This term performs a Poisson jump process that captures the projective action of the environment on the system that randomly collapses the system wavefunction into a pure system eigenstate. The trajectory average of Eq. 73 with a large number of realizations (jump trajectories) generates results identical to ρS (t) described by the Lindblad master equation in Eq. 9. The equivalence of these two descriptions can be viewed as the correspondence between the stochastic quantum state diffusion equation (Eq. 73) and the deterministic Wigner Fokker-Planck equation (which can be written in the Lindblad master equation form of Eq. 9). The L-MFE method, on the other hand, does not collapse trajectories onto a single system state, which avoids large changes in the magnitudes of the coefficients. Further, the change in magnitude of the coefficients is deterministic, whereas the magnitude of the coefficients in the Monte Carlo wavefunction method is stochastic. Further, the phases of the coefficients in L-MFE only slightly vary between time steps with no large jumps. When explicitly considering ĤC + ĤQC , the stochastic Schrödinger equation approach can encounter numerical instabilities due to large changes of the electronic coefficients, whereas the L-MFE approach provides a stable numerical integration of the equation of motion due to the small changes of phase in the coefficients. The L-MFE approach, in addition, can be easily combined with any mixed quantumclassical or semiclassical approach.