Exploring New Algorithms for Molecular Vibrational Spectroscopy Using Physics-Informed Program Synthesis

Inductive program synthesis (PS) has recently begun to emerge as a useful new approach to automatically generate algorithms in quantum chemistry, as demonstrated in recent applications to the vibrational Schrödinger equation for simple model systems with one or two degrees-of-freedom. Here, we report a new physics-informed approach to inductive PS that is more conducive to the generation of discrete variable representation algorithms for real molecular systems. The new framework ensures separability of the kinetic and potential operators and does not require an exact solution to compare synthesized algorithmic predictions with. Algorithms with a tridiagonal matrix structure are generated via a variational-based stochastic optimization procedure. Crucially, through an extensive testing procedure, we demonstrate that variationally synthesized algorithms perform just as well as those generated using a target function. Assuming a direct product representation of normal coordinates, these algorithms are applied to three triatomic molecules. In total, we identify a set of seven PS algorithms that accurately reproduce the vibrational spectra of H₂O, NO₂, and SO₂, as predicted by Colbert-Miller and sine-DVR algorithms.