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Abstract:
We present a generalized non-Hermitian equation of motion (nH-EOM) to go beyond standard trajectory
surface hopping dynamics. The derivation is based on the Born-Huang expansion of the total wave function and
the polar representation of the nuclear factor. The nH-EOM contains two additional terms, a skew symmetry term
iΓ with dissipation operator Γ to account for decoherence, and a kinetic-energy renormalization term to account
for phase shifts, without destroying the invariance to the choice of representation. Numerically, the nH-EOM can
still be solved efficiently using a semiclassical approximation in the framework of Tully’s fewest-switches surface
hopping (FSSH) algorithm. Applications to model Hamiltonians demonstrate improved performance over the
standard FSSH approach, through comparison to exact quantum results.
