Quantum dynamics in multistate harmonic models using tensor-train thermofield dynamics and semiclassical mapping dynamics

Abstract

We present quantum dynamics of the multi-state harmonic (MSH) model using numerically exact tensor-train (TT)-based calculations. The MSH model provides a general framework for mapping a realistic system onto an effective model Hamiltonian, which is defined in extended spatial dimensions, ensuring consistent reorganization energies between all state pairs. Its analytic structure allows efficient propagation of wavepackets via a rank-adaptive TT-KSL scheme and rigorous finite-temperature dynamics via TT-thermofield dynamics. These exact results are used to benchmark various approximate semiclassical and mixed quantum–classical dynamics, including the linearized semiclassical (LSC), symmetrical quasiclassical, classical mapping models (CMMs), mean-field Ehrenfest, and fewest-switches surface hopping dynamics. We systematically explore the parameter space of the MSH model by changing electronic coupling, reorganization energy, reaction free energy, and the nuclear characteristic frequency. In the adiabatic-inverted regime, strong electronic coupling and low reorganization energy lead all approximate methods to converge with the exact TT results. In contrast, discrepancies emerge in the nonadiabatic or normal regimes, where resolution-of-identity LSC and CMMs provide the reliable predictions. This study establishes the MSH model as a powerful tool for validating nonadiabatic dynamics methods in complex condensed-phase systems.