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

Avoided crossings between quasidegenerate rovibrational states in the Doppler-free twophoton excitation of the 14’ mode in the S, 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 AK have been reported experimentally between an initially prepared “light” state ( 14’ in zeroth order) and dark states, namely, one which in zeroth order is a 5’10’ 16’ state, the other being in zeroth order a 6’11’ and/or possibly a 3’ 16’ 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 5X5 (forcouplingto5’10116’)anda3X3 (forcouplingto6*11’or3’16’) matrixofthe transformed Hamiltonian, each of which can also be described, if desired, to a very good approximation by a 2 X 2 matrix. The coupling element V, and the difference of the rotational constants for the light and dark states (A& are obtained from the plots of line position vs J(J -I1) obtained. For the 14’ to 5’10’16’ and for the 14’ to 6*11’ couplings the theoretical results are in reasonable agreement with the experimental results, no adjustable parameters being employed. For a coupling of 14’ to 3’ 16l the calculated V, would be much too high compared with experiment (a factor of lo), the coupling involving the exchange of only three instead of four vibrational quanta. A situation in which the 14’ state is coupled to the 6*11’ state to yield an avoided crossing and off-resonantly coupled to the 3’ 16’ 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.