Taylor-mode automatic differentiation for constructing molecular rovibrational Hamiltonian operators

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.