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.