Quantum dynamics

Methods to solve time-dependent Schrödinger equations for molecules.

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>

1. Adiabatic Nuclear Quantum Dynamics

Exact methods:

  • Split-operator method
  • Discrete variable representation

Semiclassical methods:

  • Quantum trajectory method

2. Non-adiabatic molecular dynamics

Exact quantum dynamic with multiple electronic surfaces.

  • Split-operator method in the diabatic representation

Mixed quantum-classical methods

  • Surface-hopping method