Nonadiabatic Conical Intersection Dynamics in the Local Diabatic Representation with Strang Splitting and Fourier Basis.

We develop and implement an exact conical intersection nonadiabatic wave packet dynamics method that combines the local diabatic representation, Strang splitting for the total molecular propagator, and discrete variable representation with uniform grids. By employing the local diabatic representation, this method captures all nonadiabatic effects, including nonadiabatic transitions, electronic coherences, and geometric phase. Moreover, it is free of singularities in the first and second derivative couplings and does not require the electronic wave function to be continuous with respect to the nuclear coordinates. We further show that in contrast to the adiabatic representation, the split-operator method can be directly applied to the full molecular propagator with the locally diabatic ansatz. The Fourier series, employed as the primitive nuclear basis functions, is universal and can be applied to all types of reactive coordinates. The combination of local diabatic representation, Strang splitting, and Fourier basis allows numerically exact modeling of conical intersection quantum dynamics directly with adiabatic electronic states that can be obtained from standard electronic structure computations.