Interplay of Jahn–Teller and pseudo-Jahn–Teller vibronic dynamics in the benzene cation

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Abstract
The static and dynamic aspects of the vibronic interaction of the B̃ 2E2g and C̃ 2A2u electronic states of C6H+6 are analyzed. In the approximation of linear vibrational and vibronic coupling, the model Hamiltonian for this system comprises eight nonseparable vibrational modes, six of which are degenerate (two of A1g symmetry, four of E2g symmetry, and two of E2u symmetry). The coupling constants are estimated from existing ab initio SCF and semiempirical (CNDO/S) calculations. The topology of the adiabatic potential‐energy surfaces of this class of model Hamiltonians is investigated. It is shown that the model exhibits a variety of conical intersections which dominate the vibronic dynamics. The dynamical problem is solved with simultanteous inclusion of six vibrational modes, four of which are degenerate (the Jahn–Teller coupling of two of the E2g modes is negligible). Hamiltonian matrices with dimensions up to 6×106 are diagonalized using the Lanczos algorithm. After some adjustments of coupling constants, the calculation reproduces well the complex structure of the overlapping B̃ 2E2g–C̃ 2A2u bands in the photoelectron spectrum of benzene. The vibronic structure of the lower‐energy E2g band is dominated by a two‐mode Jahn–Teller effect in the B̃ state. At higher energy, the marked diffuseness of the ‘‘C̃ 2A2u band’’ is shown to be a consequence of complete vibronic mixing with the lower‐lying B̃ state. Based on the numerical solution of the full problem, the reliability of approximations (neglect of nonseparability of modes, introduction of a single effective pseudo‐Jahn–Teller mode) is assessed. A time‐dependent analysis reveals an ultrafast decay of the population of the C̃ state on a time scale of about 20 fs, followed by quasiperiodic recurrences which are damped on a time scale of a few hundred femtoseconds. These findings underline the importance of conical intersections and strong nonadiabatic effects also for larger molecules such as aromatic hydrocarbons. They demonstrate that nowadays a full quantum treatment is feasible also for these larger systems.