Geometric phase effects in H+O2 scattering. I. Surface function solutions in the presence of a conical intersection

Abstract

The general vector potential (gauge theory) approach for including geometric phase effects in accurate 3D quantum scattering calculations in hyperspherical coordinates is presented. A hybrid numerical technique utilizing both the DVR (discrete variable representation) and the FBR (finite basis representation) is developed. This method overcomes the singular behavior of the vector potential terms giving accurate surface function solutions to the complex Hermitian nuclear Schrödinger equation. The hybrid DVR/FBR technique is applied explicitly to HO2 for zero total angular momentum. The resulting complex surface functions include the geometric phase effects due to the C2v conical intersection. The O2 permutation symmetry is implemented to give real double-valued surface functions which exhibit both even and odd symmetry. The surface function eigenvalues are compared to calculations without the geometric phase. The results indicate that geometric phase effects should be significant for H+O2 scattering even at low energies.