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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Organic compounds with conjugated double bonds show strong absorption features in the UV–visible region of the electromagnetic spectrum attributed to π → π* electronic excitations. Generally, a UV–vis absorption spectrum is recorded as a plot of absorbance vs wavelength. The wavelength of maximum absorbance, which manifests as a peak in the absorption spectrum, is denoted as λmax.
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Computational optimal transport for molecular spectra: The fully continuous case.

Nathan A Seifert1,2, Kirill Prozument1, Michael J Davis1

  • 1Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.

The Journal of Chemical Physics
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Summary

Optimal transport offers a novel method for comparing molecular spectra, providing a more accurate measure of spectral differences than traditional approaches. This technique, using transport distances and maps, enhances quantitative spectral analysis and aids in refining theoretical models.

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Area of Science:

  • Computational chemistry
  • Spectroscopy
  • Data analysis

Background:

  • Comparing molecular spectra is crucial for understanding chemical systems.
  • Existing distance measures may not fully capture spectral differences.
  • Optimal transport provides a robust mathematical framework for comparing distributions.

Purpose of the Study:

  • To introduce and detail the application of computational optimal transport for analyzing differences between continuous molecular spectra.
  • To demonstrate the advantages of transport distances over conventional metrics for spectral comparison.
  • To explore the utility of transport maps for detailed spectral analysis and model refinement.

Main Methods:

  • Application of computational optimal transport algorithms to continuous molecular spectra.
  • Derivation and utilization of transport distances as a spectral difference metric.
  • Generation of transport maps to visualize and quantify spectral variations.
  • Analysis of model spectra and a real-world example (SO2 electronic absorption spectrum).

Main Results:

  • Transport distances are shown to be a more appropriate measure of spectral difference in many cases.
  • Transport maps provide detailed insights into spectral discrepancies.
  • The methodology allows for the adjustment of theoretical spectra (e.g., band origin, resolution) to match experimental data.
  • Successful application to comparing theoretical and experimental electronic absorption spectra of SO2.

Conclusions:

  • Computational optimal transport is a powerful tool for quantitative spectral comparison.
  • Transport distances and maps offer significant advantages over traditional methods.
  • This approach facilitates the refinement of theoretical molecular spectra based on experimental data.
  • Future applications in computational chemistry and spectroscopy are promising.