BCSH incorporates phase and branching corrections to the traditional FSSH. The phase correction algorithm was originally proposed by Shenvi and coworkers to correct the relative phase between Gaussian wavepacket (WP) components on different PESs arising from their distinct motions. The electronic Hamiltonian ˆ( ; ) where η is a positive number to be determined according to energy conservation. If the adiabatic potential energy oI state i is larger than the total energy such that energy conservation cannot be satisfied, η is set to an infinitesimally small positive value. In this way, the equations of motion for adiabatic coefficients in Eq. ( ) are replaced by