Quantum dynamics at conical intersections in solution. II. Multiconfigurational wavefunction dynamics at finite temperature

The multiplicative neural network (m-NN) potentials described in Paper I [Błasiak et al., J. Chem. Phys. 163, 124108 (2025)] are employed to carry out multi-layer multi-configuration time-dependent Hartree simulations of the dynamics at a conical intersection including environmental effects. For a model of cis-trans isomerization in a protonated Schiff base, vibronic effects induced by intramolecular torsional and bond-length-alternation modes act concertedly with a collective environmental mode, which plays the role of an effective tuning mode. The latter is coupled to a residual environment, and the combination of the effective and residual modes conforms to an overdamped Brownian oscillator type spectral density. Thermal averages are included by the thermofield dynamics approach, in line with the thermal Hamiltonian developed in Paper I. The m-NN potentials, modeled according to the regularized diabatic states representation, permit an accurate representation of the vibronic coupling Hamiltonian beyond a linear vibronic coupling model. The initial excited-state dynamics is determined by the approach to a curved conical intersection seam, followed by a strongly dissipative phase leading to equilibration in the adiabatic ground state. The characteristic inertial time scale of the environment impacts not only the time of approach to the conical intersection seam but also the isomerization yield. The present study makes first steps toward extending the m-NN approach to a treatment of collective environmental non-equilibrium evolution on par with intramolecular excited-state nonadiabatic dynamics.