Non-adiabatic perturbation theory of the exact factorization

Area of Science:

• Quantum Chemistry
• Theoretical Physics
• Computational Chemistry

Background:

• The Born-Oppenheimer approximation simplifies molecular quantum mechanics by separating electron and nuclear motion.
• Accurate descriptions of electron-nuclear correlations are crucial for understanding molecular dynamics and spectroscopy.
• Existing methods struggle to fully capture nonadiabatic effects, particularly in systems with degeneracies.

Purpose of the Study:

• To introduce a novel nonadiabatic perturbation theory (NAPT) for electron-nuclear systems.
• To provide a theoretical framework that goes beyond the standard Born-Oppenheimer approximation.
• To develop a method that systematically includes electron-nuclear correlation effects.

Main Methods:

• Exploiting the small electronic-to-nuclear mass ratio as a perturbation parameter.
• Treating electron-nuclear correlation terms within the exact factorization framework.
• Developing a finite-order truncation scheme for the perturbation theory.

Main Results:

• Demonstrated that NAPT preserves the normalization of the electronic factor and gauge covariance.
• Successfully calculated nonadiabatic corrections to the Berry phase in Jahn-Teller systems.
• Showcased NAPT's ability to distinguish between topological and geometric Berry phases.

Conclusions:

• NAPT offers a robust and accurate approach for studying nonadiabatic quantum dynamics.
• The method provides valuable insights into electron-nuclear coupling and its impact on molecular properties.
• NAPT is particularly effective for systems exhibiting conical intersections and complex topological phases.