Exploring New Algorithms\nfor Molecular Vibrational\nSpectroscopy Using Physics-Informed Program Synthesis

Inductive program\nsynthesis (PS) has recently begun to\nemerge as\na useful new approach to automatically generate algorithms in quantum\nchemistry, as demonstrated in recent applications to the vibrational\nSchrödinger equation for simple model systems with one or two\ndegrees-of-freedom. Here, we report a new physics-informed approach\nto inductive PS that is more conducive to the generation of discrete\nvariable representation algorithms for real molecular systems. The\nnew framework ensures separability of the kinetic and potential operators\nand does not require an exact solution to compare synthesized algorithmic\npredictions with. Algorithms with a tridiagonal matrix structure are\ngenerated via a variational-based stochastic optimization procedure.\nCrucially, through an extensive testing procedure, we demonstrate\nthat variationally synthesized algorithms perform just as well as\nthose generated using a target function. Assuming a direct product\nrepresentation of normal coordinates, these algorithms are applied\nto three triatomic molecules. In total, we identify a set of seven\nPS algorithms that accurately reproduce the vibrational spectra of\nH<sub>2</sub>O, NO<sub>2</sub>, and SO<sub>2</sub>, as predicted by\nColbert–Miller and sine-DVR algorithms.