Tetrahedrane, calculations

Since the structure of tetra-tert-butyltetrahedrane (19) has not been experimentally determined (128), one needs some courage to make predictions about it. Nevertheless, it seems likely that C—C, bond will be twisted from a gauche value (0(CCC,jMe) = 60°, point group) because of severe crowding among the tert-butyl groups at the tetrahedrane nucleus. MM calculations predict a structure with a 0 value near 45° T symmetry) to be 4 kcal/mol more stable than the gauche conformation (130). 

For the practical design of hypersurfaces, i.e. cuts through the (3n-6)dimensional hyperspace, some hints are outlined. The main purpose, however, is to illustrate the usefulness of hypersurface calculations especially for the detection, identification and characterization of unstable molecules. Examples chosen comprise the structure of RS-C=C-SR, the relative stability of thioacroleine isomers C,H S, the structural changes accompanying the oxidation of hydrazine and some of its derivatives, the isomerization of tetrahedrane to cyclobutadiene both thermally as well as on oxidation, the predicted existence of F SS and nonexistence of CI2SS or H2SS, and, finally, some aspects of the thermal decomposition of methyl and vinyl azides. 

In order to further substantiate the spectroscopic result and to gain more insight into both the thermal rearrangement of the neutral tetrahedrane and the structural change accompanying the one-electron oxidation to its radical cation, MNDO closed and open shell hypersurface calculations have been performed (30). 

Figure 4. One-dimensional MNDO isomerization pathways for tetra-methyl tetrahedrane and its radical cation. For the definition of the coordinate a cf. ( ) Cl denotes calculations including limited configuration interaction (see text).

It has to be pointed out, however, that additional valence isomers (CR)4 such as cyclopropenyl carbene, are found in local energy minima, if other cuts through the 54 dimensional hyperspace are calculated (30) - in agreement with compounds isolated recently e.g. from the reactions of both isomers, tetra (tert. butyl) tetrahedrane and cyclobutadiene, with tetracyanoethylene (32). 

FIGURE 1. The strain energies of the tetrahedrane and [n]prismane system (M2 H2 ) calculated at the HF/6-31G level for M = C and Si and the HF/DZ(d) level for M = Ge and Sn. Reprinted with permission from Reference 10. Copyright 1995 American Chemical Society... 

Although the ultimate bridged bicyclobutane system, tetrahedrane (8), has resisted synthetic efforts to date, its tetralithio derivative (9) is claimed" to be a product of low temperature ( —45°C) photolysis of dilithioacetylene in liquid ammonia. Calculations suggest that the most stable structure of tetralithiotetrahedrane should have a lithium cation centered at each of the four faces of the tetraanion rather than at the corners as indicated by structure (9). 

The second is the existence of the dication of variously substituted cyclobutadienes Ab initio quantum chemical calculations indicate that at least the parent dication, 42, is significantly non-planar (43). This is suggestive of some 1,3-bonding although one would hesitate to describe this ion as bicyclobutane-1,3-diium (44) vide infra). Perhaps even more reluctantly, one may describe this species as the dication of tetrahedrane (45) where both electrons have been removed from the same C-C bond. Indeed, the closed shell (or singlet) dication of tetrahedrane will lack strict tetrahedral symmetry because of unequal orbital occupancies and resulting Jahn-Teller distortion It is presumably this C-C bond... 

Table I summarizes the calculated strain energies of compound of the type E H , where n is 4, 6, and 8 and E is C, Si, Ge, and Pb, derived from homodesmic reactions (16b). The strain energies of silicon and carbon tetrahedranes are very similar (140 kcal/mol). However, replacement of the three-membered rings by four-membered rings results in a significant decrease in strain energy 140.3 (Si4H4) > 118.2 (SieHe) > 99.1 (SigHg)...

Figure 7 Calculated HF/STO-5G electrostatic potential on the molecular surface of tetrahedrane (41). Projections of bonds are indicated by solid black lines. Three ranges of V(r) are depicted lightest shading is for V(r) < - 9 kcal/mol darke.st is for - 9 < V(r) < 0 kcal/mol intermediate is for V(r) > 0 kcal/mol.

Alkorta and Elguero found that there is good correlation between PAs calculated by B3LYP/6-311-I--I-G computations and available gas phase experimental measurements. There was also good correlation with solution pA values. Based on these correlations, they made the interesting prediction that the as yet unknown hydrocarbon tetrahedrane would be comparable to water in acidity. 

Despite the highly unusual structure of tetrahedrane, 3, the problem of its synthesis had been formulated more than 70 years ago (96). The first review article on tetrahedrane (97) appeared almost simultaneously with the paper describing the first synthesis of its tetra-t-butyl derivative 77 (5), which, until recently (98), remained the only tetrahedrane derivative known. On the basis of MM calculations using different force fields Hounshell and Mislow predicted T symmetry for 77 (99). Minkin etal. (17c) discussed the synthesis, reactions, and stability of 3 and 77 pointing out that high kinetic stability of the latter molecule is partly due to unfavorable steric repulsions in the... 

This simple correlation diagram is in accord with more sophisticated molecular orbital calculations carried out for tetrahedrane The PE spectrum of tetra t-butyl-tetrahedrane has been recorded recently It confirms the orbital model insofar as the first band has been assigned to le. The recorded Jahn-Teller split of 0.7 eV corroborates this assignment. 

The connecting CC bond in 16 is (from X-ray analysis) 1.436 A long. This is shorter even than a typical sp -sp CC single bond calculated B3LYP/6-3IG CC bond lengths, which are accurate to within about 0.01 A [43] are sp -sp, 1.535 (butane central bond), sp -sp, 1.458 (1,3-butadiene), sp-sp, 1.369 (1,3-bntadiyne). The short bond in 16 is expected from the high s character of the exocyclic carbon orbitals of the tetrahedrane system. 

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