High-order expansion of T2×t2 Jahn–Teller potential-energy surfaces in tetrahedral molecules

Abstract

Methods from Jahn-Teller theory and invariant theory have been combined for the construction of analytic diabatic potential-energy surfaces of triply degenerate states in tetrahedral molecules. The potentials of a threefold degenerate electronic state of T(2) symmetry, subject to the T(2)xt(2) or T(2)x(t(2)+t(2)) Jahn-Teller effect in a three-dimensional or six-dimensional space of nuclear coordinates, respectively, are considered. The permutation symmetry of four identical nuclei is taken into account in the polynomial expansion of the diabatic surfaces. Symmetry adapted polynomials up to high orders are explicitly given and a simple combinatorial scheme was developed to express terms of arbitrary order as products of a small number of polynomials which are invariant under the permutation of identical nuclei. The method is applied to the methane cation in its triply degenerate ground state. The parameters of the analytic surfaces have been fitted to accurate ab initio data calculated at the full-valence CASSCF/MRCI/cc-pVTZ level. A three-sheeted six-dimensional analytic potential-energy surface of the (2)T(2) ground state of CH(4) (+) is reported, which involves terms up to eighth order in the degenerate stretching coordinate, up to 12th order in the degenerate bending coordinate, and up to fourth order in the stretch-bend coupling.

Hydrocarbon σ‐radical cations

“…Various theoretical methods and approaches have been used to model properties and reactivities of hydrocarbon radical cations. They range from the early use of qualitative molecular orbital diagrams,42 extended Huckel method,43 and self‐consistent field molecular orbital (SCF‐MO) calculations44,45 to the following methods commonly used nowadays: DFT, Møller–Plesset perturbation theory (MPn), configuration interaction (CI), coupled cluster (CC), complete active space self‐consistent field (CASSCF)/complete active space with a second order perturbation theory (CASPT2),46,47 and CASSCF/multireference configuration interaction (MRCI) 48…”

“…Methane radical cation demonstrates highly fluxional behavior48,62 as the barrier for interconversion of two degenerate C 2v ‐minima via a C s ‐symmetrical transition structure (TS) is very low [1.1 kcal/mol MP4/6–31G(d,p)//MP2/6–31G(d,p)] 58. The ESR19 and high‐resolution zero‐kinetic‐energy photoelectron (PE) spectroscopy63 of CD 2 H 2 •+ all support a C 2v ‐symmetrical ground state of 1 •+ .…”

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

“…[30][31][32][33][34][35][36][37] While the expansions are traditionally 38 truncated at the second order and the resultant Hamiltonians can describe JT and pJT interactions to a qualitative accuracy, a growing number of studies, both theoretical and experimental, have shown inadequacies of the low-order expansions. 17,22,23,[38][39][40][41][42][43][44][45][46][47][48] Motivated by the importance of the high-order expansions, we endeavour to derive general expansion formulas of the JT and pJT Hamiltonian operators up to arbitrary order. [49][50][51][52] In Ref.…”

Analysis of geometric phase effects in the quantum-classical Liouville formalism

“…However, the diabatic representation within a finite electronic subspace cannot be obtained 18 for a general polyatomic system (N atoms > 2), so one has to resort to approximate diabatiza-tion schemes. [19][20][21][22][23][24][25][26][27] To remain in the unambiguous adiabatic representation, Mead and Truhlar 28 (MT) proposed to compensate for the GP of individual nuclear states by attaching an extra phase factor e iλ (R) , where λ(R) is a function that increases by π on encircling a closed path around the CI seam. This approach was successfully implemented [29][30][31] and applied to many real molecules by Kendrick.…”