The STD model was proposed by Subotnik to quantify the decoherence effects in multidimensional cases. We choose the initial conditions as x 0 = -4, y 0 = 0, k x = 10, k y = 0 and place the WP on the upper PES to investigate the performance of our consistent method to construct the density matrix in multidimensional systems. According to the exact quantum results obtained by DVR, we can identify important branching events and generation of WPs during the dynamics (see Figure ). At t = 1000 au, the initial WP labeled with 1 (i.e., WP-1) on the upper PES enters the interaction region and gets reflected, generating WP-2 and WP-3 on the lower PES (see Figure ). Along with the reflection of WP-1 on the upper PES, WP-2 gets transmitted on the lower PES. This is the first branching event, following which WP-1 and WP- 11F and 11G). After t = 2300 au, WP-3 and WP-4 are scattered by the barrier on the lower PES, while WP-5 continues to move along with WP-1 and the second branching event is completed (see Figures and).