Bonding between strongly repulsive metal atoms

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Bonding between strongly repulsive metal atoms: an oxymoron made real in a confined space of endohedral metallofullerenes†‡ Alexey A. Popov,*a,b Stas M. Avdoshenko,c Angel Martín Pendás,d and Lothar Dunscha 5

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Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX DOI: 10.1039/b000000x Endohedral metallofullerenes (EMFs) are able to encapsulate up to four metal atoms. In EMFs, metal atoms are positively charged because of the electron transfer from the endohedral metal atoms to the carbon cage. It results in the strong Coulomb repulsion between the positively charged ions trapped in the confined inner space of the fullerene. At the same time, in many EMFs, such as Lu2@C76, Y2@C79N, M2@C82 (M = Sc, Y, Lu, etc.), Y3@C80, or Sc4O2@C80, metals do not adopt their highest oxidation states, thus yielding a possibility of the covalent metal-metal bonding. In some other EMFs (e.g., La2@C80), metal-metal bonding evolves in the result of the electrochemical or chemical reduction, which leads to the population of the metal-based LUMO with pronounced metal-metal bonding character. This Article highlights different aspects of the metal-metal bonding in EMFs. It is concluded that the valence state of the metal atoms in dimetallofullerenes is not dependent on their third ionization potential, but is determined by their ns2(n−1)d1→ns1(n−1)d2 excitation energies. Peculiarities of the metal-metal bonding in EMFs are described in terms of molecular orbital analysis as well as topological approaches such as Quantum Theory of Atoms in Molecules and Electron Localization Function. Interplay of Coulomb repulsion and covalent bonding is analyzed in the framework of Interacting Quantum Atom approach.

A Introduction The class of fullerenes which have atoms, ions or clusters in their inner space is referred to as endohedral fullerenes.1-6 Especially well know are endohedral metallofullerenes (EMFs) for group III metals, such as Sc, Y, and lanthanides, and in this article we will limit the discussion only to these metals as providing the highest variability in terms of the structure of the metal cluster as well as the valence states of metal atoms. Historically, the first synthesized and studied structures were mono- and dimetallofullerenes (di-EMFs).7 After a one decade of endohedral fullerene research it became clear that the structural assignments for di-EMFs done solely on the base of mass-spectrometry are ambiguous, since di-EMFs cannot be distinguished from another class of EMFs with metal-carbide clusters.8 For instance, di-EMFs "M2@C84" (M = Sc, Y) were proved to be carbide clusterfullerenes [email protected], 10 However, a certain number of genuine di-EMFs are now unambiguously structurally characterized, including Lu2@C76,11 several M2@C82 structures (e.g., Sc2@C82,12 Y2@C82,9 Er2@C8213-15), and a family of M2@C2n di-EMFs based on early lanthanides (M = La, Ce, Pr; 2n = 72, 78, 80).16-22 The largest structurally characterized MIII-di-EMF known so far is La2@C10023 (the same structure is believed to be in Dy2@C10024, 25) while mass-spectrometry showed that the structures up to La2@C138 are formed.23 Although several EMFs with three encapsulated metal atoms have been reported (Er3C74,26 Tb3C80,27 Y3C80,28 or Dy3C9824),

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their characterization is mostly limited to mass-spectrometry data, and there has been no experimental evidence showing whether the isolated species with three metal atoms are conventional trimetallofullerenes (tri-EMFs) or carbide clusterfullerenes (as now proved for Sc3C2@C80,29 which was believed to be Sc3@C82 for more than a decade after its discovery in 199230). DFT studies showed that Y3C80 is most likely a conventional trimetallofullerene Y3@C80-Ih(7) since this structure is much more stable than Y3C2@C78 isomers.28 Although endohedral clusters in EMFs can comprise up to four metal atoms, the large number of metal atoms can be achieved only in the form of the clusters with non-metals,6 such as nitrogen in M3N@C2n,3, 4, 31-40 CH in Sc3CH@C80,41 carbide unit in M2–4C2@C2n,8-10, 29, 42-44 cyano group in Sc3NC@C78,80,45, 46 oxygen in Sc4O2,3@C80,47, 48 or sulfur in [email protected], 50 The first studies of the electronic structures of EMFs soon after their discovery revealed that these molecules are characterized by an electron transfer from the metal atoms to the carbon cage. In particular, transfer of three electrons is characteristic for such monometallofullerenes as Sc@C82, Y@C82, or [email protected], 3, 4, 51-54 The endohedral metal atoms thus adopt the highest oxidation state (+3), and the metal-cage interactions can be formally described as ionic. In a similar way, the ionic model can be applied to other kinds of EMFs.55-57 For di-EMFs such as La2@C80, this model implies a 6-fold negatively charged fullerene C806− encapsulating two La3+ ions.58 Although these numbers should not be taken literally (a large degree of covalent metal-cage d-π bonding decreases these charges a lot),56, 59-67 [journal], [year], [vol], 00–00 | 1

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there is no doubt that metal atoms in EMFs do bear a sufficiently high positive charge to induce strong Coulomb repulsion when two or more metals are encapsulated inside one carbon cage.68, 69 For instance, a repulsion energy of two point charges of +1.65 (the Bader charge of La in La2@C80) placed at the distance of 3.83 Å (DFT-optimized La–La distance in La2@C80) is as high as 10 eV. Although metal atoms are certainly not the point charges, and exact electron density distribution should be taken into account for a more precise evaluation of repulsion energy, this conservative estimation shows that the order of this value is comparable to the dissociation energy of the strongest covalent bonds (e.g., 9.8 eV in N270). It is thus clear that the metal atoms in polymetallic EMFs tend to be as far from each other as possible and the metal cluster would prefer to dissociate completely, but the carbon cage restricts their separation. It is also not surprising that the large number of metal atoms in EMFs can be easier realized with non-metals: the latter bear a negative charge (the formal charge of nitrogen in nitride clusterfullerenes is −3; oxygen, sulphur, and carbide unit C2 all have a formal charge of −2) and hence partially compensate Coulomb repulsion between the metal atoms; there is also a large covalent contribution to the metal-nitrogen (oxygen, sulphur, etc.) bonding.67 Importantly, even when we consider the metals which usually exhibit a 3+ oxidation state (Sc, Y), a lower oxidation state is evident in a significant fraction of EMFs (e.g., di-EMFs M2@C82 or oxide clusterfullerene Sc4O2@C80). The lower oxidation state implies that the outer valence electrons are not completely transferred from the metal to the carbon cage, and thus they can be either localized, or form an intermetallic bond. Another option potentially leading to the metal-metal bonding is found in EMFs like La2@C80, whose LUMO is localized on the metal atoms.71 In this case, an electrochemical or chemical reduction of the EMFs formally proceeds through the carbon cage and populates the endohedrally-localized LUMO (such redox reactions are called in cavea or endohedral electron transfer, see recent review72), which usually exhibits a pronounced metal-metal bonding character. EMFs thus provide an interesting situation – on the one hand, metal atoms are strongly repulsive due to Coulomb interaction; on the other hand, they can form intermetallic covalent bonds. These phenomena and their interplay as well as the factors determining the valence state of metal atoms in di-EMFs are reviewed in this Article.

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B Dimetallofullerenes 45

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B.1 M2@C76 and M2@C82 (M = Sc, Y, Lu): M(II) or M(III)? The electron transfer from metal atoms to the carbon cage has a crucial influence on the molecular structure of EMFs. Charging changes relative stabilities of fullerene isomers, and as a result, different isomers are found for EMFs with different formal charge of the cage. For instance, while C82-C2(3) is the most abundant structure for the empty fullerene,73 the main and minor isomers of MIII@C82 have C2v(9) and Cs(6) cages,74-76 respectively, C3v(8) is usually the most abundant cage for EMFs with four-fold charged cage (e.g., M2C2@C82) followed by Cs(6) and C2v(9) isomers,9, 10, 15, 77 while nitride clusterfullerenes M3N@C82 (M = Gd and other lanthanides) with six-fold charged 2 | Journal Name, [year], [vol], 00–00

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cage are based on the C82-Cs(39663) isomer.78 Here and below the fullerene isomers are labelled by their symmetry and the number according to the spiral algorithm.79 To simplify comparison to the results of the previous works, we use two-fold numbering system: the short notation is used for the isomers obeying isolated pentagon rule (IPR), whereas the full numbering system is employed for the non-IPR isomers.65 The changes in the cage isomeric structures of EMFs depending on the cluster/cage size finds perfect parallels with the relative stability of the isomers of the empty fullerenes in appropriate charge state, and this correspondence was used many times before to find the most suitable carbon cages for new EMFs.25, 58, 80-86 But this rule can be also reversed and used to determine the formal charge of the cage in EMF based on its isomeric structure. So far, there has been no direct proof of the divalent state of metal atoms in diEMFs such as M2@C82, and hence the charge state of metal atoms in some EMFs is subject to a controversy as will be discussed below. To illustrate the correspondence between the charge state of the carbon cage (and, consequently, of the metal atoms), here we consider the results of the studies of two diEMFs, M2@C76 and M2@C82 (M = Sc, Y, Lu). Lu2@C76 has been characterized by 13C NMR by Shinohara et al. and its Td(2) isomeric structure is determined unambiguously.11 The authors proposed that the oxidation state of Lu is +3, but recent computational study of Lu2@C76 by Yang et al. showed that it is more likely to be +2 with Lu–Lu bond.87 The structure of Sc2@C76 is more ambiguous: its 13C NMR spectrum has ca 38 lines,88 which points to a two-fold symmetry (Cs, C2 or Ci) and excludes both IPR isomers with D2(1) and Td(2) symmetry. Extended DFT study showed that the non-IPR Cs(17490) isomer is more suitable for the six-fold charged cage, and Sc2@C76-Cs(17490) is indeed the most stable;82 this cage isomer was also found in the nitride clusterfullerene [email protected] It might be thus supposed that Sc in Sc2@C76 is in the +3 oxidation state. Table 1 lists the most stable isomers of C76 in the −4 and −6 charged states and their relative energies and HOMO-LUMO gaps computed at the PBE/TZ2P level.82, 83 The most stable C764− isomer is Td(2) followed by C2v(19138) with a large gap in relative energy of 66 kJ/mol.87 This value is already sufficiently large to conclude that other isomers have no practical importance. For C766−, energy distribution of isomers is rather dense. Three isomers, Cs(17490), C2v(19138), and Td(2), have particular low relative energies (0, 17, and 21 kJ/mol, respectively) and can be considered as possible hosts for two M3+ atoms. The other C766− isomers are noticeably less stable (∆E > 50 kJ/mol).82, 83 The Table 1 also lists relative energies and HOMO-LUMO gaps of corresponding Sc2@C76, Y2@C76, and Lu2@C76 isomers. Surprisingly, depending on the metal involved, M2@C76 di-EMFs fall into two groups. Relative stabilities of Sc2@C76 and Y2@C76 isomers are rather similar and correlate well with the relative energies of C766− isomers, however the HOMO-LUMO gaps of di-EMFs are significantly smaller than those in C766−. M2@C76Cs(17490) is the most stable structure for both Sc and Y. On the contrary, relative energies of the isomers of Lu2@C76 are drastically different from those of Sc2@C76 and Y2@C76 and correspond well to the stabilities of C764− isomers, while their HOMO-LUMO gaps are also somewhat smaller than in


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Fig. 1 DFT-computed MO energy levels in M2@C76-Td(2) (left panel) and M2@C76-Cs(17490) (right panel) compared to those of Sc2 and Lu2. Occupied MOs are black, vacant – cyan. Metal-based MOs in M2@C76 and corresponding MOs in M2 dimers are encircled in magenta (Sc) and green (Lu). Outermost figures show M–M bonding MOs in Lu2@C76-Td(2) (left) and Sc2@C76-Cs(17490) (right) with corresponding MOs of the Lu2 and Sc2 dimers. 5

Table 1 DFT-computed relative energies (∆E) and HOMO-LUMO gaps of the lowest energy isomers of C764−,6− and M2@C76 (M = Sc, Y, Lu). C764−

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Sc2@C76

Y2@C76

Lu2@C76

cage

∆E, kJ/mol

gap, eV

∆E, kJ/mol

gap, eV

∆E, kJ/mol

gap, eV

∆E, kJ/mol

gap, eV

∆E, kJ/mol

gap, eV

Cs(17490) C2v(19138) Td(2) C1(17465)

81.1 65.6 0.0 115.3

0.54 0.17 0.92 0.35

0.0 16.8 20.8 53.9

1.12 0.78 0.14 0.89

0.0 51.3 24.0 61.5

0.72 0.11 0.29 0.41

0.0 34.2 25.9 64.5

0.30 0.09 0.34 0.06

66.7 50.6 0.0 93.9

0.16 0.17 0.72 0.13

corresponding C764− structures. The most stable isomer of Lu2@C76 has the Td(2) carbon cage.87 Thus, in the M2@C76 EMFs, each Sc and Y atom donates 3 electrons to make the cage six-fold charged, whereas each Lu atom donates only two electrons. At the first glance this situation is counter-intuitive because the third ionization potential of Sc (24.76 eV) is 3.8 eV higher than that of Lu (20.96 eV),89 and it might be expected that Sc rather than Lu should easier form the divalent state. Moreover, third ionization potentials of Y (20.52 eV) and Lu are similar, and it is not clear why Y behaves likes Sc and not like Lu in di-EMFs. To clarify these points, in Figure 1 we plot the MO energy levels in C76-Td(2) and C76-Cs(17490) and corresponding isomers of Sc2@C76 and Lu2@C76. Td(2) isomer in the neutral state is subject to Jahn-Teller distortion, resulting in lower symmetry and lifting of the HOMO-LUMO degeneracy. The molecule still has two-fold degenerate LUMO/LUMO+1 with a very small HOMOLUMO gap, but the gap between LUMO+1 and LUMO+2 is 0.83 eV, which corresponds to the HOMO-LUMO gap of 0.92 eV in C764−-Td(2). It is thus not surprising that the transfer of four electrons from metal atoms to C76-Td(2) (i.e. occupation of lowenergy LUMO and LUMO+1) results in the stable di-EMF structure as it is found for Lu2@C76-Td(2).11, 87 Lu atoms form an intermetallic bond, and localized Lu–Lu bonding MO is the HOMO of the di-EMF (Fig. 1). Its energy is very close to the energy of the highest-occupied cage orbital, and the HOMOLUMO gap of Lu2@C76-Td(2) is close to that of C764−-Td(2). This journal is © The Royal Society of Chemistry [year]

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The non-IPR C76-Cs(17490) isomer has three low-lying LUMOs followed by the gap of 1.12 eV between LUMO+2 and LUMO+3. Hence, for this cage, transfer of six electrons is preferred to stabilize its electronic structure,90 and it is the situation found in Sc2@C76-Cs(17490). The HOMO-LUMO gap of Sc2@C76 is much smaller than that of C766− because the LUMO of Sc2@C76 is essentially a Sc–Sc bonding orbital and its energy is below that of the lowest-unoccupied cage MO (Fig. 1). The questions which remain non-clarified by this analysis are: (i) why are six electrons (and not four as would be preferable) are transferred to the carbon cage in Sc2@C76-Td(2)? (ii) why are four electrons (and not six) transferred to the carbon cage in Lu2@C76-Cs(17490)? The answer to these questions becomes evident when MO energy levels in the Sc2 and Lu2 dimers are compared to those of fullerenes (Fig. 1). When only valence electrons are considered, both metals have similar ns2(n−1)d1 atomic ground states, but the electronic structure of their dimers is different: the ground state of Sc2 is a quintet (4s)σg2(3d)πu2(3d)σg1(4s)σu1, while for Lu2 it is a triplet (6s)σg2(6s)σu2(5d)πu2 (detailed studies of the electronic structures of the dimers using experimental data and high level ab initio calculations were reported earlier91-98). In both cases, the high spin state results in a significant spin polarization, so that the spin-up and spin-down orbitals of the same type are split. The energy levels of the four highest energy single-occupied MOs (SOMOs) of both dimers are higher than −4 eV, which is well [journal], [year], [vol], 00–00 | 3

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above the energies of the empty fullerene LUMOs. Hence, transfer of these four electrons from the metal dimers to the carbon cage is natural both for Sc2 and Lu2. The most apparent difference between Lu2 and Sc2 is in the energy of the two lowest energy spin-up and spin-down SOMOs, which form a doubleoccupied MO of the (ns)σg type. Since these SOMOs fall into the energy range of the frontier orbitals of the fullerenes, their energies appear to be of paramount importance for the determination of the valence state of metals in di-EMFs. As can be seen in Fig. 1, in Lu2 these SOMOs are ca 1 eV lower in energy than in Sc2, and this difference is responsible for the alternation of the metal valence in Sc- and Lu-di-EMFs. The higher energy of the σg MO in Sc2 means that Sc2 tends to transfer six electrons (although the energies of the cage MOs are also important, see below), whereas the low energy of this MO in Lu2 results in the preference of the divalent state with Lu−Lu bond. Y2 has quintet ground state similar to Sc2, and its MO energies and oxidation state in di-EMFs are close to those of Sc2 (Fig. 2). The main factor which thus determines the valence state of the metal atoms in di-EMFs is the electronic state of the metal dimer in the free form, and in particular the energy of the (ns)σg2 MO. To form the Sc2 dimer in the quintet electronic state, one Sc atoms should be in the ground 4s23d1 state, while the other one should be excited to the 4s13d2 state.91 The 4s23d1→4s13d2 excitation energy in Sc, 1.43 eV (analogues value for Y is 1.36 eV),99 can be compensated by the energy gain due to formation of the quintet state of the dimer. At the same time, the 6s25d1→6s15d2 excitation of Lu requires too much energy, 2.34 eV,99 and this value can not be balanced by the quintet state of the dimer. As a result, the ground triplet state of Lu2 is obtained by the bonding of two Lu atoms in their ground 6s25d1 states. For comparison, 6s25d1→6s15d2 excitation energy of La is only 0.33 eV,99 and La2 dimer has a singlet (6s)σg2(5d)πu4 ground state formed by two La atoms in their excited 6s15d2 state. The energy of the (6s)σg2 MO in La2 is −3.2 eV, which is even higher than the (ns)σg2 MO energies in Sc2 and Y2 (Fig.1, 2), and hence a trivalent state of La in di-EMFs is the only choice. In short, the valence state of the metal atoms in di-EMFs is not dependent on their third ionization potential (as it is known for monometallofullerenes),100, 101 but is mainly determined by their ns2(n−1)d1→ns1(n−1)d2 excitation energies. The lower this energy, the easier a trivalent state is formed. Although the energy of the (ns)σg2 MO of the metal dimer is the main factor, the role of the carbon cage in determining the valence state of metal atoms should not be underestimated. To illustrate this fact, we compare a series of Sc, Y, and Lu di-EMFs with C82 carbon cage. As mentioned above, C82 provides the broadest variability of the stable isomeric structures in dependence on the charge state. The most stable C824− isomers are C3v(8), C2v(9), and Cs(6) with the relative energies of 0, 12, and 35 kJ/mol, respectively (Table 2, see also refs. 49, 55, 65). These isomers are proved experimentally for EMFs with 4-fold charged carbon cage (carbide,10, 102, 103 sulfide,49, 104 and oxide clusterfullerenes105 as well as some di-EMFs9, 12-14). The relative energy of the fourth most stable C824− isomer, C2v(39705), is as high as 82 kJ/mol,65 and hence less stable isomers can be taken out of consideration. For C826−, four aforementioned isomers are also among the most stable ones, and the list of the stable

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structures also includes the non-IPR Cs(39663) isomer (Table 2).82 Experimentally, only the Cs(39663) cage was found in the nitride clusterfullerenes with the 6-fold charged cage.78 MO energies of the five C82 isomers plotted in Figure 2 show that the C82-C3v(8) isomer is especially suitable for a four-electron transfer because of the low-energy LUMO and LUMO+1 and the highest LUMO+1/LUMO+2 gap exceeding 1 eV.55 Cs(6) and C2v(9) isomer are less suitable because of the higher energies of LUMO and LUMO+1 as well as much smaller LUMO+1/LUMO+2 gaps. Among these three isomers, C2v(9) has the lowest energy of the LUMO+2, and it is not surprising that in the −6 charge state it becomes the most stable. However C2v(39705) and Cs(39663) isomers are even more suitable for the 6-fold electron transfer because they have three low energy LUMOs and high LUMO+2/LUMO+3 gaps (Fig. 2).82 Table 2 also lists the relative energies of Sc2@C82, Y2@C82, and Lu2@C82 isomers with C3v(8), C2v(9), Cs(6), C2v(39705), and Cs(39663) cages. For all studied metals, M2@C82-C3v(8) is the most stable isomer, and in all structures metal atoms are in the divalent state. That is, the LUMO+2 energy of C3v(8) is higher than the energy of the M–M bonding MO, and this MO remains occupied even for Sc and Y. However, the difference in the energy of the (ns)σg2 MOs of Sc2, Y2, and Lu2 is still inherited in the HOMO-LUMO gaps of M2@C82 (Table 2). The M–M bonding MO in M2@C82-C3v(8) is HOMO, and due to its high energy in Sc2@C82 and Y2@C82 their HOMO-LUMO gaps (0.57 and 0.26 eV, respectively) are much lower than in C824−-C3v(8) (0.93 eV). In Lu2@C82-C3v(8), the Lu–Lu bonding MO is more than 0.5 eV lower in energy, and hence the HOMO-LUMO gap of the molecule, 1.23 eV, is considerably larger. Cs(6) and C2v(9) isomers of M2@C82 can be described in a similar way except for the fact that in Y2@C82 these isomers are almost isoenergetic to C3v(8), while in Sc2@C82 and Lu2@C82 they are somewhat less stable but remain within the energy range of 25 kJ/mol. In this case it is probably related to the ionic radii of the metals (Sc 2.6 eV). This journal is © The Royal Society of Chemistry [year]

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www.rsc.org/xxxxxx Table 7 IQA intra-cluster interaction energies (in eV) in Sc4O2@C800, 2− and Sc4O26+, 4+ Sc4O2@C802−

Sc4O2@C80 Vxc

Vcl

Einter

Vxc

Vcl

Einter

Vxc

Vcl

Einter

Vxc

Vcl

Sc1–Sc1' Sc1–Sc2 Sc2–Sc2' Σ(Sc–Sc) a

9.54 11.12 14.73 68.76

−0.91 −0.21 −0.13 −1.88

10.45 11.33 14.86 70.64

3.97 9.13 13.81 51.98

−1.42 −0.58 −0.12 −3.88

5.39 9.13 13.93 55.85

10.80 16.87 23.15 101.42

−2.11 −0.40 −0.24 −3.95

12.91 17.27 23.39 105.37

3.33 9.03 15.53 54.99

−3.24 −1.29 −0.20 −8.58

6.57 10.32 15.73 63.56

Sc1–O Sc1–O' Sc2–O Σ(Sc–O) a

−17.58 −7.85 −18.96 −126.68

−3.15 −0.16 −2.65 −17.24

−14.42 −7.69 −16.30 −109.44

−13.03 −2.79 −6.27 −0.13 −17.15 −3.03 −107.19 −17.97

−10.24 −6.14 −14.12 −89.22

−18.40 −8.31 −19.63 −131.94

−4.08 −0.26 −3.24 −21.63

−14.33 −8.05 −16.39 −110.31

−14.90 −6.08 −17.73 −112.91

−3.58 −0.22 −3.56 −21.84

−11.32 −5.86 −14.18 −91.07

7.77

−0.68

8.45

−0.62

9.02

6.35

−0.67

7.03

6.63

−0.58

7.22

−50.15

−19.80

−30.35

−46.81 −22.46

−24.35

−24.17

−26.25

2.08

−51.29

−31.00

−20.28

Σ(Sc4O2) a

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Sc4O24+

Einter

O–O'

5

Sc4O26+

a

8.40

Σ denotes a sum of all pairwise interactions of a given type.

Charging of EMF molecules should have obvious effects on the energies of M–M interactions: i) reduction of atomic charges (and hence decrease of the repulsive Vcl term; ii) increase of the M–M bonding and hence Vxc. Comparison of the interaction energies of the neutral and anionic forms of La2@C80 and La2@C100 shows that the first effect is ca two times larger (∆Vcl = −2.04 and –2.70 eV) than the second one (∆Vxc = −1.05 and –1.13 eV). At the same time, total M–M interaction energies in the anions of La2@C80 and La2@C100 are still more positive than Einter in M2@C82 molecules (Table 6). Formation of NNAs in the tri-EMFs raises a question of the stabilizing role of the pseudoatoms. Both Vcl and Vxc terms in the metal-pseudoatom interactions are negative, and the values listed in Table 6 show that Vcl is dominating over Vxc (−2.47 vs −0.45 eV in Y3@C80 and −0.19 vs −0.07 eV in La3@C110+). However, Einter values of metal-pseudoatom interaction are considerably smaller than the energy of M–M repulsion, and net interaction energies of M3 clusters in Y3@C80 and La3@C110+ are 10.7 and 11.0 eV, respectively. IQA analysis also allows estimation of a stabilizing role of the non-metals in clusterfullerenes. Table 7 lists Einter, Vcl and Vxc values for Sc4O2@C80, Sc4O2@C802−, Sc4O26+ and Sc4O24+. As can be seen, all Sc–Sc interactions in Sc4O2@C80 are strongly repulsive: Einter values are even larger than in di-EMFs because of the higher atomic charges (hence Vcl ≈ 11–15 eV), and weaker covalent bonding (|Vxc| < 0.9 eV). As a result, the net energy of the Sc–Sc interactions in the cluster is as high as 68.8 eV (Vxc contribution is only −1.9 eV). At the same time, Einter values for Sc–O interaction are large and negative since on the one hand, scandium and oxygen have opposite charges leading to strongly stabilizing ionic interactions (Vcl ≈ −14–16 eV), on the other hand, there is a strong covalent Sc–O bonding (see Table 5 and discussion in Section D) with Vxc values of ca −3 eV. Thus, Sc–O interactions stabilize the cluster by ΣEinter(Sc, O) = −126.7 eV This journal is © The Royal Society of Chemistry [year]

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(Vcl = −109.4 eV and Vxc = −17.2 eV). Although O–O interaction is repulsive (Vcl = 8.5 eV and Vxc = −0.7 eV), net Einter value for all intracluster interactions in Sc4O2@C80 is as high as −50.1 eV, from that ionic bonding contributes −30.3 eV, and −19.8 eV is added by covalent term. In the Sc4O2@C802− dianion, net Vxc term is further increased to −22.5 eV, but the Vcl is decreased to −24.4 eV because of reduced atomic charges (Table 5). Interestingly, in the "naked" Sc4O26+ cluster, Coulomb Sc–Sc repulsion is increased, whereas ionic term in Sc–O bonding is decreased (atomic charges are more positive both for Sc and for oxygen). For the whole cluster, Vcl(Sc, Sc) and Vcl(Sc, O) terms compensate each other resulting in Einter ≈ Vxc. Since both Vxc(Sc, Sc) and Vxc(Sc, O) terms in the ion are somewhat higher than in the clusterfullerene, the net Vxc energy in Sc4O26+ (−26.3 eV) is higher than in Sc4O2@C80.

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The inner voids in fullerenes can serve as a container for different atoms and clusters, often in rather peculiar electronic states. The carbon cage thus provides a natural "laboratory" for the study of unusual systems and interactions, which can be hardly realized or stabilized outside the fullerene. One of such specific interactions is the bonding between metal atoms in endohedral metallofullerenes. In fact, the idea that interactions between highly repulsive positively charged metal atoms in endohedral dimetallofullerenes (di-EMFs) can be discussed in terms of bonding might look questionable. In this work we summarized results of different approaches, in particular MO analysis as well as QTAIM and ELF topological analyses to show that covalent bonds between metal atoms in EMFs do exist and that their parameters are not much different from those of other chemical bonds between the metal atoms. Moreover, bond critical points for M–M bonds are characterized by negative values of the density Laplacian, which is a usual situation for covalent bonds between the first raw [journal], [year], [vol], 00–00 | 15

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elements but rarely observed for metal-metal bonds. The balance between covalent bonding and Coulomb repulsion was highlighted using Interacting Quantum Atom formalism within QTAIM. IQA analysis shows that the covalent bonding contribution to the total interaction energy is much smaller than the repulsive ionic term, which results in the net repulsion between the metal atoms. For clusterfullerenes such as Sc4O2@C80, IQA analysis also shows how metal-metal repulsion is balanced by metal-oxygen Coulomb attraction of similar or even larger magnitude. As far as the general possibility of covalent bonding between metal atoms in EMFs is solidified, the next question is "What are the rules governing the valence state of metal atoms in di-EMFs"? It is known that in some di-EMFs metal are in the 3+ oxidation state (e.g., La2@C80), while in other di-EMFs metal prefers a divalent state with intermetallic bond (e.g., Lu2@C76, M2@C82). Surprisingly, up to now there was no concise description of the factors affecting the meta-metal bonding in EMFs. In this Article we showed that the valence state of the metal atoms in di-EMFs is determined by an energy matching between the lowest energy valence MO of the metal dimer, which usually has a (ns)σg2 character, and the energies of the cage MOs. In due turn, the energy of the MO in the metal dimer correlates with the ns2(n−1)d1→ns1(n−1)d2 excitation energy of the free metal atom. Hence, this energy, rather than the third ionization potential, largely determines the valence state of metal atoms in the diEMFs. Since the M–M bonding orbitals in di-EMFs inherit significant ns-component from the (ns)σg2 MO of the metal dimers, the presence of such M–M bonds can be verified straightforwardly by ESR spectroscopy of the cation-radicals via large hyperfine coupling constants. Likewise, when the M–M bonding is absent in the neutral state of the di-EMF but appears in the anionic state (i.e. when M–M bonding orbital is LUMO as in La2@C2n), ESR spectra of anion-radicals can be used to prove formation of the M–M bonds. It is also necessary to note that for lanthanide-based di-EMFs, determination of the valence state of metal atoms by XAS can be ambiguous since it is usually focused on the 3d→4f excitation pattern, whereas the M(II) states in diEMFs can have the same 4f-configuration as in M(III). Since Coulomb repulsion is the dominant term in metal-metal interactions, metal atoms in EMFs show a tendency to be as far from each other as possible. This results in exotic situation when metal-metal bonds can be exceptionally long and raises the question on the natural limits of such bonding at long distances. In this Article we showed that covalent bonding between La atoms in charged states of La2@C100 can be established at the La–La distances of ca 5 Å. At the same time, no bonding is expected in the charged forms of La2@C120 with the La–La distances approaching 8 Å. Further study of these phenomena to close the gap between the bonding at 5 Å and the absence of bonding at 8 Å can hardly be done within DFT and will require the use of multiconfigurational ab initio approaches. Interesting evolution of the metal-metal bonding situation was also found when the number of endohedral metal atoms was increased to three. In tri-EMFs such as Y3@C80, metal-metal bonding results in the formation of non-nuclear attractor, and metal atoms form bond paths to the pseudoatom rather than to each other. NNA is persistent even at large inter-atomic distances


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as showed the study of La3@C110. Very specific Sc–Sc bonding situation develops in the oxide clusterfullerene Sc4O2@C80 upon charging. While only two Sc atoms are covalently bonded in the neutral state of the molecule, bonding pattern becomes very complex in the dianion. In particular, exotic situation with two bond paths between the same pair of Sc atoms is revealed, while bond paths between other atoms are highly curved. Sc atoms interact via three-centre bonds, and each oxygen-free face of the Sc4 tetrahedron coordinates a half of an electron pair.

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A.A.P. is thankful to DFG (project PO 1602/1-1) for financial support. Research Computing Center of Moscow State University is acknowledged for time on supercomputer "SKIF-Chebyshev". Authors are thankful to Ulrike Nitzsche for assistance with local computational resources in IFW Dresden.

Notes and references a

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Department of Electrochemistry and Conducting Polymers, LeibnizInstitute for Solid State and Materials Research (IFW Dresden), D-01171 Dresden, Germany. Fax: +49 351 4659 745; Tel: +49 351 4659 658; E-mail: [email protected] b Chemistry Department, Moscow State University, Moscow 119992, Russia. c School of Materials Engineering, Purdue University, West Lafayette, Indiana, USA. d Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006-Oviedo, Spain † In memoriam Richard F. W. Bader (1931–2012) ‡ Computations of the lowest energy isomers of empty charges fullerenes as well as di-EMFs M2@C76 and M2@C82 were performed at the PBE170 level using PRIRODA code171, 172 as reported in earlier works.49, 80-83 For QTAIM and ELF analysis, all studied molecules were first optimized at the PBE/TZVP173, 174 level (with SDD effective core potentials for La175 and Lu176, 177), and then point energy computations were performed at the PBE level with scalar-relativistic ZORA correction178 and specially-tailored full-electron TZVP-quality basis set179, 180 implemented in Orca (Version 2.8).181 To ensure sufficient flexibility of the basis set in the studies of La2@C100, La2@C120, and La3@C110, additional basis functions were added at the centre of the molecules. QTAIM and ELF analyses were performed employing AIMAll182 and TopMod,183, 184 respectively. For IQA analysis, Promolden and AIMAll were employed. Visualization of the structures and isosurfaces was done with Chemcraft,185 VMD,186 and Vesta.187 1. 2.

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