Topologically Correct Quantum Nonadiabatic Formalism for On-the-Fly Dynamics

Area of Science:

• Quantum dynamics
• Computational chemistry
• Theoretical chemistry

Background:

• Quantum nonadiabatic dynamics simulations are crucial for understanding chemical reactions.
• The adiabatic representation, common in electronic structure calculations, simplifies these dynamics.
• Conical intersections in this representation introduce geometric (Berry) phases that complicate accurate nuclear dynamics modeling.

Purpose of the Study:

• To analyze two distinct approaches for simulating quantum nonadiabatic dynamics within the adiabatic representation.
• To investigate how these approaches handle geometric and Berry phases, particularly in the context of conical intersections.
• To determine the suitability of each method for large-scale quantum dynamics simulations.

Main Methods:

• Utilizing the time-dependent variational principle for dynamics calculations.
• Employing the adiabatic representation derived from electronic structure programs.
• Comparing an approach with globally parameterized adiabatic electronic functions against one using localized nuclear basis functions (e.g., frozen-width Gaussians).

Main Results:

• The approach using global parametric dependence of electronic functions fails to capture the geometric phase without a gauge transformation.
• The second approach, employing localized nuclear basis functions, naturally accounts for the geometric phase.
• This natural inclusion of the geometric phase is due to the electronic functions lacking global nuclear coordinate dependence.

Conclusions:

• The method employing localized nuclear basis functions offers a more robust and natural treatment of geometric phases in quantum nonadiabatic dynamics.
• This approach is advantageous for simulating large systems where conical intersections are prevalent.
• Accurate modeling of nuclear dynamics near conical intersections is significantly improved by naturally incorporating geometric phases.