W.H. Henneker

Exactly solvable models for vibronic coupling in molecular spectroscopy. III. The pseudo Jahn–Teller effect

A model system consisting of two electronic manifolds coupled through a nontotally symmetric mode of vibration is solved exactly and self‐consistently by the method described in Paper I [J. Chem. Phys. 65, 2071 (1976)]. As in I, the model is defined in terms of harmonic diabatic potentials, but the restriction to harmonic adiabatic potentials, applied in I, is lifted here. As a result, the adiabatic coupling operator which has the same analytical form as in I, can assume a much wider range of values. It leads to adiabatic potentials which in general are anharmonic and may exhibit a double minimum. The coupling is taken to be an odd function of the vibrational coordinate so that it describes the (pseudo‐) Jahn–Teller effect. Absorption and emission spectra are calculated for selected combinations of four spectroscopic parameters: (1) the electronic energy gap; (2) the diabatic harmonic frequency difference; (3) a linear adiabatic coupling parameter; and (4) a nonlinear (quasiquadratic) adiabatic coupling p...

Resonance Raman scattering in molecular dimers

A systematic study is initiated of resonance Raman scattering in molecular systems with overlapping electronic absorption bands. Resonance Raman spectra, excitation profiles, and depolarization ratios are calculated for a simple molecular dimer in which the two overlapping Franck–Condon progressions are related through the permutational symmetry of the dimer. The model used is highly idealized, but can be solved exactly for a complete range of intermolecular coupling strengths. In the weak and strong intermolecular coupling regions, the exact results are compared with the physically more transparent results obtained from a low‐order perturbation treatment. The spectra and profiles show properties characteristic of both totally symmetric and nontotally symmetric modes. The profiles and polarization dispersion curves are subject to both electronic and vibronic interference effects. Anomalous extrema of the depolarization ratio are often found to coincide with minima rather than maxima in the excitation prof...

Non-condon effects in the X→A electronic absorption band system of sulphur dioxide☆

Abstract The anomalously long bending-mode progressions observed in the X → A absorption band of SO 2 are interpreted as a non-Condon effect due to a large change in OSO angle between the coupled A and B states.

Resonance Raman excitation profiles and depolarization dispersion curves, and their use in the analysis of vibronically coupled excited states

The relationship between vibronic coupling and resonance Raman scattering is studied on a model system consisting of two excited electronic states coupled by a non‐totally‐symmetric mode of vibration. Scattering cross sections and depolarization ratios are calculated as a function of the wavelengths of the incident and scattered light, giving rise to Raman excitation profiles and Raman spectra, respectively. The model system allows exact solution for arbitrary values of the electronic energy gap between the coupled states, of their vibrational frequencies, and of linear and nonlinear adiabatic coupling parameters. The results are reported in the form of three‐dimensional graphs for combinations of parameter values typical for weak, strong, and intermediate vibronic coupling. They are compared with previous results, based on simpler models and/or more approximate solution methods. In addition, they are related to the results obtained for the molecular dimer [J. Chem. Phys. 63, 5475 (1975)], which is the pr...

Quantitative interpretation of the absorption and emission spectra of 1,8‐diphenyl‐1,3,5,7‐octatetraene

Diagonalization of two‐state, two‐mode Hamiltonian matrix accounts quantitatively for the absorption and emission spectra of 1,8‐diphenyl‐1,3,5,7‐octatetraene observed by Ikeyama and Azumi [J. Chem. Phys. 76, 5762 (1982)].

Accurate Compton profiles for H2 and D2 including the effects of electron correlation and molecular vibration and rotation

Accurate isotropic Compton profiles J (q,R) for H2(X 1Σ+g) are calculated for 22 internuclear separations from the 126 configuration wavefunctions of Liu. These profiles, supplemented by the united atom and separated atom profiles, are then rigorously averaged over vibration–rotation wavefunctions computed by direct numerical solution of the radial Schrodinger equation using nearly exact potential energy curves including adiabatic and relativistic corrections. These averages are performed for a large number of vibration–rotation states of H2 and the ground vibration–rotation state of D2. It is shown that the effects of averaging Compton profiles over vibration–rotation states are significant and cannot be neglected. The isotope effect is shown to be smaller than the vibration–rotation effect. The peak of the calculated H2 Compton profile for the ground vibration–rotation state is found to be in excellent agreement with the very recent high energy electron impact measurements of Lee. A number of expansion ...

Theory of resonance Raman scattering beyond the Condon approximation for a system with two modes of different symmetry

A theoretical study is presented of resonance Raman excitation profiles and depolarization dispersion curves for a molecule with two Raman‐active normal modes of vibration and three electronic states. The modes are taken to be of different symmetry, one totally and the other non‐totally symmetric. The three electronic states are the ground state and a pair of excited states coupled through the non‐totally symmetric mode. The energy gap separating the pair is allowed to vary from zero (Jahn–Teller limit, strong coupling) to large values (Herzberg–Teller case, weak coupling). The totally symmetric coordinate is allowed to assume different equilibrium values not only between the ground state and the resonant state, but also between the two coupled excited states. As a result, the effective coupling depends indirectly on the totally symmetric coordinate, causing breakdown of the Condon approximation. The effect of this breakdown is demonstrated by calculating excitation profiles for all one and two quantum tr...

Resonance raman scattering in molecules with vibronically coupled excited states

Abstract Resonance Raman excitation profiles and depolarization dispersion curves are studied for molecules with closely spaced electronic states coupled by nontotally symmetric vibrational coordinate.

Resonance Raman scattering in molecules with double minimum potentials

Abstract Resonance Raman excitation profiles and depolarization dispersion curves are calculated for model systems exhibiting pseudo Jahn-Teller and pseudo Renner-Teller effects.

Theoretical study of the low-lying electronic states of MgH

Abstract Ab initio CI calculations have been performed for the X 2 Σ + , A 2 Π, and B′ 2 Σ + states of MgH, correlating only the three valence electrons. This procedure is found to give good agreement with experimental data. In particular, we find that the B′ state is weakly bound with r e ≈ 4.9 au and exhibits strong mixing with the ground state at this distance.