QSLE-v1.0: A New\nSoftware Package for the Calculation\nof Coupled Quantum-Classical Dynamics in Condensed Phases Based on\na Stochastic Approach

Recently, a stochastic version of the quantum-classical\nLiouville\nequation has been proposed [Campeggio, J.; Cortivo, R.; Zerbetto,\nM. J. <i>Chem. Phys.</i> <b>2023</b>, <i>158</i>, 244104], to compute the coupled quantum-classical dynamics of molecules\nin condensed phases. The approach, called quantum-stochastic Liouville\nequation (QSLE), is based on coupling the time evolution of electronic\nstates to a stochastic description of the relevant (classical) nuclear\ncoordinates. Natural internal coordinates are used, i.e., bond lengths,\nbond angles, and dihedral angles. The approach is tailored to directly\npropagate the populations of the electronic states over time, based\non a classical Fokker–Planck equation for the nuclear degrees\nof freedom coupled to a master equation for the jumps among the electronic\nstates. The QSLE is a multiscale approach requiring many ingredients\nto be assembled in order to carry out the numerical solution. To make\nthe approach accessible, a software package that handles the main\n(and most cumbersome) details of the numerical workflow has been implemented\ninto the software package QSLE-v1.0, which is introduced in the present\npaper. Here, it is considered the case of one torsional nuclear coordinate\nand two nonadiabatic electronic potential energy surfaces. This is\na very basic model for interpreting photoisomerization or charge transfer\nphenomena, but despite its simplicity, it can be applied even in complex\nsystems where the relevant quantum/classical parts affecting the phenomena\nunder study are highly localized. A sand-box model system for describing\nphotoisomerization processes is reported to demonstrate the usage\nof the software package. QSLE-v1.0 is open source and distributed\nunder the GPLv2.0 license.