A classical mechanical study of the geometric phase effect in chemical reactions

The general hyperspherical formulation of the vector potential arising due to an arbitrary position of the conical intersection of the adiabatic potential energy hypersurfaces of an A + BC type reactive system is considered. We treat the operators in the Hamiltonian (with or without vector potential) as classical variables and see 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. Though the absolute peak position of the rotational distributions (with and without geometric phase) obtained by quasi-classical trajectory (QCT) calculations differs from this QM calculation, the physical effect is the same. The present calculations require little computational effort.