We first introduce diabatization by deep neural network (DDNN). The DDNN method is based on a diabatic potential energy matrix (DPEM), whose eigenvalues are the adiabatic potential energies. The diagonal elements 𝐔 !,## of the DPEM at geometry j are the diabatic potential energies, and the off-diagonal elements 𝐔 !,#$ are called diabatic couplings. Because the elements of the DPEM are smooth and the adiabatic potentials are not smooth, the strategy adopted is to fit the DPEM and recover the adiabatic potentials by diagonalization. An For an L-layer DDNN, the input layer for geometry n is 𝐚 ) * , the hidden layers are 𝐚 ) + to 𝐚 ) ,-+ , the DPEM layer is 𝐚 ) ,-* , and the adiabatic potential energy layer is 𝐚 ) , . The propagation from the input layer to hidden layers is done by