Computing excited states of molecules using normalizing flows

TL;DR

This paper introduces a novel method using normalizing flows to learn optimal vibrational coordinates, significantly improving the accuracy and efficiency of calculating highly excited vibrational states in molecules.

Contribution

The paper presents a new approach leveraging normalizing flows to optimize vibrational coordinates, enhancing basis-set convergence and transferability across basis truncations.

Findings

Accurately computes 100 lowest vibrational states of molecules.

Improves basis-set convergence and coordinate transferability.

Enhances vibrational state separability for better quantum number assignment.

Abstract

Calculations of highly excited and delocalized molecular vibrational states are computationally challenging tasks, which strongly depends on the choice of coordinates for describing vibrational motions. We introduce a new method that leverages normalizing flows -- parametrized invertible functions -- to learn optimal vibrational coordinates that satisfy the variational principle. This approach produces coordinates tailored to the vibrational problem at hand, significantly increasing the accuracy and enhancing basis-set convergence of the calculated energy spectrum. The efficiency of the method is demonstrated in calculations of the 100 lowest excited vibrational states of H$_2$S, H$_2$CO, and HCN/HNC. The method effectively captures the essential vibrational behavior of molecules by enhancing the separability of the Hamiltonian and hence allows for an effective assignment of approximate quantum numbers. We demonstrate that the optimized coordinates are transferable across different levels of basis-set truncation, enabling a cost-efficient protocol for computing vibrational spectra of high-dimensional systems.