2. Propagate the dynamics based on Eq. 69. In particular, for the e L Ĥ ∆t part, use Eq. 61 to propagate the forward and backward electronic coefficients, and Eq. 62 to compute the nuclear force to update nuclear DOFs; for the e L L∆t k /2 part, use Eq. A3 to update the coefficients to describe the Lindblad loss dynamics.