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Theory of anharmonically modified Coriolis coupling in the S1 state of benzene and relation to experiment

Helman, Adam and Marcus, R. A. (1991) Theory of anharmonically modified Coriolis coupling in the S1 state of benzene and relation to experiment. Journal of Chemical Physics, 95 (2). pp. 872-888. ISSN 0021-9606. doi:10.1063/1.461095.

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Avoided crossings between quasidegenerate rovibrational states in the Doppler-free two-photon excitation of the 141 mode in the S1 excited state of benzene are treated theoretically. Two sets of avoided crossings in plots of spectral line frequency vs J at a given K and DeltaK have been reported experimentally between an initially prepared "light" state (141 in zeroth order) and dark states, namely, one which in zeroth order is a 51101161 state, the other being in zeroth order a 62111 and/or possibly a 31161 state, implicated earlier by Neusser et al. The identification of these states makes the phenomenon an excellent candidate for treatment of the avoided crossing via a Van Vleck transformation, no other basis set states being needed for the diagonalization in order to extract the important features. Two successive transformations are used for handling direct coupling and coupling via virtual states. The dominant calculated contribution to the coupling is, jointly, Coriolis plus cubic–cubic anharmonic interactions between vibrational modes.Playing less of a role are Coriolis terms in which the inverse moment of inertia tensor is expanded up to quadratic terms in the coordinates. There results a 5×5 (for coupling to 51101161 ) and a 3×3 (for coupling to 62111 or 31161 ) matrix of the transformed Hamiltonian, each of which can also be described, if desired, to a very good approximation by a 2×2 matrix. The coupling element V0 and the difference of the rotational constants for the light and dark states (DeltaB) are obtained from the plots of line position vs J(J+1) obtained. For the 141 to 51101161 and for the 141 to 62111 couplings the theoretical results are in reasonable agreement with the experimental results, no adjustable parameters being employed. For a coupling of 141 to 31161 the calculated V0 would be much too high compared with experiment (a factor of 10), the coupling involving the exchange of only three instead of four vibrational quanta. A situation in which the 141 state is coupled to the 62111 state to yield an avoided crossing and off-resonantly coupled to the 31161 state would be consistent with some experimental results and not affect the reasonable agreement of the slope difference and splitting for the avoided crossing plots.

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Marcus, R. A.0000-0001-6547-1469
Additional Information:© 1991 American Institute of Physics (Received 11 December 1990; accepted 28 January 1991) It is a pleasure to acknowledge the support of this research by the National Science Foundation. One of us (A.H.) is particularly indebted to the California Institute of Technology for the award of a Bantrell Fellowship. The present research was stimulated by the work of Professor Schlag and Professor Neusser and Dr. Riedle, and we are pleased to acknowledge very helpful discussions with them and with Dr. Alexei Stuchebrukhov. This paper is Contribution No. 8364 of the Arthur Amos Noyes Laboratory of Chemical Physics.
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Deposited On:15 Mar 2006
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