High-order expansion of T₂× e Jahn-Teller potential-energy surfaces in tetrahedral systems

A high-order expansion of the three potential-energy surfaces of the T2×e Jahn-Teller effect in tetrahedral systems is presented. It is shown that the expansion of the vibronic matrix can be obtained from two diagonal matrices determined from symmetry-invariant polynomials. The method is applied to the methane cation in its triply degenerate electronic ground state, which is known to exhibit an exceptionally strong Jahn-Teller effect. The potential-energy surfaces exhibit a highly anharmonic structure and multiple seams of intersections, rendering a high-order expansion of the potential matrix indispensable. An analytic expansion of the potential-energy surfaces up to 10th order has been fitted to accurate ab initio data.