Carbon–carbon π antibonding effects on the thermochemistry of alkanes, elucidated by angular overlap and MO calculations

Abstract

It is postulated that the enthalpies of formation of alkanes can be rationalised quantitatively in terms of an additive bond energy scheme with a constant C–H term (taking the methane value of 415.8 kJ mol⁻¹) while the C–C bond energy is dependent upon the π-antibonding effects of the highest occupied molecular orbitals (HOMOs). This antibonding effect can be treated by angular overlap methods with two adjustable parameters, e_π^′(HH) (which represents the magnitude of the effect where the 2p_π orbitals concerned are engaged in σ-overlap only with hydrogen 1s orbitals) and e_π^′(HC) (where one 2p_π orbital is σ-bonded to hydrogen atoms and the other to carbon atoms); e_π^′(CC) is deemed to be zero, so that the C–C bond energy in the absence of any π antibonding effect takes the diamond value (357.4 kJ mol⁻¹). The values for e_π^′(CH) and e_π^′(HH) are obtained from the experimental enthalpies of formation of C₂–C₆ alkanes having no 1,4 steric interactions. It is then possible to calculate bond energy terms for each of the types of bonds C_X –C_Y [X, Y = P(primary), S(secondary), T(tertiary), Q(quaternary)]. These yield calculated enthalpies of formation for alkanes C_nH_2n+2 (n = 2–8) in excellent agreement with experiment in the absence of significant steric interactions. Corrections for 1,4 steric repulsion are needed for C_S–C_Q , C_T–C_T and C_T–C_Q bonds but not for C_S–C_T . The HOMOs in CH_4−nMe_n (n = 2, 3) obtained from semi-empirical MO calculations (PM3) have the same relative orbital energies (b₂>a₁>b₁ for n = 2, a₁>e for n = 3) as found in the angular overlap calculations, and there is a clear correlation between the antibonding effects as measured by MO eigenvalues and the empirical thermochemical parameters. There is also an unexpectedly good agreement between the atomic fractional charges in alkanes calculated by Mulliken population analysis of the PM3 MOs and those obtained by electronegativity equilibration.