Theoretical analysis of hydrocarbon properties. 2. Additivity of group properties and the origin of strain energy

The theory of atoms in molecules is used to obtain electron populations and energies for the atoms in the same set of molecules studied in the preceding paper. Hydrogen is more electronegative than carbon in hydrocarbons with no geometrical strain, and the order of the relative electron-withdrawing abilities of the groups is H > CH/sub 3/ > CH/sub 2/ > CH > C. The electronegativity of a carbon increases with an increase in geometrical strain as measured by the decrease in its bond path angles from the normal value. In cyclopropane 0.05 fewer electrons are transferred from carbon to hydrogen than in the standard CH/sub 2/ group. The bridgehead carbons in the propellanes and in the most strained of the bicyclic molecules withdraw charge from CH/sub 2/ and H, and there is a flow of charge from the peripheral groups to the bridgehead region with increasing strain in these molecules. It is found that the charge distribution of a CH/sub 3/ or CH/sub 2/ group as defined by theory can appear unchanged as a transferable unit throughout a homologous series of molecules. When this occurs, the contribution of the group to the total energy of the molecule is also unchanged, and these groups account for the additivity of energy. The transfer of charge from H to C in CH/sub 2/ that occurs as C is subjected to geometric strain leads to a decrease in the energy of C but to an even greater increase in the energy of H, and the net result is a strain energy equal to the increase in energy of CH/sub 2/ relative to that of the standard.