Multiple lines of conical intersections and nondegenerate ground state in T⊗t2 Jahn–Teller systems

Abstract

We have investigated the T⊗t2 Jahn–Teller problem with linear and quadratic vibronic coupling including a fourth-order term. First, numerical calculations of the lowest vibronic states were carried out by direct diagonalization of the Hamiltonian. The results show that the energy level of the ground vibronic state, which is triply degenerate T for small quadratic coupling g values, intersects the next A level with increasing g, thus realizing the nondegenerate ground state at sufficiently large g values. This result reverses the long-standing belief that the ground vibronic state for the T⊗t2 system has the same degeneracy and symmetry T as the initial electronic state. To explain these results in terms of Berry phase requirements and conical intersections, the adiabatic potential energy surface of the system is analyzed, and the relationships among the type and number of minima, conical intersections, and relevant tunneling paths are revealed. Depending on the vibronic coupling parameter values, there are four trigonal minima and six orthorhombic saddle points, which become minima at large g values, plus ten lines of conical intersections on the lowest potential energy surface. The barriers between the minima are significantly increased near the lines of conical intersections where the Born–Huang terms diverge. For small enough quadratic coupling, only four lines of conical intersections that originate from the highest symmetry point and proceed along the four trigonal directions are significant in determining the Berry phase, and the triply degenerate ground T state is obtained. By increasing the quadratic coupling parameter, the remaining six lines of conical intersections approach the point of highest symmetry, thus allowing for alternative tunneling paths and Berry phases which lead to the nondegenerate A ground state. This explanation of the origin of the nondegenerate ground state for some range of values of the vibronic coupling parameters is strengthened by model calculations of tunneling splitting.

Complex States of Simple Molecular Systems

“…They showed that, contrary to what had been widely thought before, the ground state may be either a vibronic doublet or a singlet, depending on the distance (which is a function of the parameters in the vibronic Hamiltonian) of these trigonal ci's from the centre. (A similar instance of "quantum phase transition" was noted for a threefold degenerate system in [275] and, earlier, for an icosahedral system, in [276]). …”

BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection

“…More than two states may also interact in this manner. For example, the T × τ Jahn-Teller effect, where a triply degenerate electronic state is split by a triply degenerate molecular vibration, can be analyzed in the same way (47). Some other important cases, such as -coupling in linear molecules and pseudo-JahnTeller coupling, are described in Section 4.…”

Origin of warping in theE⊗eJahn-Teller problem: Quadratic vibronic coupling versus anharmonicity and application toNaCl:Rh2+García‐Fernández1, Берсукер2, Aramburu3 et al. 2005Phys. Rev. B744711View full textAdd to dashboardCite

“…11 In the T t 2 problem sufficiently strong quadratic terms lead to additional seams of conical intersections that change the ground state degeneracy too. 12 Important results obtained with strong quadratic coupling terms raise the question of the role of higher order terms and the convergence of the vibronic coupling approach taken in consecutive approximations. To explore this issue we begin with cubic terms of the vibronic coupling.…”