The talk will begin with an introduction to the quantum master equation (Liouville-von Neumann equation), followed by a discussion of how we have used this equation it in a semiclassical algorithm for calculating of non-Born-Oppenheimer molecular dynamics. I will also discuss the physical origin of decoherence in electronically nonadiabatic molecular dynamics and our method for estimating the decoherence time. The resulting treatment will be validated against accurate quantum dynamics for small molecular systems.