Study of the vibronic coupling in the first excited state of MgCH3 radical

Abstract

A methodology based on the crude adiabatic approximation is used to study the complete linear and quadratic vibronic coupling in the first excited state of MgCH₃ radical. Firstly we evaluate 30 integrals intervening in the formulation of the vibronic coupling and which are used to build the representation of the hamiltonian. Secondly, we diagonalize this representation to evaluate the vibronic levels. For the lowest excited vibronic states, the implied modes are Q₁(symmetric C-Mg stretching) and Q₄ (CH₃rocking). Energy gaps A₁-A₂ and A₂-ε resulting  of the splitting  due to the Jahn-Teller coupling E U e = A₁ + A₂+ ε are evaluated to 126 and 208 cm^-1, respectively. Finally we surround essential coupling parameters to simplify the study of highly excited vibronic states. In these states, the involved modes are Q₅ (antisymmetric C-H stretching) and Q₆ (antisymmetric C-H bending). The energy gaps are evaluated to 22 cm^-1 (A₂ – A₁) and 34 cm^-1 (A₂- ε) for Q₅ mode, 9 cm^-1 (A₁-A₂) and 16 cm^-1 (A₂- ε) for Q₆ mode.