Decoherence in combined quantum mechanical and classical mechanical methods for dynamics as illustrated for non-born-oppenheimer trajectories

This chapter discusses the role of decoherence in mixed quantum-classical approaches to electronically nonadiabatic chemical dynamics. The correlation of electronic and nuclear motion, which is not included in the semiclassical Ehrenfest or time-dependent Hartree method, induces decoherence in the reduced electronic density matrix, and the chapter shows how this can be modeled by adding algorithmic demixing to the Liouville-von Neumann equation. The resulting mixed quantum-classical equations of motion involve stochastically controlled, smooth, and continuous surface switching coupled to coherent propagation through each region of strong interaction of the electronic states. The chapter also reviews test results that show good agreement with fully quantum mechanical results for a diverse set of atom-diatom test cases.