Electron–vibration interactions in benzene and deuterobenzene

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Abstract
An exactly solvable model of the linear interaction of molecular vibrations with the electronic states of molecules is utilized to describe the intensity distributions in band systems observed in the ultraviolet photoelectron and ultraviolet absorption spectra of C6H6 and C6D6. From this analysis, the linear coupling constants describing the vibration‐induced energy shifts of the 1e1g(π), 3e2g(σ), and 3a1g(σ) one‐electron orbitals and of the 1B2u excited state are determined. These coupling constants also are calculated using the spectroscopic CNDO/S2 molecular‐orbital model of Lipari and Duke and the vibrational normal modes of Whiffen. The sensitivity of the calculated coupling constants to the precise form of the molecular orbital model is shown to be substantial. The CNDO/S2 model provides a semiquantitative (±50%) description of the measured coupling constants, whereas prior CNDO models (e.g., CNDO/2) predict values for these quantities deviating by as much as an order of magnitude from the measured ones. Although only linear electron–vibration coupling constants can be extracted from observed ultraviolet absorption and photoelectron spectra, the associated quadratic coupling constants can be evaluated using the molecular‐orbital model. This analysis indicates that the linear terms dominate the nuclear‐relaxation‐induced energy shifts for one‐electron orbitals but that the quadratic terms can predominate for excited electronic states. The calculated linear and quadratic coupling constants for the 1e2u(π*), 1e1g(π), 3e2g(σ), 1a2u(π), 3a1g(σ) orbitals and the 1B2u, 1B1u, and 1E2u electronic states are given for all 30 independent molecular vibrations of C6H6 and C6D6.

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