Thus, we explicitly use the trajectory average to converge to the expectation value defined in Eq. 33. This is one of the main theoretical results of the paper. Note that when c 0,ξ (t) = 0 and c 1,ξ (t) ̸ = 0, the random angle θ ξ added to the ground state is sampled from -π to π due to Eq. 71 which completely randomizes the phase of the ground state, which renders the undetermined phase factor e iφ 0 ξ irrelevant. These effective Lindblad updates of the electronic coefficients described in Eqs. 69a-69c can be combined with the Ehrenfest part of the electronic coefficients update described in Eq. 15 and Eq. 16 to describe the mixed quantum-classical dynamics subject to a Lindblad type decay. We refer to this approach as the L-MFE method for the remainder of the paper. The coefficient propagation of the L-MFE method can be expressed as