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Related Experiment Video

Updated: Jun 18, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

A singularity free surface hopping expansion for the multistate wave function.

Michael F Herman¹

¹Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA. mherman@tulane.edu

The Journal of Chemical Physics

|December 9, 2009

Summary

This summary is machine-generated.

A novel surface hopping wave function eliminates singularities, improving accuracy for nonadiabatic quantum dynamics. This method enhances calculations near electronic state crossing energies, crucial for understanding chemical reactions.

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Area of Science:

Quantum Chemistry
Theoretical Chemistry
Computational Chemistry

Background:

Surface hopping methods are vital for simulating nonadiabatic molecular dynamics.
The primitive semiclassical surface hopping wave function is accurate but suffers from turning point singularities.
These singularities reduce accuracy near diabatic electronic state crossing energies.

Purpose of the Study:

To derive and test a singularity-free surface hopping wave function.
To improve the accuracy of nonadiabatic dynamics simulations, especially near crossing points.
To provide a more robust computational tool for quantum chemistry.

Main Methods:

Developed a singularity-free surface hopping wave function by partitioning the coordinate axis into small steps.
Approximated adiabatic electronic energy surfaces as linear functions within each step.
Utilized matching conditions at step boundaries to determine state-change and reflection amplitudes.

Main Results:

The derived surface hopping wave function is free of turning point singularities.
Numerical tests on a one-dimensional model demonstrate high accuracy across all energies.
Accuracy is maintained even when the system's energy is near the crossing energy of diabatic electronic surfaces.

Conclusions:

The singularity-free surface hopping wave function offers a significant improvement over previous methods.
This approach enhances the reliability of nonadiabatic dynamics simulations.
It provides a more accurate computational tool for studying complex chemical processes.