  Quantum molecular dynamics requires an accurate representation of the
molecular potential energy surface from a minimal number of electronic
structure calculations, particularly for nonadiabatic dynamics where excited
states are required. In this paper, we employ pseudospectral sampling of
time-dependent Gaussian basis functions for the simulation of non-adiabatic
dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics
tests the Schr\"{o}dinger equation with $N$ Dirac delta functions located at
the centers of the Gaussian functions reducing the scaling of potential energy
evaluations from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. By projecting the
Gaussian basis onto discrete points in space, the method is capable of
efficiently and quantitatively describing nonadiabatic population transfer and
intra-surface quantum coherence. We investigate three model systems; the
photodissociation of three coupled Morse oscillators, the bound state dynamics
of two coupled Morse oscillators, and a two-dimensional model for collinear
triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian
method is in quantitative agreement with numerically exact calculations. The
results are promising for nonadiabatic molecular dynamics in molecular systems
where strongly correlated ground or excited states require expensive electronic
structure calculations.
