Computational optimal transport for molecular spectra: The semi-discrete case

Area of Science:

• Computational chemistry
• Spectroscopy
• Applied mathematics

Background:

• Comparing discrete theoretical spectra (e.g., stick spectra) to continuous experimental spectra is a significant challenge in molecular spectroscopy.
• Traditional methods like least-squares fitting can be difficult to apply due to the nature of continuous and discrete data.
• Optimal transport theory provides a mathematical framework for comparing probability distributions, which can be adapted for spectral analysis.

Purpose of the Study:

• To investigate the application of computational optimal transport for quantitatively comparing discrete and continuous molecular spectra.
• To introduce and explain the concept of semi-discrete optimal transport in the context of molecular spectroscopy.
• To demonstrate the utility of optimal transport distance for spectral analysis using synthetic and experimental data.

Main Methods:

• Utilizing the optimal transport distance, specifically tailored for the semi-discrete case, to compare spectral data.
• Developing a tutorial on applying semi-discrete optimal transport to molecular spectra.
• Analyzing synthetic spectra to understand the impact of frequency resolution on spectral comparison.
• Applying the method to compare a theoretical stick spectrum with an experimental electronic absorption spectrum of sulfur dioxide (SO2).

Main Results:

• The study demonstrates that optimal transport provides a robust metric for comparing discrete and continuous molecular spectra.
• Calculations show how the frequency resolution of continuous spectra influences the transport distance to discrete spectra.
• The optimal transport distance was successfully used to compare experimental and theoretical SO2 spectra.
• A refined theoretical value for the SO2 band origin was proposed, showing improved agreement with experimental observations.

Conclusions:

• Computational optimal transport, specifically semi-discrete optimal transport, is a powerful and versatile tool for quantitative spectral comparison.
• This method offers advantages over traditional techniques, particularly when dealing with discrete and continuous spectral data.
• The application to SO2 spectra highlights the potential for improving theoretical models and spectral analysis in computational chemistry and spectroscopy.