The geometric phase effect in chemical reactions: A quasiclassical trajectory study

The hyperspherical formulation of the vector potential arising due to the presence of a conical intersection in the adiabatic potential energy hypersurface of an ${\mathrm{A+B}}_2$ type reactive system is considered. We wish to treat the operators in the Hamiltonian (with or without vector potential) as classical variables and have seen the same direction of the relative shift in the peak position of the rotational distribution as in the quantum mechanical (QM) calculations by Kuppermann and Wu [Chem. Phys. Lett. 205, 577 (1993)]. Though the absolute peak position of the rotational distributions (with and without geometric phase) obtained by quasiclassical trajectory (QCT) calculations differ from this QM calculation, the physical effect nevertheless becomes transparent once again by our calculation which requires very little computational effort.