Quantal and semiclassical analysis of vector correlation in molecular photodissociation

General semiclassical expressions for state multipoles and multipole moments have been obtained by the correspondence principle. The expression derived for low-rank multipole moments is identical with that obtained by comparing quantal and classical formulae for one- and two-photon absorption intensity of diatomic molecules [D. A. Case, G. M. McClelland, and D. R. Herschbach, Mol. Phys. 35, 541 (1978)]. For molecular photodissociation, quantal expressions for multipole moments have been obtained by formal expansion of the density matrix by the state multipoles of fragment angular momentum both in the velocity-fixed (VF) and the transition dipole moment fixed (μF) frames. The formulas derived in the two frames were proved to be equivalent. Semiclassical formulas have been also obtained in VF and μF frames by approximating the quantal multipole moments with the semiclassical expressions. The expression thus obtained in the μF frame is in agreement with that reported by Dixon [J. Chem. Phys. 85, 1866 (1986)].

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