The Curl–Divergence equations for the electronic non-adiabatic coupling terms: study of the C2H molecule and the H2+H system

This Letter is part of an effort to use the Curl equations to calculate non-adiabatic coupling terms, subject to ab initio boundary conditions. As examples we consider two-state, planar, systems characterized by two coordinates, θ and q and treat the corresponding non-adiabatic coupling terms, namely, τθ(q,θ) and τq(q,θ). The theory, which yields τq(q,θ) once τθ(q,θ) is given, is applied to three cases: an analytical model and two ab initio treatments – one for the C2H molecule and one for the H+H2 molecular system. In all three cases encouraging agreements were obtained between the theoretical τq(q,θ) values and the ab initio ones.