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

An efficient and accurate double-valued (DV) boundary condition based on the Jacobi coordinate system is proposed to incorporate the geometric phase (GP) effect in adiabatic calculation for the A + B 2 reaction within the time-dependent wave packet framework. In this approach, the scattering region is divided into two parts, and two sets of spherical harmonic function bases with different symmetries are employed in each region. Compared with the traditional vector potential method, which includes the GP effect but suffers from singularity problems, the DV boundary condition eliminates these singularities, making it more efficient. Typical triatomic reactions involving a T-shaped conical intersection, such as H + O 2 and H + D 2, are studied using the DV boundary condition and other methods that include the GP effect. A comparative study clearly demonstrates the advantages of the DV boundary conditions. Because of its simplicity, the DV boundary condition is expected to be implemented in more complex reactions, including tetratomic reactions.