Mixed quantum-classical molecular dynamics: Aspects of the multithreads algorithm

The mixed quantum-classical Liouville equation is derived from a semiclassical perspective starting from the full quantum Schrödinger equation. An asymptotic numerical scheme for solving the equation is discussed which relies on propagating swarms of interacting “threads” which represent the density matrix or other observable. It is demonstrated that this “multithreads” method performs extremely well on simple one-dimensional model systems designed to test nonadiabatic molecular dynamic methods, yielding essentially exact results for a variety of models.