An Efficient Neural Network Architecture for Molecular Vibrational States: From Rigid Molecules to Molecular Complexes

Abstract Accurately solving the nuclear Schrödinger equation for molecular complexes exhibiting noncovalent interactions remains a challenge due to the exponential scaling of basis sets and the presence of strongly anharmonic, large-amplitude motions. Recently, we proposed a neural network (NN) method to tackle high-dimensional vibrational problems and successfully applied it to C3H8 in full dimensionality; however, applying the method to molecular complexes has been hindered by difficulties in representing delocalized wave functions across multiple minima. In this work, we present a substantially improved NN-based methodology that overcomes these limitations through two key developments: (i) a novel NN architecture specifically designed to capture the asymptotic behavior and delocalization characteristics of weakly bound complexes, and (ii) an efficient training protocol that optimizes the variance of local energies. We demonstrate that this approach achieves subcm–1 accuracy for the vibrational ground and excited states of CH4 with substantially fewer parameters than the previous method requires. Crucially, for the prototypical water dimer (H2O)2, the new method successfully computes both ground state and intramolecular excited states with ∼1 cm–1 accuracy using ∼6000 NN parameters. This work establishes a robust and scalable framework for performing full-dimensional, fully coupled vibrational calculations on molecular complexes, providing an efficient approach for accurate spectroscopic predictions of such systems.