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Circulant orbitals for atoms and molecules.

R G Parr1, M B Chen

  • 1Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27514.

Proceedings of the National Academy of Sciences of the United States of America
|March 1, 1981
PubMed
Summary

Circulant orbitals offer a new perspective on closed-shell systems by transforming canonical Hartree-Fock orbitals. These orbitals yield electron densities close to the average and a Hermitian circulant Fock matrix.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Canonical Hartree-Fock orbitals are fundamental in electronic structure calculations.
  • Understanding orbital properties is crucial for accurate molecular modeling.

Purpose of the Study:

  • To introduce and analyze circulant orbitals derived from Hartree-Fock orbitals.
  • To investigate the properties of electron density and the Fock matrix for these new orbitals.

Main Methods:

  • A unitary transformation, specifically the discrete Fourier transform, was applied to canonical Hartree-Fock orbitals.
  • The properties of the resulting circulant orbitals and their associated Fock matrix were analyzed.

Main Results:

  • Circulant orbitals result in electron densities closely approximating the average total electron density.

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  • The Fock matrix for circulant orbitals is a Hermitian circulant matrix, distinct from the diagonal matrix of canonical orbitals.
  • The states generated by applying the Fock operator to circulant orbitals are uniformly distributed in Hilbert space.

    • Conclusions:

    • Circulant orbitals provide an alternative representation of electronic structure in closed-shell systems.
    • The mathematical properties of circulant orbitals and their Fock matrix offer insights into electronic distributions and state behavior.