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Optimal Transport Distances to Characterize Electronic Excitations.

Annina Z Lieberherr1, Paola Gori-Giorgi2,3, Klaas J H Giesbertz2

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Summary

This study introduces a new optimal transport diagnostic (Θ) for classifying electronic excitations in computational chemistry. While showing promise, Θ has limitations with charge transfer and Rydberg excitations, suggesting combined approaches for better accuracy.

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Area of Science:

  • Computational Chemistry
  • Theoretical Chemistry
  • Quantum Mechanics

Background:

  • Classifying electronic excitations from simulations is crucial for computational and mechanistic studies.
  • Optimal transport distances offer a powerful framework for classification tasks.

Purpose of the Study:

  • To propose and evaluate a novel diagnostic (Θ) based on Sinkhorn divergence for electronic excitation characterization.
  • To compare the performance of Θ against the established Λ diagnostic and their combination.

Main Methods:

  • Utilized Sinkhorn divergence from optimal transport to develop the Θ diagnostic.
  • Employed a k-nearest neighbors (k-NN) classification algorithm.
  • Assessed performance on labeling electronic excitations, including Rydberg and charge transfer types.

Main Results:

  • The new diagnostic (Θ) showed limitations, particularly for charge transfer excitations in small molecules.
  • Rydberg excitations were poorly separated across all tested methods.
  • A length-scale-normalized version of Θ correlated well with the Λ diagnostic for Gaussian basis sets.

Conclusions:

  • The proposed diagnostic (Θ) offers a new perspective but requires further refinement for broad applicability.
  • Combined optimal transport and overlap diagnostics with alternative metrics show the most potential for future excitation classification.