The hyperbolic matrix method for wave packet treatment of atomic and molecular dynamics

The hyperbolic matrix method for the treatment of atomic and molecular nuclear dynamics is derived by means of the wave packet technique within the Born–Oppenheimer approach formalism. This method allows one to calculate the evolution of a wave packet by means of the product of usual matrices instead of the time propagation of matrix exponentials. We provide a detailed description of this method, considering Tully’s model as an example. We also show good agreement with the Landau–Zener model application