The multiple bonding in heavier group 14 element alkene analogues is stabilized mainly by dispersion force effects

Computations on the heavier group 14 dimetallenes [E{CH(SiMe3)2}2]2 and [E{N(SiMe3)2}2]2 (E = Ge, Sn, or Pb) and their respective monomers indicated that empirically observed dimerization is principally driven by attractive dispersion forces.


Introduction
The synthesis of the lower valent group 14 element dialkyls :E{CH(SiMe 3 ) 2 } 2 (E ¼ Sn and Pb) in 1973 1 and the corresponding isoelectronic amido derivatives: E{N(SiMe 3 ) 2 } 2 (E ¼ Ge, Sn, and Pb) in 1974 2,3 were landmark events in the evolution of modern main group chemistry. The alkyl derivatives in particular were to exert a great inuence on the perception of bonding between heavier main group elements because of their unprecedented structures and chemical behavior. Both the amides and alkyls were shown to exist as monomers in benzene solution 1,2 and in the vapor phase. [4][5][6] But whereas the amides remained monomeric as solids, 5,7 the alkyl derivatives displayed unusual E-E bonded dimeric structures in the solid state. [8][9][10][11] Although they are heavier congeners of substituted ethylenes, their group 14 atoms were found to have non-planar coordination, and the structures displayed a centrosymmetric trans-pyramidalized (or folded) conguration (Fig. 1a), as well as E-E bond lengths that did not display the extent of shortening expected for double bond formation. [8][9][10][11] The original interpretation of the (at the time) peculiar E-E bonding was based on either a double donor-acceptor bond (Fig. 1b) or a valence bond resonance structure (Fig. 1c). The bonding can be viewed also in terms of a pseudo (also called 2 nd -order) Jahn-Teller mixing 12,13 of the p-bonding and s* levels which occurs upon a transbending distortion (i.e. a vibration) of the E-E frameworks. The mixing of a bonding and antibonding orbital generates a molecular orbital with lone-pair character, and hence a pyramidalized coordination for E. This interaction takes place more readily in the heavier main group element derivatives because the bonds become increasingly long (weaker) as a result of larger Pauli repulsions between core electrons as the group is descended. Consequently, the energy difference between the s* and p orbitals also decreases, and hence the extent of their interaction increases. The trans-folding, which weakens the E-E bond, is oen sufficient to cause dissociation of the double bond of the heaviest tin and lead species to two monomeric metallanediyls. However, dissociation is less common in their germanium analogues and for the iconic disilenes, rst reported in 1981, 14 dissociation is rare and the silicon coordination is generally close to planar. [15][16][17] In addition to the aforementioned bonding models, there is the broadly-applicable CGMT approach, 18 which focuses on the energetics of double bond formation. It is based on the fact that the double bonded species are formed from two constituent carbene-like metallanediyl units. This allows the bond energies and molecular geometry to be rationalized in terms of the singlet-triplet excitation energies of the metallanediyl monomers. 19 The investigation and rationalization of bonding in these and related multiple-bonded compounds has been a topic of broad interest [15][16][17] that continues to the present day. 20 These compounds, and others in neighboring groups, 21 marked a departure from the widely-assumed notion that heavier main group elements did not form double or triple bonds to each other. 22 The key development that enabled their stabilization was the use of sterically large hydrocarbon substituents 23 that blocked their decomposition via association or elimination reactions. In the numerous reviews and discussions of heavier main group multiple bonds, the focus has been almost exclusively on details of the interaction between the two heavier elements, i.e. the orbitals likely to be involved in the multiple bonds, their relative energies, their likely bonding character, and the extent of the overlap. However, recent work, mainly on carbon compounds that carry bulky substituents, 24,25 has shown that attractive dispersion interactions between the C-H moieties of the substituents also play a large role in the stabilization of sterically crowded molecules. This attraction is exemplied by the stabilization of the substituted ethane {C(C 6 H 3 -3-,5-Bu t 2 ) 3 } 2 , which has a long central single C-C bond of 1.67Å and is stabilized via dispersion force interactions between the Bu t groups, whereas the corresponding C-C bonded, less hindered, unsubstituted species (CPh 3 ) 2 (i.e. the C-C bonded dimer of the Gomberg radical) is unknown. 26 Despite these developments, the realization of importance of the dispersion interactions between the C-H moieties of substituent ligands to the stability of inorganic and organometallic compounds is not widespread. However, several reports have shown that such forces are very important for the bonding and structure of a variety of species. [24][25][26][27][28][29][30][31][32][33][34][35] We showed recently that attractive dispersion forces were of key importance in the association of sterically crowded phosphinyl and arsinyl radicals to the corresponding diphosphanes and diarsanes. 35 We now describe the results of density functional theory calculations with and without dispersion force contributions for the monomeric dialkyls and diamides E{CH(SiMe 3 ) 2 } 2 and E{N(SiMe 3 ) 2 } 2 (E ¼ Ge, Sn, or Pb) as well as the corresponding E-E bonded dimers. The calculations without the inclusion of dispersion force effects revealed that the E-E bonding energies are low for the tetraalkyls, and insufficient to stabilize their dimeric structures under ambient conditions. In contrast, the inclusion of dispersion force resulted in large increases in the binding energies. Application of the same protocols to the amido compounds also afforded lower binding energies that are insufficient to sustain the dimeric structures under ambient conditions.

Computational methods
All calculations were carried out using the Gaussian 09 program. 36 Geometry optimization was performed with hybrid density functional theory (DFT) at the B3PW91 (ref. 37) level by using the 6-311+G(2d) basis set for Ge, the [4333111/433111/43] basis set augmented by two d polarization functions (d exponents 0.253 and 0.078) for Sn, 38 the SDD basis set and its effective core potential for Pb, 39 and the 6-31G(d,p) 38,39 basis set for other atoms. In order to estimate the dispersion effects, geometries were reoptimized with the dispersion-corrected B3PW91-D3 method. 40 Geometry optimization was also performed at the B97-D3 level. 40,41 Single-point MP2 (second-order Møller-Plesset perturbation theory) 42 energy calculations were performed on B3PW91-D3 optimized geometries. The basis set superposition errors (BSSE) were estimated with the counterpoise method. 43 Enthalpy (H), entropy (S), and free energies (G) as well as zero point energies (ZPE) were estimated using calculated harmonic vibrational frequencies and BSSE corrected energies.

Results and discussion
Computational data for the alkyl monomers and dimers, E{CH(SiMe 3 ) 2 } 2 and [E{CH(SiMe 3 ) 2 } 2 ] 2 (E ¼ Ge, Sn, or Pb) The calculated structural parameters at various levels of optimization for the alkyl-substituted germanium, tin, and lead monomers and dimers are presented in Table 1 and 2 respectively. The E{CH(SiMe 3 ) 2 } 2 (E ¼ Ge or Sn) monomers have the syn, syn orientation of the -CH(SiMe 3 ) 2 alkyl groups in the gas phase, as shown in Fig. 2a. At present, no gas phase electron diffraction data are available for the Pb{CH(SiMe 3 ) 2 } 2 monomer. However, in Table 1 we have given the experimental parameters for Pb{CH(SiMe 3 ) 2 } 2 , derived from a syn, syn Pb{CH(SiMe 3 ) 2 } 2 unit within the [Pb{CH(SiMe 3 ) 2 } 2 ] 2 (ref. 11) 'dimer'. In the X-ray structures of the germanium and tin crystalline dimers the E{CH(SiMe 3 ) 2 } 2 (E ¼ Ge or Sn) 8-10 units have a syn, anti conformation, as shown in Fig. 2b. In contrast, the Pb{CH(SiMe 3 ) 2 } 2 units within the lead 'dimer' have the aforementioned syn, syn conguration, as shown in Fig. 2c, i.e. the same conguration as those experimentally observed for the germanium and tin dialkyl monomers in the gas phase. 10 The calculated bond lengths and angles are generally close to those observed experimentally. This statement is particularly true for the X-ray crystal structures of the germanium and tin dimers, where the experimental structural parameters and E-E bond lengths (Ge-Ge ¼ 2.347(2) A 9 ; Sn-Sn ¼ 2.768(1)Å 10 ) are reproduced with good accuracy. Exceptions to this generalization involve the calculated torsion angles between the methane C-H bonds and the central EC 2 (E ¼ Ge or Sn) plane in the germanium and tin monomers, and the C-Ge-C angle in the germanium monomer, which is somewhat high. For the torsion angle in the germanium and tin monomers, the discrepancy is almost 20 in the germanium and 6-8 in the tin monomer. Unfortunately, in the monomeric structures which are measured from GED (gas electron diffraction) data, no standard deviations were given. However, standard deviations of 2 were listed for the EC 2 angle, and it is reasonable to suppose the standard deviation for the torsion angle for the methane C-H bonds would be larger than this value. We replicated the optimization with the HCECH torsion angles xed at the experimental values of 2 (E ¼ Ge) and 15 (E ¼ Sn). As shown in Table S1, † this increased the binding energy by 10.7 kcal mol À1 for Ge, but only 2.5 kcal mol À1 for tin. Thus, the HCECH torsion angle has signicantly larger effect in the germanium dimer, consistent with its more sterically-congested structure. It is worthwhile to recall that the calculations on the dimers are for the molecules in isolation (i.e. in the gas phase), and take no account of the effects of neighboring molecules (i.e. packing forces), which can also be expected to exert some effect on their structure.
The calculated Pb-Pb separation and C-Pb-C angle in the dimeric lead structure differ considerably from the experimentally measured values. The experimental Pb-Pb distance of 4.129(1)Å in the crystal structure of the [Pb{CH(SiMe 3 ) 2 } 2 dimer 11 is far longer than the sum of single bond covalent radii of 2.88Å expected for a Pb-Pb single bond. 44 Furthermore, the calculated Pb-Pb distances using the B3PW91-D3 method is 3.241Å and, by the B97-D3 method, it is 3.256Å. These distances are over 1Å shorter than the experimentally measured value, and suggest a very weak interaction between the lead atoms of the Pb{CH(SiMe 3 ) 2 } 2 units in the crystal structure. Nevertheless, long interactions of this type between the heavier main group elements can be signicant. 45 In spite of the observed deviation in Pb-Pb separation, the experimental and calculated C-Pb-C angles of the lead dimer are in good agreement with each other. If it is assumed that the Pb{CH(SiMe 3 ) 2 } 2 units within the lead dimer are syn, syn monomers, that is to say the long Pb-Pb interaction is ignored, the structural parameters given for Pb{CH(SiMe 3 ) 2 } 2 in Table 1 are obtained. It can be seen that the calculated C-Pb-C angles of 96.6 (B3PW91), 92.2 (B3PW91-D3), or 92.0 (B97-D3) are also close to the experimentally-measured value of 93.4 (2) . Moreover, this angle also resembles those calculated (range 98.4-94.2 ) for the C-Sn-C angle in the Sn{CH(SiMe 3 ) 2 } 2 monomer (cf. C-Sn-C ¼ 97(2) by GED). In effect, the data suggest that the Pb{CH(SiMe 3 ) 2 } 2 units within the lead dimer are behaving essentially as weakly interacting plumbylene monomers, rather than as a Pb-Pb multiple bonded diplumbene.
It was noted above that the experimentally-determined orientation of the -CH(SiMe 3 ) 2 groups of the E{CH(SiMe 3 ) 2 } 2 units within the germanium and tin dimers are syn, anti and the computational data in Table 2 and 3 have been made on the basis of this orientation. However, it is possible to perform similar computations with the assumption of syn, syn orientation in the E{CH(SiMe 3 ) 2 } 2 units. The results of these calculations are given in Tables S2 and S3. † The changed orientation results in longer E-E distances and smaller binding energies of 18.9 (Ge) and 20.0 (Sn) kcal mol À1 at the B3PW91-D3 level with BSSE and ZPE corrections, which can be compared to the values of 28.7 (Ge) and 26.3 (Sn) kcal mol À1 in Table 3. In effect, the changed orientation of the substituents results in binding energies that are ca. 10 kcal mol À1 lower than the syn, anti conguration values. These energy differences are somewhat smaller than the 16.4 kcal mol À1 calculated for the corresponding changes in the energy of the [P{CH(SiMe 3 ) 2 } 2 ] 2 / 2P{CH(SiMe 3 ) 2 } 2 process upon relaxation of the congurations from syn, anti to syn, syn. 35 The difference in values can be rationalized, at least in part, in terms of the reduced inter E{CH(SiMe 3 ) 2 } 2 unit steric crowding because of the larger sizes of germanium and tin in comparison to that of phosphorus.
It is also informative to consider the effect of altering the orientation of the CH(SiMe 3 ) 2 groups of the [Pb{CH(SiMe 3 ) 2 }] 2 dimer to the syn, anti orientation observed for the lighter congeners; the data in Table S4 † reect calculations in this orientation. The resultant Pb-Pb distance is consistently shorter than in both the experimental and computational results in the syn, syn orientation; the dispersion corrected distance of 2.956Å (B3PW91-D3) approaches the sum of the covalent radii indicating a signicant degree of Pb-Pb bonding. Table 1 Calculated and experimental structural data for E{CH(SiMe 3 ) 2 } 2 (E ¼ Ge, Sn, or Pb) monomers in syn, syn configuration  Also noteworthy is the effect upon the C-Pb-C angle which is calculated to widen signicantly (91.3 versus 106.6 at the B3PW91-D3 level); likely a consequence of steric clash between the SiMe 3 groups of the ligand. Such an angle, however, would also optimize Pb-Pb bonding by increasing the p-character of the Pb lone pair. That the Pb{CH(SiMe 3 ) 2 } dimer does not adopt such a conformation must suggest the nature of the Pb{CH(SiMe 3 ) 2 } 2 dimer is that of two weakly interacting plumbylene monomers wherein signicant s-character of the lone pair enforced by the narrow C-Pb-C angles (93.4(2) ) lead to "closed-shell" interactions between the Pb atoms.

Calculated thermodynamic data for the dissociation of the [E{CH(SiMe 3 ) 2 } 2 ] 2 dimers
The data for the dissociation of the dimeric [E{CH(SiMe 3 ) 2 } 2 ] 2 to two E{CH(SiMe 3 ) 2 } 2 monomers are summarized in Table 3. . Taken together, the calculated energies strongly suggest that the major portion of the binding energy for the germanium, tin, and lead dimetallenes are a result of attractive dispersion forces between the -CH(SiMe 3 ) 2 ligands. Calculation of the free energy changes (DG) at 25 C and 1 atm for the dissociation of the dimers, without dispersion force correction, affords values of À17.8, À14.8, and À9.9 kcal mol À1 for the germanium, tin, and lead derivatives respectively. In other words, dissociation is favored in all cases. Application of the dispersion-corrected B3PW91-D3 method changes these DG values to +9.4, +7.1, and À1.7 kcal mol À1 . Thus, the dimeric structures become favored for the germanium and tin species, but remains slightly disfavored for lead. These ndings are in accord with the relatively long element-element distances experimentally observed for the germanium and tin dimers, and the very weak interaction in the case of the lead species. The DG energies calculated for the dissociation of germanium and tin alkyls at the temperatures and pressures at which the GED data sets were collected, i.e. 428 K and 0.1 Torr for the germanium dialkyl and 393 K and 0.1 Torr for the tin dialkyl, were À7.2 and À6.1 kcal mol À1 .
These negative values are consistent with the monomeric structures observed in the vapor phase.
There has been only one report of an experimental determination of energies associated with the monomer-dimer equilibrium of the E 2 R 4 (E ¼ Ge, Sn, or Pb; R ¼ CH(SiMe 3 ) 2 ) series. 46 This was accomplished by variable-temperature NMR spectroscopy of [Sn{CH(SiMe 3 ) 2 } 2 ] 2 and the behavior of the 13 C shis for the methine carbons in the monomers and dimers. This allowed calculation of DH ¼ 12.8 kcal mol À1 and DS ¼ 33 cal K À1 mol À1 for the dissociation. These experimental values differ considerably from those calculated (cf. DH ¼ 27.0 kcal mol À1 and DS ¼ 66.7 cal K À1 mol À1 ). At present, the reason for the discrepancy between the experimental and calculated values is unclear, and more data will be required to establish the expected values for similarly-substituted monomer-dimer equilibria. For example, signicantly higher DS values of 75 and 66 cal mol À1 K À1 have been determined for the dissociation of the [M{N(SiMe 3 ) 2 } 2 ] 2 (M ¼ Fe or Co), which carry -N(SiMe 3 ) 2 substituents that are isoelectronic to CH(SiMe 3 ) 2 . 47,48 The dissociation of the digermene [Ge(C 6 H 2 -2,4,6-Me 3 ){C 6 H 2 -2,4,6-(CH(SiMe 3 ) 2 ) 3 }] 2 was studied by electronic spectroscopy which revealed a DH value of 14.7(2) kcal mol À1 and a DS value of 42.4 cal mol À1 K À1 . 49 A rationalization for the observed congeneric variation can thus be constructed wherein the interplay between the effects of   The syn, anti conformation adopted by germanium and tin yields an increased interligand steric congestion, 33 and thus other factors must stabilize the adoption of this orientation in the dimers. In contrast, such stabilization must be insufficient in the case of the lead congener which results in the adoption of a less crowded syn, syn orientation and consequent attenuation of metal-metal bonding. This conclusion is supported by the fact that the seven-membered ring dialkyl lead(II) species PbC(SiMe 3 ) 2 SiMe 2 CH 2 CH 2 SiMe 2 C(SiMe 3 ) 2 , 50 which has a very similar substitution pattern to that in [Pb{CH(SiMe 3 ) 2 } 2 ] 2 and a C-Pb-C angle of 117.1 (2) , has no Pb-Pb contact shorter than 8.911Å. Furthermore, the Sn(II) dialkyl SnC(SiMe 3 ) 2 (CH 2 ) 2 C(SiMe 3 ) 2 , 51 featuring the tin atom in a ve-membered ring structure and a C-Sn-C angle of 86.7(2) , is also monomeric. Here the C(SiMe 3 ) 2 moieties have a syn, syn-like conformation analogous to the vapor phase structure of Sn{CH(SiMe 3 ) 2 } 2 and the lead congener in all cases. These data suggest that a syn, syn orientation precludes strong M-M contact and thus any dimerisation must emerge principally from dispersion interactions.
In the case of the germanium and tin congeners, two factors clearly stabilize the sterically unfavorable adoption of a syn, anti orientation; the strength of dispersion forces and the degree of metal-metal bonding. The dispersion interactions in these dimers is evidently optimized between different ER 2 fragments favoring dimerisation, as evidenced by the increase in C-E-C angle when dispersion corrected (Ge ¼ 109.9 (B3PW91), 111.8 (B3PW91-D3); Sn ¼ 109.8 (B3PW91), 111.2 (B3PW91-D3)). These data reinforce that dispersion effects are the principal driving force for dimerisation in these species and act as a scaffold for metal-metal bonding.
In contrast, the application of a dispersion correction to the lead structure yields, in the case of the experimentally consistent syn, syn orientation a contraction of the C-M-C angle (96.8 (B3PW91), 91.3 (B3PW91-D3)) or in the case of the putative syn, anti orientation a negligible change (106.3 (B3PW91), 106.6 (B3PW91-D3)). These data are a likely consequence of the increase in E-C bond length down group 14, precluding dimerfavoring dispersion interactions in the Pb case, and instead favoring intramonomer interactions which cannot stabilize the steric clash introduced by a syn, anti orientation of the ligands. Furthermore, this narrowing of the C-Pb-C angle increases the s-character of the Pb centered lone pair, disfavoring metalmetal bonding further indicating that any Pb-Pb interactions are closed-shell in nature.

The amido monomers E{N(SiMe 3 ) 2 } 2 (E ¼ Ge, Sn, or Pb)
The calculated and experimental structural parameters for the three monomeric amido derivatives E{N(SiMe 3 ) 2 } 2 (E ¼ Ge, Sn, or Pb) are provided in Table 4. Diffraction data for both the gas (GED) and crystalline phases (X-ray), which show that each has a monomeric structure, are listed. The experimental data for the gas and crystalline phases differ considerably in their N-E-N angles and the dihedral angles between the EN 2 and NSi 2 coordination planes. It can also be seen that the N-E-N angle is much more sensitive to the identity of the central atom (E) in the vapor phase than in the solid state. Furthermore, the N-E-N angle is signicantly narrower for the tin and lead compounds in the vapor phase than in the solid state. Such differences have been attributed to the changed ligand orientation in the gas phase, where the NSi 2 planes are essentially perpendicular to the EN 2 plane. 5,7 This may minimize steric repulsion because of the parallel orientation of the NSi 2 planes. However, it would give inefficient packing in the solid state. As a result, the -NSi 2 ligand planes are tilted with respect to the EN 2 plane in the crystal structure. In addition, they have close intramolecular contacts as well as different E-N-Si angles for the 'inner' (wider E-N-Si angle) and 'outer' (narrower E-N-Si angle) SiMe 3 groups. The differences are ca. 12.3 for the Ge, ca. 11 for the Sn, and ca. 8.5 for the lead species. Inspection of the theoretical data show that there is good agreement with the calculated bond lengths for both the vapor and crystal phase structures. However, for the key N-E-N and E-N-Si angles, there is good agreement only in the case of the X-ray crystallographic data, where the calculated bond lengths, N-E-N angles, and the different 'inner' and 'outer' E-N-Si angles are faithfully reproduced in the calculations. The X-ray data show that the shortest E-E distances in the three crystal structures are 5.36Å (Ge), 4.96Å (Sn), and 6.663Å (Pb). In the tin structure, the relative orientation of the tins is head to head between the closest monomers, and although there is a 0 torsion angle between the perpendiculars to the SnN 2 planes, there is a displacement of the units with respect to each other such that imaginary lines bisecting the SnN 2 angles are parallel to each other but are 0.52Å apart.

Structural and thermodynamic data for the putative amido dimers [E{N(SiMe 3 ) 2 } 2 ] 2
The calculated structural parameters and dissociation energies of the putative [E{N(SiMe 3 ) 2 } 2 ] 2 dimers at various levels of optimization are given in Table 5. The calculated structural parameters for the E{N(SiMe 3 ) 2 } 2 units within the dimers are close to those calculated for the monomeric structures which match those experimentally determined by X-ray crystallography. The E-E distances undergo large contractions when dispersion force corrections are included. However, the shortest distances calculated for the germanium and tin amido dimers, even with the inclusion of such forces at the B3PW91-D3 level, are signicantly longer (by ca. 1.4 and 0.7Å) than the measured values and the values calculated at the same level for the alkyl dimers. The metal-metal distance calculated for the amideligated lead dimer (3.714Å) by the B3PW91-D3 method is ca. 0.5Å longer than the corresponding calculated distance (3.241Å) in the dialkyl lead dimer. These distances indicate considerably weaker interactions between the group 14 elements for the amido derivatives. Thermodynamic data (Table 5) for the amido dimers also provide further evidence for weak association. The binding energies calculated without the inclusion of dispersion forces for the germanium, tin, and lead amido dimers at the B3PW91 level yield negative values of À5.0, À3.5, and À4.1 kcal mol À1 , respectively, and show that the E-E interaction is disfavored (cf. positive values of 5.6, 12.0, and 0.1 for the alkyls, Table 1). In other words, monomeric structures are favored in each case. However, at the B3PW91-D3 level, which includes dispersion force effects, the energies change to 8.4, 19.8, and 15.6 kcal mol À1 . Using the B97-D3 method affords similar but somewhat lower values of 7.9, 16.4, and 12.5 kcal mol À1 . Single point MP2 calculations yield corresponding values of 5.1, 15.6, and 3.9 kcal mol À1 . The overall picture that emerges from the calculations on the amides is that the dimerization tendency is present but weaker than it is in the alkyls, and that the driving force for the association of the monomers is due to dispersive attraction forces the -N(SiMe 3 ) 2 ligands. Further calculations on the thermodynamics of dissociation show that the DG energies for the process are À16.4, À18.0, and À10.8 kcal mol À1 at 25 C and 1 atm, so that dissociation and monomeric structures are favored under these conditions. These ndings are, of course, consistent with the structural and physical data. The much weaker E-E interactions in the amides in comparison with the alkyls is probably a result of electronic and steric factors. The more electronegative -N(SiMe 3 ) 2 ligand causes a larger HOMO-LUMO separation on the E atom, which would lower the extent of orbital interaction between the monomers. Also, the congurational differences between the -CH(SiMe 3 ) 2 and -N(SiMe 3 ) 2 (no syn, syn-syn, anti congurational change is possible for the amido ligands) may lead to greater steric hindrance, and hinder the association of the two monomeric fragments in the case of the amido ligand.

Persistent dimers of stannylenes: the case of [Sn{SiMe t Bu 2 } 2 ] 2
With these analyses in hand, it is informative to consider other stannylenes in the literature. Whilst a plethora of such species have been reported, the vast majority are monomeric in solution, and many with extremely sterically demanding ligands remain monomeric in the solid state. 14 One notable exception is [Sn{SiMe t Bu 2 } 2 ] 2 , described by Sekiguchi, Apeloig and co-workers in 2006. 52 This species persists as a dimer in solution and, in contrast to the vast majority of literature examples, reacts as a dimer. It has a very short Sn-Sn distance of 2.6683(10)Å and essentially planar coordinated tin atoms, but the tin coordination planes subtend an angle of 44.62(7) with respect to each other. This led the authors to propose that the Sn-Sn bonding was a result of a triplet-triplet interaction between the two stannylenes on the basis of calculations on the model species Sn 2 (SiMe 3 ) 4 . While no full molecule calculations have been reported for [Sn{SiMe t Bu 2 } 2 ] 2 to investigate dispersion force contributions, a qualitative assessment can be made. One notable feature of dispersion force interactions is their dependence on length-scale and they are thought to be highly attenuated beyond the sum of the van der Waals radii of the interacting atoms. 53 Thus, a qualitative assessment of  (Fig. 3). In the former case, two notable observations can be made-a number of monomer-monomer dispersion interactions are apparent, supporting the observed dimerisation in the solid state. Furthermore, whilst a syn, anti conformation is sterically disfavoured, a signicant number of dispersion interactions can be observed between the ligands on each Sn{CH(SiMe 3 ) 2 } 2 unit indicating that such a sterically unfavourable conformation is partly stabilised by dispersion interactions.
In the case of [Sn{SiMe t Bu 2 } 2 ] 2 , several dispersion interactions are evident between each of the interacting Sn{SiMe t Bu 2 } 2 fragments, and they occur with greater frequency than in the [Sn{CH(SiMe 3 ) 2 } 2 ] 2 species. Whilst the report 52 of [Sn{SiMe t Bu 3 } 2 ] 2 provides an extensive electronic rationale for Sn-Sn interactions being responsible for its observed dimeric structure and short Sn-Sn distance, it is likely that dispersion forces are also of importance in stabilising the persistent dimeric nature of this compound.
To check this hypothesis, our initial full molecule calculations (see Table S5 †) on [Sn{SiMe t Bu 2 } 2 ] 2 conrm the presence of a shorter tin-tin bond (2.647Å) than that in [Sn{CH(SiMe 3 ) 2 } 2 ] 2 . However, the calculations show that the binding energy increases from 25.8 to 46.8 kcal mol À1 with inclusion of dispersion effects, and that the DG of dissociation at 25 C and 1 atm is increased from 8.3 to a value of 26.5 kcal mol À1 upon inclusion of the dispersion correction, indicating that the dispersion force attraction is of key importance in maintaining the dimeric structure.

Conclusions
The calculations have shown that the interplay between dispersion force attraction, steric repulsion and elementelement bonding stabilize the dimeric structures. Although the E-E distances indicate E-E bonding is present in the germanium and tin dimers, and possibly the lead dimer, the bonding is weak, and represents a relatively small fraction of the binding energy. The results emphasize the importance of including attractive dispersion force interactions in consideration of multiple bonded heavier main group element species where sterically encumbering ligands are employed in their stabilization. 28 Furthermore, these effects act in harmony with a variety of other stabilizing and destabilizing effects (e.g. packing or conformational) which are notable particularly for the -CH(SiMe 3 ) 2 ligand. A similar analysis for the non-dissociating distannene [Sn{SiMe t Bu 2 } 2 ] 2 shows that in this molecule also, the dispersion forces are of key importance in its stabilization. These studies provide an initial framework for the analysis of metal-metal bonding which takes into account these more subtle effects. Although much effort has been expended in development of bonding models for the multiple bonds between heavier main group elements, it seems both probable and ironic that the dispersion force attraction forces exceed those of the multiple bonds in many instances and that a variety of more subtle interactions including packing effects are of key importance for the understanding of their bonding.