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Variations of the Hartree-Fock fractional-spin error for one electron
Hugh G A Burton1, Clotilde Marut2, Timothy J Daas3
1Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, United Kingdom.
Fractional-spin errors in density functional approximations, like Hartree-Fock, are reduced in one-electron systems. Methods like unrestricted and generalized Hartree-Fock minimize these errors by localizing electrons or rotating spin coordinates.
Area of Science:
- Quantum Chemistry
- Computational Physics
Background:
- Fractional-spin errors are a known issue in approximate density functionals.
- These errors are often linked to strong static correlation effects.
Purpose of the Study:
- To investigate the Hartree-Fock fractional-spin error in one-electron systems.
- To analyze error minimization strategies using different ensemble densities and the generalized Hartree-Fock approach.
Main Methods:
- Examining restricted and unrestricted ensemble densities.
- Utilizing the exact generalized Hartree-Fock representation.
- Studying the hydrogen atom and H+2 cation.
Main Results:
- Unrestricted and generalized Hartree-Fock schemes reduce fractional-spin errors by localizing electrons or rotating spin coordinates.
- A similarity was found between the Coulomb hole in He-like ions and density depletion from fractional-spin errors in hydrogen.
Conclusions:
- The study provides insights into minimizing fractional-spin errors in quantum chemistry calculations.
- Understanding these errors is crucial for developing more accurate density functionals.
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