Effects of higher order Jahn-Teller coupling on the nuclear dynamics

Abstract

In this paper effects of higher order Jahn-Teller coupling terms on the nonadiabatic dynamics are studied. Of particular interest is the case when the potential energy surfaces of the degenerate state show pronounced anharmonicity. In order to demonstrate the effects a two-dimensional E multiply sign in circle e Jahn-Teller model system is treated which is based on the e(') stretching vibration of the photoactive (2)E(') state of NO(3) as a realistic example. The sixth order E multiply sign in circle e Jahn-Teller Hamiltonian is derived in the diabatic representation which is valid for any system with a C(3) rotation axis. This diabatization scheme is compared to lower-order Jahn-Teller Hamiltonians and to symmetry adapted as well as ad hoc approximations. Lower-order potentials result in pronounced quantitative and qualitative differences in the dynamics, including differences in the evolution of mean values, the autocorrelation functions (and thus the corresponding spectra), and the electronic population evolution. In the particular example treated, the results of fourth and fifth order potentials are very similar to the sixth order reference system. In contrast, the approximate sixth order Hamiltonians, though the corresponding adiabatic surfaces seem to be nearly identical, results in pronounced differences. The possible consequences for the dynamics of realistic systems with higher dimensionality are briefly discussed.

On the construction of quasidiabatic state representations of bound adiabatic state potential energy surfaces coupled by accidental conical intersections: Incorporation of higher order terms

“…There have been a limited number of studies that have included higher order terms for coupled potential energy surfaces. [6][7][8][9][10][11][12] In this work, we consider the addition of anharmonic terms to the fully quadratic vibronic coupling model in the case where the conical intersections are accidental and the low-lying seams of the conical intersection are spatially separated from the global minimum on the ground state potential energy surface. This is accomplished using an extension of our previously reported 4 algorithm for determining fully quadratic, quasidiabatic bound-state Hamiltonians (H d ).…”

Jahn–Teller and spin–orbit coupling effects in transition-metal trifluorides

“…In principle, a two-mode JT + PJT model Hamiltonian can be derived by an expansion up to sixth or higher-order, which provides an accurate description of the (E ′ + A ′ 1 ) × (e ′ + e ′ ) three-state conical intersection problem. 74,89 The analysis of the PJT effect and its dynamic consequences (radiationless decay of the 4 E ′ excited state to the 4 A ′ 1 ground state) is, however, beyond the scope of the present work. …”

“…The first systematic treatment of the E × e JT problem considering the large-amplitude nuclear displacement was developed by Viel and Eisfeld. 74 It was shown that a higher-order expansion (beyond second-order) can significantly improve the accuracy of the JT PE surfaces. 74 The sixth-order expansion of electrostatic JT Hamiltonian (extension of (2.15) up to sixth-order) in the real representation reads 74…”

“…The expressions for U (n) , W (n) and Z (n) are given in Appendix A (up to sixth order for a single e-mode). 74 …”

“…(3.26)) are given by 74 U (0) = a 1 (0) U (1) = 0 U (2) = a 1 (2) [Q x 2 + Q y 2 ] U (3) = a 1 (3) [2Q x 3 − 6Q x Q y 2 ] U (4) = a 1 (4) [Q x 4 + 2Q x 2 Q y 2 + Q y 4 ] U (5) = a 1 (5) [2Q x 5 − 4Q x 3 Q y 2 − 6Q x Q y 4 ] U (6) = a 1 (6) …”