The adiabatic‐to‐diabatic transformation angle and topological phases for strongly interacting states: Solution with four states

A few years back T. Vértesi et al. (J Phys Chem A 2005, 109, 3476) gave an elegant procedure to derive the adiabatic‐to‐diabatic transformation angle (ADT‐angle) for lowest two states, γ₁₂, in presence of their interaction with the higher states. In this article, we explicitly solved the coupled differential equations involving the ADT‐angles describing the mixing of four interacting states for the first time to get all the ADT‐angles, γ_ij's (including the γ₁₂) associated with well‐defined topological phases. In application to a suitable configuration space (CS) of a molecular system, we have demonstrated well‐defined Berry phases (Berry M. V., R Soc London Ser A 1984, 45, 392) for an isolated system with as many as four strongly interacting states. © 2012 Wiley Periodicals, Inc.