Taylor-mode automatic differentiation for constructing molecular rovibrational Hamiltonian operators

TL;DR

This paper introduces an automated method utilizing automatic differentiation to construct high-order Taylor series expansions of rovibrational Hamiltonian operators for molecules, enabling efficient matrix element evaluations across various coordinate systems.

Contribution

It presents a novel framework that leverages Python's JAX library for automatic differentiation to generate rovibrational operators in a flexible and computationally efficient manner.

Findings

Automated generation of high-order Taylor expansions for rovibrational operators.

Efficient evaluation of matrix elements in product basis sets.

Flexible application to arbitrary molecules and coordinate systems.

Abstract

We present an automated framework for constructing Taylor series expansions of rovibrational kinetic and potential energy operators for arbitrary molecules, internal coordinate systems, and molecular frame embedding conditions. Expressing operators in a sum-of-products form allows for computationally efficient evaluations of matrix elements in product basis sets. Our approach uses automatic differentiation tools from the Python machine learning ecosystem, particularly the JAX library, to efficiently and accurately generate high-order Taylor expansions of rovibrational operators. The implementation is available at https://github.com/robochimps/vibrojet.