A Double-Valued Boundary Condition for Incorporating the Geometric Phase into Adiabatic Calculation

Area of Science:

• Chemical Physics
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Geometric phase (GP) effects are crucial in understanding chemical reactions, particularly those involving conical intersections.
• Traditional methods for including GP effects, like the vector potential method, often suffer from singularity problems, limiting their efficiency and applicability.
• Accurate theoretical modeling of chemical dynamics requires robust methods to handle complex quantum phenomena.

Purpose of the Study:

• To propose and validate an efficient and accurate double-valued (DV) boundary condition for incorporating the geometric phase (GP) effect in adiabatic calculations.
• To address the singularity issues present in traditional methods for including GP effects.
• To demonstrate the applicability and advantages of the DV boundary condition for typical triatomic reactions.

Main Methods:

• Development of a double-valued (DV) boundary condition utilizing the Jacobi coordinate system.
• Division of the scattering region into two parts with distinct spherical harmonic function bases.
• Application of the time-dependent wave packet framework for adiabatic calculations.
• Inclusion of the geometric phase (GP) effect within the DV boundary condition framework.

Main Results:

• The proposed DV boundary condition effectively incorporates the geometric phase (GP) effect without singularities.
• The method demonstrates improved efficiency compared to the traditional vector potential method.
• Accurate calculations were performed for triatomic reactions, including H + O2 and H + D2, involving T-shaped conical intersections.
• Comparative studies confirmed the advantages of the DV boundary condition.

Conclusions:

• The double-valued (DV) boundary condition offers an efficient and accurate approach for including geometric phase (GP) effects in chemical reaction dynamics.
• The method successfully overcomes singularity issues associated with previous techniques.
• The simplicity and effectiveness of the DV boundary condition suggest its potential for application to more complex reactions, including tetratomic systems.