Theoretical and Computational Study of a Complex

Award Accounts

The Chemical Society of Japan Award for 2013

Theoretical and Computational Study of a Complex System Consisting of Transition Metal Element(s): How to Understand and Predict Its Geometry, Bonding Nature, Molecular Property, and Reaction Behavior Shigeyoshi Sakaki1,2 Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606-8103

1 2

CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012

E-mail: [email protected] Received: March 31, 2015; Accepted: April 24, 2015; Web Released: May 7, 2015

Complex chemical systems consisting of transition metal element(s) are important and attractive research targets in both experimental chemistry and theoretical chemistry. Transition-metal complexes with carbon dioxide are discussed as one example, in which the coordination geometry, bonding nature, and reactivity are understood well and predicted with the HOMO and the number of d electrons. The spin-multiplicity of inverse sandwich-type dinuclear transition-metal complexes, which have been synthesized recently as a new type of compound, is discussed as another example based on CASPT2 calculations, in which the clear relationship between the spin multiplicity of its ground state and the number of d electrons is presented. Theoretical understanding of various organometallic reactions has been an important endeavor over the last two decades. Insertion reactions of olefin and carbon dioxide into M­H and M­alkyl bonds and σ-bond activation reactions are discussed with orbital interaction diagrams based on perturbation theory. In particular, detailed discussion of the characteristic features of a new type of oxidative addition to an M­L moiety (L = neutral ligand such as alkene and alkyne) and heterolytic σ-bond activation by an M­X moiety (X = anionic ligand). It is still a central challenge to elucidate the reaction mechanisms of catalytic reactions by transition metal complexes. The reaction mechanisms and electronic processes of Ru-catalyzed hydrogenation of carbon dioxide, Pt-, Rh-, and Zr-catalyzed hydrosilylations of alkene, Ir-catalyzed borylation of benzene, and the Hiyama cross-coupling reaction are analyzed based on computational results. We wish to present how to understand the mechanism based on the number of d electrons and the energy of d orbitals in discussion. Also, the importance of solvation and crystalline effects in the theoretical study of transition-metal complexes is discussed based on our recent theoretical studies of mixed-valence complex and a single crystal of a Pt(II) complex.

1. Introduction Complex chemical systems which consist of transition metal element(s) are important research targets in modern chemistry. One can find interesting and flexible geometries, chemical bonds, molecular properties, and reaction behaviors in those systems. Those interesting features deeply relate to the electronic structure. In this regard, theoretical and computational studies are indispensable to understand the chemistry of complex systems with transition metal element(s). Let me consider a catalytic reaction by transition metal complex such as Pd-catalyzed cross-coupling, which is an important and useful synthetic reaction mediated by a transition-metal complex.1 The first step of this catalytic reaction is the oxidative addition of an R­X σ-bond (R = aryl and X = bromine or iodine in many cases) to a Pd(0) complex to afford a Pd(II)­R species. The second step is trans-metallation between Pd(II)­R and R¤­ Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

M species (R¤ = aryl or vinyl in many cases; M = B, Si, Cu, etc.), and the final is reductive elimination of R­R¤. In these elementary steps, a stable σ-covalent bond is broken and/or formed. It is of considerable interest how the stable σ-bond reacts with the transition metal element. Also, to understand this catalytic reaction and to find a better catalytic system, we need correct knowledge of the intermediates and transition states of these reactions. However, it is not easy to experimentally observe and investigate such intermediates because of the high reactivity. Moreover, it is not possible to detect the transition state experimentally in this type of complex reaction. On the other hand, theoretical and computational study can provide meaningful information about the geometries, stabilities, reaction processes, and electronic structures of these species; even if such information is presented on a model system, it is very helpful for us to understand the catalytic reaction. In this regard, many theoretical and computational studies have been

© 2015 The Chemical Society of Japan | 889

O

O C

C MLn

MLn

O

C

O

MLn

O

O (A) η2-side-on coordination

(B) η1-C coordination

(C) η1-O end-on coordination

Scheme 1. Three coordination modes of transition-metal complexes of carbon dioxide.

Metal moiety Toluene Metal moiety Scheme 2. Typical inverse sandwich-type dinuclear chromium complex of toluene. Reprinted with permission from Ref. 5a. Copyright 2007 American Chemical Society.

reported in the last two decades.2,3 Also, we can find many interesting complex systems consisting of transition metal element(s) which attract a lot of interest from the viewpoint of physical chemistry and molecular science because of new and unusual chemical bond, geometry, molecular propertyies, and high reactivity. One good example are transition-metal complexes of carbon dioxide (Scheme 1).4 Some of the carbon dioxide complexes have an η2-side-on C=O coordination structure, while some of them have an η1-C coordination structure. Considering the presence of a lone-pair orbital at the O atom, the η1-O end-on coordination is also considered possible. It is of considerable interest to elucidate the factors to determine the coordination structure. Another example are inverse sandwichtype dinuclear transition metal complexes (Scheme 2).5 In these complexes, the organic moiety is sandwiched by two metal moieties unlike usual sandwich complex such as ferrocene and chromocene in which a metal is sandwiched by two organic moieties. In these complexes, very high spinmultiplicities, septet for M = Cr and quintet for M = V, have been experimentally reported, interestingly.5 This is surprising because the closed-shell singlet ground state is found in many organometallic compounds. To understand their geometries and molecular properties, we need correct knowledge of their electronic structures. Such complex systems consisting of transition metal element(s) are still challenging research targets in theoretical and computational chemistry due to the reasons described below: (i) The first one is their complicated electronic structures. Though density functional theory (DFT) has been very often applied to various transition metal systems, DFT is not always 890 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

reliable and a post Hartree­Fock method must be employed several times in the theoretical study of complex systems consisting of transition metal element(s). This is because significantly large electron correlation effects are present in many complex systems. One good example is a metal­metal multiple bond. In organic molecules, a triple bond is the maximum bond order. In transition metal complexes, the presence of a quadruple bond bearing a dσ2dπ4dδ2 configuration was previously proposed by Cotton.6 Recently, the sextuple bond (in a formal sense) of Cr2 and U2 has been theoretically investigated.7,8 These compounds are of considerable interest, because the bond order of six is now the largest. In these metal­metal multiple bonds, we need to employ multi-reference computational methods such as CASPT2 to take the very large static correlation effects into consideration.7­9 (ii) The second one is the flexible geometry and bonding nature which are sensitive to the metal, ligand, and even atmosphere such as solvent and molecular crystal. Because of the flexibility, we need to consider varieties of geometry and electronic structure, which require careful examination and also heavy computational costs. (iii) The third one is the difficulty in analysis of computational results due to the presence of d orbitals. In usual organic molecules, we can easily find σ- and π-orbitals. In transition-metal complexes, on the other hand, the participation of d orbitals makes bonding complicated. One important purpose of theoretical study is to find general and fundamental understanding based on electronic structures. Because one can expect that the nature of complex systems consisting of transition metal element(s) largely depend on the d orbital shape, d orbital energy, and the number of d electrons, it is desirable to analyze and present general understanding based on the d orbital energy, the d orbital size, and the number of d electrons. But, such analysis is not easy. From the above discussion, one can easily understand that the theoretical and computational study of complex systems consisting of transition metal element(s) is still challenging even now. In section 2 of this review article, we wish to report several theoretical and computational studies of geometries, bonding nature, and molecular properties of such interesting transitionmetal complexes as carbon dioxide complexes and inverse sandwich-type dinuclear transition-metal complexes. In the next section 3, we will report theoretical studies of important organometallic reactions, in which insertion reaction and σbond activation are mainly discussed. In section 4, we will discuss the theoretical study of typical catalytic reactions by transition-metal complexes such as Pt-, Rh-, and Zr-catalyzed hydrosilylation of ethylene, Ru-catalyzed hydrogenation of carbon dioxide, and Ir- and Pd-catalyzed cross-coupling reactions. In the last section 5, we will discuss our recent theoretical © 2015 The Chemical Society of Japan

studies of large complex systems such as metal­organic framework (MOF), transition-metal complexes in molecular crystal, and mixed-valence complexes in solution. Throughout this article, I wish to present general and fundamental understanding and also theoretical prediction. 2. Geometry, Bonding Nature, Reactivity, and d-Electron Configuration of Transition-Metal Complexes 2.1 Transition-Metal Complexes of Carbon Dioxide. Recently, the interaction and reaction between carbon dioxide and transition-metal complex has attracted much interest, because of the problem of carbon dioxide. As mentioned in the Introduction, we find three possible coordination structures in transition-metal complexes of carbon dioxide depending on the metal (Scheme 1).4 Though we theoretically investigated transition-metal complexes of carbon dioxide quite some time ago, we believe it is valuable to remember the relation between the coordination structure and d orbital occupation, because such discussion is useful for understanding conversion reactions of carbon dioxide into useful chemicals and finding new reactions. An intermolecular interaction between two molecules A and B can be considered to be separated into electrostatic (ES),

(A) K[Co(R-salen)(CO2)]a)

(C) Ni(PCy3)2(CO2)c)

exchange repulsion (EX), charge transfer (CT) from A to B, that of B to A, and polarizations (PLs) of A and B, in general. These interactions have been evaluated at the Hartree­Fock level with Kitaura­Morokuma energy decomposition analysis (EDA).10 In the case of transition metal complexes, the CT and PL could not be separated well, because coordinate bonds are somewhat stronger than hydrogen bonds and charge-transfer adducts.11 In such cases, the CT(A¼B) term was evaluated combined with the PL(B) term of the B fragment. We applied this analysis to transition-metal complexes of carbon dioxide, where a total complex was separated into a carbon dioxide moiety and a remaining metal moiety.12 The EDA results of [Co(alcn)(CO2)]¹ (alcn: NH­CH­CH­CHO¹) are discussed here, as an example.12b In this compound, X-ray analysis clearly shows that the CO2 moiety coordinates with the Co center in an η1-C coordination structure (Figure 1A).13 However, the reason why this Co(I) complex has the η1-C structure was unclear. The Hartree­Fock calculation indicates that η1-C coordination is more stable than η2-side-on in this Co(I) complex, where the geometry optimization of the η2-side-on structure was carried out under some constraints; if not, the η2side-on structure changed to the η1-C structure during the optimization. Though the electron correlation effects increase

(B) RhCl(As^As)2(CO2)b)

(D) Mo(PMe3)4(CO2)2 d)

(E) NbCp’2(CH2SiMe3)(CO2) e)

Figure 1. Several experimentally reported transition metal complexes with carbon dioxide. a) Reprinted with permission from Ref. 13b. Copyright 1982 American Chemical Society. b) The As^As represents a chelate diarsine ligand, o-phenylenebis(dimethylarisine). Reprinted with permission from Ref. 14. Copyright 1983 American Chemical Society. c) Reprinted with permission from Ref. 15. Copyright 1975 Royal Society of Chemistry. d) Reprinted with permission from Ref. 16b. Copyright 1991 American Chemical Society. e) Cp¤ represents methylcyclopentadienyl anion. Reprinted with permission from Ref. 17. Copyright 1981 Royal Society of Chemistry. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan | 891

2.0

z

M

y x

d x 2- y 2 dz2

dxy

dyz

dzx

–

(A) d-d Orbital separation of [Co(alcn)] dxz

Orbital energy/eV

0.0

M

-2.0 -4.0 -6.0 -8.0 -10.0 -12.0 -14.0 -16.0

180

160

140

120

OCO angle

Figure 2. The in-plane π, nonbonding π, and π* orbitals of CO2 and their orbital energy changes with O­C­O bending.a) a) DFT(B3LYP)/6-311G* was employed.

z x

Ni dyz

(PR3)2 Ni R3P

PR 3

(B) d-d Orbital separation of Ni(PR3)2

Scheme 3. Schematic representation of d­d orbital splitting of [Co(alcn)]¹ and Ni(PR3)2 (Three other d orbitals are omitted for brevity).

the binding energy of carbon dioxide with the transition metal center, the relative stability is not influenced very much by the correlation effects.18 This result suggests that the EDA analysis at the Hartree­Fock level is meaningful for discussing relative stabilities of several coordination modes. The EDA analysis provides us with several important features, as follows;12 (1) the electrostatic stabilization (ES) is smaller in the η1-C structure than in the η2-side-on one, (2) the exchange (EX) repulsion is smaller in the η1-C structure than in the η2-side-on one, and (3) the stabilization by CT(Co ¼ CO2) + PL(CO2) is larger in the η1-C structure than in the η2-side-on one. Hence, the larger stability of the η1-C coordination structure arises from the smaller EX repulsion and the larger CT(Co ¼ CO2) + PL(CO2) stabilization than those of the η2-side-on one. These results of EDA are easily understood by considering the d electron configuration and frontier orbitals. [Co(alcn)(CO2)]¹ has a square pyramidal structure, in which the Co center has a d8 electron configuration. According to ligand field theory, the dx2
y2 orbital exists at the highest energy in this structure (Scheme 3A). The next is the dz2 orbital. When the energy gap between the dx2
y2 and dz2 orbitals is small, this complex has a triplet ground state. However, the dz2 is doubly occupied and 892 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

thereby the dx2
y2 is empty in [Co(alcn)(CO2)]¹, because the η1-C coordinated CO2 moiety is σ-electron-withdrawing, as will be discussed below. The remaining dxz, dyz, and dxy orbitals are doubly occupied and exist at lower energies than the dz2 . As shown in Figure 2, the LUMO of CO2 is a π* orbital, to which the carbon pπ orbital contributes much greater than the oxygen pπ orbital. In the η1-C coordination complex, the in-plane π* orbital becomes very low in energy because the O­C­O angle considerably decreases in the complex. Hence, this LUMO overlaps well with the dz2 of [Co(alcn)]¹ to form a strong CT interaction from the Co to the CO2 moiety in the η1-C coordination structure (Scheme 4A). In the η2-side-on structure, the LUMO of CO2 overlaps well with the dxz orbital to form a charge-transfer (CT) interaction (Scheme 4B). But, the dxz exists at a lower energy than the dz2 , as was discussed above, which is not favorable for the CT from the Co to the η2-side-on coordinated CO2. It is concluded that the large CT(Co ¼ CO2) in the η1-C structure arises from the fact that the HOMO of [Co(alcn)] is dz2 . If the dxz is the HOMO, the CT(M ¼ CO2) is strong in the η2-side-on structure because the dxz can overlap well with the LUMO of CO2 in this structure. The ES term is easily understood in terms of charge distribution. In CO2, the C atom is positively charged but the O atom is negatively charged (Scheme 4C). Because the Co center is positively charged in [Co(alcn)]¹, the η1-C coordination structure is not favorable for the ES interaction with the Co center, while the η2-side-on structure is not very bad for the ES interaction because the positively charged C and the negatively charged O atoms interact with the Co center. The EX term becomes large when the doubly occupied d orbital of [Co(alcn)]¹ overlaps with the doubly occupied orbital of CO2. In the η1-C coordination structure, the in-plane nonbonding π orbital (HOMO) of CO2 overlaps with the dxz orbital of [Co(alcn)]¹ but does not with the dz2 orbital because of the different symmetry (Scheme 4D). Also, the in-plane π bonding orbital of CO2 overlaps well with the dz2 orbital but does not with the dxz orbital because of the different symmetry. In the η2side-on structure, on the other hand, the in-plane π orbital of CO2 can overlap with both the dxz and dz2 and also the in-plane nonbonding π orbital of CO2 can overlap with these two d orbitals. Hence, the EX repulsion is larger in the η2-side-on © 2015 The Chemical Society of Japan

(A) η1-C mode

(B) η2-side-on mode

η2-side-on mode

(C) NBO Charges

η1-C mode

(D) Exchange Repulsion

Scheme 4. Schematic representations of the interaction between [Co(R-salen)]¹ and CO2. Reprinted with permission from Ref. 12b. Copyright 1987 American Chemical Society. Table 1. Qualitative Understanding of Each Interaction in η1-C, η2-side-on, and η1-O Coordination Structures of Transition-Metal Complex of Carbon Dioxide Coordination modes η -C 1

η2-side-on

η1-O

ES Unfavorable in general Not bad in general

Large Stabilization

than in the η1-C structure, when the dσ and dπ orbitals are doubly occupied. Considering these features, general conclusions are summarized in Table 1.19 This simple table provides us with clear understanding and prediction of the coordination structure of CO2. For instance, we can easily understand the reason why [RhCl(As^As)2(η1-CO2)] (As^As: o-phenylenebis(dimethylarsine))14 has an η1-C coordination structure, based on Table 1. In this complex, Rh has +I oxidation state with a d8 electron configuration. Because [RhCl(As^As)2(CO2)] has an octahedral-like structure, the LUMO is the dx2
y2 orbital and the HOMO is a dz2 orbital expanding toward CO2 and three nonbonding dπ orbitals are doubly occupied like in [Co(R-salen)(CO2)]¹ (Scheme 3A). According to Table 1, this electronic structure is not favorable for the η2-side-on but favorable for Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

Each Interaction EX Small Destabilization in general Large destabilization when dσ is doubly occupied Small destabilization

CT(M ¼ CO2) Large stabilization when dσ is HOMO. Large stabilization when dπ is HOMO Small stabilization

the η1-C coordination structure, which is the reason why the η1-C coordination structure is taken in [RhCl(As^As)2(CO2)]. [Ni(PCy3)2(CO2)] has an η2-side-on structure (Figure 1).15 In Ni(PCy3)2 with a bending P­Ni­P moiety, the dπ orbital is HOMO (Scheme 3B), because the Ni(0) has a d10 electron configuration and the dxz orbital is destabilized in energy by the antibonding overlap with the lone pair orbitals of phosphines. Note that the dyz and other d orbitals are nonbonding or nearly nonbonding with the lone pair orbitals of phosphines. The presence of this HOMO is favorable for the CT in the η2-side-on coordination structure. Because the dσ orbital is doubly occupied, the EX repulsion is large in this η2-side-on complex, but the stabilization by the CT compensates well the destabilization by the EX repulsion, leading to the formation of the η2-side-on carbon dioxide complex. [Mo(PR3)4(CO2)2] has two η2-side-on © 2015 The Chemical Society of Japan | 893

C O Rh

: Increase in electron density : Decrease in electron density (A) Difference density map

(B) HOMO contour map

Figure 3. The HOMO and the difference density of [RhCl(AsH3)4(CO2)]. Reprinted with permission from Ref. 21. Copyright 1989 American Chemical Society.

coordinated CO2 molecules,16 which is surprising because the coordinate bond of carbon dioxide is believed to be weak. In this complex, the Mo center has 0 oxidation state with a d6 electron configuration. In the octahedral-like d6 complex, the HOMO is dπ (dxy , dxz, and dyz) but the dσ is empty (Scheme 3A, left-hand side). This situation is the best for the η2-side-on coordination. Hence, two CO2 molecules can coordinate with the Mo center. [Cp2Nb(SiR3)(CO2)] has also an η2-side-on structure.17 In this complex, the Nb has +III oxidation state with a d2 electron configuration. Its two d electrons occupy one d orbital which expands between two Cp planes, avoiding the strongly electrondonating CH2SiR3 ligand. Hence, the doubly occupied dπ orbital can overlap with the in-plane π* orbital of CO2. In this complex, the dπ orbital is doubly occupied and the dσ is empty, which is the best situation for the η2-side-on structure like [Mo(PR3)4(CO2)2] (Table 1). As briefly discussed here, Table 1 is useful for understanding and predicting the coordination structure of carbon dioxide with transition metal complex. Here, we wish to briefly mention that η1-C coordinated CO2 is a typical Z-ligand, which now attract a lot of interest in coordination and organometallic chemistry.20 The idea of Z ligands was proposed first by Green in 1995,20a but essentially the same coordinate bond was found and discussed in detail before that.12b 2.2 Reactivity of Transition-Metal Complexes with Carbon Dioxide. The next issue to be discussed is the reactivity of CO2 coordinated with the transition-metal complex. Interestingly, the electrophilic attack on CO2 is enhanced in [RhCl(As^As)2(CO2)] despite the Lewis acidity of CO2.14 We theoretically investigated the electronic structure and reactivity of [RhCl(AsH3)4(CO2)] which is a model of [RhCl(As^As)2(CO2)].21 In this work, the Hartree­Fock and MP2 methods were employed because this work had been carried out previously. Theoretical calculations showed that the electrophilic attack on the O atom of carbon dioxide more easily occurs in 894 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

this complex than in free CO2, which is consistent with experimental reports. Interestingly, the electron density increases very much around the O atom of carbon dioxide (Figure 3A), though the O atom does not directly interact with the Rh center. This is the origin of the enhanced reactivity of carbon dioxide to electrophilic attack. The HOMO is responsible for this increase in electron density around the O atom of carbon dioxide, as follows; in the η1-C coordination structure, the doubly occupied dσ orbital overlaps with the π orbital of CO2 in an antibonding way because the π orbital exists at a lower energy than the Rh dσ orbital but overlaps with the π* orbital of CO2 in a bonding way because the π* orbital exists at a higher energy than the Rh dσ orbital (Scheme 5A). These orbital mixings can be understood with perturbation theory. The bonding and antibonding overlaps correspond to the charge transfer from the Rh dσ to the CO2 π* orbital and the exchange repulsion between the Rh dσ and the CO2 π orbitals, respectively. Because the phase of the pπ orbital of the C atom is reverse between the π and π* orbitals, the pπ orbital component of the C atom decreases in the HOMO (Scheme 5B). On the other hand, the pπ orbital component of the O atom increases in the HOMO, because the phase of the oxygen pπ orbital is the same in the π and π* orbitals. As a result, the pπ component of the O atom is larger than that of the C atom in the HOMO (Figure 3B), which leads to the presence of higher electron density around the O atoms than around the C atom. Both the large pπ component of the O atom in the HOMO and the increased electron density around the O atom are favorable for electrophilic attack on the O atom. This is the reason why the electrophilic attack easily occurs at the O atom in the η1-C coordinated CO2 complex. Essentially the same frontier orbital was reported in the theoretical study of a nickel(I) carbon dioxide complex.22 Because of the presence of this frontier orbital, the protonation of the O atom easily occurs in the nickel(I) η1-C coordinated CO2 © 2015 The Chemical Society of Japan

π∗

Table 2. The Spin Multiplicity of the Ground State in the Inverse Sandwich-Type Complexes of Benzene for the First-Row and Second-Row Transition Metal Elements

dx2-y2 dz2 dxz dyz

nπ

Spin multiplicity

Sc 1

Ti 3

V 5

Cr 7

Mn 9

Spin multiplicity

Y 1

Zr 3

Nb 5

Mo 1 (or 3)

Tc 3

Fe 1

dxy π RhCl(As ^As)2

CO2

RhCl(As ^As)2(CO 2) (A)

d-orbital mixing with π and π * orbitals of CO2

+

(B)

+

Schematic representation of HOMO

Scheme 5. Orbital interactions of π and π* orbitals of carbon dioxide with the doubly occupied dσ orbital of Rh in [RhCl(AsR3)4(CO2)]. Reprinted with permission from Ref. 21. Copyright 1989 American Chemical Society. CO2

e−

+ LNi(I)

2+ LNi(II)

O LNi(III)

+

CO

C O

LNi(II) CO

2+

H+ OH−

OH LNi(III) C

2+

e−

O

Scheme 6. Experimentally and theoretically proposed electrochemical reduction of CO2 to CO.22,23c

complex, as was experimentally suggested in the Ni(cyclam)catalyzed electrochemical reduction of CO2 to CO (cyclam: saturated cyclic amine containing four amine moieties)23 (Scheme 6). Also, the theoretical study clearly revealed that after the protonation, further one-electron reduction easily Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

occurs to induce the C­O bond scission to afford CO and OH¹ anion in Ni(cyclam)-catalyzed electrochemical reduction of CO2 (Scheme 6).22,23 These computational results22 provide theoretical evidence for the experimentally proposed reaction mechanism.23 Re-catalyzed photochemical reduction of CO2 to CO24 attracts a lot of recent interest.25 Though the reaction mechanisms are unclear, recent elegant experiments have provided clear indications of the active species and mechanisms.26 Based on experimental findings, a similar reaction mechanism to Scheme 6 was proposed, while the CO2 coordination mode is not clear. Essentially the same mechanism was experimentally proposed in the electrochemical reduction of CO2 to CO catalyzed by a palladium complex.27 In all these mechanisms, the coordinated CO2 undergoes protonation and then OH¹ anion dissociates from CO upon the second one-electron reduction, indicating that the protonation of CO2 is one crucial step in photo- and electrochemical reductions of CO2 to CO. Hence, the orbital interaction diagram of Scheme 5 is important for understanding these catalytic reactions and the reason why the protonation is accelerated by the η1-C coordination of CO2. 2.3 Electronic Structure and Flexible Spin Multiplicity of Inverse Sandwich-Type Dinuclear Transition-Metal Complexes. One of the important characteristic features of transition-metal complexes is the presence of a variety of spin multiplicities. One good example is an inverse sandwich-type dinuclear transition-metal complex such as (¯-η6: η6-C7H8)[M(DDP)]2 (M = Cr or V; DDP: β-diketiminate HC(C(Me)NC6H3i-Pr)2; C7H8: toluene) and its analogues synthesized by Tsai et al.5a,5b and Theopold et al.5c (Scheme 2). Interestingly, inverse sandwich-type benzene (or toluene) complexes of dinuclear vanadium and chromium have ground states of quintet and septet spin multiplicities, respectively. These spin multiplicities are understood to be abnormally high because organometallic compounds tend to have a closed-shell singlet ground state in many cases. Considering that the electron correlation effects are in general large in multi-nuclear metal complexes, we investigated the inverse sandwich-type dinuclear transition-metal complexes with the DFT and CASPT2 methods,28 where an AIP (HN­(CH)3­NH: AIPH: (Z)-1-amino3-iminoprop-1-ene) was employed as a model of DDP. In the benzene complexes of vanadium and chromium, DFT, CASSCF, and CASPT2 methods reproduce well the experimentally reported spin multiplicity in the ground state, as shown in Table 2. It is of considerable interest to understand the reason why such high spin multiplicities are possible in their ground states. The schematic molecular orbital diagram is useful for understanding the reason, even though the electron correlation effects are large in some cases. In the M(AIP) moi© 2015 The Chemical Society of Japan | 895

[M(AIP)] 2 (C6H6)[M(AIP)] 2

Benzene

φ11 LUMO1 LUMO2

z x

φ12

φ9

π2*(d xz), π2(d xz)

φ10 φ7 φ8

π1*(d yz), π1(dyz) δ2*(d xy), δ2(dxy)

φ6

φ5

δ1*(d x2-y2), δ1(dx2-y2) σ*(dz2 ), σ(dz2)

φ3 φ4 φ1

φ2

(A) Molecular orbital diagram of (C6H6)[M(AIP)]2

φ1

φ2

φ3

φ4

φ5

φ6

φ7

φ8

φ9

φ10

φ11

φ12

(B) Molecular orbitals of (C6H6)[M(AIP)]2 Scheme 7. MO diagram of the inverse sandwich complex of benzene. Reprinted with permission from Ref. 28a. Copyright 2010 American Chemical Society.

ety, the dxz orbital of metal overlaps well with the antibonding pair of N lone pair orbitals of the AIP ligand to form very stable bonding and very unstable antibonding MOs (Scheme 7) for x and z axes. The very stable bonding MO is doubly occupied by two lone pair electrons of the AIP ligand. The very unstable antibonding MO mainly consisting of the dxz orbital exists at a very high energy; see π2(dxz) and π2*(dxz) in the right-hand side of Scheme 7. The dyz orbital is somewhat destabilized in energy by a π-type antibonding overlap with the π orbital of the AIP. The dxy and dx2
y2 orbitals are moderately destabilized in energy by a δ-type antibonding overlap with the π orbital of the AIP. The dz2 is destabilized little in energy because the lone pair of AIP overlaps with the positive phase part of dz2 and also with the negative phase part of dz2 . These four d orbitals are close to each other in energy. In the inverse sandwich-type complex, these d orbitals form bonding and antibonding pairs with each other because two M(AIP) moieties are involved in 896 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

one molecule (Scheme 7). In these bonding and antibonding pairs, only the antibonding pair can overlap with the π* MOs of benzene due to the symmetry. The most stable º1 MO consists of the δ-type bonding overlap between the metal dxy orbitals and one of the LUMOs of benzene (Schemes 7A and 7B). Another δ-type bonding º2 MO is formed by the bonding overlap between the metal dx2
y2 and the remaining LUMO of benzene. Their antibonding counterparts º9 and º10 MOs exist at high energies in an unoccupied level. Between these bonding and antibonding MOs, nearly nonbonding º3 to º8 MOs exist. The º11 and º12 mainly consisting of the dxz exist above the º9 and º10 MOs, because these MOs are destabilized very much in energy by the antibonding overlap with the AIP lone pairs, as was discussed above. In (¯-η6: η6-C6H6)[Cr(AIP)]2, the Cr has +I oxidation state with five d electrons. Hence, totally ten d electrons occupy these MOs. The two bonding º1 and º2 MOs are doubly occupied. The remaining six electrons occupy the

© 2015 The Chemical Society of Japan

nearly nonbonding º3 to º8 MOs. Because these nonbonding MOs have similar orbital energy, six electrons occupy six MOs with a parallel spin. This electronic structure corresponds to a septet, which was experimentally observed.5 Interestingly, the DFT and MRMP2 methods indicate that the spin multiplicity of the ground state is calculated to increase from a closed shell singlet to a septet, when going from Sc(I) to Cr(I) (Table 2). This interesting feature is understood by considering the d electron occupation in the MOs of Scheme 7A, as follows: In these complexes, the metal has +I oxidation state in a formal sense. Because Sc(I) has a d2 electron configuration, in total four d electrons occupy the stable º1 and º2 MOs, and thereby, this complex has a closed-shell singlet ground state. Ti(I) has a d3 electron configuration, and thereby, two more d electrons occupy º3 to º8 MOs. Because these º3 and º8 MOs are nearly degenerate, two d electrons in the º3 and º4 MOs have the same spin to afford a triplet ground state. In the V(I) complex, two more d electrons occupy the º5 and º6 MOs, to afford a quintet ground state, which is consistent with the experimental results. In the Cr(I), two more d electrons occupy the º7 and º8 MOs to afford a septet ground state, as was discussed above. However, the spin multiplicity of the Mn(I) complex depends on the DFT functional;28a in the B3LYP calculation, the ground state has a quintet spin multiplicity, while in the B3LYP*, BP86, and PW91 calculations, the ground state has a nonet spin multiplicity. The nonet state is favorable from the exchange interaction between many parallel spins, but the quintet state is favorable from the orbital occupation at the low energy. Because these two electronic states are comparable in energy, some of the functionals cannot reproduce correctly the relative energies of these two states. We performed MRMP2 calculations on this complex and found that the ground state is nonet. The nonet spin multiplicity is understood to be very high in this type of small molecule. The MO scheme of the Mn compelx is somewhat different from those of the Sc to Cr complexes; in the Mn complex, the º11 and º12 MOs mainly consisting of the Mn dxz orbital are found below the º9 and º10 MOs, because the d orbital energy decreases when going from the left-hand side to the right-hand side in the periodic table.29 In the CASSCF calculations of the Mn complex, these d MOs are involved in the active space. More interesting is the Fe(I) analogue. The MRMP2 calculations indicate that the Fe(I) complex has an open-shell singlet ground state but a triplet state is moderately less stable than the open-shell singlet. These results are completely different from the spin multiplicities of the Cr and Mn complexes. The electronic structure is not simple in this Fe(I) complex. In the inverse sandwich-type benzene complexes of dinuclear 4d metals, the spin multiplicity of the ground state increases from a closed-shell singlet to a quintet when going from Y to Nb but then decreases to a singlet at Mo (Table 2).28b This means that the position of the maximum spin multiplicity shifts to the left-hand side in the periodic table and its spin multiplicity decreases to quintet which is much lower than the nonet spin state of the Mn complex. These interesting differences between 3d and 4d metals arise from the differences in size between 3d and 4d orbitals; as well known, the size of a 4d orbital is larger than that of 3d,29 which leads to a larger d­d orbital energy gap and thereby the ground state tends to take a lower spin Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

multiplicity in the inverse sandwich complexes of 4d metals than in the complexes of 3d metals. The inverse sandwich-type dinitrogen complexes of Cr(I) and Fe(I) have a similar structure to those of the inverse sandwich-type complexes of benzene. However, their effective magnetic moments are 3.9 and 7.9 ¯B, respectively,30,31 which correspond to the spin state between triplet and quartet in the Cr complex and septet in the Fe complex. These spin multiplicities are completely different from those of the inverse sandwichtype complexes of benzene. We investigated these dinitrogen complexes with the CASPT2 method and found several interesting results in spin multiplicity;32 (i) In the Cr(I) complex, the ground state is open-shell singlet, while triplet, quintet, and septet states are close in energy to the singlet. (ii) The effective magnetic moment corresponds to the thermal average of those spin multiplicities. (iii) In the Fe(I) complex, the ground state is septet in contrast to the open-shell singlet spin multiplicity of the inverse sandwich-type Fe complex of benzene. (iv) The dinitrogen ligand has a considerably negative spin population in the Fe(I) complex, while it has negligibly small spin population in the Cr(I) complex even at high spin state. To save space, we will skip detailed discussion here but mention that these differences are clearly interpreted in terms of the presence of a nonbonding d orbital in the inverse sandwich-type complex of dinitrogen; in the Fe(I) complex, the nonbonding d orbital is singly occupied, which induces spin-polarization to stabilize the high spin state. This spin polarization is the origin of the negative spin density on the dinitrogen moiety. In the Cr(I) complex, the nonbonding d orbital is unoccupied because of the smaller number of d electrons, and thereby spin polarization is not induced and the high spin state is not stabilized enough by exchange interaction. This nonbonding d orbital is formed in the dinitrogen complex but not in the benzene complex because the π* orbital is different between dinitrogen and benzene molecules. In other words, the spin multiplicity of these inverse sandwich-type complexes is sensitive to the bridging ligand and the number of d electrons. This is a good example of the flexible electronic structure of transition-metal complexes. As discussed above, the multinuclear transition-metal complexes are of considerable interest in coordination chemistry, physical chemistry, and molecular science. Also, many multinuclear complexes have been investigated experimentally. We can expect the theoretical studies of such multinuclear complexes will make a new advancement in coordination chemistry and molecular science. 3. Electronic Processes of Important Elementary Steps in Catalytic Cycles The catalytic reaction by transition-metal complexes occurs through several common elementary steps such as oxidative addition of σ-bond, migratory insertion reactions of C­C and C­O double and/or triple bonds into M­H and M­R bonds, reductive elimination, and so on. We theoretically investigated these important elementary steps. Here, we wish to discuss theoretical studies of two important elementary steps; one is the migratory insertion of carbon dioxide. Though we investigated this migratory insertion reaction quite some time ago, we selected this reaction here because the ethylene and acetylene

© 2015 The Chemical Society of Japan | 897

Figure 4. Transition state of CO2 insertion into Cu(I)­H and Cu(I)­CH3 bonds. Bond distance is in angstroms and bond angle is in degrees. Reprinted with permission from Ref. 33d. Copyright 1995 American Chemical Society.

Scheme 8. Schematic representation of orbital overlap between the HOMO of the M­R moiety (R = H or CH3) and the LUMO of CO2. Reprinted with permission from Ref. 33d. Copyright 1995 American Chemical Society.

insertion reactions have been investigated in many theoretical studies but the CO2 insertion has been investigated only in our work to our knowledge. Also, CO2 insertion is now important in CO2 conversion reactions. Another is σ-bond activation. We systematically investigated various σ-bond activation reactions because σ-bond activation reactions are important in catalytic reactions by transition metal complexes. 3.1 Migratory Insertion of CO2 and C2H4 into M­H and M­CH3 Bonds. Because we performed this theoretical study long ago, the geometry was optimized at the Hartree­Fock level and the energy changes were evaluated with MP4(SDQ).33 The CO2 insertion into a Cu(I)­H(hydride) and Cu(I)­ CH3 bonds were selected as models, because the CO2 insertion into the Cu(I)­alkyl bond was experimentally reported when we started this theoretical study.34,35 In the transition state, the C atom of CO2 is approaching the H (or CH3) coordinated with the Cu center and one O atom of CO2 is also approaching the Cu center (Figure 4). This four-center transition state is found in general migratory insertion reactions. In the CO2 insertion into the Cu(I)­CH3 bond, the position and orientation of the CH3 ligand deviates much more from the original than in the insertion into the Cu(I)­H bond. This is because the H ligand has a spherical 1s valence orbital but the CH3 ligand has a directional sp3 valence orbital. To make a better overlap with the directional sp3 orbital, the CH3 position must move downward and its orientation must change toward the C of CO2 (Scheme 8). Consistent with the geometry in the transition state, the activation barrier is considerably smaller in the CO2 insertion into the Cu(I)­H bond (7.9 kcal mol¹1) than into the Cu(I)­CH3 bond (15.7 kcal mol¹1), where the activation barrier is defined as a difference in MP4(SDQ)-calculated potential 898 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

energy between the transition state and the precursor complex. The same trend is found in the activation barrier of the ethylene insertion into the Cu(I)­H and Cu(I)­CH3 bonds; the activation barrier is 2.0 and 25.3 kcal mol¹1 for these insertion reactions, respectively. From these results, one can expect that the CO2 insertion into the Cu(I)­OR bond occurs easily because the lone pair orbital of the OR group can participate in the interaction with CO2. Actually, the CO2 insertion into the Cu(I)­OH bond was calculated to occur without barrier. The changes in electron population provide us with good understanding of the electronic process of the CO2 insertion reaction. As shown in Figure 5A, the electron population of the CO2 moiety considerably increases and the electron population of the Cu­H moiety considerably decreases as the reaction proceeds from CuH(PH3)2 + CO2 1A to the Cu­OCOH species (4A to 6A), indicating that the CT from the Cu­H moiety to CO2 plays crucial roles in the CO2 insertion. It should be noted that the O1 atomic population increases more than the C1 and O2 atomic populations. This is a little bit surprising, because one can expect that the C1 atom receives more electron population than the O1 and O2 atoms because it directly interacts with the H ligand of CuH(PH3)2. Similar population changes are observed in the C2H4 insertion into the Cu(I)­H bond (Figure 5B); the electron population of C2H4 considerably increases, that of the Cu­H moiety considerably decreases, and the C1 atomic population increases more than the C2 despite the C1 not directly interacting with the H ligand. The difference density maps clearly show that the electron density increases around the O1 and O2 atoms but rather decreases around the C1 atom in the CO2 insertion (Figure 6A). In the C2H4 insertion reaction, essentially the same features are observed in electron density (Figure 6B). The frontier orbital plays crucial roles in these population changes (Figures 6C and 6D), the HOMO mainly consists of the π* orbital of CO2/C2H4 and the H 1s orbital. This HOMO corresponds to the CT from the Cu­H moiety to the π* orbital of CO2/C2H4. We calculated much simpler model systems consisting of CO2/C2H4 and H¹ (Figures 6E and 6F). The HOMOs of these model systems are essentially the same as those of the total system in Figures 6C and 6D. Based on these results, it is concluded that the HOMO of the transition state mainly consists of the 1s orbital of the H(hydride) ligand and the π* orbital of CO2/C2H4. Because the H(hydride) 1s orbital exists at a higher energy than the π orbital of CO2/C2H4 but at a lower energy than the π* orbital of CO2/C2H4, the H 1s orbital forms a bonding overlap with the π* orbital of CO2/C2H4 and an antibonding overlap with the © 2015 The Chemical Society of Japan

CO2 C2H4 O1

C1

O2 C

C2

H H Cu Cu (A) CO2 Insertion into Cu(I)-H of CuH(PH3)2

(B) C2H4 Insertion into Cu(I)-H of CuH(PH3)2

Figure 5. Electron population changes in CO2 and C2H4 insertions into the Cu(I)­H bond. Reprinted with permission from Ref. 33d. Copyright 1995 American Chemical Society.

π orbital of CO2/C2H4, which leads to the orbital mixing (Scheme 9). Apparently, the pπ orbital of the O1 is enhanced but that of the C is decreased by this orbital mixing. As a result, the electron population increases much more on the O1 atom than on the C atom in the CO2 insertion. In the C2H4 insertion, the pπ orbital of the C1 is similarly enhanced but the pπ orbital of the C2 is reduced in the HOMO, which leads to the larger increase in the C1 atomic population than in the C2. In both the CO2 and C2H4 insertion reactions, this type of CT interaction plays crucial roles, which will be discussed below in the section of theoretical studies of catalytic reactions. These features are commonly found in the migratory insertion reactions of carbon dioxide, ethylene, and acetylene. The Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

orbital mixing here is essentially the same as that shown in Scheme 5; both are based on perturbation theory, indicating that this type of orbital mixing based on the perturbation theory is indispensable for understanding many organometallic reactions. 3.2 σ-Bond Activation Reactions. σ-Bond activation is involved in many catalytic reactions as a key proces.3,36 For instance, in palladium-catalyzed cross-coupling reactions, the first step is the oxidative addition of the σ-bond of organohalide to a palladium(0) complex, the second step is transmetallation in which the metal­carbon and the palladium­halide bonds are broken but palladium­carbon and metal­halide bonds are formed, and the last step is reductive elimination in which a © 2015 The Chemical Society of Japan | 899

Scheme 9. Important orbital interactions found in the CO2 insertion into the Cu(I)­H bond. Reprinted with permission from Ref. 33d. Copyright 1995 American Chemical Society.

Figure 6. Difference density maps and contour maps of HOMOs in CO2 and C2H4 insertion reactions into the Cu(I)­H bond and the contour maps of HOMOs of model systems, H¹ + CO2 and H¹ + C2H4. Reprinted with permission from Ref. 33d. Copyright 1995 American Chemical Society.

new carbon­carbon bond is formed; in other words, all three steps are σ-bond activation or its reverse reaction. In my understanding, almost all σ-bond activation reactions are classified into the following two categories:3,36a The first one is the σ-bond activation by a metal center only and the second one is the σ-bond activation by a metal­ligand moiety. The latter one can be understood as ligand-assisted σ-bond activation. The former category is further classified into two sub-categories; concerted oxidative addition to the metal center (eq 1a) and stepwise oxidative addition via nucleophilic attack of metal center to substrate (eq 1b). The concerted oxidative addition is well known, because it has been theoretically investigated for long time since the first geometry optimization of the transition state by Kitaura, Obara, and Morokuma.37 MLn þ R1 ­R2 ! MðR1 ÞðR2 ÞLn (1a) 1 1 1 1 1 1 (1b) MLn þ R ­X ! ½MðR ÞLn X ! MðX ÞðR ÞLn MðX2 ÞLn þ R1 ­R2 ! MðR1 ÞLn £ðX2 ­R2 Þ or MðR1 ÞLn þ ðX2 ­R2 Þ (2a) MðR2 C¼CR2 ÞLn þ R1 ­R2 ! MðCR2 CR2 R1 ÞðR2 ÞLn (2b)

900 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

The stepwise oxidative addition via nucleophilic attack (eq 1b) was first theoretically investigated by Rzepa and co-workers concerning the oxidative addition of alkynyl and aryl carbon­ fluorine σ-bonds to palladium(0) complex in solvent.38 The second category, ligand-assisted σ-bond activation, is also classified into two sub-categories; in one sub-category, an anion X2 ligand participates in the σ-bond activation, as shown in eq 2a. In the other, a neutral ligand such as alkene or alkyne participates in the reaction, as shown in eq 2b. In the reaction of eq 2a, one part (R2) of the substrate is bound with the anion X2 ligand to afford X2­R2 in the product side, which either weakly interacts with the M center or dissociates from the M center. In both cases, the metal oxidation state does not change at all because one X2 anion ligand is bound with the metal center in the reactant side and one anionic R1 is bound with the M center in the product side. This type of reaction was theoretically investigated by Siegbahn39 and our groups.40 In the reaction of eq 2b, the alkene or alkyne ligand is converted to the alkyl or vinyl ligand in the product side, respectively. Because the metal is coordinated with two anionic alkyl (or vinyl) and R2 ligands in the product, the metal oxidation state increases by +2 in this reaction. In other words, this reaction is understood as oxidative addition to a metal­ligand (M­L) moiety. Though this type of reaction has been very limited, two examples are found in experimental reports, to our knowledge;41,42 One is the O­H σ-bond activation of water by silabenzene complex of Cr41 and another is the H­H σ-bond activation by nickel(0) borane complex.42 In two old theoretical works, this type of reaction was reported, though the reaction was not recognized clearly as the oxidative addition to an M­L moiety.43,44 In this section, we wish to discuss characteristic features of these σ-bond activation reactions. 3.2.1 Concerted Oxidative Addition (eq 1a): The transition state of the concerted oxidative addition was previously optimized by Morokuma and co-workers in the oxidative addition of H2 to Pt(PH3)2, as mentioned above.37 Since then, theoretical work of concerted oxidative addition has been

© 2015 The Chemical Society of Japan

(A) Concerted oxidative addition of methane to Pt(PH3)2

H

H3

H H

C

z

x

(A) Schematic figure of HOMO of transition states of H-H and C-H oxidative addition

dπ

(occ)

78.4%

σ∗ 11.4% σ 0.6% (unocc) (occ)

(B) Composition of HOMO of transition states of C-H oxidative addition to a Ti(IV)-N bond

(C) Non-planar transition states of Si-C and C-C oxidative addition to Pt(PH3)2

Scheme 10. The HOMO of the transition state of the concerted oxidative addition of the C­H σ-bond to Pt(PH3)2. Reprinted with permission from Refs. 46f and 48. Copyright 1998 and 2007 American Chemical Society.

Changes in NBO population

Changes in NBO population

reported by many theoretical groups.45 Our group also theoretically investigated the oxidative addition of C­H, Si­H, Si­ C, and Si­B σ-bonds.46 In many oxidative addition reactions to a d10 metal complex ML2 (M = Pt, Pd, or Ni; L = phosphine etc.), the transition state is planar. This planar transition state is consistent with the orbital interaction diagram proposed by Tatsumi and co-workers;47 because the CT interaction from the doubly occupied d orbital to the antibonding σ*-MO of the σbond plays crucial roles in the oxidative addition, the σ*-MO wants to overlap with the HOMO. In the oxidative addition to the two-coordinate ML2 complex of a d10 metal, the dxz orbital is the HOMO of ML2 with a bending L­M­L angle (Scheme 3B), and thereby, the planar structure is favorable for the overlap between the σ*-MO and the dxz (Scheme 10A). Actually, the planar transition states were reported in the oxidative additions of the H­H,37 C­H, and Si­H σ-bonds.46a,46b Consistent with this orbital interaction, the Pt atomic population considerably decreases and both the H and CH3 electron populations considerably increase in the reaction (Figure 7A). These population changes are consistent with the understanding that the metal oxidation state increases by +2 in the reaction. Also, these results suggest that the CT plays crucial roles in the concerted oxidative addition. However, clear evidence has not been provided for the orbital participation. In the oxidative addition of the C­H σ-bond of methane to Pt(PH3)2, we analyzed what MOs of the Pt(PH3)2 and methane participate in the HOMO of the transition state and found that the HOMO of the transition state mainly consists of the HOMO(dπ) of Pt(PH3)2 and the C­H σ*-antibonding MO (Scheme 10B).48 This is a clear evidence that the CT from the doubly occupied dπ orbital of the metal center to the σ*-antibonding MO plays crucial roles in the concerted oxidative addition of the C­H σbond of methane to a platinum(0) complex Pt(PR3)2. However, the transition state is not always planar; for instance, the oxidative addition of the C­Si and C­C σ-bonds (eqs 3a and 3b) occurs through a nonplanar transition state (Scheme 10C).46f

(B) Heterolytic σ-bond activation of benzene by Pd(η2-O2CH)2

Figure 7. Population changes of the oxidative addition and heterolytic σ-bond activation reactions. Reprinted with permission from Refs. 40 and 48. Copyright 2000 and 2007 American Chemical Society. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan | 901

Scheme 11. The LUMO of distorted R­CN which is the same as that in the transition state of the concerted oxidative addition of R­CN to Ni(PMe3)2. Reprinted with permission from Ref. 51. Copyright 2007 American Chemical Society.

PtðPH3 Þ2 þ H3 C­SiR3 ! cis-½PtðCH3 ÞðSiR3 ÞðPH3 Þ2 

(3a)

ðR ¼ H, Me, or ClÞ (3b) PtðPH3 Þ2 þ H3 C­CH3 ! cis-½PtðCH3 Þ2 ðPH3 Þ2  This result is against our understanding based on the orbital interaction of Scheme 10A. To elucidate the reason for the nonplanar transition state, the oxidative addition of the Si­C σbond to Pt(PH3)2 was carefully investigated with three kinds of substituent (H, Me, or Cl) on the Si atom. The important features are summarized below: (i) the transition state is nonplanar in all these substrates, (ii) the nonplanar geometry starts to change to planar when the σ-bond is almost broken, (iii) when a more bulky substituent is introduced on the Si atom, the transition state deviates more from the planar structure, and (iv) the transition state is always planar in the oxidative addition of H­H, C­H, and Si­H σ-bonds. From these observations, it is reasonably concluded that the planar transition state is favorable for orbital interaction but the nonplanar one is favorable for steric repulsion. The planar or nonplanar transition state is determined by steric factors, orbital interactions, the position of the transition state such as late- or early-transition state; note that in the late transition state the σ-bond is almost broken, which is favorable for the planar geometry. One important advance in the concerted oxidative addition was achieved recently by the Jones group.49 They succeeded in the concerted oxidative addition of Ph­CN to a Ni(0) complex (eq 4), NiðPR3 Þ2 þ Ph­CN ! cis-½NiðCNÞðPhÞðPR3 Þ2 

ð4Þ

which is of considerable interest because the strong C­CN bond is broken. This activation reaction was theoretically investigated by the Jones group50 and our group.51 The key factor of this oxidative addition is understood to be the orbital mixing between the C­CN σ*-antibonding MO and the C­N π*-MO:51 In the transition state, R­CN distorts from the linear to a bent geometry. In such a nonlinear geometry, the π* MO of the CN triple bond can mix into the antibonding C­CN σ*-MO (Scheme 11).51 Because of this orbital mixing, the σ*-component appears in the LUMO and the CT from the dπ orbital of Ni to the LUMO leads to the weakening of the C­CN σ-bond. This C­CN σ-bond activation was applied to such catalytic reactions as Ni-catalyzed carbocyanation of alkyne by the Nakao­Hiyama group.52 We theoretically investigated the reaction mechanism;53 the first step is the oxidative addition of the C­CN σ-bond of Ph­CN to a nickel(0) complex and the second one is the alkyne insertion into the Ni(II)­Ph bond. The alkyne insertion into the Ni­CN bond is very difficult, because of the strong Ni­CN bond. The last step is the C­CN reductive elimination. The rate-determining step is the oxidative addition of the C­CN bond to a nickel(0) complex. Hence, the Ph­CN 902 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

σ-bond activation is a key step in this catalytic reaction. This is one reason why Ni(PR3)2 is used as a catalyst; note that the Ni(0) complex exhibits high reactivity in concerted oxidative addition. Another new advance in this field is the acceleration of the concerted oxidative addition of C­CN σ-bond by Lewis acid, which was also reported by the Jones group.49b The nickel/ Lewis acid system was applied to Ni-catalyzed reactions by the Nakao­Hiyama group54 and Kurahashi­Matsubara group.55 We theoretically investigated the reaction mechanisms of Ni(0)catalyzed [6-2+2] cycloaddition reaction of isatoic anhydrides with alkynes and Ni(0)-catalyzed decyanative [4+2] cycloaddition.56 In these theoretical studies, we found that Lewis acid accelerates the C­C σ-bond cleavage by enhancing the CT from the metal to the C­C σ*-antibonding MO. We believe that the use of Lewis acid is very powerful to achieve σ-bond activation and perform catalytic reaction via σ-bond activation. 3.2.2 Stepwise Oxidative Addition via Nucleophilic Attack of Metal Center to Substrate (eq 1b): The first theoretical study of this type of oxidative addition was carried out by Rzepa and co-workers with DFT, where the COSMO method was employed to incorporate solvation effects.38 They found that a zwitterion-type σ-complex is formed through nucleophilic attack of Pd(0) to a carbon atom of substrate before σ-bond cleavage. However, it is not clear whether σbond cleavage occurs in one step or in a stepwise manner via nucleophlic attack. Also, they recognized that the presence of electron-withdrawing substituent and the solvation are important for the nucleophilic attack. Two years later, Ziegler and co-workers theoretically investigated the oxidative addition of phenyliodide (Ph­I) to Pd(P^P) (P^P: bis(dimethylphosphino)ethane or bis(dimethylphosphine)biphenyl) in solution,57 where the PCM method was employed to consider the solvation effects. They found that the iodide is dissociating from the substrate and Pd center in the transition state. This result indicates that the oxidative addition occurs via nucleophilic attack. We also theoretically investigated a similar oxidative addition of methyliodide to a Pt(II) complex [PtBr2(NH3)2] (eq 5a),58 which is a model reaction of eq 5b reported by Pudapphatt et al.59 In this work, the solvation effect was incorporated with the RISM-SCF method.60 ½PtðCH3 Þ2 ðNH3 Þ2  þ CH3 I (5a) ! trans-½PtðCH3 Þ3 ðIÞðNH3 Þ2  ½PtðCH3 Þ2 ðbpyÞ þ RX ! trans-½PtðCH3 Þ2 ðRÞðXÞðbpyÞ (5b) ðRX ¼ CH3 I or PhCH2 BrÞ Interestingly, methyliodide undergoes the nucleophilic attack of the Pt center (Figure 8). It should be noted that the transition

© 2015 The Chemical Society of Japan

Figure 8. Geometry changes in the oxidative addition of methyliodide to a Pt(II) complex. Bond distances are in angstrom. Reprinted with permission from Ref. 58. Copyright 2008 Elsevier B.V. All right reserved.

state TS23 is essentially the same as that of the usual transition state of the SN2 substitution reaction; see the CH3 moiety takes a planar geometry and the Pt­C­I moiety is almost linear. After TS23, the iodide anion dissociates from the CH3 group. However, the iodide anion does not completely dissociate from the Pt complex but it is staying around the Pt center to move to the position trans to the CH3 group; in other words, a separated species 4a is much less stable than an ion-pair species 4b (Figure 8). The final product has a trans-form, which is different from the cis-product of the concerted oxidative addition. It should be noted that the geometry of [Pt(CH3)2(NH3)2] does not distort very much in TS23, which will be discussed below. The comparison between stepwise and concerted oxidative addition was recently made in the theoretical study of the reaction between BBr2(OSiMe3) and M(PMe3)2 (M = Pd or Pt),61 where DFT was employed with PCM for incorporating solvation effects. Interestingly, a trans product was experimentally observed in this oxidative addition of a B­X σ-bond (X = halogen) to a metal complex,62 which is different from that of the concerted oxidative addition. The DFT calculation showed that trans-[PtBr{BBr(OSiMe3)}(PMe3)2] is directly produced by the stepwise oxidative addition to Pt(PMe3)2, which is consistent with the experimental observation. In the transition state, the Br dissociates from the B center, to afford an ion pair intermediate [Pt{BBr(OSiMe3)}(PMe3)2]Br, as shown in TS3,5-Pt of Figure 9 (lower part). It should be noted that the dissociating Br anion does not form any interaction with the Pt center. This transition state is essentially the same as that of an SN2 reaction. The concerted oxidative addition was also investigated (Figure 9, upper part). Its transition state TS3,4-Pt indicates characteristic features of the concerted oxidative addition; the B­Br distance is considerably elongated, the P­Pt­P Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

angle considerably decreases to 140°, and the dihedral angel between the PtP2 plane and the B­Br bond is 45°. These features are essentially the same as those observed in the concerted oxidative additions of the C­C and Si­C σ-bonds to Pt(PH3)2.46f The product of this oxidative addition is a cis[PtBr{BBr(OSiMe3)}(PMe3)2], which isomerizes to a transform through a transition state TS4,5-Pt. This isomerization occurs on the singlet potential energy surface, unexpectedly, despite the triplet being the ground state in a tetrahedral-like d8 system. This is because the boryl group is extremely electrondonating to destabilize very much one d orbital; remember that one d orbital is empty in a closed-shell singlet d8 system. Thus, the isomerization occurs on the singlet potential energy surface. An important difference in transition state of the B­Br σbond cleavage between the stepwise oxidative addition and the concerted one is observed in the P­Pt­P angle; in TS3,5-Pt of the stepwise oxidative addition, it is 160° which is considerably larger than that in TS3,4-Pt of the concerted oxidative addition. This difference arises from the difference in the orbital interaction between TS3,5-Pt and TS3,4-Pt. In the concreted oxidative addition, the dπ orbital interacts with the antibonding σ*-MO of the substrate, as discussed above. To form a strong CT interaction, the dπ orbital energy must become higher. To raise the dπ orbital energy, the P­Pt­P angle becomes smaller; remember that the lone pair orbitals of two phosphines interact with the dπ orbital in an antibonding way to destabilize it in energy (Scheme 3B). This is one of the characteristic features of the concerted oxidative addition. In the nucleophilic attack involved in the stepwise oxidative addition, on the other hand, the doubly occupied dσ orbital of Pt(PMe3)2 interacts with the empty p orbital of the B atom. To form a strong CT inter© 2015 The Chemical Society of Japan | 903

Figure 9. Geometry changes in the oxidative addition of BBr2(OSiMe3) to Pt(PMe3)2. Bond distances are in angstroms. Reprinted with permission from Ref. 63. Copyright 2013 American Chemical Society.

action, the dσ orbital must exist at a high energy; note that BBr2(OSiNe3) is a Z-ligand because the empty 2p orbital of the B atom forms a σ-type CT interaction. The P­Pt­P bending does not necessarily occur to raise the dσ orbital energy because lone pair orbitals of two phosphines overlap well with the dσ orbital at the P­Pt­P angle of 180°; though the P­Pt­P angle somewhat decreases in TS3,5-Pt, this geometry distortion occurs to reduce the steric repulsion between Pt(PMe3)2 and BBr2(OSiMe3). Hence, the P­Pt­P angle is considerably larger in TS3,5-Pt than in TS3,4-Pt. Also, the geometry of Pt(CH3)2(NH3)2 does not distort very much in TS23 of the nucleophilic attack of the Pt center to CH3I; see above and Figure 8. In the oxidative addition to Pt(PMe3)2, the stepwise reaction occurs more easily than the concerted one, because the isomerization of cis-[PtBr{BBr(OSiMe3)}(PMe3)2] to a trans-form needs a large activation energy. In the oxidative addition to Pd(PMe3)2, concerted oxidative addition occurs more easily than stepwise because the SN2-like transition state becomes higher in energy than the transition state for the cis­trans isomerization of [PdBr{BBr(OSiMe3)}(PMe3)2]. This difference is understood, as follows: Because the Pd d orbital is more stable in energy than the Pt d orbital, the dσ orbital of non-distorted Pd(PMe3)2 does not exist at a sufficiently high energy.29 Hence, the P­Pd­ P angle must decrease to raise the dπ orbital energy enough to strongly form the CT to the substrate. In such Pd(PR3)2 with a bent structure, concerted oxidative addition is more favorable than stepwise via nucleophilic attack, because the dπ orbital becomes the HOMO in the bent structure. These results lead to the conclusions; (i) the solvation effect is crucial to stabilize the transition state and ion-pair intermediate in the stepwise oxidative addition via nucleophilic attack of a metal center, indicating that the use of polar solvent is recommended. A theoretical method which incorporates the solvation effects must be employed in the calculation. (ii) The dσ orbital must exist at a high energy for the stepwise oxidative addition via nucleophilic attack. The metal complex with the Zligand has a dσ orbital at a high energy; for instance, Pt(PMe3)2 which can perform a stepwise oxidative addition forms an 904 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

adduct [Pt(PMe3)2(AlCl3)] with a typical Z-ligand AlCl3. In this adduct, the CT from the Pt dσ orbital to the empty 3p orbital of AlCl3 contributes to the interaction.64 The metal complex with η1-C coordinated CO2 has a doubly occupied dσ orbital at a high energy, as was discussed above. Considering the above discussion, one can expect that such metal complexes can be applied to this type of stepwise oxidative addition reaction via nucleophilic attack. 3.2.3 Heterolytic σ-Bond Activation (eq 2a): As discussed above, one important feature of this heterolytic σbond activation reaction is that the metal oxidation state does not change at all, which is completely different from the oxidative addition (eqs 1a and 1b). In my understanding, this reaction was first reported by the Fujiwara­Moritani group long ago.65 However, the importance of this reaction was not recognized and the electronic process was unclear for a long time. We theoretically investigated this heterolytic C­H σ-bond activation of benzene by palladium(II) formate complex Pd(η2-O2CH)2 and clearly displayed the electronic process and the important driving force,40 where Pd(η2-O2CH)2 was employed as a model of Pd(OAc)2 used experimentally. As shown in Figure 10, the first step is the formation of a palladium(II)­benzene complex I1, which occurs through a transition state TS1a. In the next step, the C­H σ-bond activation occurs through a transition state TS1b to afford a palladium(II) phenyl complex [Pd(η2-O2CH)(Ph)(HCOOH)] P1, in which a formic acid weakly coordinates with the Pd center. In TS1b, the H atom is moving from the Ph group toward the O atom of formate and its position is almost intermediate between them. The electron population changes are interesting. As shown in Figure 7B, the electron population of the Ph group decreases in the palladium(II)­benzene complex I1 because the CT occurs from the benzene to the Pd(II). Then, its electron population considerably increases when going from I1 to the product P1 through TS1b. On the other hand, the H atomic population considerably decreases when going to the product. The Pd atomic population somewhat increases in the reaction. These features are very much different from the population changes observed in the concerted oxidative addi© 2015 The Chemical Society of Japan

Figure 10. Geometry changes in the heterolytic C­H σ-bond activation of benzene by Pd(II) bisformate complex. Reprinted with permission from Ref. 40. Copyright 2000 American Chemical Society.

Pd(PMe3)2

+

H-Ph

cis-Pd(Ph)(H)(PMe3)2

BD(C-H) = 119.0

BD(Pd-H) = 49.5 BD(Pd-Ph) = 51.4

Pd(η η2-O2CH)2

+

Pd(Ph)(η2-O2CH)(HCOOH)

BD(Pd-O) = 23.2

BD(C-H) = 119.0

H-Ph

BD(O-H) = 107.0 BD(Pd-Ph) = 51.4

Scheme 12. Bond energies (in kcal mol¹1)a) related to heterolytic C­H σ-bond activation by [Pd(η2-O2CH)2]. a) CCSD(T)-calculated values are presented.

tion in which the electron populations of R (Me, Ph etc.) and H groups considerably increase but the Pt atomic population considerably decreases (Figure 7A). Based on these results, we named this reaction heterolytic C­H σ-bond activation. The theoretical study showed that this reaction occurs with a moderate activation barrier and significantly large exothermicity, while the concerted oxidative addition to a palladium(0) complex occurs with a considerably large activation barrier and significantly large endothermicity. In general, palladium(0) complexes are not reactive very much for the concerted oxidative addition because its d10 electron configuration is very stable; in other words, the d orbital exists at a low energy in a palladium atom.29 The bond energies provide us with clear understanding of the reason why the hetelolytic C­H σ-bond activation easily occurs (Scheme 12). In the concerted oxidative addition, only the C­H σ-bond of benzene is broken in the reactant side but the Pd­Ph and Pd­H bonds are newly formed in the product side. In the heterolytic activation, the C­H bond and one of the Pd­O bonds in the Pd­η2-O2CH moiety are broken in the reactant side but the Pd­Ph and O­H bonds are Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

formed in the product side. Though one of the Pd­O bonds must be broken in the heterolytic activation, this bond is not very strong because the Pd­η2-O2CH moiety changes to the Pd­η1-OCOH by the Pd­O bond breaking; note that the Pd­O bond in the Pd­η1-O2CH moiety is stronger than that of the Pd­ η2-OCOH bond. Also, the very strong O­H bond is formed in the product, which is much stronger than the Pd­H bond. Hence, the heterolytic C­H σ-bond activation can occur easily, in contrast to the concerted oxidative addition which is difficult in the case of Pd(0) complex. The important conclusions are summarized below:40 (i) The concerted oxidative addition of the C­H bond of benzene to Pd(PMe3)2 occurs with a large activation energy and endothermicity, indicating that the concerted oxidative addition to a palladium(0) complex is difficult. (ii) On the other hand, the heterolytic C­H σ-bond activation by a palladium(II) formate complex easily occurs with a moderate activation barrier and significantly large exothermicity. (iii) The driving force of this reaction is the formation of a strong O­H bond. (iv) The population changes clearly show that the H atom becomes positively © 2015 The Chemical Society of Japan | 905

charged and the Ph group becomes negatively charged in the reaction, indicating that the C­H σ-bond activation occurs in a heterolytic manner. And, (v) the Pd oxidation state does not change at all unlike it in the oxidative addition. All these are important characteristic features of the heterolytic σ-bond activation. Though we named this reaction heterolytic σ-bond activation, other names have also been employed for this type of reaction;66 those names are internal electrophilic substitution (IES),67 concerted metalation­deprotonation (CMD),68 and ambiphilic metal­ligand activation (AMLA).69 Our computational results are consistent with these names, too: This reaction can be understood to be an intramolecular electrophilic attack (IES) of the Pd center to a benzene π-electron system because the Pd atomic population increases in the reaction. Also, the H atom of benzene is substituted for by Pd in the palladium(II)­ benzene complex. In this regard, this is an internal electrophilic substitution. However, the electron population of the phenyl group increases in the reaction, which is not consistent with the name electrophilic substitution. The CMD is a good name because the benzene simultaneously undergoes metalation and deprotonation in the reaction. However, this name is limited to reactions in which H atom participates. Considering that this type of heterolytic σ-bond activation is found in many cases, as will be discussed below, a general name is better. Also, the name of AMLA is reasonable because a palladium atom and one formate (in real a system, acetate) participate in the reaction through a six-member ring including a C­H bond to be broken. Though the name has not been fixed yet, to our knowledge, we believe that the heterolytic σ-bond activation is the best because this name is general and clearly represents the electronic process. There remains one important issue to be investigated. It is the orbital interaction which participates in the heterolytic σbond activation. Though this important orbital interaction was briefly discussed in the theoretical work of the C­H σ-bond activation of benzene by Pd(η2-O2CH)2,40 the discussion was presented without evidence. The orbital interaction has been clearly discussed in our recent theoretical work on the C­H σbond activation of methane by a titinum(IV)­imido complex;48 see eq 6. ðMe3 SiOÞ2 Ti¼NHðSiMe3 Þ þ H­CH3 ! ðMe3 SiOÞ2 TiðCH3 Þ-NH2 ðSiMe3 Þ

ð6Þ

This reaction and similar ones were theoretically investigated previously with Hartree­Fock and DFT methods.70 We investigated this reaction with the DFT, MP2 to MP4(SDQ), and CCSD(T) methods. MP2 to MP4(SDQ) exhibit fluctuation in activation barrier and reaction energy, because the reactant containing a Ti­N double bond is not represented well by these methods. On the other hand, CCSD(T) and DFT provide similar values. DFT with B3PW91 functional shows that this reaction occurs with a moderate activation energy of 14.6 kcal mol¹1 and significantly large exothermicity of 22.7 kcal mol¹1, where potential energy is employed in discussion. The population changes indicate that the C­H σ-bond is cleaved in a heterolytic manner (Figure 11A), the H atomic population considerably decreases, while the electron population of the CH3 group considerably increases. The Ti atomic population considerably 906 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

increases when going from the reactant to the transition state but then moderately decreases when going to the product from the transition state. These features are similar to the population changes in the heterolytic σ-bond activation by Pd(η2-OCH)2. The HOMO of the transition state mainly consists of the C­H σ-bonding MO and σ*-antibonding MO of CH4 and the dπ­pπ bonding MO between the Ti and N atoms (Scheme 13A), where the dπ­pπ bonding MO is the HOMO of (Me3SiO)2Ti=NH(SiMe3). Because the C­H σ-bonding MO of CH4 exists at a lower energy but the C­H σ*-antibonding MO exists at a higher energy than the dπ­pπ bonding MO of (Me3SiO)2Ti=NH(SiMe3), this dπ­pπ bonding MO forms a bonding overlap with the C­H σ*-antibonding MO but an antibonding overlap with the C­H σ-bonding MO. Because of these orbital mixings, the participation of the H 1s orbital decreases but that of the C 2p orbital increases in this HOMO (Scheme 13B). As a result, the H atom becomes positively charged and the C atom becomes negatively charged. The negatively charged C atom induces the CT from the C 2p orbital to the empty dz2 of the Ti to reduce the electron density on the C atom and increase the Ti atomic population (Scheme 13C). This CT leads to the formation of the Ti­C bond. These orbital mixings reasonably explain all of the changes in electron distribution and geometry observed in the heterolytic σ-bond activation reaction. It is concluded that these orbital interactions are the origin of the heterolytic σ-bond activation reaction. Interestingly, similar orbital interactions play crucial roles in the 2+2 coupling reaction between the Ti­imido bond and acetylene (eq 7). The experimental work was reported by Wolczanski and co-worker.71 We theoretically investigated this reaction with DFT, CCSD(T), and CASPT2 methods.72 Though the MP2-MP4 methods provided considerably different energy changes from other methods, the DFT, CCSD(T), and CASPT2 presented similar energy changes.

(Me3SiO)2Ti=NH(SiMe3) + RC≡CR RC=CR (Me3SiO)2Ti

NH(SiMe3) ð7Þ

The electron population changes of this reaction are interesting (Figure 11B); the Cα atomic population considerably increases, while the Cβ atomic population considerably decreases. The Ti atomic population considerably increases when going from the reactant to the transition state but then moderately decreases when going to the product from the transition state. These population changes are essentially the same as those of the C­H σ-bond activation reaction by a titanium(IV) imido complex. The orbital interactions shown in Scheme 14 induces the above mentioned population changes; the Ti­N dπ­pπ bonding MO overlaps with the acetylene π orbital in an antibonding way and with the acetylene π* orbital in a bonding way because the Ti­N dπ­pπ bonding MO exists at a higher energy than the acetylene π MO but at a lower energy than the acetylene π* MO. These orbital mixings are essentially the same as those in Scheme 13. It is of considerable interest that essentially the same orbital pictures and population changes are observed between two different reactions, the heterolytic C­H σ-bond activation and the 2+2 coupling reactions. This is because the Ti­N dπ­pπ bonding MO plays crucial roles in both reactions. © 2015 The Chemical Society of Japan

(A) C-H σ-bond activation by (Me3SiO)2Ti(=NSiMe3) 1

(B) 2+2 Coupling between 2-butyne and (Me3SiO)2Ti(=NSiMe3) 1

Figure 11. Population changes in the C­H σ-bond activation of methane by a Ti­imido complex and the 2+2 coupling reaction between acetylene and Ti­imido complex. Reprinted with permission from Refs. 48 and 72. Copyright 2010 American Chemical Society.

σ∗ 10.4% (unocc)

dπ−pπ

σ

(occ)

10.3%

δ−

δ+

56.8%

(occ)

dπ−pπ

56.8%

σ∗ 10.4% (unocc)

(occ)

(B) Polarization of the C-H bond

σ

(occ)

dz2

σ

7.3%

(occ)

10.3%

10.3%

(unocc)

dz2 7.3% (unocc) (A) Composition of HOMO

(C) CT from CH4 toTi(IV)

Scheme 13. Important orbital interaction in the heterolytic C­H σ-bond activation. Reprinted with permission from Ref. 48. Copyright 2007 American Chemical Society. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan | 907

(A)

(B)

Scheme 14. Orbital interaction scheme in the 2+2 coupling reaction between the Ti(IV)­N and C¸C triple bonds. Reprinted with permission from Ref. 72. Copyright 2010 American Chemical Society.

Many theoretical studies have reported that the H­H σbond activation by hydrogenases and their models occurs in a heterolytic manner.73 In this regard, transition metal dinuclear complexes were synthesized as those models.74 Matsumoto, Tatsumi, and co-workers synthesized a hydroxo/sulfido-bridged ruthenium­germanium heterodinulcear complex and found that this compound is reactive for the H­H σ-bond activation of dihydrogen.75 We theoretically investigated the H­H σ-bond activation reaction by this heterodinuclear complex, using the ONIOM(DFT:MM) method and found that the H­H σ-bond activation occurs in a heterolytic manner and both the Ru atom and the Ge­OH group participate in the activation.76 The anionic group directly bound with the transition metal participates in many heterolytic σ-bond activation reactions. But in this reaction, it should be noted that the OH group which does not coordinate with the metal but is bound with the heavy maingroup element participates in the σ-bond activation reaction. This result suggests that one can perform heterolytic σ-bond activation with a variety of compounds which have a metal and an electronegative group even separated from the metal. Considering the reports discussed above, it is concluded that various heterolytic σ-bond activation reactions can be found with various new compounds and that such heterolytic σ-bond activation plays crucial roles in catalytic reactions and biological reactions. Though the C­H σ-bond activation by metal oxide also occurs in a heterolytic manner,77,78 detailed explanation is omitted here to save space. 3.2.4 Oxidative Addition to an M­L Moiety (L = Neutral Ligand) (eq 2b): This type of oxidative addition had not been recognized as a σ-bond activation reaction before we discussed it.3,36 One good example is an Si­H σ-bond activation by [Cp2Zr(C2H4)] (Cp: C5H5)44 (eq 8): ½Cp2 ZrðC2 H4 Þ þ H­SiH3 ! ½Cp2 ZrðSiH3 ÞðCH2 CH3 Þ or ½Cp2 ZrðHÞðCH2 CH2 SiH3 Þ ð8Þ ½PdðPH3 Þ2 ðC2 H2 Þ þ RS­BðORÞ2 ! ½PdðSRÞfCH¼CHBðORÞ2 gðPH3 Þ2  ð9Þ Though very strong π-back-donation interaction is formed between the Zr center and ethylene in [Cp2Zr(C2H4)], it is unlikely that the ethylene moiety becomes dianion. This means that the oxidation state of the Zr center is considered to be +II in [Cp2Zr(C2H4)]. In [Cp2Zr(H)(CH2CH2SiH3)] and [Cp2Zr(SiH3)(CH2CH3)], the oxidation state of the Zr center is 908 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

apparently +IV because Cp, H, alkyl, and silyl are considered to be anions in a formal sense. Hence, this reaction can be understood to be an oxidative addition of the Si­H σ-bond to the Zr­(C2H4) moiety. Essentially the same feature was found in the reaction between [Pd(PH3)2(C2H2)] and thioborane (eq 9).43 In the left-hand side of eq 9, the Pd center takes 0 oxidation state but in the right-hand side +II oxidation state because the SR and vinyl (­CH=CHB(OR)2) groups bound with the metal atom are considered to be anions in a formal sense. The reaction between [Cp2Zr(C2H4)] and H­SiH3 easily occurs with a small activation barrier and significantly large exothermicity, as shown in Figure 12. In the transition state leading to the formation of [Cp2Zr(SiH3)(CH2CH3)] (the upper half of Figure 12), silane is very distant from the Zr center, suggesting that this is a transition state for the approach of silane to the Zr center. After that, [Cp2Zr(SiH3)(CH2CH3)] is formed without any transition state, indicating that the Si­H σ-bond can be broken without any barrier. Also, [Cp2Zr(H)(CH2CH2SiH3)] is formed through a five-center transition state (the lower half of Figure 12), in which the Si­H σ-bond cleavage is in progress. Though detailed analysis has not been made yet, the contour map of the HOMO of the transition state provides us with a reasonable understanding of orbital interaction scheme which plays crucial roles in the reaction (Figure 13). In the transition state leading to the formation of [Cp2Zr(SiH3)(CH2CH3)], the dπ­π* bonding MO of [Cp2Zr(C2H4)] starts to form bonding overlaps between the Zr center and SiH3 group and between the ethylene carbon and the silane H atoms (Figure 13A). One can understand that this HOMO is constructed by the bonding overlap between the Si­H antibonding σ*-MO and the dπ­π* bonding MO of [Cp2Zr(C2H4)] (Figure 13B). In the transition state leading to the formation of [Cp2Zr(H)(CH2CH2SiH3)], the dπ­π* bonding MO of [Cp2Zr(C2H4)] forms bonding overlaps between the Zr center and the H atom of silane and between the ethylene carbon and the SiH3 group (Figure 13C). This HOMO is considered to be constructed by the bonding overlap between the Si­H antibonding σ*-MO and the dπ­π* bonding MO of [Cp2Zr(C2H4)] (Figure 13D), in which the Si­H bond takes a reverse orientation to that of Figure 13B. In experimental works, two examples are found of this type of oxidative addition to an M­L moiety, as mentioned above. The first experimental example, to my knowledge, is the © 2015 The Chemical Society of Japan

Figure 12. Si­H σ-bond activation of silane by [Cp2Zr(C2H4)]. Bond distances are in Angstroms. In parentheses are relative potential energy (in kcal mol¹1) to [Cp2Zr(C2H4)] + SiH4. Reprinted with permission from Ref. 44b. Copyright 2004 American Chemical Society.

reaction of water with a chromium(0) silabenzene complex (Scheme 15).41 In the intermediate, the OH group is bound with the Si atom and the H atom is bound with the Cr center, indicating that the oxidation state of the Cr increases to +II. The reductive elimination of the H atom on the Cr and the C atom of the silacyclohexadienyl group occurs to produce a silanol. In an experiment with D2O, one D atom is introduced in the product. This result indicates that the H­D exchange between the chromium(II) hydride and D2O occurs easily. Also, Peters and coworkers reported that a nickel(0) borane complex [Ni{MesB(o-Ph2PC6H4)2}] performs the H­H σ-bond activation to afford a nickel(II) hydride borohydride complex [Ni(H){MesBH(o-Ph2PC6H4)2}] (Scheme 16).42 In the product, the oxidation state of the Ni center increases to +II, because the hydride and the borohydride are considered to be anions in a formal sense. These observations indicate that this reaction is understood to be oxidative addition to an M­L moiety. We theoretically investigated63 the H­H σ-bond activation reaction by the nickel(0) borane complex reported by Peters.42 In the nickel(0) borane complex [Ni{MesB(o-Ph2PC6H4)2}], the Ni center has a distorted three-coordinate structure, which is not usually observed in nickel(0) complexes (Figure 14). This is because the empty 2p orbital of the B atom interacts with the doubly occupied d orbital of the Ni center to form a CT interaction from the Ni to the empty 2p orbital of the borane. The C=C double bond of one phenyl group also coordinates with the Ni center. The first step of the reaction is coordination Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

of dihydrogen with the Ni center, which occurs with a moderately positive Gibbs reaction energy (2.8 kcal mol¹1) to afford a dihydrogen σ-complex. In this complex, the Ni­Ph distance is somewhat elongated but the Ni­B distance is elongated a little. In the transition state (TS2/3 in Figure 14), the H1 atom is approaching the Ni center and the H2 atom is approaching the B atom, where the H1­H2 distance is considerably elongated to 0.997 ¡. A similar dihydrogen σ-complex and transition state were reported in the DFT study by Peters and co-workers.42b In the product, the H1 atom coordinates with the Ni center as a hydride ligand and the H2 atom bridges the B and Ni atoms. The B atom has a tetrahedral-like structure, indicating that the borate is formed and its H atom interacts with the Ni atom as one ligand; in other words, these features clearly show that this reaction is understood to be an oxidative addition of the H­H σ-bond to a Ni(0)­borane moiety. In the transition state, considerable CT occurs from the H­H σ-bonding MO to the empty 2p orbital of the borane and also somewhat occurs from the Ni doubly occupied d orbital to the H­H σ*-antibonding MO (Figure 15). Because the former CT is unexpectedly strong, the H2 molecule is somewhat positively charged in the transition state, despite this being oxidative addition to an M­L moiety. This characteristic feature comes from the presence of the empty 2p orbital of the borane. This 2p orbital interacts with the Ni center in the reactant, but in the transition state, its orientation changes toward the H2 atom. Thereby, the Ni doubly occupied 3d orbital does not need to form a CT with the © 2015 The Chemical Society of Japan | 909

C

C Zr Zr

H Si

R

RR

(A) HOMO of transition state leading to Cp2Zr(SiH3)(C2H5)

(B) Schematical orbital picture

C

C Si Zr

(C) HOMO of transition state leading to Cp2Zr(H)(CH2CH2SiH3)

H

(D) Schematic orbital picture

Figure 13. Contour maps of the HOMO of the transition states of eq 7a. Contour values are 0.0, «0.0125, «0.025, «0.0375, and so on (in e1/2 au¹3/2), where the Hartree­Fock method was employed. Reprinted with permission from Ref. 44b. Copyright 2004 American Chemical Society.

Tbp = 2,4,6-substituted phenyl group

Scheme 15. O­H σ-bond activation of water by chromium(0) silabenzene complex. Reprinted with permission from Ref. 41. Copyright 2010 American Chemical Society.

borane 2p orbital and starts to form the CT interaction with the H­H σ*-antibonding MO, which is indispensable for the H­H σ-bond activation. In the oxidative addition of the Si­H σ-bond to [Cp2Zr(C2H4)], the Si­H σ*-antibonding MO overlaps with the Zr dπ 910 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

Scheme 16. H­H σ-bond activation by nickel(0) borane complex. Reprinted with permission from Ref. 42. Copyright 2012 American Chemical Society.

and the ethylene π* orbitals in a bonding way, as was discussed above. This interaction is similar to the interaction of the H­H σ*-antibonding MO with the Ni doubly occupied d orbital. However, the participation of the Si­H σ-bonding MO was not clearly found in the oxidative addition of the Si­H σ-bond to [Cp2Zr(C2H4)]. In the oxidative addition of the H­H σ-bond to the nickel(0) borane complex, on the other hand, the H­H σ-bonding MO apparently participates in the interaction with © 2015 The Chemical Society of Japan

Figure 14. Geometry changes in the H­H σ-bond activation by a nickel(0) complex [Ni{MesB(o-Ph2PC6H4)2}]. Bond length is in angstroms. In parentheses are the Gibbs energy change (in kcal mol¹1) relative to the reactant. Reprinted with permission from Ref. 61. Copyright 2012 American Chemical Society.

Figure 15. Electron populations of important MOs of [Ni{MesB(o-Ph2PC6H4)2}] and dihydrogen molecule. Reprinted with permission from Ref. 61. Copyright 2012 American Chemical Society.

the empty p orbital of the borane. In this regard, the orbital interaction scheme of the oxidative addition to an M­L moiety is a little bit different between these two examples. Further detailed analysis is necessary. Essentially the same C­H σ-bond activation was recently proposed in the Ni-catalyzed hydroarlyation of unactivated alkenes by Hartwig, Eisenstein, and co-workers.79 In this reaction, the C­H σ-bond of arene reacts with a nickel(0) alkene Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

moiety to afford a nickel(II) alkyl aryl intermediate. They discussed this elementary step as a proton transfer. However, calling this oxidative addition of the C­H σ-bond of arene to a Ni(0)­alkene moiety is also reasonable, because the oxidation state of Ni increases to +II in the reaction in a formal sense. Considering these reactions, one can expect that the oxidative addition to an M­L moiety is an important elementary step in the catalytic cycle. Because the experimental examples have © 2015 The Chemical Society of Japan | 911

been limited, further experimental studies are indispensable to broaden the potential application of this oxidative addition reaction. Further theoretical study is also necessary, because the fundamental features such as orbital interaction and driving force are not clear. In particular, it is necessary to clarify what factors are favorable for a typical concerted oxidative addition to a metal center and what factors are favorable for this type of oxidative addition to an M­L moiety.

is metathesis between Ru­(η1-OCOH) and H­H bonds, which occurs through either four-center or six-center transition state (see the left-hand side of Scheme 17). These four possible reaction courses were theoretically investigated and the metathesis via a six-center transition state was found to be the most favorable. The DFT method with B3PW91 functional underestimates the stabilization of the ruthenium(II) carbon dioxide adduct and thereby the activation barrier of the CO2 insertion step compared to the MP4(SDQ) method. Based on the MP4(SDQ)-calculated values, it is concluded that the ratedetermining step is the CO2 insertion into the Ru­H bond; in the DFT-computational results, the CO2 insertion and the sixcenter metathesis occur with comparable activation barrier. The experiments showed that the reaction rate depends on the pressure of dihydrogen gas, which suggests that molecular dihyrogen participates in the rate-determining step.81b,81c This experimental finding is seemingly inconsistent with the computational result that the rate-determining step is the CO2 insertion. However, the calculated energy changes provide an understanding consistent with the experimental finding; because the CO2 insertion is endothermic, the coordination of dihydrogen is necessary to stabilize the ruthenium(II) η1formate species. This means that the reaction rate depends on the concentration of dihyrogen in the solution, as experimentally observed. The metathesis between the Ru­(η1-OCOH) and H­H bonds is a typical heterolytic H­H σ-bond activation because one H atom of dihydrogen changes to a proton of formic acid and the other H atom changes to a hydride bound with the Ru(II) center. Actually, the Hα atomic population increases very much and the Hβ one decreases very much in the reaction (Figure 16), where the Hα and Hβ represent hydrogen atoms which become a proton of formic acid and a hydride, respectively (Scheme 18). The Ru atomic population somewhat increases. These population changes are essentially the same as those found in the C­ H σ-bond activation of benzene by the palladium(II) formate complex (Figure 7B).40 These results suggest that the heterolytic σ-bond activation plays crucial roles as a key step in this catalytic reaction.

4. Theoretical Studies of Catalyses of Transition-Metal Complexes As mentioned in the introduction, theoretical and computational study is now indispensable for understanding catalytic reactions by transition-metal complexes.2,3 In this section, we wish to report some typical examples of our theoretical studies of catalytic reactions, discuss what characteristic features are disclosed by theoretical and computational studies, and present theoretical predictions. 4.1 Catalyses for CO2 Conversion Reactions. The first example is the catalytic hydrogenation of carbon dioxide into formic acid. The prototype of this reaction was reported some time ago by Inoue and co-workers,80 and a remarkable breakthrough was achieved about 20 years ago by Ikariya, Noyori, and co-workers, because they succeeded in providing extremely large turn-over numbers.81 Since then, this reaction is one of the most attractive CO2 conversion reactions.82 We theoretically investigated this catalytic reaction to provide clear understanding of the reaction mechanism because many possibilities were found in the catalytic cycle83 (Scheme 17), it is likely that the active species of this catalytic reaction is a ruthenium(II) dihydride complex [Ru(H)2(PMe3)3], because this complex was experimentally employed as one of the catalysts. The first step is CO2 insertion into the Ru­H bond to afford a ruthenium(II) formate species [Ru(H)(OCOH)(PMe3)3]. In the next step, one of the plausible reactions is reductive elimination of formic acid because one hydride ligand still remains on the Ru center. This reaction occurs through either three-center or five-center transition state (see the right-hand side of Scheme 17). Another plausible reaction HCOOH

LnRu H

Oxidative Addition H2 H LnRu

HCOOH H H LnRu

Reductive Elimination

O

CO2

H H

C H O

LnRu H

H Six-Centered σ -Bond Metathesis

H2

O C

O

HCOOH

HCOOH

LnRu

CO2 Insertion

H LnRu

H Four-Centered σ -Bond Metathesis H2 LnRu H

O

C

O C O H H

O C H O

L = PR 3

O

H

Scheme 17. Four possible catalytic cycles of Ru-catalyzed hydrogenation of carbon dioxide. 912 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan

Here, I wish to mention the reasons why four-center and six-center transition states are possible and why the six-center transition state is more favorable than the four-center one in the metathesis between the Ru­(η1-OCOH) and H­H bonds. Because each of two O atoms of the formate has a lone-pair orbital, both four- and six-center transition states are possible. In the four-center transition state, the lone pair orbital of the O atom, which is used for the coordinate bond with the Ru center, must change its direction toward the hydrogen 1s orbital, as shown in Scheme 18A. This geometry change leads to the weakening of the Ru­O coordinate bond. In the six-center transition state, on the other hand, the lone pair of the terminal O atom starts to form a bonding overlap with the hydrogen 1s orbital, where the Ru­(η1-OCOH) bond is not weakened very much (Scheme 18B). Such transition state is much more favorable than the four-center transition state. This is the reason why the metathesis occurs via the six-center transition state. In the Rh(I)-catalyzed hydrogenation of carbon dioxide, not the six-center metathesis but the four-center one was proposed as an important elementary step.84 This is because the metathesis occurs with nearly no barrier in this reaction.

We have one more question, if the reductive elimination does not play any role in the CO2 hydrogenation into formic acid. To provide the answer, we theoretically investigated Rh(III)- and Rh(I)-catalyzed hydrogenations of carbon dioxide and made comparison of them with the Ru(II)-catalyzed reaction.85 In the Rh(III)-catalyzed reaction, the final step is the reductive elimination, while in the Rh(I)-catalyzed reaction, both the metathesis and the oxidative addition of the second dihydrogen molecule followed by the reductive elimination of formic acid occur with a similar activation energy. These interesting differences are understood based on the M­H bond energy: Because the Rh(III)­H bond energy is small, the reductive elimination can occur with a moderate activation barrier. However, the Ru(II)­H bond is stronger than the Rh(III)­H. Such a strong Ru(II)­H bond makes the reductive elimination difficult because the strong Ru(II)­H bond must be broken in the reductive elimination. Because the Rh(I) complex is very reactive for the oxidative addition of dihydrogen molecule, a rhodium(III) dihydride η1-formate complex is easily formed. After that, the reductive elimination easily occurs because the Rh(III)­H bond is not strong. Also, the metathesis can occur with a moderate activation energy because the strong Rh(I)­H and O­H bonds are formed simultaneously with the H­H and Rh(I)­H bond breaking. In other words, both the metathesis and the oxidative addition of H2 followed by the reductive elimination are possible in the case of Rh(I) complex. From these theoretical studies, it is reasonable to conclude that the M­H bond energy determines which of reductive elimination and metathesis is the final step releasing formic acid. Recently, the Pd-86a and Ni-catalyzed carboxylations of phenyl chloride with carbon dioxide87 and the Ni-catalyzed carboxylation of benzyl chloride were experimentally reported86b (Scheme 19). In the Ni-catalyzed reactions, either Mn or Zn powder was added, interestingly. Consistent with this reac-

Cl

COOH NiCl2(PR3)2/Mn

Figure 16. NBO population changes in the six-membered metathesis between the Ru­(η1-OCOH) and H­H bonds which is an important elementary step in Ru-catalyzed hydrogenation of carbon dioxide. Reprinted with permission from Ref. 83b. Copyright 2012 American Chemical Society.

+ CO2

Scheme 19. Ni-catalyzed carboxylation of phenyl chloride with carbon dioxide.

Scheme 18. Schematic orbital interaction in four- (A) and six-center (B) transition states of metathesis between the Ru­(η1-OCOH) and H­H σ-bonds. Reprinted with permission from Ref. 83a. Copyright 2000 American Chemical Society. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan | 913

Ph-Cl

1/2 Mn(COOPh)2

0

Ni (PPh3)2 Oxidative Addition

One-electron reduction 1/2 Mn

(PPh 3)2NiII(Ph)Cl (PPh3)2

NiICOOPh 1/2 Mn

CO2 insertion (PPh3 )2NiIPh CO2

One-electron reduction 1/2 MnCl2

Scheme 20. Experimentally proposed and theoretically elucidated catalytic cycle of Ni-catalyzed carboxylation of phenyl chloride with carbon dioxide. Cited from Ref. 89a. Reproduced by permission of The Royal Society of Chemistry (RSC).

tion condition, the presence of Ni(I) species was experimentally proposed.86b,87 This is somewhat surprising for us, because the Ni(I) oxidation state is not stable and has not been proposed in catalytic cycles except for a few of limited examples.88 It is of considerable interest to elucidate the reason why an unusual Ni(I) species is involved in the catalytic reaction. We theoretically investigated both reactions.89 In the carboxylation of phenyl chloride, the first step is the oxidative addition of Ph­Cl to a nickel(0) complex [Ni(PPh3)2] (Scheme 20). This reaction easily occurs with a small Gibbs activation energy to afford a nickel(II) chloro phenyl complex [NiCl(Ph)(PPh3)2]. Because the CO2 insertion into the Cu(I)­Me bond was calculated to occur with an activation barrier of about 15 kcal mol¹1, as was discussed above,33 we expected that the CO2 insertion into the Ni(II)­Ph bond can occur with a similar activation energy. However, its Gibbs activation energy is very large (31.7 kcal mol¹1), indicating that the CO2 insertion into the Ni(II)­Ph bond is difficult. One-electron reduction of [NiCl(Ph)(PPh3)2] with Mn easily occurs with a considerably negative ¦G° value (¹21.7 kcal mol¹1) to afford a nickel(I) phenyl complex [NiPh(PPh3)2]. This nickel(I) complex undergoes CO2 coordination to afford a nickel(I) carbon dioxide complex [Ni(Ph)(CO2)(PPh3)2] in which CO2 coordinates with the Ni center in an η2-side-on manner. In this complex, the CO2 insertion into the Ni(I)­Ph bond easily occurs with a very small ¦G°‡ value of 2.6 kcal mol¹1 and a considerably negative ¦G° value of ¹32.3 kcal mol¹1 to afford a nickel(I) benzoate species [Ni(η2O2CPh)(PPh3)2]. The last step is one-electron reduction of [Ni(η2-O2CPh)(PPh3)2]. All these computational results provide evidence of the experimentally proposed reaction mechanism (Scheme 20) and a clear explanation why the Mn powder is necessary in the reaction. One of the important results here is that the CO2 insertion into the Ni(II)­Ph bond needs a large activation energy but the insertion into the Ni(I)­Ph bond easily occurs with a very small activation energy. The reason was clearly discussed in terms of the CT interaction from the Ni­Ph moiety to CO2. As discussed above, the CO2 insertion into the 914 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

M­R bond needs the CT interaction from M­R to CO2.33 The Ni(I)­Ph species is more favorable for such CT than the Ni(II)­ Ph species because the HOMO of the Ni(I)­Ph intermediate exists at a higher energy than that of the Ni(II)­Ph; in other words, the Ni(I)­Ph species is more electron-rich than the Ni(II)­Ph. Ni-catalyzed carboxylation of benzyl chloride with carbon dioxide also occurs with essentially the same catalytic cycle.86b In this case, it is noted that MgCl2 is added to the reaction system unexpectedly. We do not know clear reasons why MgCl2 must be added to the reaction system and what role MgCl2 plays in the reaction. This reaction was theoretically investigated with the DFT method recently and several important features were disclosed:89b (i) Carbon dioxide coordinates with the Ni(I) center to afford a nickel(I) carbon dioxide complex [Ni(Ph)(η2-CO2)(PCp3)2] 8 (Figure 17). (ii) MgCl2 interacts with the O atom of the CO2 coordinated with the Ni(I) to stabilize this CO2 complex 12 by 13.0 kcal mol¹1. (iii) The CO2 insertion into the Ni(I)­CH2Ph bond needs a larger activation barrier than that into the Ni(I)­Ph bond. This is because the sp3 carbon atom is less reactive for the insertion reaction than the sp2 carbon; remember that the sp3 carbon must change its position and orientation in the insertion reaction because of its directional sp3 valence orbital, as was discussed above,33 but the carbon atom of the phenyl group has an sp2 valence orbital and a pπ orbital; note that the pπ orbital can participate in the CT to the π* orbital of CO2 to accelerate the CO2 insertion reaction. (iv) MgCl2 plays crucial roles in accelerating the CO2 insertion into the Ni(I)­CH2Ph bond. Because MgCl2 is a Lewis acid, MgCl2 interacts with the O atom of CO2 which coordinates with the Ni(I) center. This interaction stabilizes the orbital energy of the CO2 moiety to enhance the CT interaction and also stabilizes the system due to the electrostatic interaction. As a result, the CO2 insertion into the Ni(I)­CH2Ph bond occurs with a smaller ¦G°‡ value of 6.4 kcal mol¹1 in the presence of MgCl2 than that (8.6 kcal mol¹1) in the absence of MgCl2 (Figure 17). Also, the transition state TS12-13 in the presence of MgCl2 is much more © 2015 The Chemical Society of Japan

/ Figure 17. Geometry and energy changes in the CO2 insertion into the Ni­CH2Ph bond in [Ni(CH2Ph)(PPh3)2]. Cited from Ref. 89b. Reproduced by permission of The Royal Society of Chemistry (RSC).

Ni(acac)2/Zn/MgBr2

Scheme 21. Ni-catalyzed double carboxylation of alkyne with carbon dioxide.

stable than that TS8-9 in the absence of MgCl2 by 12.0 kcal mol¹1. These results indicate that MgCl2 plays crucial roles to accelerate the CO2 insertion into the Ni(I)­C(sp3) bond. Recently, double carboxylation of alkyne was accomplished by Fujiwara, Tsuji, and co-workers (Scheme 21).90 In this reaction, MgBr2 was necessary, too. The DFT calculations show that MgBr2 plays crucial roles as an innocent additive to accelerate the CO2 insertion into the Ni(I)­vinyl bond like MgCl2. This is one of the important reasons why the doublecarboxylation was successful in the presence of MgBr2. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

Summarizing the above results, the catalytic cycles for CO2 fixation are constructed by CO2 insertion into M­H and M­R bonds, reductive elimination between η1-OCOR and hydride, or metathesis of M­(η1-OCOR) with dihydrogen. One of the new features is the acceleration of CO2 insertion by Lewis acid such as MgCl2 and MgBr2. This new result suggests that Lewis acids can be applied to the CO2 insertion reaction and similar insertion reactions, as well as the σ-bond cleavage via oxidative addition which was discussed in the section of concerted oxidative addition. Another new feature is the use of Ni(I) © 2015 The Chemical Society of Japan | 915

Pt & Rh; Easy

R 3Si H

H2 Reductive Elimination

[M]

Oxidative Addition

[M]

H SiR 3 CH 2

CH 3 [M]

H H

CH 2 SiR 3 Reductive Elimination

CH 2 CH SiR 3

β-Hydrogen Abstraction

Chalk-Harrod

CH 2

SiR 3

Insertion into Pt-H is easy but that into H Pt-SiH3 is very [M] SiR 3 difficult. Modified Chalk-Harrod H 2C CH 2 Insertion into H Ethylene [M] SiR3 Rh-silyl is not very Insertion C C difficult. H H [M]

H C C H2 H2

2

2

Pt: C2H5-SiH3 reductive elimination is more difficult than H-CH2CH2SiH3 one. Rh: C2H5-SiH3 reductive elimination is more difficult in Rh case than in Pt case.

Scheme 22. Chalk­Harrod and modified Chalk­Harrod mechanisms of Pt-catalyzed hydrosilylation of ethylene. Reprinted with permission from Ref. 92. Copyright 2002 American Chemical Society.

species to accelerate the CO2 insertion into the Ni­R bond. This idea can be applied to the other insertion reaction. 4.2 Catalyses for Hydrosilylation of Alkene. Hydrosilylation is an important reaction to synthesize organosilicon compounds. Two important reaction mechanisms have been experimentally proposed; one is the Chalk­Harrod mechanism which occurs via oxidative addition of silane to a low-valent transition-metal complex to afford a transition metal hydride silyl complex, alkene insertion into a metal­hydride bond to afford a metal alkyl silyl complex, and reductive elimination of silyl and alkyl groups to afford a hydrosilylated compound91 (Scheme 22). Another is the modified Chalk­Harrod mechanism (or variant Chalk­Harrod mechanism).93 The first step is the same as that of the Chalk­Harrod mechanism. Then, alkene is inserted into a metal­silyl bond to afford a metal hydride silyl complex. The last step is reductive elimination of alkyl and hydride groups to afford a hydrosilylated compound. Besides these two mechanisms, the Glaser­Tilley mechanism94 and σ-bond metathesis mechanism95 have been proposed. In the Glaser­Tilley mechanism, alkene reacts with the Si­H bond of silane or silyl which coordinates with a metal. In the σ-bond metathesis mechanism, an active species is a metal­alkene complex which reacts with an Si­H bond of silane to afford a metal alkyl hydride species and then either reductive elimination or metathesis with the second silane occurs to produce a hydrosilylated product. These mechanisms are classified in terms of the reaction of alkene with active species. Here, we wish to focus on the Chalk­Harrod, modified Chalk­Harrod, and σ-bond metathesis mechanisms. The Chalk­Harrod mechanism was proposed for Ptcatalyzed hydrosilylation of alkene, while the modified Chalk­Harrod mechanism was proposed for Rh-catalyzed hydrosilylation of alkene. This is because vinylsilane was 916 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

formed little as a by-product in the Pt-catalyzed reaction but somewhat in the Rh-catalyzed reaction. Note that the formation of vinylsilane is evidence of alkene insertion into a metal­silyl bond because it is formed through alkene insertion into an M­ silyl bond followed by β-H abstraction (Scheme 22). In the theoretical study of the Chalk­Harrod mechanism, we used the MP2 method for geometry optimization and the MP4SDQ for evaluation of energy change, where Pt(PH3)2 was employed as a model of catalyst to save CPU time; note that we carried out this work some time ago.96 In the Chalk­Harrod mechanism, the first step is the oxidative addition of the Si­H σ-bond of silane to a zero-valent platinum complex Pt(PH3)2, which easily occurs with nearly no barrier to afford cis-[Pt(H)(SiH3)(PH3)2], as discussed above.46a,46b The second step is ethylene insertion into either the Pt­H bond or the Pt­silyl bond. The ethylene insertion into the Pt­H occurs much more easily than into the Pt­silyl bond to afford [Pt(CH2CH3)(SiH3)(PH3)] (Scheme 22). Though the final alkyl­silyl reductive elimination is more difficult than the H­alkyl reductive elimination, the ethylene insertion into the Pt­silyl bond needs a much higher activation energy than the alkyl­silyl reductive elimination. As a result, the Chalk­Harrod mechanism is more favorable than the modified Chalk­Harrod mechanism in the Pt catalyst. In the theoretical study of Rh-catalyzed hydrosilylation, we employed [RhCl(PH3)2] as a model catalyst and trimethylsilane HSiMe3 as a substrate.92 We found interesting similarities and differences between Pt- and Rh-catalyzed hydrosilylations; (i) the oxidative addition of silane easily occurs in both catalysts, (ii) the ethylene insertion into the Rh­H bond more easily occurs than into the Rh­silyl bond like the Pt case, but the insertion into the Rh­silyl is not very difficult unlike in the Pt case, (iii) the silyl­alkyl (Me3Si­C2H5) reductive elimination is more difficult than the hydride­alkyl (H­CH2CH2SiMe3) © 2015 The Chemical Society of Japan

Transition state

Product

(A) Ethylene insertion into Pt-SiH3 bond

Product

Transition state (B) Ethylene insertion into Rh-SiMe3 bond

Figure 18. Comparison of transition state between ethylene insertion into Pt(II)­silyl and that into Rh(III)­silyl bonds. Reprinted with permission from Refs. 92 and 96b. Copyright 1998 and 2002 American Chemical Society.

elimination in both catalysts, but the silyl­alkyl reductive elimination is more difficult in the Rh catalyst than the ethylene insertion into the Rh­silyl bond. As a result, the modified Chalk­ Harrod mechanism is more favorable than the Chalk­Harrod mechanism in the case of Rh catalyst. One important reason for the modified Chalk­Harrod mechanism is that the ethylene insertion into the Rh­silyl bond is not very difficult, compared to that of the Pt case. The reason is easily found by inspecting the transition state geometry. Because cis-[Pt(H)(SiH3)(PH3)2] with a planar geometry is formed by the oxidative addition of silane, ethylene must coordinate with the Pt center at the position trans to the H(hydride) to be inserted into the Pt­silyl bond (Figure 18A); note that the intermediate cis-[Pt(H)(SiH3)(PH3)2] is a Pt(II) complex with a d8 electron configuration and thereby it has a planar structure. In such case, the Pt­alkyl bond is formed at the position trans to the H(hydride) ligand by the insertion reaction (Figure 18A). This geometry is not favorable for stabilizing the transition state and the product because the H(hydride) has very strong trans-influence. Note that in the ethylene insertion into the Pt­H(hydride) bond, the alkyl group is formed at the position trans to the silyl group, but the insertion into the M­H bond is intrinsically easy because of the spherical 1s valence orbital of the H ligand (Scheme 8). In the Rh case, also cis-[Rh(H)(SiMe3)Cl(PH3)2/3] is formed by the oxidative addition of silane. Alkene coordinates with the Rh center to afford a six-coordinate Oh-like Rh(III) complex because the Rh(III) center has a d6 electron configuration. In the six-coordinate structure, ethylene does not need to take the Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

position trans to the H(hydride) ligand but can take the position trans to phosphine, leading to the formation of the Rh­alkyl bond at the position trans to phosphine (Figure 18B). Because the trans-influence of phosphine is weaker than that of the H(hydride), the ethylene insertion into the Rh­silyl bond occurs with a lower activation barrier than in the Pt case. On the other hand, the silyl­alkyl (Me3Si­CH2CH3) reductive elimination needs a larger activation barrier in the Rh case than in the Pt case. In the Pt case, the transition state has a pseudo-tetrahedral structure to avoid the steric repulsion between the silyl­alkyl moiety and phosphine ligands; remember a similar nonplanar transition state is found in the Si­C oxidative addition to Pt(PH3)2 to reduce the steric repulsion.46f In the Rh case, the deviation from the Oh-like structure is not easy, because such deviation is suppressed by the presence of six ligands in the Ohlike structure. This means that the differences between Pt and Rh cases arise from the difference in the number of d electrons between Pt(II) and Rh(III). In the Rh case, the Rh(III) hydride silyl intermediate has a six-coordinate structure because it is a d6 system, which is favorable for the ethylene insertion into the Rh(III)­silyl bond but not favorable for the silyl­alkyl reductive elimination. In the Pt case, the Pt(II) hydride silyl intermediate must have a four-coordinate planar structure because it is a d8 system. This structure is not favorable for the alkene insertion into the Pt­silyl bond but favorable for the silyl­alkyl reductive elimination because of the less congested transition state. Recently, the Rh-catalyzed hydrosilylation of alkene was theoretically investigated with the DFT method.97 In this case, © 2015 The Chemical Society of Japan | 917

Scheme 23. Reaction mechanism of Cp2Zr-catalyzed hydrosilylation of ethylene. Reprinted with permission from Ref. 44b. Copyright 2004 American Chemical Society.

the Chalk­Harrod mechanism was concluded to be more favorable than the modified Chalk­Harrod mechanism. This result is seemingly inconsistent with our results. However, it should be noted that not the phosphine ligands but the strongly electron-donating carbene ligands coordinate with the Rh center. In such case, the ethylene must take the position trans to the carbene ligand even if ethylene avoids the position trans to the H(hydride). As a result, the ethylene insertion into the Rh­silyl bond does not occur easily and the modified Chalk­Harrod mechanism becomes unfavorable. This suggests that the reaction mechanism is controlled by using various ligands. The σ-bond metathesis mechanism was investigated in the Cp2Zr-catalyzed hydrosilylation of ethylene in the comparison with the Chalk­Harrod and modified Chalk­Harrod mechanisms,44 because this mechanism was proposed experimentally in the Cp2Zr-catalyzed hydrosilylation of alkene.95 The final results are summarized in Scheme 23. Apparently, the ethylene insertion process going from [Cp2Zr(H)(SiH3)] to [Cp2Zr(H)(CH2CH2SiH3)] is not involved in this Scheme, indicating that the modified Chalk­Harrod mechanism is excluded here. This insertion reaction has a very large activation barrier. The ethylene insertion into the Zr­H bond occurs with a very small activation barrier to afford [Cp2Zr(C2H5)(SiH3)]. However, the Chalk­Harrod mechanism is not exactly the same as the typical one, as follows: The simple reductive elimination of silyl and alkyl groups (H3Si­C2H5) does not occur from this species because of the very large activation barrier and endothermicity. The next step is either ethylene-assisted reductive elimina918 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

tion affording [Cp2Zr(C2H4)] and a hydrosilylated product CH3CH2SiH3 or metathesis with one more silane affording [Cp2Zr(H)(SiH3)] and the same hydrosilylated product. Thusformed [Cp2Zr(C2H4)] reacts with silane to afford either [Cp2Zr(H)(CH2CH2SiH3)] or [Cp2Zr(SiH3)(C2H5)], which was discussed above as the oxidative addition to an M­L moiety. [Cp2Zr(H)(CH2CH2SiH3)], which is the same intermediate as that of the modified Chalk­Harrod mechanism, undergoes either the ethylene-assisted reductive elimination or the metathesis with silane. It is of considerable interest to elucidate the reason why such a complicated reaction mechanism is possible in the Cp2Zr catalyst. This complicated mechanism arises from the facts that the simple reductive elimination is difficult but both ethyleneassisted reductive elimination and metathesis are possible. One important reason for the difficulty in the simple reductive elimination is that the d orbital of the Zr center exists at a high energy; see Supporting Information Table S2 and discussion there.29 One of the important features of transition metal elements is that the ionization potential increases and the d orbital energy becomes lower when going from the left-hand side to the right-hand side in the periodic table.29 Because the Zr 4d orbital exists at a high energy, Cp2Zr which is the product of the simple reductive elimination is not stable. However, the ethylene-assisted reductive elimination leads to the formation of a stable [Cp2Zr(C2H4)] complex, in which the strong backdonation from the Zr 4d orbital to the ethylene π* MO is formed due to the presence of the Zr 4d orbital at high energy; compare

© 2015 The Chemical Society of Japan

Scheme 24. Comparison among simple reductive elimination, ethylene-assisted reductive elimination, and σ-bond metathesis in Cp2Zr-catalyzed hydrosilylation of ethylene. Reprinted with permission from Ref. 44b. Copyright 2004 American Chemical Society.

the simple reductive elimination (top reaction in Scheme 24) and the ethylene-assisted reductive elimination (the second reaction in Scheme 24). As a result, the ethylene-assisted reductive elimination easily occurs, compared with the simple reductive elimination without ethylene coordination. Though only the Si­C bond is formed in the simple reductive elimination, the Zr­H and Zr­SiH3 bonds are formed in addition to the formation of the Si­C bond in the metathesis; see the last reaction in Scheme 24. Though the Si­H bond is broken in the metathesis, the Zr­H and Zr­SiH3 bonds are formed and the sum of their bond energies is larger than the Si­H bond energy. This is because the oxidative addition to Cp2Zr is significantly exothermic; in other words, the Zr wants to take +IV oxidation state. In the metathesis, the Zr oxidation state does not need to return to +II but keeps +IV. Hence, the metathesis easily occurs. It is reasonable to conclude that this complicated catalytic cycle results from the small ionization potential of the early transition metal element. In conclusion, the reaction mechanism of hydrosilylation depends on the number of d electrons in the cases of Pt and Rh complexes; the Chalk­Harrod mechanism is favorable in the Pt system because of the presence of a d8 Pt(II) intermediate. In the Rh case, the modified Chalk­Harrod mechanism is favorBull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

able because of the presence of a d6 Rh(III) intermediate. However, the Chalk­Harrod mechanism becomes more favorable than the modified Chalk­Harrod one even in the Rh case when strongly donating ligands coordinate with the Rh.97 In the early transition metal complexes, the metathesis mechanism becomes favorable, in which the d orbital energy is one of the important factors for determining the reaction mechanism. 4.3 Catalyses for Cross-Coupling and Related Reactions. Pd-catalyzed cross-coupling is one of the most important organic reactions for C­C bond formation.1 In this regard, several theoretical studies have been reported.98 Hiyama crosscoupling reaction (eq 10)99 is of considerable interest from the viewpoint of reaction mechanism, because this reaction is unexpectedly accelerated by the presence of fluoride anion. R1 ­CH¼CH­I þ R2 ­CH¼CH­SiR3 3 Pdð0Þ=½Nt Bu4 F









! R1 ­CH¼CH­CH¼CH­R2 þ I­SiR3 3 ð10Þ We theoretically investigated the Hiyama cross-coupling reaction with the DFT method, where we employed Pd(PMe3)2 as a model of catalyst and vinyliodide CH2=CHI and vinylsilane CH2=CHSiMe3 as substrates.100 The first step is the oxidative addition of vinyl iodide CH2=CH­I to a palladium(0) complex (Scheme 25), which occurs easily to afford a palladium(II)

© 2015 The Chemical Society of Japan | 919

iodide vinyl complex cis-[Pd(CH=CH2)(I)(PMe3)2] with a moderate activation barrier. The next step is substitution of vinylsilane for phosphine to afford [Pd(CH=CH2)(I)(PMe3)(CH2=CHSiMe3)] in which the C=C double bond of vinylsilane coordinates with the Pd center. Then, transmetallation occurs in [Pd(CH=CH2)(I)(PMe3)(CH2=CHSiMe3)] to afford a palladium(II) bis-vinyl complex [Pd(CH=CH2)2(I-SiMe3)(PMe3)] in the absence of fluoride anion. In this transmetalla-

Scheme 25. Reaction mechanism of Hiyama cross-coupling reaction. Reprinted with permission from Ref. 100. Copyright 2008 American Chemical Society.

6b (0.0) (A) In the absence of fluoride

26

tion, the Si­C bond is broken and the Pd­vinyl and Si­I bonds are formed. Also, the Pd­I bond is converted to a weak Pd­ (ISiMe3) bond. The final step is the reductive elimination of butadiene derivative, which also easily occurs with a moderate activation energy because the Pd(0) is stable due to the low d orbital energy, as was reported previously.45d,46e,101,102 This is because a d10 electron configuration is stable in Pd; see Table S2 in Supporting Information.29 It is noted that the transmetallation has a large activation barrier in the absence of fluoride anion; see Figure 19A for geometry and energy changes. This is a rate-determining step. In the presence of fluoride anion, we investigated two possibilities; in one, the iodo ligand is substituted by the fluoride ligand to afford a palladium(II) fluoro vinyl complex [Pd(F)(CH=CH2)(PMe3)2]. This substitution was calculated to occur easily. In [Pd(F)(CH=CH2)(PMe3)(CH2=CHSiMe3)], the transmetallation occurs with a much smaller activation barrier (14.9 kcal mol¹1) and considerably large exothermicity (¹15.7 kcal mol¹1), indicating that the transmetallation is kinetically and thermodynamically accelerated very much by the fluoride ligand. This reaction is essentially the same as the heterolytic σ-bond activation reaction which was discussed above; note that the vinyl group becomes anionic in the product because it is bound with the Pd center but the SiMe3 group becomes cationic because it is bound with the fluorine atom in the product. From this example, one can understand that the heterolytic σ-bond activation plays important roles in catalytic reaction, again. In

TS6b/7b

(45.8)

TS26/27

(0.0) (12.7) (B) In the presence of tetramethylammonium fluoride [NMe4]F

7b (25.6)

27 (-24.8)

Figure 19. Geometry and energy changes in transmetallation of the Hiyama cross-coupling reaction. In parentheses are energy change including solvation effects. Reprinted with permission from Ref. 100. Copyright 2008 American Chemical Society. 920 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan

Ecov ¼ fð¾A
¾B Þ2 þ 4¢2 g1=2 2

 j¾A
¾B j þ 2¢ =j¾A
¾B j

Scheme 26. Bond energies related to transmetallation. Reprinted with permission from Ref. 100. Copyright 2008 American Chemical Society.

another reaction course, fluoride anion attacks the Si center of vinylsilane from the outside to accelerate the transmetallation. As shown in Figure 19B, the fluoride anion is approaching the Si center and the vinyl group is moving from the Si center toward the Pd center in the transition state. Also, it is noted that the SiMe3 moiety is almost planar and the fluoro and vinyl groups take axial positions. These geometrical features are essentially the same as those of the transition state of SN2 substitution reaction. The structure around the Si center is trigonal bipyramidal, which is similar to the hypervalent Si species. It is of considerable importance to elucidate the reason why the transmetallation is accelerated by the fluoride anion. In the absence of fluoride anion, the Si­I bond is formed and the Pd­I bond is converted to the Pd­(ISiMe3) bond (Scheme 26A). In the fluoride complex, the strong Si­F bond is formed and the strong Pd­F bond is converted to a weak Pd­(FSiMe3) bond (Scheme 26B). When the fluoride anion attacks the Si center of trimethylvinylsilane from the outside, the Pd­I bond is kept in the reaction but the strong Si­F bond is formed (Scheme 26C). In the latter two cases, the transmetallation easily occurs with a moderate activation barrier and significantly large exothermicity, because the very strong Si­F bond is formed. In other words, the formation of the very strong Si­F bond is the driving force for the transmetallation. This is the same as that of the heterolytic C­H σ-bond activation of benzene by palladium(II) formate complex, which was discussed above.40 Though it is well known that the Si­F bond is strong, the reason has not been clear. The next issue to be discussed is the reason why the Si­F bond is strong. We previously reported that the covalent bond energy (¦Ecov) is approximately represented by the simple equation eq 11, based on the simple Hückel MO method:102,103 Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

(11a) (11b)

where ¾A and ¾B are energies of valence orbitals of A and B, respectively, and ¢ is a resonance integral. When «¢« is much smaller than «¾A ¹ ¾B«, eq 11a can be converted to eq 11b. These equations indicate that the bond energy is large when the difference between ¾A and ¾B is large. Apparently, the sp3 orbital of SiMe3 radical exists at a higher energy than the valence orbitals of fluorine and iodine atoms and the valence orbital of fluorine is much lower than that of iodine. Hence, the «¾A ¹ ¾B« is much larger in the fluorine than in the iodine, and thereby, the Si­F bond energy is much larger than the Si­I one. Based on this discussion, not only fluoride anion but also anions that have a valence orbital at a low energy accelerates the transmetallation. One can expect that the OH anion, carboxylate anion, and similar anions bearing an electronegative element are useful for this reaction like fluoride anion. The same story can be presented for Suzuki­Miyaura crosscoupling, in which organoboronic acids and esters are used as a reagent; note that the boryl moiety has its valence orbital at a high energy because of its electropositive character. This is the reason why basic conditions are employed in the reaction; see also Ref. 98. Actually, a palladium(II) hydroxo and similar alkoxo complexes have been experimentally reported as a good catalyst for Suzuki­Miyaura cross coupling reaction.1,104,105 Because organoboronic acids and esters are used as important reagents in Suzuki­Miyaura cross-coupling reactions, various organoboronic acids and esters are necessary for Suzuki­ Miyaura cross-coupling. Recently, diborane has been applied to borylation of phenyl iodide,106 arene, and similar compounds.107­109 These reactions are also considered to be a kind of cross-coupling because a portion of diborane is bound with an organic moiety such as a phenyl group (Scheme 27). We theoretically investigated the Pd-catalyzed borylation of phenyl iodide (eq 12) with the DFT method,110 where bis(ethyleneglycolate)diborane B2(eg)2 (eg: ­OCH2CH2O­) was employed as a model of bis(pinacolato)diborane B2(pin)2 (pin: ­OCMe2CMe2O­) used in the experiment. Pdð0Þ=PR3

C6 H5 ­I þ B2 ðpinÞ2





! C6 H5 ­BðpinÞ þ I­BðpinÞ ð12Þ The first step is the oxidative addition of phenyl iodide to a palladium(0) complex Pd(PH3)2, to afford a palladium(II) iodo phenyl complex cis-[Pd(I)(Ph)(PH3)2], which is the same as the first step of the Suzuki­Miyaura cross-coupling reaction. One may have a question why the oxidative addition of diborane to a palladium(0) complex does not occur. This question is not surprising because the first step of Pt-catalyzed diborylation of alkyne with diborane is the oxidative addition of diborane to a platinum(0) complex, as proposed experimentally111 and elucidated theoretically.112 However, experiments and theoretical calculations show that the palladium(0) complex is not reactive for the oxidative addition of diborane.111­113 This is because the reactivity of palladium(0) complex is lower than that of platinum(0) complex for the oxidative addition, as was discussed above.29,45d,46e,101,102 The second step is the transmetallation between diborane and a palladium(II) phenyl complex and the last step is the reductive elimination of phenyl borane. These © 2015 The Chemical Society of Japan | 921

two steps are essentially the same as those of the Suzuki­ Miyaura cross-coupling reaction. In this reaction, basic conditions are employed like the Suzuki­Miyaura cross-coupling. Thus, it is likely that [Pd(I)(Ph)(PH3)2] is converted to [Pd(OH)(Ph)(PH3)2] under basic conditions. Diborane coordinates with the OH ligand of [Pd(OH)(Ph)(PH3)2] and then one O atom of B2(eg)2 approaches the Pd center to induce the

Scheme 27. Reaction mechanism of Pd-catalyzed borylation of organic halide. Reprinted with permission from Ref. 1c. Copyright 2008 Chemical Society of Japan.

dissociation of phosphine from the Pd center to afford an Ocoordinated diborane complex of palladium(II) (Figure 20). After that, the transmetallation occurs to produce Pd­boryl and B­OH bonds. This reaction occurs with a moderate activation barrier and significantly large exothermicity. We also investigated the transmetallation between a palladium(II) chloro phenyl complex [Pd(Cl)(Ph)(PPh3)2] and B2(eg)2 and found that the transmetalation easily occurs in the fluoro complex but with difficulty in the chloro complex. The reason is essentially the same as that of the Hiyama cross-coupling reaction. The larger reactivity of the fluoro and hydroxo complexes than that of the chloro complex arises from the fact that the HO­B(eg) and F­B(eg) bond energies are much larger than the Cl­B(eg) one like the Si­X bond. This is because the sp2 orbital of B(eg) exists at a high energy like the sp3 orbital of the silyl group. Based on these results, it is concluded that the electronegative group plays crucial roles to accelerate the transmetallation. Note that this transmetallation is also heterolytic σ-bond activation. We theoretically investigated iridium-catalyzed direct borylation of benzene with diborane (eq 13),114 and found that it is a little bit different from the two examples above. This reaction was experimentally performed first by Ishiyama, Hartwig, and co-workers107,108 and also well investigated by Smith and co-workers.109 This reaction is interesting from both synthetic chemistry and reaction mechanism viewpoints, because the C­ H bond of benzene is directly borylated, two boryl moieties of diborane are used for a product, and dihydrogen molecule H2 is produced; note that both C­H σ-bond activation and dihydrogen evolution are not easy and only one boryl group is used in the product of the Pd-catalyzed borylation of iodobenzene

Figure 20. Geometry and energy changes in transmetallation between [Pd(OH)(Ph)(PH3)2] and diborane. Reprinted with permission from Ref. 110. Copyright 2004 American Chemical Society. 922 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan

Scheme 28. Reaction mechanism of Ir-catalyzed direct borylation of benzene. Reprinted with permission from Ref. 114. Copyright 2003 American Chemical Society.

with diborane. In this catalytic reaction, an iridium(III) triboryl complex [Ir(Bpin)3(bpy)] is considered to be an active species because a stoichiometiric reaction between this complex and three-equivalent benzene molecules produces three phenylborane molecules. ½IrðBpinÞ3 ðbpyÞ

2C6 H6 þ B2 ðpinÞ2








! 2C6 H5 ­BðpinÞ þ H2 ð13Þ As mentioned above, one important question is how the C­H σ-bond of benzene is activated. Another question is why and how two boryl moieties can be used in the product. These are motivations of our theoretical study.114 The first step is the C­H σ-bond activation of benzene with [Ir(Bpin)3(bpy)]. Two possibilities must be considered; one is the oxidative addition of the C­H σ-bond to the iridium(III) complex, and another is the metathesis between the Ir­B(pin) bond and the C­H bond of benzene. DFT calculation showed that the oxidative addition of the C­H σ-bond to the Ir(III) center occurs with an activation barrier of 24.2 kcal mol¹1 to afford an iridium(V) triboryl hydride phenyl complex [Ir(Beg)3(bpy)(H)(Ph)] (Scheme 28), where we employed B2(eg)2 as a model of B2(pin)2. The transition state of the σ-bond metathesis could not be located. The next step is the reductive elimination of phenylborane, leading to the formation of an iridium(III) hydride diboryl complex [Ir(H)(Beg)2(bpy)]. This process easily occurs with a small activation barrier because the reductive elimination from a high-valent iridium(V) complex occurs easily. Thus-formed [Ir(H)(Beg)2(bpy)] easily reacts with diborane to afford an iridium(V) hydride tetraboryl complex [Ir(H)(Beg)4(bpy)] because diborane is very reactive. From [Ir(H)(Beg)4(bpy)], the reductive elimination of borane HB(eg) occurs easily to reproduce the iridium(III) triboryl complex. After diborane is consumed by the reaction, [Ir(H)(Beg)2(bpy)] starts to react with borane HB(en) to afford an iridium(V) dihydride triboryl complex, [Ir(H)2(Beg)3(bpy)]. Because HB(eg) is less reactive than diborane, borane cannot react with the iridium(III) complex until all diborane is consumed. Starting from [Ir(H)2(Beg)3(bpy)], the reductive elimination of dihydrogen occurs Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

to reproduce the original iridium(III) triboryl active species with evolution of hydrogen gas. Because the iridium(V) species are not popular in the chemistry of iridium complexes, the oxidative addition of the C­H σ-bond of benzene to [Ir(Beg)3(bpy)] is seemingly unusual. Here, we wish to discuss this process in detail. Because [Ir(Beg)3(bpy)] has an uncoordinated site, benzene approaches the Ir center at the uncoordinated site; see species I5 in Figure 21. Then, the C­H σ-bond activation occurs to afford the iridium(V) complex [Ir(H)(Ph)(Beg)3(bpy)]. This iridium(V) complex has a pseudo-pentagonal bipyramidal structure, in which one boryl and one pyridil group of bpy take the axial position and the H ligand, two boryl groups, phenyl, and another pyridyl of bpy take the equatorial position. These two boryl, phenyl, and pyridil groups on the equatorial plane are nearly perpendicular to the equatorial plane, to reduce steric repulsion. More important is to elucidate the reason why this iridium(V) complex has a closed-shell singlet ground state. In the pentagonal bipyramidal structure, two d orbitals (dxy and dx2
y2 ) in the equatorial plane and one d orbital (dz2 ) along the z axis are considerably destabilized in energy by the ligand field (Scheme 29), while two d orbitals (dxz and dyz) are not destabilized very much. Because the iridium(V) has a d4 electron configuration, its four d electrons can occupy these dxz and dyz orbitals. This electron configuration is favorable for the closed-shell singlet ground state. We have still one more important question, why an iridium(I) boryl complex does not play a role of active species, because the iridium(I) complex is more reactive for the oxidative addition than the iridium(III) complex. In other words, it is of considerable importance to elucidate the reason why this reaction does not occur through the Ir(I)­Ir(III) catalytic cycle via the iridium(III) intermediate. In the Ir(I)­Ir(III) cycle, the oxidative addition of the C­H σ-bond of benzene more easily occurs than that to the Ir(III) complex. However, the reductive elimination of dihydrogen becomes more difficult because it must occur from the iridium(III) dihydride complex. This means that the Ir(III)­Ir(V) catalytic cycle is favorable for the © 2015 The Chemical Society of Japan | 923

Figure 21. Geometry changes in oxidative addition of the C­H bond of benzene to an iridium(III) trisboryl complex [Ir(Ben)3(bpy)] to afford an iridium(V) intermediate [Ir(Ben)3(H)(Ph)(bpy)] followed by the reductive elimination of phenylborane. Reprinted with permission from Ref. 114. Copyright 2003 American Chemical Society.

Scheme 29. Schematic representation of d­d orbital splitting in the pentagonal bipyramidal iridium(V) complex. Reprinted with permission from Ref. 114. Copyright 2003 American Chemical Society.

reductive elimination of molecular hydrogen. Another important reason is that diborane is very reactive and thereby the oxidative addition of diborane easily occurs to the iridium(I) boryl species to afford the iridium(III) triboryl complex, indicating that the iridium(I) boryl complex cannot exist as a stable species under the catalytic reaction conditions. Actually, 924 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

diborane reacts even with the iridium(III) triboryl complex to afford an iridium(V) pentaboryl complex [Ir(Beg)5(bpy)] (Scheme 28). This [Ir(Beg)5(bpy)] is in equilibrium with the active species [Ir(Beg)3(bpy)]. One more reason is the presence of boryl groups in the iridium(V) intermediate because the strongly σ-donating boryl ligand stabilizes the high-valent iridium(V) complex. This type of C­H σ-bond activation followed by borylation with diborane is an attractive catalytic reaction and many reports have been presented to date108,109,115,116 because the C­ H bond activation and the functionalization are achieved at one time. One important development of this reaction is the extension to the borylation of a C(sp3)­H bond. This reaction was shown to be facile in the recently reported Ir-catalyzed C(sp3)­ H borylation of chlorosilane.116 A recent DFT study reported that the reaction occurs via oxidative addition of the C(sp3)­H bond to the iridium(III) triboryl complex followed by the reductive elimination of borylated product,117 which is essentially the same as the mechanism of Ir-catalyzed borylation of benzene. Also, the C(sp3)­H σ-bond borylation of alkylamines and alkylethers have also been demonstrated recently.118 Another important development is to achieve regioselective C­H σ-bond activation in these direct borylation reactions, which is also an important target in the chemistry of C­H activation because regioselective C­H σ-bond activation is not easy. The factors for controlling regioselectivity have been discussed in theoretical work of borylation of substituted arenes, heterocycles,119 and chlorosilane.117 In the direct borylation of alkylamines and alkylethers, the regioselectivity has been

© 2015 The Chemical Society of Japan

experimentally and theoretically well investigated.118 I wish to skip the discussion to save the space. 5. Miscellaneous Including Ligand Effects, Solvation Effects, and Crystalline Effects We must remember that the electronic structure of transitionmetal complex is flexible and thereby it can be perturbed very much by ligands and the surrounding environment. Actually, ligand effects and solvation effects are very often discussed in experiments. In this regard, it is of considerable importance to incorporate the surrounding environment into computation correctly and effectively. Also, we must notice that transition metal complexes have attracted a lot of interest as potential molecular devices recently. In such cases, the effects of neighboring molecules are important because the molecular devices are used in solid phase in many cases. Here, we wish to discuss how to incorporate the ligand effects, the solvation effects, and the crystalline effects. 5.1 Effects of Substituent in Ligand. DFT can be applied to large systems which have bulky real substituents. However, we are afraid there are several weak points in DFT calculations. For instance, DFT with B3LYP and similar functionals underestimates the binding energy of large π-conjugate systems with transition-metal complexes,120 because the dispersion interaction (London force) is not considered well by those functionals. This weak point has been solved in some new functionals by incorporating many parameters121 and/or empirical correction similar to Lenard­Jones parameters.122 But, we are concerned that the parameters are not always correct. Also, we are concerned with another weak point of the DFT method, which is found in the calculation of near-degenerate systems. Actually, DFT provides an unreasonable potential energy curve for the reaction between a non-heme catechol dioxygenase model Fe(III) complex and dioxygen, in which the CASPT2calculated potential energy curve is reasonable, semi-quantitatively at least.123 Also, the M­M multiple bond length is considerably underestimated.9c In such case, we want to employ a post-Hartree­Fock method such as CASPT2 and RASPT2. However, we must use a small model to perform the postHartree­Fock calculation because of the large cost. The ONIOM method124 is very powerful for large systems. However, it is better to employ the post-Hartree­Fock method with incorporating electronic effects of real substituents which are omitted in small models. To reproduce the electronic effect of the substituent in the post-Hartree­Fock calculation, we proposed a capping potential which we call Frontier-OrbitalConsistent Quantum-Capping Potential (FOC-QCP).125 A similar capping potential has been proposed in QM/MM calculations of proteins to reduce the boundary problem.126 In a transition metal complex, the frontier orbital of ligands play crucial roles in determining the electronic structure. In this regard, the capping potential must be determined so as to reproduce the frontier orbital energy of the ligand when some substituents are replaced by small substituents or hydrogen atoms. A similar idea has been proposed some time age in a model of phosphine ligand, in which a shift operator was employed.127 Here, the capping potential in FOC-QCP was determined by fitting the frontier orbital energy of a model system to a real system bearing a bulky substituent so as to reproduce the fronBull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

Scheme 30. The dπ orbital energy of M(PR3)2 and frontier orbital energy of phosphine ligand. Reprinted with permission from Ref. 125. Copyright 2008 American Chemical Society.

tier orbital energy with the model system. The importance of the frontier orbital energy of ligands can be easily understood by considering the ligand effect on the orbital energy of a metal complex (Scheme 30), the lone pair orbital of phosphine PR3 raises the dπ orbital energy of M(PR3)2, because the lone pair orbital forms an antibonding overlap with the metal dπ orbital (Scheme 3B). Because the lone pair of PMe3 exists at a higher energy than that of PH3, the dπ orbital energy in M(PMe3)2 is higher than in M(PH3)2. When PH3 is employed as a model instead of real phosphine, some deviation is induced in calculation and analysis. Let’s consider the CCSD(T) calculation of the oxidative addition of a C­C σ-bond to Pt(PR3)2 (R = CH3, C2H5, isopropyl, or tert-butyl), in which we must employ PH3 to save computational cost, for instance. This means that the CCSD(T) calculation is carried out with the lone pair orbital of PH3 which is at a lower energy than in a real system. On the other hand, the steric repulsion with PH3 is much smaller than that with PR3. It is likely that the CCSD(T)-calculated activation energy is overestimated by the electronic factors but underestimated by the steric factors, suggesting that the understanding of the computational results deviates from the truth. Because phosphine is used in many cases as a typical ligand and it also often contains bulky organic groups, we constructed FOC-QCPs of phosphines such as PMe3, PEt3, P(iPr)3, and P(tBu)3 (Me: methyl, Et: ethyl, iPr: isopropyl, tBu: tertiary buryl). The capping potential is defined by eq 14, where Ul(r) is the usual effective core potential for the core electrons of carbon and the second term is added to adjust the frontier orbital energy of PH3 to that of a real ligand. Ul ðrÞQCP ¼ Ul ðrÞ þ Cr n
2 expð
¦r2 Þ

ð14Þ

The reductive elimination of ethane from M(CH3)2(PR3)2 was employed in a test calculation, where the geometry changes were optimized by DFT with the B3PW91 functional. As shown in Table 3, the MP2 to MP4(SDQ) are completely wrong for this nickel complex, which is seen in general for first row transition-metal complexes. This is because electron © 2015 The Chemical Society of Japan | 925

Table 3. Activation Barrier (Ea) and Reaction Energy (¦E) of Reductive Elimination of Ethane from [M(CH3)2(PR3)2]a),b) B3PW91

R M = Ni H Me(real) Me(FOC)

MP4(SDQ)

CCSD(T)

Ea

¦E

Ea

¦E

Ea

¦E

17.7 20.4 20.2

¹13.8 ¹14.0 ¹13.5

¹86.2 ¹83.6 ¹83.5

¹110.8 ¹109.9 ¹114.7

18.7 ® 21.8

¹6.5 ® ¹5.2

a) In kcal mol¹1. These are not evaluated as the Gibbs energy change but the potential energy change. b) The steric repulsion was also re-evaluated with bulky moieties; see Ref. 125.

(B) Creutz-Taube Complex

(A) Robin-Day Classification

Scheme 31. Robin­Day Classification of mixed-valence compound and Creutz­Taube complex.

correlation effects are significantly large in the first row transition metal elements. The DFT with the B3PW91 functional provides a good trend but the reaction energy is considerably different from the CCSD(T)-calculated value, suggesting that the use of the CCSD(T) is necessary to present quantitatively correct results. The DFT calculation with the FOC-QCP for PMe3 presents almost the same results as the DFT calculation with the real PMe3, indicating that the present FOC-QCP works well to incorporate the electronic effects of the substituent. Considering these results, it is likely concluded that the CCSD(T) calculation with the FOC-QCP provides a better result. The CCSD(T) with the FOC-QCP was then applied to the coordination of CO, H2, N2, and C2H4 with dinuclear rhodium(I) complex [RhCl(PiPr3)2]2 (eq 15). ½RhClðPi Pr3 Þ2 2 þ 2H2 ! 2½RhClðPi Pr3 Þ2 ðH2 Þ

ð15Þ

The experimentally reported enthalpy changes are reproduced well by the CCSD(T) calculation with the FOC-QCP. Considering these successful results, we believe that this type of capping potential can be applied to many systems including cluster models of surfaces. Also, I wish to propose that this FOC-QCP is useful to investigate electronic effects of substituents without changing the steric effects; for instance, we can calculate a system with electron-donating substituents by shifting the frontier orbital to higher energy by this QCP without change in steric effect. 5.2 Solvation Effects. The solvation is of considerable importance in the case of transition-metal complexes because the transition-metal complex is charged several times and has many polar bonds in general. Now, the polarized continuum model (PCM) is used in many theoretical studies.128 Though this is very powerful and useful despite its small computational cost, the solvation structure cannot be calculated by this method. This means that the analysis of the solvation effects can be made only on the basis of polarizability and the cavity 926 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

of solvent and dipole moment of solute. This does not seem sufficient in the case of transition-metal complexes because the transition-metal complex has many polar bonds and polar groups in general. Another method which can be coupled with electronic structure calculation is Reference Interaction Site Model SelfConsistent-Field (RISM-SCF) method.60 In this method, the electronic structure of a solute molecule is solved by quantum mechanics in the presence of the effects of surrounding solvent molecules evaluated by the integral equation which is based on the statistical mechanics of liquid.129 Though the RISM-SCF calculation exhibits divergence several times in the calculation of transition-metal complexes in our limited experience, the problem has been solved by Yokogawa, Sato, and co-worker, using spatial electron density distribution (SEDD).130 This method was successfully applied to the stepwise oxidative addition of methyliodide to a platinum(II) complex,58 as was discussed above, and also to the hydrolysis of cis-platin.131 Considering the large size and the presence of many polar bonds in transition-metal complexes, however, the 3-dimentional (3D) RISM method132 is considered better than the RISM method, because the equation is solved at 3-dimensional meshed points surrounding a solute molecule and the averaging is made only on solvent molecules. Though this is more timeconsuming than the RISM, this method has been applied to the solvation of large systems such as protein.133 The 3D-RISM was recently combined with the post-Hartree­Fock and DFT methods. This 3D-RISM-SCF method was successfully applied to hydrolysis of cis-platin134 and 1,6-anhydrosugar formation of phenyl α- and β-D-glucosides under basic conditions.135 Mixed-valence compounds are one of the most important systems in which solvation plays crucial roles.136 As is well known, mixed-valence systems are classified into three categories, according to Robin and Day;137 in Class-I, the system has two electronic structures but one electronic structure is © 2015 The Chemical Society of Japan

never converted to another one because two potential energy surfaces do not have any interference (Scheme 31A). In other words, the transfer integral Hab is zero. In Class-II, interconversion occurs between two electronic structures with small activation energy; in other words, Hab is moderate. This means that the ground state is flexible in this Class-II compound. In Class-III, two electronic structures cannot be separated from each other and the electronic structure is delocalized; in this case, Hab is very large. Mixed-valence compounds attract a lot of interests because they are a model of electron-transfer systems138 and also are potentially useful for constructing switching materials.139 Apparently, the solvation effect is very important in mixed-valence systems, because the localized electronic structure is stabilized very much by polar solvent but the delocalized structure is influenced little by solvent. A typical example of a mixed-valence system is the Creutz­Taube complex which is a pyrazine-bridged dinuclear ruthenium complex140 (Scheme 31B). In this complex, two possible electronic structures must be considered; in the localized electronic structure (Class II), one ruthernium center has +2 oxidation state and another has +3, while in the delocalized one both ruthenium centers have +2.5 oxidation state. The former state is stabilized by polar solvent because it has a dipole moment, while the latter is not because the delocalized electronic structure does not have a dipole moment. This complex has been theoretically investigated with DFT,141 MP2,142 and CASSCF143 methods. Those studies reported that the electronic structure is delocalized, as experimentally indicated.140c Considering the near-degenerate electronic structure and the important roles of solvation, the multi-reference method must be employed with incorporation of the solvation effect. We investigated this system with a two-state mixing wavefunction.144 In this work, a solute molecule was placed in a spherical cavity surrounded by a continuous solvent medium bearing a dielectric constant of solvent and the solvation free energy was evaluated by considering the interaction of the point charge and the dipole moment of the solute with the reaction field. This calculation showed that the Creuz­Taube complex has a delocalized electronic structure corresponding to Class-III but Class-II electronic structure becomes possible when 4,4¤-bipyridine is employed as a bridging ligand instead of pyrazine. Recently, a little bit different mixed-valence phenomena were experimentally reported in salen radical complexes of Mn(III) and Ni(II), [MnIII(salcn•)]+ and [NiII(salen•)]+ (H2salcn: N,N¤-bis(3-tert-butyl-5Rsalicylidene)-1,2-cyclohexanediamine), consisting of one-electron oxidized salen radical and either Mn(III) or Ni(II).145 The geometries of these compounds are shown in Scheme 32 with schematic representation of the d electron configuration of the metal center. We theoretically investigated this system with the generalized multiconfigurational quasi-degenerate perturbation (GMC-QDPT) method, where the solvation effects were incorporated with the 3D-RISM-SCF method.146 Considering that the CASPT2 could not be applied to this system due to the large active space, this is a reasonable method for investigating the mixed-valence complex. The interesting features are found in the absorption spectrum. In the Mn(III) complexes, the small and broad absorption spectrum is observed at high energy, independent on the R and R¤ substituents on the salen ligand. In the Ni(II) Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

Scheme 32. Schematic representation of M(salen) complex and d orbital occupation. Reprinted with permission from Ref. 146. Copyright 2014 American Chemical Society.

complexes, a similar small and broad absorption spectrum is observed at high energy when R is different from R¤, but the large and sharp absorption spectrum is observed at low energy when R is the same as R¤. In Class II, the one-electron excitation occurs from one electronic structure to another one, while in Class III, one-electron excitation occurs from one delocalized electronic structure to its excited state. The former absorption spectrum is broad because the minimum in the potential energy surface is different between the ground and the excited states. On the other hand, the absorption spectrum becomes sharp in the latter case, because the minimum position in the potential energy surface is a little different between the ground and excited states. Hence, the difference in absorption spectrum between the Ni(II) complexes with R = R¤ and the Mn(III) complexes and between the Ni(II) complexes with R = R¤ and that with R º R¤ suggests that the electronic structure is different between them. The excitation energies calculated by the TD-DFT method with B3LYP, CAMB3LYP, M062X, LC-BLYP, and LC-wPBE functionals are very different from the experimental values, while only the M06 functional provides good results. Considering the large dependence of excitation energy on the functional, we employed GMC-QDPT method, where 18 orbitals were employed for the active space in the Ni(II) complex and 22 orbitals were used for the active space in the Mn(III) complex; note that the d orbitals are not involved in the active space of the Ni(II) complex because the d orbital does not participates in the excitation but the d orbitals are involved in the active space of the Mn(III) complex because they participate in the excitation. In the GMC calculation, oneand two-electron excitations are involved among all active © 2015 The Chemical Society of Japan | 927

Table 4. The GMC-QDPT-Calculated Excitation Energies (in eV) and Oscillator Strengths of Manganese(III) and Nickel(II) Complexes of Salen Radical146 Energy/Geometry

Gas/Gas RISM/RISM Expt.

(Me,Me)

Mn(III) (OMe,OMe)

0.34 1.11 0.84

0.39 1.13 0.98

(Cl,OMe) (Me,Me) Excitation energy 1.31 1.70 1.39

0.48 0.49 0.62

Ni(II) (OMe,OMe)

(Cl,OMe)

0.46 0.45 0.58

0.81 1.47 0.89

0.40 0.39

0.24 0.14

Oscillator strength Gas/Gas RISM/RISM

0.35 0.10

0.43 0.12

(A)

0.061 0.04

0.40 0.41

(B)

Figure 22. The SOMOs participating in the excitation of the manganese(III) and nickel(II) complexes with salen radical. Reprinted with permission from Ref. 146. Copyright 2003 American Chemical Society.

orbitals. As shown in Table 4, the excitation energy calculated in gas phase with gas phase geometry does not agree with the experimental value in the case of the Mn(III) complexes with R = R¤. However, the excitation energy calculated with the solvation effect agrees well with the experimental value, because the delocalized electronic structure in gas phase changes to the localized one in solution. When R is different from R¤, the excitation energy agrees well with the experimental value even in gas phase calculation with the gas-phase geometry in both Mn(III) and Ni(II) complexes. This is not surprising because the electronic structure is localized even in the gas phase when R is different from R¤ in both Mn(III) and Ni(II) complexes; in other words, the electronic structure is perturbed little by solvation. In the Ni(II) complexes, the excitation energy in the gas phase is calculated to be almost the same as that without solvation effects even when R is the same as R¤. This is because the electronic structure is delocalized in both gas phase and solution. The larger excitation energy in the localized electronic structure than in the delocalized structure is understood in terms of the solvation structure, as follows: As shown in Figure 22A, the electron excitation in the Mn(III) complex occurs from the SOMO localized on one part of the salen ligand to another SOMO localized on the other part of the salen. This excitation induces the redistribution of electron density because the negative charge moves from one part of the salen ligand to another part. The solvation structure is determined so as to stabilize the ground state, but such solvation 928 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

structure destabilizes the excited state (Figure 23A), because the electron redistribution of the excited state is completely reverse to that of the ground state; remember that the solvation structure does not change by the excitation due to the Frank­ Condon principle. In the Ni(II) complex with R = R¤, the oneelectron excitation occurs from one delocalized SOMO to another delocalized empty MO, in which the charge redistribution does not occur very much (Figure 22B). As a result, the solvation energy changes little in the Ni(II) complex (Figure 23B). Because the solvation structure stabilizes the ground state but destabilizes the excited state in the localized electronic structure, the excitation energy of the localized electronic structure is larger than that of the delocalized one. On the other hand, the solvation energy is not very much different at the ground and excited states in the delocalized electronic structure, which leads to the observation of absorption spectrum at low energy. We also investigated the solvation effects with the mean-field (MF) MD simulation,147 where solute with the 3D-RISM-SCF-UDFT/M06-optimized geometry was calculated by the GMC-QDPT, using the ensemble of solvent configurations generated by 1000 snapshots of the QM/ MM-MD trajectory with spacing of 3 ps. The excitation energy calculated with the MF-QM/MM MD method is close to that by the 3D-RISM-SCF/GMC-QDPT method. All these results clearly show that the GMC-QDPT with 3D-RISM-SCF method is useful for investigating the transition metal complex with strong solvation effect like the mixed-valence system. © 2015 The Chemical Society of Japan

(A) One-electron oxidized Ni(II)-salen radical complex

(A) High spin state without any gas molecule

(B) One-electron oxidized Mn(III)-salen radical complex

(B) Low spin state with CS2 absorption.

Figure 23. Change of solute­solvent ES interaction by excitation in one-electron oxidized Mn(III) and Ni(II)­ salen complexes with substituents (R1, R2) = (OMe, OMe) on the salen ligand. Red region represents the increase in ¦Econd avg and blue region represents the decrease in it. (a) «¦Vint SDF(r)« = 0.1 kcal mol¹1 ¡¹3. (b) «¦Vint SDF(r)« = 0.01 kcal mol¹1 ¡¹3. Reprinted with permission from Ref. 146. Copyright 2014 American Chemical Society.

5.3 Infinite Transition-Metal Complex Systems. Spincrossover complexes and metal­organic frameworks (MOFs) attract a lot of interest in modern chemistry. The Hofmann-type MOF which consists of iron(II), platinum(II), cyanide, and pyrazine (Scheme 33) exhibits low spin to high spin transition when the temperature rises, because the iron(II) center with a d6 electron configuration can take either a low spin or a high spin state. The absorption of bulky gas molecules stabilizes the high spin state even at low temperature.148 Considering that a large pore size is favorable for absorption of bulky gas molecules, this is not surprising because the metal­ligand distance is longer in high spin state than in low spin state; remember that the antibonding dσ MOs are unoccupied in low spin state but singly occupied in high spin state in iron(II) complexes. However, the absorption of carbon disulfide stabilizes the low spin state even at high temperature but the absorption of similar carbon dioxide does not induce any spin transition. This is surprising and no clear reason has been reported. We theoretically investigated the spin transition of this Hofmann type MOF.149 In general, the spin transition temperature T1/2 is represented by eq 16.150 T1=2 ¼ HðHS-LSÞ=SðHS-LSÞ

Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

ð16Þ

Scheme 33. The Hofmann-type metal­organic framework (MOF). Reprinted with permission from Ref. 152. Copyright 2013 American Chemical Society.

where ¦H(HS-LS) and ¦S(HS-LS) are enthalpy and entropy changes induced by spin transition, respectively. CS2 absorption increases the T1/2, which means that the ¦H(HS-LS) increases and/or the ¦S(HS-LS) decreases with CS2 absorption. It is unlikely that the ¦H(HS-LS) increases with CS2 absorption, we focused on the entropy change with CS2 absorption. As shown in Scheme 33A, the pyrazine moiety seems to freely rotate around its coordinate bond in the high spin state, while the rotation is suppressed in the low spin state with CS2 absorption because CS2 exists between two pyradine molecules (Scheme 33B). These results suggest that the rotational entropy of pyrazine decreases with CS2 absorption, indicating that the ¦S(HS-LS) decreases with CS2 absorption because CS2 suppresses the rotation of pyrazine even at high spin state. The rotational energy can be evaluated by solving the Schrödinger equation (eq 17) for rotation and the rotational entropy can be estimated by the rotational energies through a partition function Q.   h 2 @2 ^ þ VðªÞ  i ðªÞ ¼ Ei  i ðªÞ ð17Þ
2Iª @ª2 In eq 17, the V(º) term is the potential energy for rotation, which was calculated with a model system. As shown in Figure 24, the rotational barrier is considerably larger in the low spin state than in the high spin state and the pyrazine freely rotates around the coordinate bond in the high spin state at room temperature because the barrier is about 1­2 kcal mol¹1. This is consistent with the X-ray structure in the high spin state. The difference in ¦S(rotation) between the high spin and low © 2015 The Chemical Society of Japan | 929

-1

/kcal mol Figure 24. Potential energy of the pyrazine rotation in the model of the Hofmann-type MOF. Reprinted from Ref. 149 published in Chem. Phys. Lett.

spin states was evaluated to be about 8.3 cal mol¹1 K¹1 around room temperature. The change in T1/2 by gas absorption is represented by eq 18; T1=2 ¼ T1=2 ðCS2 Þ
T1=2 ðnonÞ ¼ HðnonÞfSðnonÞ
SðCS2 Þg =fSðnonÞ  SðCS2 Þg

ð18Þ

where ¦H(non) and ¦H(CS2) etc. represent the enthalpy change by spin transition in the absence of a gas molecule and in the presence of a CS2 molecule, respectively. The rotational entropy by pyrazine corresponds to the difference between ¦S(non) and ¦S(CS2); ¦S(rotation) = ¦S(non) ¹ ¦S(CS2). Because the ¦H(non) and ¦S(non) values have been experimentally reported for a single crystal Hofmann-type MOF,151 the ¦T1/2 could be evaluated to be about 25 K. This value is close to the experimentally reported increase in ¦T1/2. It is of considerable interest to clarify the origin of the larger rotational barrier in the low spin state than in the high spin state. We carefully investigated it with several model systems and found that not the electronic factors but the steric factors are the origin of the barrier; remember that the metal­ligand distance is shorter in the low spin state than in the high spin state, which induces larger steric repulsion between the pyridine and CN ligands in the low spin state when they are eclipsed with each other. The next important question is the reason why CS2 suppresses the rotation but CO2 cannot. To suppress the pyrazine rotation, CS2 must interact strongly with the pyrazine moiety but CO2 does not. Hence, the next task is to investigate the interactions of CS2 and CO2 molecules with the Hofmann-type MOF. As will be seen below, two interaction sites are important in this MOF; one is the position between two pyrazine ligands, which is called the pyrazine site hereafter. Another is the position between two platinum atoms, which is called the Pt site. Because it is not easy to describe the absorption at these two sites with one model, we employed two model systems shown in Scheme 34;152 the above was used to investigate the 930 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

gas absorption at the pyrazine site and the below was used to investigate the gas absorption at the Pt site. Because the dispersion interaction plays crucial roles in the interaction between a gas molecule and the pyrazine moiety,153 we must use a computational method which can represent well the dispersion interaction. Here, we employed the ONIOM(MP2.5 or SCS-MP2:DFT or HF), where either MP2.5 (average of MP2 and MP3 calculated values) or SCS-MP2 was used for the high quality region and either DFT or Hartree­Fock (HF) was used for the whole system. The MP2.5- and SCS-MP2-calculated binding energies of gas molecules with pyrazine molecule are close to the CCSD(T)-calculated values.153 We also evaluated the potential energy surface of gas absorption by the DFT with M06-2X and found that the minimum position calculated by the M06-2X functional is almost the same as that calculated by the ONIOM method but the binding energy is underestimated by the M06-2X. Also, it is noted that the binding energy depends little on the computational method employed for the whole system; in other words, both the Hartree­Fock and DFT with M06-2X and B3LYP are useful for the whole system calculation, indicating that the ONIOM procedure works well in this MOF. The S atom of CS2 takes the pyrazine position and the CS2 is parallel to the pyrazine planes (Figure 25). This position agrees well with experimental results.148 On the other hand, the C atom of CO2 takes the Pt position (Figure 25). The binding energy of CS2 is much larger than that of CO2. These results are consistent with the fact that CS2 can suppress the rotation of pyrazine because the binding energy is larger than the rotational barrier of the pyrazine molecule. We investigated these differences with energy decomposition analysis and found that the dispersion interaction with pyrazine is important in the CS2 absorption and the electrostatic interaction with the Pt atoms is important in the CO2 absorption. As a result, the absorption position is different between CS2 and CO2. This difference is interpreted in terms that this MOF has significantly large electrostatic potential in the pore and the electrostatic interaction is different between CO2 and CS2; CO2 has © 2015 The Chemical Society of Japan

(A) A model for investigating the position between two pyrazine ligands

(B) A model for investigating the position between two Pt atoms Scheme 34. Model of the Hofmann-type MOF employed in the calculation. Reprinted with permission from Ref. 152. Copyright 2013 American Chemical Society.

Binding Energy = -5.2 kcal mol–1

Binding Energy = -17.3 kcal mol–1

Figure 25. Optimized position of CS2 and CO2 molecules in the Hofmann-type MOF. Reprinted with permission from Ref. 152. Copyright 2013 American Chemical Society. Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

© 2015 The Chemical Society of Japan | 931

Table 5. Optimized Geometric Parameters (in angstroms) of trans-[PtCl2(NH3)(N-glycine)]¢H2O156

Pt(1)­Hw Pt(1)­Ow Pt(2)­Hw Pt(2)­Ow

Cluster modela) QM(4) QM(2)b) 2.69 3.09 3.60 3.30 3.50 3.56 2.39 3.11 3.42 4.51 3.32 3.67

QM/MM QM(2) 2.94 3.77 3.53 2.87 3.79 3.53

QM(4) 2.97 3.89 3.57 2.84 3.94 3.58

Expt. 2.89 3.83 3.62 2.89 3.83 3.62

a) The usual QM calculation without any MM molecule. b) QM(2) represents that two molecules are calculated in the QM region.

a negative quadrupole moment but CS2 has a positive one, and the C is positively charged in CO2 but negatively in CS2 (Scheme 4C). In these studies, we did not consider the influence of the infinite system. But, this is not very bad, because the London force is local. However, the neglect of the infinite system induces serious problem, when polar molecule and/or charged species interact(s) with the MOF. Also, we found various crystalline and amorphous systems which exhibit interesting molecular properties. One example is a spin-crossover complex which induces spin transition by temperature rise and/or photoirradiation. Previously, we theoretically investigated the potential energy surfaces of spin-crossover iron(II) and iron(III) complexes, because the potential energy surface is one important factor in spin-crossover phenomenon.154 One more good example is a vapochromic transition-metal complex which is expected to be useful as a gas sensor. Such metal complex shows absorption and/or emission change(s) by absorption of organic gas molecules in a crystal or amorphous system. To understand this phenomenon, we need to know the binding energy of a gas molecule and the geometry of the excited state. We successfully elucidated the alcohol sensor mechanism of Cu2Au trinuclear complexes, recently.155 In those theoretical studies, however, we could not incorporate the crystalline effects of the neighboring molecules. This is not very good because the potential energy surface is significantly influenced by the crystalline effects. Considering this insufficient computational procedure, we have to use a computational method which can incorporate the crystalline effects on the geometry, electronic structure, and molecular properties of the molecule in crystal. As the first step, we proposed a QM/MM computational method for molecular crystal.156 In this computational scheme, the QM method is employed for a target transition-metal complex in a unit cell. The MM method is employed for the other part, in which the steric effect is evaluated with the Lenard­Jones parameters. The electrostatic effect is calculated as an interaction between point-charges of the MM molecule and the electrostatic potential of the QM molecule which is directly calculated with the wavefunction of the QM molecule, when the MM molecule is close to the QM one. When the MM molecule is distant from the QM one, the usual point-charge approximation is employed. For the intermediate region, a switch function is employed to smoothly connect the electrostatic potential between the close and distant regions. This procedure is similar to that of the 3D-RISM-SCF method 932 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

employed for transition metal complexes.134,146 The geometry of the MM part is constructed by placing the QM molecule according to the symmetry of the crystal. The geometry optimization is carried out on the QM molecule, the QM-MM distance, and the orientation of the MM molecule (that is the lattice vectors), in a self-consistent manner under self-consistent charge distribution. We applied this method to platinum(II) and platinum(IV) complexes. In Table 5, some important geometric parameters of trans-[PtCl2(NH3)(N-glycine)]¢H2O are compared with the experimental values. The Pt(1)­Hw and Pt(1)­Ow distances are not very much different from the experimental values in the usual cluster calculation with two QM molecules even if the crystalline effects are not considered. However, these successful results seem coincidental because these geometric values deviate very much from the experimental values in the QM(4) cluster calculation with four QM molecules. Moreover, the Pt(1)­Hw and Pt(1)­Ow distances are very much different from the Pt(2)­Hw and Pt(2)­Ow, respectively, in the QM(4) calculation, despite being equivalent. On the other hand, the QM/MM calculated values agree well with experimental values and the Pt(1)­Hw and Pt(1)­Ow distances are close to the Pt(2)­ Hw and Pt(2)­Ow, respectively. These results suggest that the QM/MM computational method is powerful to investigate the molecular geometry and properties of molecules in molecular crystal. This type of QM/MM calculation will become more important in the near future because solid systems and surface problems are at the frontier of modern chemistry. 6. Perspective As discussed above, complex systems consisting of transition metal element(s) are attractive and interesting research targets for theoretical and computational studies. Also, there remain many challenging issues in such transition-metal complexes even now. First, we must recognize that a complicated electronic structure often requires us to use multi-reference computational methods incorporating both of non-dynamical and dynamic correlations. The CASPT2 and MRMP2 are representative methods. However, the size of active space is limited to less than 12 to 14. In many transition-metal complexes, we want to employ much larger active space in general. It is very important to develop a multi-reference method which can be employed effectively for a large and complicated system. In this regard, the DMRG157 and quantum Monte­Carlo method158 based on wave-function theory are expected to become much more important in the near future. The application of DMRG to transition metal complexes has been started.8c,8d,159,160

© 2015 The Chemical Society of Japan

The second issue is to incorporate effects of solvation and molecular crystalline effects. As mentioned above, the electronic structure of transition metal complex systems is flexible and thereby easily perturbed by the environment such as solvent and neighboring molecules in molecular crystal and amorphous states. Such systems are important in modern chemistry because molecular devices are used in crystal and/or amorphous contexts. Hence, we need to employ a multi-reference method incorporating environmental effects. Also, infinite systems such as MOF are now important targets in modern chemistry. Many experimentalists are trying to apply MOF to gas absorption and gas separation. In theoretical study of MOF, we need to incorporate dispersion interaction in computational methods. It is not easy to incorporate the dispersion interaction in the calculation of infinite systems. Now, plane wave calculation is possible with dispersion corrected functional PBE-D. This is one choice. But, we always want to use the post Hartree­Fock method even in such cases. At this moment, one can expect that QM/MM and ONIOM are useful for investigating such system with some modification. However, much better methods must be developed in the near future. Metal particles are interesting systems, which are neither a molecule nor bulk metal system. They exhibit interesting properties including catalysis and gas absorption and/or adsorption. The post-Hartree­Fock calculation is impossible now. Even DFT calculation is not easy because of the problem of SCF convergence. Considering interesting experimental observed phenomena, we need to calculate metal particles with 500 to 2000 atoms. As the first step, we need to improve the technique for SCF. The slow convergence maybe relates to the fundamental properties of the electronic structure, suggesting that some new idea is necessary. The surface of metal and metal oxide systems is another interesting system to which theoretical and computational studies must be applied. Now, we can apply the plane wave DFT method with the slab model. In many theoretical studies of chemical reactions, however, we want to use a post Hartree­ Fock method such as MP4, CCSD(T), CASPT2, etc. At least, we believe that the use of hybrid functionals is indispensable in theoretical study of chemical reaction on solid surfaces. For such calculations, the cluster model must be employed. However, the simple cluster model is not very good. In the cluster model, we need to make improvements; for instance, we must incorporate infinite electrostatic potential, and also, solve the QM-MM boundary problem. In the near future, theoretical and computational chemists must approach such infinite and semi-infinite systems and complex systems in solvent, crystal, and amorphous phases with post-Hartree­Fock methods. To do so, we need to make further advancements of methods, algorithms, and also models. All these are very challenging. I hope many young students will join in this field. I would like to thank the Ministry of Education, Culture, Sports, Science and Technology for providing me with Grant-in-Aids of Specially Promoted Science and Technology (No. 22000009). I am also thankful to the Japan Science and Technology Corporation (CREST “Establishment of Molecular Technology towards the Creation of New Functions” Area). Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

I wish to thank the computational center at the Institute of Molecular Science (IMS), Okazaki, Japan for using computers; most of our work discussed here was performed with the computer systems at IMS. Finally, I would like to thank all my colleagues, post-doctoral fellows, Ph.D., Master, and undergraduate students of my group at Kumamoto University and Kyoto University for their sincere efforts. Without their collaborations, I could not do any work discussed in this review article. Supporting Information This material is available electronically on J-STAGE. References 1 For instance; a) N. Miyaura, A. Suzuki, Chem. Rev. 1995, 95, 2457. b) A. Suzuki, J. Organomet. Chem. 1999, 576, 147. c) N. Miyaura, Bull. Chem. Soc. Jpn. 2008, 81, 1535. 2 For instance; a) S. Niu, M. B. Hall, Chem. Rev. 2000, 100, 353. b) M. Torrent, M. Solà, G. Frenking, Chem. Rev. 2000, 100, 439. c) T. Ziegler, J. Autschbach, Chem. Rev. 2005, 105, 2695. d) P. E. M. Siegbahn, J. W. Tye, M. B. Hall, Chem. Rev. 2007, 107, 4414. 3 a) S. Sakaki, in Theoretical Aspects of Transition Metal Catalysis, ed. by G. Frenking, Springer, Berlin, 2005, pp. 31­78. doi:10.1007/b104398. b) S. Sakaki, in Practical Aspects of Computational Chemistry II, ed. by J. Leszczynski, M. K. Shukla, Springer, 2012, pp. 391­470. doi:10.1007/978-94-007-0923-2_11. c) S. Sakaki, Y. Ohnishi, H. Sato, Chem. Rec. 2010, 10, 29. d) W. Guan, F. B. Sayyed, G. Zeng, S. Sakaki, Inorg. Chem. 2014, 53, 6444. 4 For instance; D. H. Gibson, Chem. Rev. 1996, 96, 2063. 5 a) Y.-C. Tsai, P.-Y. Wang, S.-A. Chen, J.-M. Chen, J. Am. Chem. Soc. 2007, 129, 8066. b) Y.-C. Tsai, P.-Y. Wang, K.-M. Lin, S.-A. Chen, J.-M. Chen, Chem. Commun. 2008, 205. c) W. H. Monillas, G. P. A. Yap, K. H. Theopold, Angew. Chem., Int. Ed. 2007, 46, 6692. 6 F. A. Cotton, Acc. Chem. Res. 1978, 11, 225. 7 M. Brynda, L. Gagliardi, B. O. Roos, Chem. Phys. Lett. 2009, 471, 1 and references therein for theoretical works before 2009. 8 a) K. Andersson, B. O. Roos, P.-¡. Malmqvist, P.-O. Widmark, Chem. Phys. Lett. 1994, 230, 391. b) K. Andersson, C. W. Bauschlicher, Jr., B. J. Persson, B. O. Roos, Chem. Phys. Lett. 1996, 257, 238. c) Y. Kurashige, T. Yanai, J. Chem. Phys. 2011, 135, 094104. d) Y. Kurashige, Mol. Phys., New Views 2013, 1. 9 a) L. Gagliardi, B. O. Roos, Inorg. Chem. 2003, 42, 1599. b) K. Saito, Y. Nakao, H. Sato, S. Sakaki, J. Phys. Chem. A 2006, 110, 9710. c) Y. I. Kurokawa, Y. Nakao, S. Sakaki, J. Phys. Chem. A 2009, 113, 3202. 10 K. Kitaura, K. Morokuma, Int. J. Quantum Chem. 1976, 10, 325. 11 a) K. Kitaura, S. Sakaki, K. Morokuma, Inorg. Chem. 1981, 20, 2292. b) S. Sakaki, K. Kitaura, K. Morokuma, K. Ohkubo, Inorg. Chem. 1983, 22, 104. 12 a) S. Sakaki, K. Kitaura, K. Morokuma, Inorg. Chem. 1982, 21, 760. b) S. Sakaki, A. Dedieu, Inorg. Chem. 1987, 26, 3278. 13 a) G. Fachinetti, C. Floriani, P. F. Zanazzi, J. Am. Chem. Soc. 1978, 100, 7405. b) S. Gambarotta, F. Arena, C. Floriani, P. F. Zanazzi, J. Am. Chem. Soc. 1982, 104, 5082. 14 J. C. Calabrese, T. Herskovitz, J. B. Kinney, J. Am. Chem.

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Shigeyoshi Sakaki received a Ph.D. degree from Kyoto University in 1974 under Professor K. Tarama. After working as a JSPS fellow in Kyoto University for one year, he was appointed an Assistant Professor in 1975, promoted to an Associate Professor in 1982 and a Full Professor in 1990 at Kumamoto University. He served as a Visiting Professor at the Institute for Molecular Science during 1990­1991. He moved to Kyushu University in 2001 and then Kyoto University in 2002. He also served as a Director of Fukui Institute for Fundamental Chemistry (FIFC) in Kyoto University for 2006­2010. He retired from a Full Professor position of Kyoto University in 2010. After working as a Research Professor in Institute for Integrated Cell-Material Science of Kyoto University for 2010­2011, he moved to FIFC on 2011 and he is working there as a Research Leader since then. He served as a Chief Editor of J. Compt. Chem. (2007­2011). He received the Japan Society for Molecular Science Award (2009), the Chemical Society of Japan Award (2013), and the Fukui Medal from the Asia-Pacific Association for Theoretical and Computational Chemists (2015).

938 | Bull. Chem. Soc. Jpn. 2015, 88, 889–938 | doi:10.1246/bcsj.20150119

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