Vibrational Calculations for the HD₂ First-Excited Electronic State Using a Coordinate-Transformation Technique

Abstract

We report calculations of the vibrational spectrum of HD 2 in its first-excited electronic state by using a coordinate-transformation technique. The implications of the geometric phase (GP) effect in the spectrum have been investigated. The results show that the lowest 45 vibrational levels calculated using the traditional Longuet-Higgins phase (φ/2, where φ is the pseudorotation angle) are in good agreement with those obtained by using a single-surface generalized Born-Oppenheimer equation previously reported by the authors.

Dynamics study of a three-fold pseudo-Jahn–Teller system using the extended Longuet–Higgins formalism

“…In summary, GP will appear on electronic states ψ 1 and ψ 3 , with the PES's of these two electronic states having a nonzero slope at the degeneracy locus. 39 Clearly, the GBO formalism reported here is strictly valid in the vicinity of the degeneracy seam, although generality can be warranted by invoking the fact that such regions influence in a dominant way the dynamics even when the energetics allows sampling wider areas of configuration space 44 surrounding the degeneracy point. Extension to larger manifolds is warranted by the ELH theorem.…”

Generalized Born–Oppenheimer treatment of Jahn–Teller systems in Hilbert spaces of arbitrary dimension: theory and application to a three-state model potential

“…A final remark to note that the GBO formalism reported here is strictly valid in the vicinity of the degeneracy seam, although generality is conveyed to it by invoking the fact that such regions influence in a dominant way the dynamics even when energetics allows to sample wider areas of configuration space. 30 Extension to larger manifolds is warranted by the ELH theorem. 22 This and applications to realistic potentials are in progress.…”

Adiabatic approximation and related issues including topological implications

“…(6.35), where the complex phase factor has been absorbed in the nuclear wave functions [106][107][108]. Such an approach is especially convenient for X 3type systems when using hyperspherical coordinates [36,109], although it can be generalized [40,110,111] where f = f (z; ρ 2 , ρ 3 cos 3ϕ), g = g(z; ρ 2 , ρ 3 cos 3ϕ), and w are analytic functions.…”

“…with inclusion of GP and without it. Such studies have been carried out for a wealth of systems [18,39,110,111,115,[131][132][133][134][135], with the reader being referred to the original papers for details. Suffice it to say that the nuclear SE including GP may be written asĤΦ = EΦ, whereĤ =Ĥ 0 + ιĤ 1 .…”