Ring torsional dynamics and spectroscopy of benzophenone: A new twist

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Abstract
The low energy portion of the high resolution S1←S0 fluorescence excitation spectrum of benzophenone recently reported by Holtzclaw and Pratt [J. Chem. Phys. 84, 4713 (1986)] is modeled here using a simple two-degree-of-freedom vibrational Hamiltonian. The Hamiltonian features a 1:1 nonlinear resonance between the two low frequency ring torsional modes of the molecule in its S1 state. Line positions and intensities of the two major spectral progressions are well reproduced using parameters similar to those derived from earlier matrix diagonalizations. The comparison of the theory and experiment results in a determination of the displacement of the S1 surface relative to the ground electronic state along the symmetric torsional coordinate and permits a calculation of the excitation spectra of various isotopically substituted molecules not yet measured in the laboratory. A clear picture of the relationship between the dynamics on the S1 surface and the spectroscopy of benzophenone is revealed by comparing a time domain analysis of the experimental data with wave packet dynamics on the model S1 surface. This comparison provides new insight into energy flow in the isolated molecule and permits a qualitative simulation of the effects of collisional quenching on the fluorescence spectrum. We also discuss, using a classical trajectory analysis, the resonance dynamics of the torsional modes and note the existence of heretofore undetected local modes in the high resolution spectrum.