Electronic transitions diabatic basis sets

A certain electronic transition in a polyatomic system can be equally described either within the adiabatic or within the diabatic basis set as the transitions can be induced either by the dynamic or by the static coupling,... 

The time evolution of the electronic wave function can be obtained in the adiabatic or in the diabatic basis set. At each time step, one evaluates the transition probabilities between electronic states and decides whether to hop to another siu-face. When hopping occurs, nuclear velocities have to be adjusted to keep the total energy constant. After hopping, the forces are calculated from the potential of the newly populated electronic state. To decide whether or not to hop, a Monte Carlo technique is used Once the transition probability is obtained, a random number in the range (0,1) is generated and compared with the transition probability. If the munber is less than the probability, a hop occurs otherwise, the nuclear motion continues on the same surface as before. At the end of the simulation, one can analyze populations, distribution of nuclear geometries, reaction times, and other observables as an average over all the trajectories. 

For class-1 states, a simple harmonic representation of U leads to a complete set of eigenfunctions ( ) this harmonic oscillator basis set is used to diagonalize equation (6). In this case, it is sufficient to construct U( 4>k) using a standard approach involving mass fluctuation (or nuclear ) coordinates and the corresponding electronic state dependent Hessian. The higher terms in the Taylor expansion define anharmonic contributions to the transition moments. These diabatic states are confining and only one stationary point in -space would be found for each... 

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