Mixed quantum-classical dynamics

[1] Such methods are characterized by: In the Born-Oppenheimer approximation, the ensemble of electrons of a molecule or supramolecular system can have several discrete states.

In this stationary situation, nuclei and electrons are in equilibrium, and the molecule naturally vibrates near harmonically due to the zero-point energy.

Such events create a non-equilibrium between nuclei and electrons, which leads to an ultrafast response (picosecond scale) of the molecular system.

In principle, the problem can be exactly addressed by solving the time-dependent Schrödinger equation (TDSE) for all particles (nuclei and electrons).

[2] Nevertheless, they are limited to small systems with two dozen degrees of freedom due to the enormous difficulties of developing multidimensional potential energy surfaces and the costs of the numerical integration of the quantum equations.

Most of NA-MQC dynamics methods have been developed to simulate internal conversion (IC), the nonadiabatic transfer between states of the same spin multiplicity.

Methods like TSH, in particular in the fewest switches surface hopping (FSSH) formulation, do not have an exact limit.

[11] The most common approach in NA-MQC dynamics is to compute the electronic properties on-the-fly, i.e., at each timestep of the trajectory integration.