Quantum Theory of the Intensities of Molecular Vibrational Spectra

Abstract

Formulas for the transition probabilities and hence the absolute intensities of molecular vibrational spectra are obtained from a unified quantum field treatment. The theory of infrared, Raman, and hyper-Raman spectroscopy of molecular vibrations is developed by assuming these processes occur as time-ordered steps involving the creation or destruction of one quantum of vibrational energy and changes in the occupation number of one, two, or three photons, respectively. The formulas obtained by this method for ir transitions become equivalent to the earlier treatment of Jones and Simpson if the energy difference of the ground and first excited electronic energy levels are very large relative to that of the vibrational quantum. The formulas obtained for Raman transitions are very similar to those obtained by the method originated by Albrecht and developed further by Savin; we get not only the original terms of Albrecht but also the trace terms obtained by Savin. Furthermore by using third-order time-dependent equations from the start we avoid many of the difficulties of the earlier treatments; our equations predict different conditions for the resonant Raman effect than do the earlier equations, and experiments are suggested for testing the new equations. The formula which we give for the absolute intensity of the hyper-Raman effect appears to be the first ever given.

Giant infrared absorption bands of electrons and holes in conjugated molecules

“…When all electronic excitations lie much higher than the vibrational excitation (o eg 0 4 4o a ), dipole derivatives are amplified little by electronic excitations. It is apparent in Figs 1-3 that the P 1 transitions of polarons 24,25 provide low-lying electronic states at energies near to those of the CH vibrational transitions that could amplify their IR intensities. The intensities computed here (Figs 1 and 2, Supplementary Figs S9 and S11) for the CH vibrations are much weaker than the observed CH bands, possibly because vibronic coupling to excited states is not yet incorporated into Gaussian 09 for calculation of IR intensities.…”

“…The fact that large CH bands are observed despite weak expected and computed dipole derivatives might be understood on the basis of enhanced IR intensities due to vibronic coupling 4,17,20,24,25,39 to low-energy electronic excited states. Nafie's 25 description for the transition dipole of an IR band at frequency o a multiplies the contributions of dipole ARTICLE derivatives to transition moments by a term…”

“…Theories of IR intensities [31][32][33][34] have evolved [23][24][25] to include contributions from two principal factors: dipole derivatives and proximity to electronic transitions. Substantial dipole derivatives arise when charge distributions evolve in response to vibrations 35,36 and these can become 'massive', for example, for charged solitons in polyacetylene 37,38 .…”

“…These are plausibly strong, but absolute intensities were not determined. The IRAV bands were interpreted with an amplitude theory 18,19 that has been further developed 20 along with related theories [21][22][23] including descriptions with a molecular viewpoint 24,25 . The present work takes advantage of ready determination of absolute IR absorption (extinction) coefficients in solution to find coefficients 10 times larger than that of Sakamoto et al 4 Results IR spectra of anions.…”

Evaluation of the electron–TO–phonon interaction in polar crystals from experimental data

“…In particular, methods of vibrational spectroscopy have been shown to yield reliable estimates of several fundamental microscopic parameters, including relevant constants of electron-phonon interactions (e.g., [1][2][3][4][5] and references therein).…”