Tunneling Path and Ground State Crossover in Linear T⊗(e⊕t2) and Quadratic G⊗(g⊕h) Jahn–Teller Systems

Abstract

Abstract It was believed that vibronic coupling does not alter the symmetry and degeneracy of the ground state of a Jahn–Teller (JT) system. However this conjecture was found to be untrue in the case of the icosahedral H ⊗ h system, where in strong coupling the system has a ground vibronic state of A symmetry instead of the expected H symmetry. A physical explanation to account for this ground state crossover has been given very recently by the consideration of two kinds of tunneling paths on the adiabatic potential energy surface. One path between a pair of minima is favored at strong coupling while a path between a different pair of minima is favored in weak coupling. By using the WKB approximation, it was shown that different contributions to the tunneling splitting arise from the two different paths. This gives rise to the crossover of the ground vibronic states occurring at a certain value of the coupling strength. In the cubic T ⊗( e ⊕ t 2 ) JT system a crossover has also been proposed. However, only minima having trigonal symmetry occur when the t 2 mode dominates and thus only one type of tunneling path is present so that a crossover seems to be unlikely in the reported range of coupling constants. In a second example considered here, it is shown that in the icosahedral G ⊗( g ⊕ h ) system a crossover is possible for certain combinations of linear and quadratic coupling constants. This crossover can be understood from the consideration of two kinds of competing paths between pairs of trigonal minima.