Quantum geometrical molecular dynamics

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Molecular reactive quantum dynamics are complex to model.
• Existing methods struggle with singularities arising from nonanalytic electronic states.

Purpose of the Study:

• To develop a unified and exact quantum geometric framework for molecular reactive quantum dynamics.
• To unveil the critical roles of quantum geometry in adiabatic and nonadiabatic dynamics.

Main Methods:

• Developed a numerically exact geometric quantum molecular dynamics method.
• Employed discrete local trivialization of the projected electronic Hilbert space bundle.
• Encoded the electronic quantum geometric tensor within the global electronic overlap matrix.

Main Results:

• The framework eliminates singularities from nonanalytic adiabatic electronic states.
• Atomic motion is governed by variations in electronic energies and electronic quantum geometry.
• Demonstrated the critical role of quantum geometry in both adiabatic and nonadiabatic quantum dynamics.

Conclusions:

• The developed method provides an exact and unified approach to quantum molecular dynamics.
• The strategy of discrete local trivialization is applicable to broader quantum dynamics problems, including non-Hermitian systems and arbitrary fiber bundles.