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

Abstract

Generalized Born-Oppenheimer equations including the geometrical phase effect are derived for three- and four-fold electronic manifolds in Jahn-Teller systems near the degeneracy seam. The method is readily extendable to N-fold systems of arbitrary dimension. An application is reported for a model threefold system, and the results are compared with Born-Oppenheimer (geometrical phase ignored), extended Born-Oppenheimer, and coupled three-state calculations. The theory shows unprecedented simplicity while depicting all features of more elaborated ones.

The adiabatic‐to‐diabatic transformation angle and the berry phase for coupled jahn–teller/renner–teller systems: The F + H2 as a case study

“…In contrast to the just mentioned ADT treatment by Werner et al for the F + H 2 system, most of the treatments of other molecular systems are done by applying the original BO‐NACTs 1–14, 18–23, 29–47. This study for the F + H 2 system is the first that uses BO‐NACTs for the diabatization of this system.…”

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

“…The detailed approach from Schrödinger's equation (SE) of the complete many-body problem has been discussed earlier, 40 but for the sake of completeness we will give a brief account of the equations involved in the dynamics. Consider the nuclear motion restricted to a three-state electronic manifold.…”

“…The parameters assume the values of μ = 0.58 amu, ω 0 = 5.0 × 10 13 s −1 , A = 3.0 eV, D = 6.0 eV, σ = 0.20 Å(respectively), and hence differs slightly from the one used elsewhere. 40 The degeneracy lies nearly 3.0 eV above the asymptote, and hence the calculations will be for energies below the seam. One should note that the model obeys selection rules, namely: if reduced to a two-state conical intersection, only even↔odd transitions are allowed; for the three-state coupled case, only even→even and odd→odd are permitted.…”

“…1.00 (a) 0.331 0.021 0.309 0.003 1.00 (b) 0.020 0.547 0.035 0.050 1.00 (c) 0.344 0.000 0.319 0.000 1.00 (d) 0 kinetic energies for the scattering mode. This adiabatic wave function is then propagated as a function of time by using the newly derived single surface GBO equation, 40 and the BO and Extended BO (EBO) 34,38 ones, in addition to the solution of the three-state coupled equations. 33 For this, the discrete variable representation (DVR) method 43 has been utilized, with the final wave functions at t → ∞ being projected on the asymptotic eigenfunctions of the Hamiltonian such as to obtain the state-to-state vibrational transition probabilities at different energies.…”

“…More recently, the systematic derivation of the dynamical equations for such a JT and pseudo-JT system has been communicated. 40 In the present work, we discuss the Generalized Born-Oppenheimer (GBO) formulation of such dynamical equations using the extended LH (ELH) theorem for three-fold electronic JT manifolds which is readily extendable to manifolds of arbitrary dimension. Comparisons of the dynamics using various methods on this model are also presented.…”