Semiclassical initial value representation in curvilinear coordinates

A semiclassical propagator originally defined on Euclidean space is systematically extended to general curvilinear coordinate systems. This method time-evolves nuclear wave packets on the fly in curvilinear coordinates, without prior construction of global potential energy surfaces or complicated kinetic energy operators, and enables dimensionality reduction by isolating the physically essential degrees of freedom through coordinate constraints. By propagating the dynamics in a redundant coordinate space, the coordinate singularities inherent to curvilinear systems are circumvented in a numerically robust manner. In addition, the topology of each coordinate-such as its periodicity and boundary conditions-is properly taken into account by modifying the coherent state basis of the propagator. We applied this approach to molecular motions that are difficult to describe in conventional normal coordinates-pure rotation of hydrogen and methane, rovibrational dynamics of hydrogen, and large-amplitude torsional motion of butane-and reproduced reference eigenenergies and the characteristic features of the corresponding spectra.