Simultaneous integration of mixed quantum‐classical systems by density matrix evolution equations using interaction representation and adaptive time step integrator

A density matrix evolution method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem., 97, 13464 (1993)] to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five‐level quantum harmonic oscillator. We improved the numerical performance by rewriting the Liouville–von Neumann equation in the interaction representation and so eliminated the frequencies of the unperturbed oscillator. Furthermore, replacement of the fixed time step fourth‐order Runge–Kutta integrator with an adaptive step size control fourth‐order Runge–Kutta resulted in significantly lower computational effort at the same desired accuracy. © 1996 by John Wiley & Sons, Inc.

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