The Quantum Decoherence Problem in Nonadiabatic Trajectory Methods

In this chapter we deal mainly with nonadiabatic independent trajectory approaches to the simulation of excited state dynamics. We focus on a ubiquitous shortcoming of such methods, namely overcoherence, or lack of decoherence, in the time-evolution of the electronic wavefunction and density matrix. In the mean-field approach the overcoherence affects the average potential energy surface on which the trajectory runs, yielding unphysical results, while in the surface hopping dynamics it leads to an overestimation of the couplings between electronic states. In the introduction we frame the theme of decoherence as a fundamental element of quantum theory and a real process affecting molecular dynamics. In the next section, we introduce the overcoherence problem in independent trajectory methods for nonadiabatic dynamics. In the third section, we shortly review the mean-field and surface hopping approaches, we show how decoherence can be described in the framework of Liouville-von Neumann equation, and we introduce several formulas and procedures to compute decoherence rates. In the fourth section we examine a variety of algorithms that have been proposed to correct the overcoherence in mean-field and surface hopping methods, dividing them in two classes: those based on stochastic sudden decoherence events, and those introducing smooth modifications of the (over)coherent electronic dynamics. Finally, in the last section we recall the most popular and/or promissing decoherence correction methods, and we focus on tests showing how such corrections really improve the accuracy of the nonadiabatic trajectories simulations.