Geometry at the aliphatic tertiary carbon atom: computational and experimental test of the Walsh rule

The geometrical parameters of molecules of 2-substituted 2-methylpropanes and 1-substituted bicyclo[2.2.2]octanes were calculated at the B3LYP/6-311+G(d,p) level. They agreed reasonably well with the mean crystallographic values retrieved from the Cambridge Structural Database for a set of diverse non-cyclic structures with a tertiary C atom. The angle deformations at this C atom produced by the immediately bonded substituent are also closely related to those observed previously in benzene mono derivatives (either as calculated or as derived from crystallographic data). The calculated geometrical parameters were used to test the classical Walsh rule: It is evidently true that an electron-attracting substituent increases the proportion of C-atom p-electrons in the bond to the substituent and leaves more s-electrons to the remaining bonds; as a consequence the C-C-C angles at a tertiary carbon are widened and the C-C bonds shortened. However, this rule describes only part of the reality since the bond angles and lengths are controlled by other factors as well, for instance by steric crowding. Another imperfection of the Walsh rule is that the sequence of substituents does not correspond to their electronegativities, as measured by any known scale; more probably it is connected with the inductive effect, but then only very roughly.