Born–Oppenheimer energy surfaces of similar molecules: Interrelations between bond lengths, bond angles, and frequencies of normal vibrations in alkanes

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Abstract
CH bond lengths, HCH and HCC bond angles, and CH symmetric and asymmetric stretching frequencies in alkane molecules are placed into four groups according to their occurrence in CH4, –CH3, CH2, and –CH, and are seen to vary in a regular fashion. The physical rationale offered for these variations relates them to balanced interactions between adjacent orbitals of CH and CC bonds, which are assumed to be common to all energy surfaces of alkane molecules. The regular variations are quantitatively reproduced by a consistent force field of alkanes, which in place of the usual harmonic stretching potentials uses only two Morse potentials, one for the CH bond, common to all four groups, and one for the CC bond. The correlated variation in bond lengths and bond angles, due to orbital interactions, is represented mainly by stretch–bend, stretch–stretch, and bend–bend cross terms. The resulting stretching frequencies, being dependent upon the second derivative of the Morse function, decrease with increasing bond length. The new force field yields bond lengths, bond angles, and vibrational frequencies, and reproduces the observed trend in their variation, mostly to within experimental accuracy. Remaining deviations are attributed to vicinal and higher order nonbonded interactions. Methane is included as a member of the alkane family and the new force field accounts successfully for its vibrational frequencies.