New method for calculating wave packet dynamics: Strongly coupled surfaces and the adiabatic basis

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Abstract
The nuclear dynamics on potential energy surfaces with a conical intersection is investigated on the basis of exact (numerical) integration of the time‐dependent Schrödinger equation. The ethylene cation is chosen as a typical realistic model system. Complementing earlier work we study the dynamics also in the adiabatic basis, which will be seen to allow for a more profound understanding of the decay and dephasing processes occurring in the system. The computational effort exceeds considerably that of propagation in the diabatic basis, to which previous related studies have been confined. To solve the resulting computational problems we develop and present a special multidimensional adaptation of the finite basis set method utilizing the product structure of the basis. It allows us to calculate propagation in a general potential including three vibrational modes. For the time integration a fourth order differencing scheme is introduced which is faster than the second order differencing‐scheme and predictor–corrector approaches.