Solving the vibrational Schrödinger equation with artificial neural networks

Artificial neural networks (NN) are universal function approximators and have shown great ability in computing the ground state energy of the electronic Schrödinger equation, yet NN has not established itself as a practical and accurate approach to solve the vibrational Schrödinger equation for realistic polyatomic molecules to obtain vibrational energies and wave functions for the excited states. Here we purpose an efficient approach to use NN to solve the vibrational Schrödinger equation and demonstrate the new method on CH4, a five atom molecule with 9 degree of freedom. By using a NN with < 3,000 parameters, we are able to achieve vibration energies for the ground and excited states with an accuracy of less than 1 cm-1 as compared to the reference values obtained by using more than 109 basis functions. It is anticipated the new method is capable of providing highly accurate vibrational energies and wave functions for molecules with more than 10 atoms, beyond the limit for all the existing computational approaches.