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

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Algorithm Development

Background:

• Program synthesis (PS) is an emerging technique for automatically generating algorithms.
• Previous applications of PS in quantum chemistry were limited to simple systems.
• Existing methods often require exact solutions for comparison.

Purpose of the Study:

• To develop a physics-informed inductive program synthesis framework for generating discrete variable representation (DVR) algorithms.
• To create algorithms suitable for real molecular systems without needing exact solutions.
• To validate the performance of synthesized algorithms against established methods.

Main Methods:

• A new physics-informed inductive program synthesis approach was developed.
• The framework ensures separability of kinetic and potential operators.
• Algorithms with a tridiagonal matrix structure were generated using variational-based stochastic optimization.

Main Results:

• Variationally synthesized algorithms demonstrated performance comparable to those generated using a target function.
• Seven program synthesis algorithms were identified.
• These algorithms accurately reproduced the vibrational spectra of H₂O, NO₂, and SO₂.

Conclusions:

• The developed physics-informed program synthesis framework is effective for generating accurate quantum chemistry algorithms.
• The synthesized algorithms are suitable for analyzing vibrational spectra of real molecular systems.
• This approach offers a viable alternative to traditional methods for algorithm generation in computational chemistry.