  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 non-adiabatic effects, including
nonadiabatic transitions, electronic coherences, and geometric phases.
Moreover, it is free of singularities in the first and second derivative
couplings, and does not require a smooth gauge of electronic wavefunction
phase. 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 exact modeling of conical intersection
quantum dynamics directly with adiabatic electronic states that can be obtained
from standard electronic structure computations.
