On the electron flow sequence driving the

Journal of Molecular Modeling (2018) 24: 305 https://doi.org/10.1007/s00894-018-3841-2

ORIGINAL PAPER

On the electron flow sequence driving the hydrometallation of acetylene by lithium hydride Eduardo Chamorro 1

&

Mario Duque-Noreña 1 & Savaş Kaya 2 & Elizabeth Rincón 3 & Patricia Pérez 1

Received: 29 June 2018 / Accepted: 20 September 2018 / Published online: 3 October 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract The sequence of the electronic flow driving the hydrometallation of acetylene by lithium hydride (and that of the opposite β-hydride elimination reaction from the alkenyl metal intermediate), was examined within the perspective provided by the bonding evolution theory (BET). The analysis was based on the application of catastrophe theory to the changes of the electron localization function topology along the intrinsic reaction coordinate. The description of the electronic processes occurring on the process was represented in terms of topological structural stability domains (SSDs) and the associated elementary bifurcation catastrophes. Within such a framework of representation, the Bevolution^ of the system through the different SSDs reveals the key chemical events driving the transformation, including the large polarization effect as a consequence of Pauli repulsion between ions of the positive cationic metal on the hydride domain, the activation of the CC triple bond to attack the cationic center, and the agostic stabilizing interactions involving the hardest cationic metal, followed by the attack of the hydride center. These results contribute to emphasizing the intrinsic value and usefulness of using topological-based approaches and associated tools to increase our knowledge and understanding of the subtleties underlying the electronic flow as nuclei evolve along the reaction coordinate, providing detailed and complementary insights in comparison to other interpretative tool such those based on orbital-based representations, concerning the intimate nature of the electronic rearrangement of key mechanistic processes in chemistry. Keywords Bonding evolution theory (BET) . Electron localization function (ELF) . Catastrophe theory . Hydrometallation . β-hydride elimination . Ethenyl Lithium . LiH

Introduction This paper is dedicated to Professor Pratim K. Chattaraj. His kindness friendship and professional scientific work have been always a source of endless encouragement and inspiration for our work. This paper belongs to Topical Collection P. K. Chattaraj 60th Birthday. This paper belongs to Topical Collection International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday * Eduardo Chamorro [email protected] 1

Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Universidad Andres Bello, Avenida República 275, 8370146 Santiago, Chile

2

Faculty of Science, Department of Chemistry, Cumhuriyet University, 58140 Sivas, Turkey

3

Facultad de Ciencias, Instituto de Ciencias Químicas, Universidad Austral de Chile, Las Encinas 220, 5110033 Valdivia, Chile

Hydrometallation reactions and β-hydride eliminations in alkyl or alkenyl intermediates constitute key processes in several pivotal synthetic and mechanistic approaches in organometallic chemistry [1–3]. Although it is commonly accepted that direct (uncatalyzed) processes proceed through a fourcentered transition state (TS) [4–8], the detailed knowledge about the nature of the intimate electronic rearrangement have remained a subject of open interest [9–12]. In such a context, vinyl metalloid intermediates selectively synthetized remains a highly active field of research [13, 14], driving in fact the richness of synthetic strategies within the interest of several useful applications [15–17]. Following ongoing efforts [18–29] oriented to further explore the usefulness of topological approaches for representing chemical bonding concepts within a position-space representation of molecular systems, here we focus on the variation of

305 Page 2 of 12

the electronic pattern driving the reaction mechanism. Within this context, we applied the so-called bonding evolution theory (BET) to characterize chemical transformations [30–32]. Our aim was to elucidate the sequence of the electronic flow driving such a key hydrometallation processes by examining the reaction of acetylene by lithium hydride taken as one of simplest models for the general interconversion process (i.e., Fig. 1) [11, 33–39]. Within the BET framework, Thom’s catastrophe theory (CT) [40–43] concepts are applied to identify and characterize changes in topological patterns associated with the evolution of the gradient field of the electron localization function (ELF) [44–47], along a chosen reaction path [18, 31, 32, 48–51]. ELF is a local function describing the relative electron pair (de)localization associated to a given electron density [45, 46, 52]. Within the current DFT level of approximation, ELF can be interpreted as the relative local excess of kinetic energy density arising from the Pauli principle [44–47, 52–54]. Basin-dependent electron populations as well as variancerelated descriptors, useful for rationalizing electron delocalization have been obtained by integrating the one-electron and two-electron density probabilities in the volume of ELF basins [44–47, 52, 53, 55–57]. In this way, BET provides a unique understanding of the behavior of any dynamic system in terms of bifurcations related to the changes of the gradient field of a well characterized local function along the chosen reaction coordinate (see recent examples [18, 32, 49, 58, 59]). The system evolution is sketched into a sequential series of structural stability domains (SSDs) defined in terms of the number and type of critical points [18, 30, 59–62]. SSDs enclose in fact all sequential configurations of the evolving reacting system having the same number and type of critical points of the gradient field of ELF. The turning points separating each pair of SSDs can be therefore identified and characterized in terms of discontinuities or elemental bifurcation catastrophes [30, 42]. In the context of representation that ELF provides for chemical bond and associated concepts (i.e., the basins of

Fig. 1 Reaction processes for the direct hydrometallation of alkynes 1 (path A) and the associated β-hydride elimination from alkenyl intermediates 2 (path B) via a concerted four-membered transition structure (TS). The simplest system (R = R’ = H, M = Li) is taken to be examined within a bonding evolution theory (BET) perspective as a

J Mol Model (2018) 24: 305

attractors derived from the topological analysis of ELF can be identified to bonding concepts of the Lewis theory [23, 44, 54, 63–65]), the reaction mechanism become rationalized in terms of an ordered sequence of events corresponding to electronic rearrangements driving the creation and/or annihilation of chemical meaningfully entities associated to both non-bonding or bonding regions (e.g., Blone pairs^, Bbond pairs^, etc.).

Computational details Geometry optimization using analytical gradients [66–69] and the associated characterization (via frequency calculations) of all stationary points involved in the hydrometallation of acetylene by lithium hydride depicted in Fig. 1 were obtained at the B3LYP functional [70, 71] with the 6–31++G(d,p) basis set by using the Gaussian 09 package of programs [72]. The chosen level of theory is adequate for characterizing all relevant electronic effects expected for the reaction path evolution of the target system that includes only Li, C, and H atoms. Given that the ELF topology (i.e., the position of the critical points associated to its gradient field) is invariant to the level of theory calculation [73], it seems reasonable to expect that this good property be transferable to the BET analysis and characterization of such an electronic rearrangement [74, 75]. The intrinsic reaction coordinate (IRC) [76, 77], which corresponds to the minimum energy reaction pathway in mass-weighted Cartesian coordinates connecting the TS and its reactants and products, has been calculated using a standard integration method [68, 69]. The topological analysis of ELF along the IRC [76, 77] has been performed using Topmod [78] and Multiwfn [79]. Elemental catastrophe theory concepts are then applied in order to identify the sequential SSD and corresponding bifurcation catastrophes [30, 48, 50, 51, 60–62, 80, 81].

representative example for the electronic rearrangement driven such a key processes. The main focus is directed to uncover the precise nature of the sequence of electronic flux driven bond formation/bond breaking processes along the transformation

J Mol Model (2018) 24: 305

Results and discussion Within the realm of BET, the reaction of hydrometallation of acetylene by lithium hydride emerges as one process characterized by fold (F†), cusp (C and C†) and elliptic umbilic (U) elementary catastrophes. It is convenient to recall at this point that the fold F† singularity is associated with the transformation of a non-critical point into an attractor and a saddle point, increasing by one the total number of basins in the system. The cusp C† catastrophe corresponds to the transformation of an attractor into two attractors and a saddle point, also increasing by one the total number of basins, whereas the cusp C bifurcation merges two attractors and a saddle point into an attractor, decreasing by one the total number of basins in the system. Finally, the elliptic umbilic U catastrophe can be simply associated to changes in the synaptic order of a given basin without changing the total number of basins in the system [18, 30, 42, 60]. The energy profile for the hydrometallation of acetylene by lithium hydride process along the IRC is presented in Fig. 2, revealing the nine structural stability domains that have been identified (SSDs, labelled from I to IX) on the basis of changes in the number and type of valence basins arising from the topological analysis of the electron localization function (ELF) for each examined configuration of system evolving along the chosen IRC pathway. Note that the TS configuration is found to be located within the SSD-V.

Fig. 2 Relative energy (kcal mol −1 ) along the intrinsic reaction coordinate (IRC) for the hydrometallation of acetylene by lithium hydride 1 resulting in ethenyl lithium 2 via a four-membered TS. The structural stability domains (SSDs) are labelled from I to IX, separated by blue (acetylene + lithium hydride side) and red (alkenyl metalloid intermediate side) vertical lines. The positions of the specific configurations separating the different SSDs are indicated on the top axis by the labels p1–p8. The corresponding positions of the intrinsic reaction coordinate are: p1 −1.98693, p2 −0.99450, p3 −0.33149, p4 −0.11051, p5 +0.44199, p6 +0.77350, p7 +2.76074, p8 +3.3599

Page 3 of 12 305

Figure 3 reports the variation of the electron populations associated to the ELF valence basins of selected points of the IRC for the hydrometallation reaction of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The populations of most relevant valence basins for selected points of the IRC including those separating the different SSDs are reported in Table 1. Along the hydrometallation path, i.e., 1 → TS→2, the first structural stability domain (SSD-I) is characterized by structures with seven attractors, providing three core basins C(C1), C(C2), C(Li), two disynaptic valence basins V(H1,C1), V(H2,C2), one monosynaptic valence protonated basin V(H3), and one trisynaptic valence basin V(C1,C2, Li). SSD-I reveals itself as the initial stage of interaction of the metallic center and the C1C2 triple bond. The existence of a trisynaptic signature for the C1C2 region and the cationic metal is clearly present along this domain, where indeed the metal hydride is properly represented as an ionic structure with the explicit charge separation Li+H−. The electron population at the V(H3) monosynaptic valence basin decreases only slightly from 1.95e to 1.93e along SSD-I. The first catastrophe, at the turning point p1, corresponds to an elliptic umbilic U bifurcation identified with the change of the synaptic order of the V(H2,C2) valence basin. In the second structural stability domain (SSD-II), also with seven basins, a trisynaptic basin V(H2,C2,Li) identifies the interaction of the C2–H2 single bond region (which localize 2.30e) with the cationic metallic center. In this domain, the V(H3) continues to decrease up to 1.89e. The third structural stability domain (SSD-III) is characterized by the appearance of a new disynaptic valence basin V(C1,Li), increasing to eight the total of basins in the system. Henceforth, the turning point at p2 has been identified with a fold F† catastrophe. The electron population at V(C1,Li) increases along SSD-III from 0.47e to 0.92e starting the initial formation of the C1–Li bonding interaction, which will continuously grow up until the end of the path. The fourth structural stability domain (SSD-IV) starts with a split of the trisynaptic V(C1,C2,Li) valence basin becoming here represented as V1,2(C1,C2,Li), increasing to nine the total number of basins. The turning point at p3 is therefore identified with a cusp C† catastrophe. The electron population at the V(H3) basin reaches 1.78e. The fourth catastrophe, at the turning point p4, starting the fifth structural stability domain (SSD-V), corresponds to a new elliptic umbilic U bifurcation identified with the transformation of the monosynaptic V(H3) valence basin into the disynaptic V(H3,Li) one. The electron population integrated at this basin decrease in SSD-V from 1.77e to 1.69e. The transition structure belongs to this SSD-V. In the TS, the V(H3,Li) basin integrating 1.75e is associated to the LiH-bond-forming

305 Page 4 of 12

J Mol Model (2018) 24: 305

Fig. 3 Electron populations integrated in the valence basins arising from the topological analysis of the electron localization function for selected points along the IRC associated to the hydrometallation reaction of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The positions of the specific configurations separating the different SSDs are indicated on the top axis by the labels p1–p8. The SSDs are separated by blue

(acetylene + lithium hydride side) and red (alkenyl metalloid intermediate side) vertical lines. The small population associated to the asynaptic basin appearing in the SSD-VI is interpreted as being part of the V(H3,Li) valence basin in the process that turns it into a trisynaptic one, i.e., V(H3,C2,Li) in the SSD-VII

interaction, two trisynaptic basins V1,2(C1,C2,Li) integrating to 4.48e, are associated to C1C2 bonding region, which remains in interaction with the metallic center. A V(H2,C2,Li) basin integrating 2.28e is also observed to associated with the interaction of the C2H2 bonding region with the metallic center. These results indicate that, along the process from 1 to TS, the sequence of the electronic rearrangement is essentially associated to the formation of a new bonding interaction between the Li and C1 centers [82, 83]. This is revealed by a clear disynaptic basin V(C1,Li). On progressing in such a pathway, agostic interactions of the cationic metal center with the C1C2 and C2H2 bonding regions is also evidenced. The sixth structural stability domain (SSD-VI) is characterized by the creation of a new attractor in the vicinity of C1, increasing to ten the number of basins. The turning point at p5 is therefore identified with a fold F† catastrophe. This basin (formally identified as asynaptic) is related to the very initial stage of formation of the C1–H3 bonding interaction. Note that the very small population associated with such an asynaptic basin (i.e., which varies from 0.05e to 0.16e) can be straightforwardly related as part of the V(H3,Li) valence basin in the process that turns it into a trisynaptic one, i.e., V(H3,C2,Li), in the

next SSD. The seventh structural stability domain (SSDVII) is reached after two simultaneous cusp C and elliptic umbilic U catastrophes at the turning point p6, providing the trisynaptic V(H3,C2,Li) and the change of synaptic order associated to the now disynaptic V(H2,C2) valence basins, respectively, while reducing to nine the total number of basins in the system. This domain ends the agostic interaction between the Li and H2 centers. The eighth structural stability domain (SSD-VIII) is reached after an elliptic umbilic catastrophe U at the turning point p7, which changes the synaptic order of the two valence disynaptic basins associated to the now C1 = C2 double bound. This domain remarks the end of any interaction of the unsaturated C1C2 bond region and the metallic center. The next bifurcation catastrophe corresponds to a new elliptic umbilic U at the turning point p8, which is associated to the change of the synaptic order of the newly formed C2-H3 bond, providing the ninth structural stability domain (SSD-IX) in which further stabilization of the ethenyl lithium product will provide the final alkenyl metal configuration 2. A simple representation for the sequence of SSDs characterizing the hydrometallation of acetylene by lithium hydride yielding ethenyl lithium is depicted in Fig. 4a, where the number of attractors of ELF and

Page 5 of 12 305

J Mol Model (2018) 24: 305 Table 1 Variation in valence electron localization function (ELF) basin populations (number of electrons) for selected points along the intrinsic reaction coordinate (IRC; in units of amu 1 / 2 .Bohr) for the IRC 1

hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2 via a four-membered transition structure (TS)

V(H1.C1) V(H2.C2) V(H2.C2.Li) V(C1.Li) V(H3) V(H3.Li) V(Asyn) V(H3.C2.Li) V(H3.C2) V1.2(C1.C2.Li) V1.2(C1.C2)

−3.080 2.24

2.29

1.95

5.29

−2.095 2.23

2.30

1.93

5.32

1.93 1.93

5.32 5.33

p1 −1.987 2.23 −1.878 2.22

2.30 2.30

−1.105 2.19 p2 −0.994 2.18

2.30 2.29

0.47

1.89 1.88

5.40 4.95

−0.884 2.17

2.30

0.59

1.87

4.84

−0.442 2.14 P3 −0.331 2.12

2.30 2.29

0.92 0.99

1.82 1.8

4.60 4.57

−0.221 2.12 p4 −0.110 2.11

2.29 2.28

1.06 1.11

1.78

TS

0.000 2.10

2.28

p5

0.331 2.07 0.442 2.06

p6

0.552 2.07 0.663 2.06 0.774 2.06

p7

p8 2

1.77

4.53 4.50

1.17

1.75

4.48

2.27 2.26

1.37 1.42

1.69 1.68

0.05

2.25 2.23 2.22

1.48 1.55 1.6

1.66 1.64

0.09 0.16

0.884 2.06

2.21

1.658 2.650 2.761 2.868

2.06 2.02 2.01 2.01

2.12 2.09 2.09 2.09

3.276 2.01 3.360 2.01 3.489 2.01

2.09 2.09 2.09

4.37 4.30

1.82

4.24 4.14 4.08

1.65

1.84

4.02

2.01 2.29 2.31 2.32

1.95 2.07 2.07 2.07

3.64

2.36 2.36 2.37

2.07

3.30 3.30 3.28 2.08 2.08

3.24 3.24 3.24

The bold entries are associated to the configuration points 1, p1, p2, p3, p4, TS, p5, p6, p7, p8 and 2.

associated synaptic order is sketched [30, 48, 50, 51, 60–62, 80, 81]. The synaptic order in each case is represented by the number of lines (continuous or dashed) connecting them to the associated core attractors C1, C2 and Li. The activation region from 1 to TS (i.e., SSD I to SSD IV) is characterized by the fast (given the small calculated activation energy) interaction driving the formation of the Li–C1 bond. In the process, the lithium center is observed to coordinate as a cationic species that is stabilized by electron rearrangement from the C1C2 triple bond to form the V(C1,Li) attractor and associated basin. An agostic interaction between the metallic center and the C2–H2 bonding region is also present. In the domain of SSD IV, the C1C2 triple bond associated until that point with a single attractor begins to evolve into a double bond characterized by two attractors. The deactivation path, i.e., SSD VII to SSD IX, is essentially identified with the formation of the H3–C2 bond and the structural stabilization of the

ethenyl lithium intermediate. Note that, in such a representation, the Bmigrating^ center H exists as a monosynaptic basin V(H3) along the SSDs I to IV. The new bond H3–C2 is formed after the TS is reached, and the process is always Bassisted^ by the lithium center, as revealed by the nature of a trisynaptic valence basin V(H3,C2,Li) along the structural stability domains VI– VIII. Such an interpretation given in terms of the sequence of topologically defined structural stability domains, emphasizing a visually appealing picture for rationalizing the rearrangement that complements and expands the arguments invoked from within the traditional molecular orbital paradigm [4, 5, 11, 33–39]. In order to provide a complementary insight about the progress of the reaction, geometrical parameters as well as energy differences associated to the evolution of the reacting system along each SSD is provided in Fig. 4b. Note indeed that at the current level of theory this process is predicted to be a favored exergonic reaction with free energy changes for

305 Page 6 of 12

J Mol Model (2018) 24: 305

a

SSD-I

SSD-III

SSD-II V(H3)

Li V(H1,C1)

C1

Li C2

V(H2,C2)

U C2

C1

V(H2,C2,Li)

C2

SSD-V

SSD-IV

SSD-VI

Li

Li

F+

V(Asyn)

C2

C1

C2

Li

V(H3,Li)

U C1

C+

F C1

V(C1,C2,Li)

Li

V(C1,Li)

C1

[CU]

C2

V1,2(C1,C2,Li)

SSD-VII Li

SSD-IX

SSD-VIII Li

V(H3,C2,Li)

Li U

U C2

C1

C2

C1

V(H3,C2)

C1

C2

V1,2(C1,C2)

b

(1) P1 p2 p3 p4 p5 p6 p7 p8 (2)

C1-C2 1.210 1.214 1.220 1.230 1.235 1.250 1.261 1.349 1.353 1.349

C1-LI 2.442 2.293 2.167 2.106 2.088 2.051 2.033 1.910 1.875 1.948

Interactomic distances (Å) LI-C2 LI-H3 H3-C2 2.439 1.621 4.025 2.257 1.628 2.903 2.201 1.630 2.519 2.167 1.627 2.253 2.156 1.624 2.161 2.134 1.618 1.921 2.123 1.616 1.771 2.092 1.778 1.125 2.167 1.941 1.117 2.900 3.061 1.094

H1-C1 1.069 1.066 1.069 1.071 1.072 1.075 1.076 1.094 1.093 1.100

H2-C2 1.069 1.070 1.066 1.066 1.067 1.070 1.073 1.097 1.096 1.095

−1 activation and reaction of ΔG‡0 and 298 ¼ 6:99 kcal mol −1 0 ΔG298 ¼ −28:79 kcal mol . The activation entropy is val−1 ued in ΔS ‡0 K−1, in agreement with a 298 ¼ −7:45 cal mol process via a cyclic TS. Although the enthalpy difference between the reactant complex formed by lithium hydride and acetylene and isolated reactants is evaluated in ΔH 0298 ¼ −8:23 kcal mol−1, there are no essential differences in terms of free energies, i.e., ΔG0298 ¼ −0:11 kcal mol−1 within the

C2-C1-LI 75.5 72.9 75.3 76.0 76.1 76.3 76.3 77.8 82.7 122.2

C1-LI-H3 166.8 126.3 113.2 104.7 101.8 94.4 89.8 71.6 69.2 44.1

Planar angles (°) LI-H3-C2 H3-C2-C1 9.4 82.0 50.7 110.1 59.6 112.0 113.7 65.6 67.7 114.3 73.6 115.7 77.5 116.5 89.3 121.3 85.8 122.4 71.2 122.5

H1-C1-LI 106.1 113.4 118.1 125.1 127.6 134.0 137.7 164.9 163.4 126.1

H2-C2-H3 105.8 66.8 72.2 78.2 80.3 85.3 88.2 107.1 109.4 113.2

DFT framework. These findings agrees with the experimental available evidence pointing out that hydrometallation to alkynes is fast and indeed accounts for the lack of studies associated to alkenyl β-hydride eliminations from the corresponding metal complexes [82, 83]. The planar four-membered TS is characterized by only one imaginary frequency, i.e., 577.8i cm−1. The motion along such a frequency reveals that most of nuclei displacement at the position of TS are associated primarily with the displacement of the migrating H center and the

Page 7 of 12 305

J Mol Model (2018) 24: 305

ƒFig. 4

a BET representation of the electron localization function (ELF) attractors along the sequence of SSDs characterizing the B3LYP/6–31 + G(d,p) IRC associated to the hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The corresponding bifurcation catastrophes separating each SSD are identified over the arrows. The fold catastrophe F† splits a non-critical point into an attractor and a saddle point, increasing by one the total number of basins. The cusp catastrophe C merges two attractors and a saddle point into an attractor, decreasing by one the total number of basins, whereas the C† splits an attractor into two attractors and a saddle point, increasing by one the total number of basins. The elliptic umbilic catastrophe U is identified with changes in the synaptic order without changing the total number of basins. Attractors for the core basins, C(Li), C(C1), and C(C2), are represented by single labels Li, C1, and C2, respectively. The attractors associated to disynaptic and trisynaptic basins are represented by black circles. The synaptic order of a given basin is associated to the number of lines connecting such a valence attractors with the core ones. Note that the attack of the hydride center is represented by the evolution of a purely monosynaptic V(H3) basin into the disynaptic protonated V(H3,C2) one, including the formation of both disynaptic V(H3,Li) and trisynaptic V(H3,C2,Li) basins in the process (see the text for details). b Sequence of molecular configurations associated to the SSDs for the hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The value of the energy change (in kcal mol−1) associated to the evolution of the reacting system along each SSD is also reported. Note that the greatest energy change is located on the deactivation path (i.e., SSD-VII, −34.97 kcal mol−1) and corresponds to the process of formation of the new H3–C2 bond

change of hybridization at the carbon atoms. The DFT geometrical parameters of TS, namely, dC1-C2 = 1.237 Å, dC1-Li = 2.080 Å, d Li-H3 = 1.623 Å, d C2-H3 = 2.114 Å, d C1-H1 = 1.072 Å, and dC2-H2 = 1.067 Å; AH3-C2-C1 = 114.6°, ALi-C1C2 = 76.2°, ALi-C1-H1 = 128.9°, AH3-C2-H2 = 81.3°, DH3-Li-C1C2 = 0.000°, DH3-C2-C1-H2 = 180.000°, are close to the already known for this system at the Hartree Fock level of theory [4, 5]. The reaction mechanism can henceforth be described using the suggested notation [18, 30] in terms of bifurcation catastrophes associated with the key chemical events along the IRC pathway as: C2H3Li: 9-UF†C†UF†[CU]UU-0: C2H3Li [18, 30, 42, 60]. The evolution of the ELF topology plotted in the planar reaction center at representative points of each SSD is depicted in Fig. 5. The ELF representation at the chosen DFT level of theory reveals the nature of the electron density rearrangement featuring key characteristics driving the hydrometallation process [1–3]: (1) a large polarization effect of the positive cationic metal on the anionic V(H3) domain which appears strongly Bdeformed^ as a result of the Pauli repulsion between ions [44–47, 52–57] (e.g., Fig. 5a), (2) the activation of the C1C2 triple bond to attack the cationic center (e.g., Fig. 5b–e), and (3) the attack of the hydride center on C2 (e.g. Fig. 5g–h) and the final configurational evolution towards the alkenylmetal intermediate (e.g., Fig. 5i–j).

a

SSD-I (at IRC = - 3.08051)

b

SSD-II (at IRC = -1.98693)

Fig. 5 Color-filled maps of the ELF in the molecular plane defined by the C1–C2–Li centers for selected points within the different SSDs along the IRC for the hydrometallation of acetylene by lithium hydride 1, resulting in ethenyl lithium 2 via a four-membered TS. The values of the ELF are mapped on a red-green-blue color scale indicated on the left of each representation. In these maps. The contour lines for the values 0.50 (outer) and 0.80 (inner) are represented in bold. The ELF representation at the chosen level clearly reveals the nature of the electron density rearrangement driven by the motion of the cationic lithium center

305 Page 8 of 12

J Mol Model (2018) 24: 305

c

e SSD-V (at IRC = -0.11051)

SSD-III (at IRC= -0.9945)

f SSD-VI (at IRC= 0.44199)

d

SSD-IV (at IRC = -0.33149)

Fig. 5 (continued)

Fig. 5 (continued)

Conclusions Hydrometallation of HC≡CH by Li+H− and the reverse process associated with the β-hydride elimination in the alkenyl system H2Cβ = CαHLi was characterized in terms of the sequence of SSDs arising from the topological analysis of ELF theory. The bifurcation catastrophes separating the sequential SSDs were identified and characterized within the language of

Thom’s catastrophe theory framework. The results provide evidence that, on the metallation pathway (i.e., the fast—energetically favorable—hydrometallation of an alkyne), activation of the CC triple bond is the key factor enabling bond formation of the Li–Cα bonding. This is then followed by the formation of the Cβ–H single bond as a result of the attack on the hydride center. The agostic stabilizing interactions between the cationic center and the CC and C–H bonding regions along the path are identified as key processes along the reaction path. Within such a framework of interpretation, the

Page 9 of 12 305

J Mol Model (2018) 24: 305

i SSD-IX (at IRC= 3.3599)

g SSD-VII (at IRC = 0.7735)

j SSD-IX (at the configuration of the optimized ethenyl lithium)

Fig. 5 (continued) h SSD-VIII (at IRC = 2.76074)

Fig. 5 (continued)

References 1.

lithium cation plays a key role by driving the direction of the electron flow rearrangement. These results further exemplify [18–29] the usefulness of BET methodology, providing detailed mechanistic insights beyond the representation of a given chemical reaction (as described by a chosen coordinate) in terms of useful but frequently oversimplified curly arrows [4–8, 84, 85], a conclusion that, concerning purely electronic effects and density rearrangements, is proposed to extend also to related organometallic systems [13–17]. Acknowledgments We acknowledge the continuous support provided by Fondo Nacional de Ciencia y Tecnología (FONDECYT - Chile) through Projects 1181582 (EC) and 1180348 (PP).

2.

3.

4.

5.

Komine N, Hirano M, Komiya S (2015) Markovnikov-selective hydrometallation catalyzed by mono(phosphine)palladium(0) complexes: synthesis and reactivity of heterodinuclear hydridopalladium intermediate. J Synth Org Chem Jpn 73:616–631. https://doi.org/10. 5059/yukigoseikyokaishi.73.616 Jambor R, Lycka A (2017) Organosilicon and -germanium hydrides in catalyst-free hydrometallation reactions. Eur J Inorg Chem 4887–4898. https://doi.org/10.1002/ejic.201700630 Frihed TG, Furstner A (2016) Progress in the trans-reduction and trans-hydrometalation of internal alkynes. Applications to natural product synthesis. Bull Chem Soc Jpn 89:135–160. https://doi.org/ 10.1246/bcsj.20150317 Chen B, Zhao CD, Huang JA (1990) The irc method in chemicalreactions .3. Reaction ergodography for the addition of lih dimer to acetylene. Acta Chim Sin 48:209–215 Zhao CD, Chen B, Huang JA (1989) Reaction ergodography for the additions of hli and its dimer to acetylene. Int J Quantum Chem 36: 5–14. https://doi.org/10.1002/qua.560360103

305 Page 10 of 12 6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

Kaufmann E, Sieber S, Schleyer PV (1989) Abinitio models for metalation and hydrogenolysis reactions involving organo-lithium compounds. J Am Chem Soc 111:121–125. https://doi.org/10. 1021/ja00183a021 Kaufmann E, Schleyer PV, Houk KN, Wu YD (1985) Abinitio mechanisms for the addition of CH3Li, HLi, and their dimers to formaldehyde. J Am Chem Soc 107:5560–5562. https://doi.org/10. 1021/ja00305a058 Houk KN, Paddonrow MN, Rondan NG, Wu YD, Brown FK, Spellmeyer DC, Metz JT, Li Y, Loncharich RJ (1986) Theory and modeling of stereoselective organic-reactions. Science 231:1108– 1117. https://doi.org/10.1126/science.3945819 Gilmore K, Mohamed RK, Alabugin IV (2016) The Baldwin rules: revised and extended. Wiley Interdiscip Rev Comput Mol Sci 6: 487–514. https://doi.org/10.1002/wcms.1261 Xie JB, Li QL, Shi WJ, Ren FD, Song H (2015) Theoretical studies on H-M center dot center dot center dot pi (M=H, Li, Na, K) interactions involving the pi-electron donors, C2H2, C2H4 and C6H6. Indian J Chem A 54:709–719 Fohlmeister L, Stasch A (2015) Alkali metal hydride complexes: well-defined molecular species of saline hydrides. Aust J Chem 68: 1190–1201. https://doi.org/10.1071/ch15206 Fressigne C, Lhermet R, Girard AL, Durandetti M, Maddaluno J (2013) Influence of the acetylenic substituent on the intramolecular carbolithiation of alkynes: a DFT theoretical study. J Org Chem 78: 9659–9669. https://doi.org/10.1021/jo4012893 Dudziec B, Marciniec B (2017) Double-decker silsesquioxanes: current chemistry and applications. Curr Org Chem 21:2794– 2813. https://doi.org/10.2174/1385272820666151228193728 Pawluc P, Prukala W, Marciniec B (2010) Silylative coupling of olefins with vinylsilanes in the synthesis of pi-conjugated double bond systems. Eur J Org Chem 219–229. https://doi.org/10.1002/ ejoc.200900883 Nakajima Y, Shimada S (2015) Hydrosilylation reaction of olefins: recent advances and perspectives. RSC Adv 5:20603–20616. https://doi.org/10.1039/c4ra17281g Cheng C, Hartwig JF (2015) Catalytic silylation of unactivated C-H bonds. Chem Rev 115:8946–8975. https://doi.org/10.1021/ cr5006414 Frogneux X, Jacquet O, Cantat T (2014) Iron-catalyzed hydrosilylation of CO2: CO2 conversion to formamides and methylamines. Cat Sci Technol 4:1529–1533. https://doi.org/10.1039/ c4cy00130c Domingo LR, Rios-Gutierrez M, Perez P, Chamorro E (2016) Understanding the 2n+2n reaction mechanism between a carbenoid intermediate and CO2. Mol Phys 114:1374–1391. https://doi.org/ 10.1080/00268976.2016.1142127 Lopez L, Ruiz P, Castro M, Quijano J, Duque-Norena M, Perez P, Chamorro E (2015) Understanding the thermal dehydrochlorination reaction of 1-chlorohexane. Revealing the driving bonding pattern at the planar catalytic reaction center. RSC Adv 5:62946–62956. https://doi.org/10.1039/c5ra10152b Chamorro E, Ruiz P, Quijano J, Luna D, Restrepo L, Zuluaga S, Duque-Norena M (2014) Understanding the thermal 1s,5s hydrogen shift isomerization of ocimene. J Mol Model 20. https://doi.org/ 10.1007/s00894-014-2390-6 Rincon E, Zuloaga F, Chamorro E (2013) Global and local chemical reactivities of mutagen x and simple derivatives. J Mol Model 19: 2573–2582. https://doi.org/10.1007/s00894-013-1799-7 Domingo LR, Chamorro E, Perez P (2010) Understanding the high reactivity of the azomethine ylides in 3+2 cycloaddition reactions. Lett Org Chem 7:432–439 Domingo LR, Chamorro E, Perez P (2010) Understanding the mechanism of non-polar diels-alder reactions. A comparative elf analysis of concerted and stepwise diradical mechanisms. Org Biomol Chem 8:5495–5504. https://doi.org/10.1039/c0ob00563k

J Mol Model (2018) 24: 305 24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40. 41. 42.

Domingo LR, Chamorro E, Perez P (2008) Understanding the reactivity of captodative ethylenes in polar cycloaddition reactions. A theoretical study. J Org Chem 73:4615–4624. https://doi.org/10. 1021/jo800572a Domingo LR, Chamorro E, Perez P (2008) An understanding of the electrophilic/nucleophilic behavior of electro-deficient 2,3-disubstituted 1,3-butadienes in polar diels-alder reactions. A density functional theory study. J Phys Chem A 112:4046–4053. https://doi.org/ 10.1021/jp711704m Fuentealba P, Chamorro E, Santos JC (2007) Understanding and using the electron localization function. In: Toro-Labbe A (ed) Theoretical and computational chemistry. Elsevier, Amsterdam, p 57–85 Chamorro E, Notario R, Santos JC, Perez P (2007) A theoretical scale for pericyclic and pseudopericyclic reactions. Chem Phys Lett 443:136–140. https://doi.org/10.1016/j.cplett.2007.06.025 Chamorro E, Fuentealba P, Savin A (2003) Electron probability distribution in aim and elf basins. J Comput Chem 24:496–504. https://doi.org/10.1002/jcc.10242 Chamorro E (2003) The nature of bonding in pericyclic and pseudopericyclic transition states: thermal chelotropic decarbonylations. J Chem Phys 118:8687–8698. https://doi.org/ 10.1063/1.1566740 Krokidis X, Noury S, Silvi B (1997) Characterization of elementary chemical processes by catastrophe theory. J Phys Chem A 101: 7277–7282. https://doi.org/10.1021/jp9711508 Andres J, Berski S, Silvi B (2016) Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (elf) analysis to valence-shell electron-pair repulsion (vsepr) inspired interpretation. Chem Commun 52: 8183–8195. https://doi.org/10.1039/c5cc09816e Andres J, Gonzalez-Navarrete P, Safont VS, Silvi B (2017) Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory. Phys Chem Chem Phys 19: 29031–29046. https://doi.org/10.1039/c7cp06108k Ashby EC, Noding SA (1980) Hydrometalation .6. Evaluation of lithium hydride as a reducing agent and hydrometalation agent. J Org Chem 45:1041–1044. https://doi.org/10.1021/jo01294a024 Pi R, Friedl T, Schleyer PV, Klusener P, Brandsma L (1987) Representative metalation and reduction reactions of the superactive metal-hydrides LiH, NaH, and KH. J Org Chem 52: 4299–4303. https://doi.org/10.1021/jo00228a027 Pons JM, Santelli M (1988) Reductions promoted by low valent transition-metal complexes in organic-synthesis. Tetrahedron 44: 4295–4312. https://doi.org/10.1016/s0040-4020(01)86132-9 Klusener PAA, Brandsma L, Verkruijsse HD, Schleyer PV, Friedl T, Pi R (1986) Superactive alkali-metal hydride metalation reagents— LiH, NaH, and KH. Angew Chemie-Int Ed Engl 25:465–466. https://doi.org/10.1002/anie.198604651 Kowalski CJ, Lal GS (1986) Lithium hydride addition to ynolate anions—the mechanism of reductive ester homologation. J Am Chem Soc 108:5356–5357. https://doi.org/10.1021/ja00277a057 Hong ZH, Ong DY et al (2016) Understanding the origins of nucleophilic hydride reactivity of a sodium hydride-iodide composite. Chem Eur J 22:7108–7114. https://doi.org/10.1002/chem. 201600340 Xu F, Peng LF et al (2015) One-shot double amination of sondheimer-wong diynes: synthesis of photo luminescent dinaphthopentalenes. Org Lett 17:3014–3017. https://doi.org/10. 1021/acs.orglett.5b01293 Thom R (1994) Structural stability and morphogenesis: an outline of a general theory of models. Westview, London Zeeman EC (1976) Catastrophe theory. Sci Am 234:65. https://doi. org/10.1038/scientificamerican0476-65 Woodcock AER, Poston A (1974) Geometrical study of elementary catastrophes. Springer, Berlin

Page 11 of 12 305

J Mol Model (2018) 24: 305 43.

Gilmore R (1993) Catastrophe theory for scientists and engineers. Dover, New York 44. Savin A, Nesper R, Wengert S, Fassler TF (1997) ELF: the electron localization function. Angew Chemie Int Ed 36:1809–1832 45. Silvi B, Savin A (1994) Classification of chemical-bonds based on topological analysis of electron localization functions. Nature 371: 683–686. https://doi.org/10.1038/371683a0 46. Savin A, Silvi B, Colonna F (1996) Topological analysis of the electron localization function applied to delocalized bonds. Can J Chem 74:1088–1096. https://doi.org/10.1139/v96-122 47. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular-systems. J Chem Phys 92: 5397–5403. https://doi.org/10.1063/1.458517 48. Andres J, Berski S, Domingo LR, Polo V, Silvi B (2011) Describing the molecular mechanism of organic reactions by using topological analysis of electronic localization function. Curr Org Chem 15: 3566–3575 49. Adjieufack AI, Ndassa IM, Patouossa I, Mbadcam JK, Safont VS, Oliva M, Andres J (2017) On the outside looking in: rethinking the molecular mechanism of 1,3-dipolar cycloadditions from the perspective of bonding evolution theory. The reaction between cyclic nitrones and ethyl acrylate. Phys Chem Chem Phys 19:18288– 18302. https://doi.org/10.1039/c7cp01016h 50. Andres J, Gonzalez-Navarrete P, Safont VS (2014) Unraveling reaction mechanisms by means of quantum chemical topology analysis. Int J Quantum Chem 114:1239–1252. https://doi.org/10.1002/ qua.24665 51. Krokidis X, Vuilleumier R, Borgis D, Silvi B (1999) A topological analysis of the proton transfer in H5O2+. Mol Phys 96:265–273. https://doi.org/10.1080/002689799165891 52. Silvi B (2002) The synaptic order: a key concept to understand multicenter bonding. J Mol Struct 614:3–10. https://doi.org/10. 1016/s0022-2860(02)00231-4 53. Savin A, Becke AD, Flad J, Nesper R, Preuss H, Vonschnering HG (1991) A new look at electron localization. Angew Chemie-Int Ed 30:409–412. https://doi.org/10.1002/anie.199104091 54. Grin Y, Savin A, Silvi B (2014) The elf perspective of chemical bonding. In: Frenking G, Shaik S (eds) The chemical bond: fundamentals and models. Wiley-VCH, Weinheim, pp 345–382 55. Matito E, Silvi B, Duran M, Sola M (2006) Electron localization function at the correlated level. J Chem Phys 125:024301. https:// doi.org/10.1063/1.2210473 56. Ponec R, Chaves J (2005) Electron pairing and chemical bonds. Electreon fluctuation and pair localization in ELF domains. J Comput Chem 26:1205–1213. https://doi.org/10.1002/jcc.20257 57. Ayers PW (2005) Electron localization functions and local measures of the covariance. J Chem Sci 117:441–454. https://doi.org/ 10.1007/bf02708348 58. Nouri A, Zahedi E, Ehsani M, Nouri A, Balali E (2018) Understanding the kinetics and molecular mechanism of the curtius rearrangement of 3-oxocyclobutane-1-carbonyl azide. Comput Theor Chem 1130:121–129. https://doi.org/10.1016/j.comptc. 2018.03.019 59. Cmikiewicz A, Gordon AJ, Berski S (2018) Characterisation of the reaction mechanism between ammonia and formaldehyde from the topological analysis of elf and catastrophe theory perspective. Struct Chem 29:243–255. https://doi.org/10.1007/s11224-0171024-x 60. Berski S, Andres J, Silvi B, Domingo LR (2003) The joint use of catastrophe theory and electron localization function to characterize molecular mechanisms. A density functional study of the dielsalder reaction between ethylene and 1,3-butadiene. J Phys Chem A 107:6014–6024. https://doi.org/10.1021/jp030272z 61. Polo V, Andres J, Berskit S, Domingo LR, Silvi B (2008) Understanding reaction mechanisms in organic chemistry from catastrophe theory applied to the electron localization function

62.

63. 64.

65.

66.

67.

68.

69.

70.

71.

72. 73.

74.

75.

76.

77. 78.

79.

80.

topology. J Phys Chem A 112:7128–7136. https://doi.org/10. 1021/jp801429m Berski S, Ciunik LZ (2015) The mechanism of the formation of the hemiaminal and schiff base from the benzaldehyde and triazole studied by means of the topological analysis of electron localisation function and catastrophe theory. Mol Phys 113:765–781. https:// doi.org/10.1080/00268976.2014.974702 Savin A (2005) On the significance of elf basins. J Chem Sci 117: 473–475. https://doi.org/10.1007/bf02708351 Savin A (2005) The electron localization function (ELF) and its relatives: interpretations and difficulties. J Mol Struct THEOCHEM 727:127–131. https://doi.org/10.1016/j.theochem. 2005.02.034 Ayers PL, Boyd RJ et al (2015) Six questions on topology in theoretical chemistry. Comput Theor Chem 1053:2–16. https://doi.org/ 10.1016/j.comptc.2014.09.028 Schlegel HB (1982) Optimization of equilibrium geometries and transition structures. J Comput Chem 3:214–218. https://doi.org/ 10.1002/jcc.540030212 Schlegel HB (1995) Geometry optimization on potential energy surfaces. In: Ryarkony DR (ed) Modern electronic structure theory. World Scientific Publishing, Singapore Gonzalez C, Schlegel HB (1990) Reaction-path following in massweighted internal coordinates. J Phys Chem 94:5523–5527. https:// doi.org/10.1021/j100377a021 Gonzalez C, Schlegel HB (1991) Improved algorithms for reactionpath following: higher-order implicit algorithms. J Chem Phys 95: 5853–5860. https://doi.org/10.1063/1.461606 Lee CT, Yang WT, Parr RG (1988) Development of thecollesalvetti correlation-energy formula into a functional of the electron-density. Phys Rev B 37:785–789. https://doi.org/10.1103/ PhysRevB.37.785 Becke AD (1993) Density-functional thermochemistry. 3. The role of exact exchange. J Chem Phys 98:5648–5652. https://doi.org/10. 1063/1.464913 Frisch MJ, Trucks GW et al (2010) Gaussian 09, revision C.01. Gaussian, Inc., Wallingford CT Fuentealba PC, Chamorro E, Santos JC (2007) Chapter 5 understanding and using the electron localization function. In: ToroLabbe A (ed) Theoretical aspects of chemical reactivity. Elsevier, Amsterdam, pp 57–85 Zhao Y, Schultz NE, Truhlar DG (2006) Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J Chem Theory Comput 2:364–382. https://doi.org/10.1021/ct0502763 Zhao Y, Truhlar DG (2008) Density functionals with broad applicability in chemistry. Acc Chem Res 41:157–167. https://doi.org/ 10.1021/ar700111a Hratchian HP, Schlegel HB (2005) Chapter 10. Finding minima, transition states, and following reaction pathways on ab initio potential energy surfaces. In: Dykstra CE, Frenking G, Kim KS, Scuseria G (eds) Theory and applications of computational chemistry: the first 40 years. Elsevier, Amsterdam Fukui K (1981) The path of chemical-reactions—the IRC approach. Acc Chem Res 14:363–368. https://doi.org/10.1021/ar00072a001 Noury S, Krokidis X, Fuster F, Silvi B (1999) Computational tools for the electron localization function topological analysis. Comput Chem 23:597–604. https://doi.org/10.1016/s0097-8485(99)00039x Lu T, Chen F (2012) Multiwfn: a multifunctional wavefunction analyzer. J Comput Chem 33:580–592. https://doi.org/10.1002/ jcc.22885 Andres J, Gracia L, Gonzalez-Navarrete P, Safont VS (2015) Chemical structure and reactivity by means of quantum chemical

305 Page 12 of 12 topology analysis. Comput Theor Chem 1053:17–30. https://doi. org/10.1016/j.comptc.2014.10.010 81. Berski S, Andres J, Silvi B, Domingo LR (2006) New findings on the diels-alder reactions. An analysis based on the bonding evolution theory. J Phys Chem A 110:13939–13947. https://doi.org/10. 1021/jp068071t 82. Gogsig TM (2012) New discoveries on the β-hydride elimination. Springer, Berlin 83. O'Reilly ME, Dutta S, Veige AS (2016) Beta-alkyl elimination: fundamental principles and some applications. Chem Rev 116: 8105–8145. https://doi.org/10.1021/acs.chemrev.6b00054

J Mol Model (2018) 24: 305 84.

85.

Klimenko NM, Bozhenko KV, Strunina EV, Rykova EA, Temkin ON (1999) Ab initio calculations of minimum-energy pathways of the nucleophilic addition of the H− anion, LiH molecule and Li+/H− ion pair to acetylene and methylacetylene. J Mol Struct THEOCHEM 490:233–241. https://doi.org/10.1016/s01661280(99)00102-5 Houk KN, Rondan NG, Schleyer PV, Kaufmann E, Clark T (1985) Transition structures for additions of LiH and MeLi to ethylene and acetylene. J Am Chem Soc 107:2821–2823. https://doi.org/10. 1021/ja00295a053