Time‐dependent solution of molecular quantum systems using multiwavelet

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We solve the time‐dependent Schrödinger equation (TDSE), time‐dependent Hartree‐Fock equations (TDHF), and time‐dependent Density Functional Theory DFT(TDDFT) [Runge and Gross, Phys Rev Lett 1984, 52, 997] equations of general electronic/muonic systems using a multiresolution multiwavelet (MRMW) basis set. The stable solution of these timedependent equations with relatively large time step is obtained using the Cayley formalism with the MRMW basis set. The Cayley operator corresponding to each axis is applied to the direct‐product basis set or a subset of the direct‐product basis set to obtain high efficiency for multidimensional cases. The method is tested by applications to the simulation of electron and muon dynamics of simple molecular systems in the framework of Ehrenfest dynamics employing classical point charge nucleus approximation. Stable solutions of the equations for the quantum and classical particles are obtained.