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Updated: Jun 12, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Exploring Ground and Excited States Via Single Reference Coupled-Cluster Theory and Algebraic Geometry.

Svala Sverrisdóttir1, Fabian M Faulstich2

  • 1Department of Mathematics, The University of California, Berkeley, California 94720, United States.

Journal of Chemical Theory and Computation
|September 17, 2024
PubMed
Summary
This summary is machine-generated.

Computational chemists explored coupled cluster (CC) equations, finding multiple solutions accurately describe excited states. This research on four-electron systems advances quantum chemistry root structure understanding.

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Area of Science:

  • Computational quantum chemistry
  • Algebraic geometry
  • Theoretical chemistry

Background:

  • Coupled cluster (CC) equations are fundamental in computational quantum chemistry.
  • Understanding the root structure of CC equations is crucial for accurate chemical predictions.
  • Previous studies have not fully explored the complete solution set of CC equations.

Purpose of the Study:

  • To investigate the intricate root structures of coupled cluster (CCD and CCSD) equations.
  • To compare computed CC roots against theoretical upper bounds for accuracy and efficiency.
  • To assess the capability of single-reference CC methods in approximating excited state energies.

Main Methods:

  • Utilized algebraic geometry techniques, including monodromy and parametric homotopy continuation.
  • Calculated the full solution set of CC equations.
  • Focused on dissociation processes of four-electron systems: (H2)2, H4, and lithium hydride.

Main Results:

  • Computed CC roots were compared against established theoretical upper bounds.
  • Multiple CC roots were found to accurately describe excited state energies.
  • For systems like lithium hydride, CC methods approximated both excited state energies and the states themselves with high accuracy.

Conclusions:

  • The study provides significant insights into the root structure of CC equations.
  • CC methods demonstrate a strong capability in describing excited states accurately.
  • This work enhances the understanding and application of CC theory in computational chemistry.