Local mode combination bands and local mode mixing

Abstract

Side bands appear in the local‐mode (LM) overtone vibrational spectra of many substances, including the aromatic and aliphatic hydrocarbons. Many of these side bands are interpretable as being LM–LM combination bands of various C–H oscillators in these molecules. The simultaneous excitation of two LM’s represents the most commonly observed transition of the many LM–LM combinations possible. However, such transitions are strictly forbidden as long as the dipole moment and Hamiltonian operators are separable within the LM subspace. The consequences of the breakdown of each of these separabilities is investigated. Application is made to detailed new spectra for benzene (containing the prototypical aromatic C–H oscillator) and tetramethylsilane (containing a prototype of the aliphatic primary C–H oscillator). Multisite terms in the dipole operator are treated empirically and are able to rationalize the intensities of binary LM combination bands. Inter‐LM coupling terms in the Hamiltonian are taken from previous ab initio calculations and normal mode analysis. The Hamiltonian is diagonalized within a truncated basis of LM (anharmonic) eigenfunctions. The new eigenfunctions explain not only the appearance of the side bands correctly, but also account for energy splittings in the spectra, particularly conspicuous at low quantum numbers. Separability for both operators is found to be a good zeroth‐order approximation for both molecules, but somewhat less so for tetramethylsilane whose methyl substituents contain three LM oscillators sharing a common atom.