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.

Visible absorption spectrum of liquid ethylene

“…This effect has been attributed to an increase in the local mode anharmonic interaction through the lighter CX2 group (22). The same conclusions have been reached as to the effect of anharmonic coupling in tetramethylsilane (23). We would expect ethylene to follow the mass progression of the dihalomethanes to the extent that the large force constant of the C==C bond results in a rigid C=C unit that decouples the C-H local modes of vibration.…”

“…20 and references cited therein). This model was subsequently extended to the alkanes (21) and the model compounds CH2F2, CH2C12, CH2Br2, CH212 (22), and tetramethylsilane (23). The additional structure observed in these spectra in comparison to the benzene spectrum was interpreted as due to a mixing of local and normal modes of vibration.…”

Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra

“…Many previous studies have indeed focused on the changes in spectra induced by the normalto-local bifurcation. 2,37,38,[93][94][95][96][97][98][99][100][101][102][103][104][105][106] As emphasized earlier in this article, the condition for a bifurcation to take place is that at least two modes are coupled by a systematic nonlinear offdiagonal resonance. It must be emphasized that an accidental near degeneracy of some pairs of states, which is absolutely unavoidable, does not lead to systematic changes of the spectrum over wide regions of energy (see, e.g., HCO and refs 27 and 107).…”

The influence of “communicating states” on the dissociation yield in theS 1 of benzene

“…Albrecht et al [65] and Siebrand et al [24,66] show that the CH oscillators are essentially uncoupled. Other work indicates mixing of the local modes in benzene [67][68][69][70]. Halonen [70] took into account the spread of the fundamental term values.…”