On transition rates in surface hopping.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Trajectory Surface Hopping (TSH) is a widely adopted quantum-classical algorithm for simulating nonadiabatic molecular dynamics.
• A rigorous theoretical derivation for TSH, particularly its classical limit from combined quantum electron-nuclear dynamics, remains elusive.
• Understanding the theoretical basis of TSH hopping rules is crucial for advancing molecular dynamics simulations.

Purpose of the Study:

• To elucidate the theoretical underpinnings of the widely used hopping rules in Trajectory Surface Hopping (TSH).
• To formally derive the transition rates governing the hopping process in nonadiabatic molecular dynamics.
• To provide a rigorous justification for the empirical effectiveness of TSH algorithms.

Main Methods:

• Utilizing a Gaussian wave packet limit to analyze the dynamics.
• Deriving transition rates for the hopping process at an avoided level crossing.
• Concentrating on the formal aspects of TSH to establish its theoretical basis.

Main Results:

• The derivation successfully retrieves essential features of standard TSH algorithms.
• Identified non-zero electronic transition rates at avoided crossings.
• Derived electronic transition rates that are linear in nonadiabatic coupling vectors and include velocity rescaling for energy conservation.

Conclusions:

• The study provides a formal derivation for TSH, grounding its theoretical basis.
• The derived hopping rules align with key aspects of standard TSH implementations.
• This work offers fundamental insights into the physics governing nonadiabatic molecular dynamics and TSH simulations.