Initial Conditions for Surface Hopping Trajectories from the VSCF-Wigner distribution

In trajectory surface hopping (TSH) simulations, initial conditions are typically generated using harmonic Wigner distributions, which assume independent harmonic normal modes. While this assumption fails for anharmonic systems, it remains unclear under which conditions harmonic Wigner sampling becomes unreliable in photochemical simulations and whether anharmonicity alone is a sufficient criterion for reconsidering the use of harmonic Wigner sampling. In the present study, we introduce a sampling strategy based on vibrational self-consistent field (VSCF) theory to construct a VSCF Wigner quasiprobability distribution that incorporates anharmonic effects while retaining mode separability. Analytical expressions are derived in both harmonic and distributed Gaussian bases enabling the implementation in TSH simulations. The method is applied to malonaldehyde and methylhydroperoxide, which exhibit moderate and strong anharmonicity, respectively. For malonaldehyde, VSCF-based and harmonic Wigner sampling yield similar results, indicating that harmonic Wigner sampling remains reliable despite the anharmonicity. In methylhydroperoxide (MHP), where torsional motion strongly influences the excited-state character, VSCF Wigner sampling gives results comparable to the quantum thermostat approach while offering a computationally efficient and systematically improvable route to initial-condition sampling.