Existence of strictly diabatic basis sets for the two‐state problem

Abstract

Some new properties of the nonadiabatic coupling elements are derived, in particular the orthogonality and gauge invariance of their longitudinal and transverse components. A method for constructing a strictly diabatic basis set that makes both the transverse and longitudinal components of the nonadiabatic coupling elements of the two-state problem vanish identically and is based on introducing overlap between the electronic states in the vicinity of the crossing seam is proposed.

Geometric phase effect at N‐fold electronic degeneracies in Jahn–Teller systems

“…(16), the general adiabatic electronic wave vectors {|ψ I ( r ; R )〉} can be represented by a one‐parameter orthogonal transformation of the initial electronic wave vectors | E x ( r )〉 and | E y ( r )〉; R represents the full set of nuclear coordinates. For the two‐state problem, one has or, in matrix form, where γ( R ) is the mixing angle 16, 17, 29 (this has been shown 17 to be equivalent, up to a constant, to the so‐called adiabatic to diabatic transformation angle 30–33). We observe that ψ i ( i = 1, 2) are real and that they change sign over a closed loop around the degeneracy point.…”