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Numerical Methods for a Kohn-Sham Density Functional Model Based on Optimal Transport.

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This study presents numerical methods for strictly correlated electrons (SCE) models, extending beyond radial symmetry. We developed and applied these methods to the H2 molecule, improving the understanding of electron correlation in quantum chemistry.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Density functional theory (DFT) approximations struggle with strongly correlated electrons.
  • The strictly correlated electrons (SCE) framework offers an alternative by minimizing Coulomb repulsion.
  • Previous numerical studies were limited to radially symmetric electron densities.

Purpose of the Study:

  • To develop and analyze numerical discretizations for SCE density functional models.
  • To extend SCE methods to non-radially symmetric electron densities.
  • To apply these methods to a realistic molecular system, the H2 molecule.

Main Methods:

  • Mathematical derivation of self-consistent Kohn-Sham-SCE equations.
  • Construction of an efficient numerical discretization for N=2 electrons.
  • Application to the H2 molecule in its dissociating limit.

Main Results:

  • Successful implementation of numerical discretizations for SCE models beyond radial symmetry.
  • Demonstration of the method's applicability to the H2 molecule.
  • Insights into the behavior of strongly correlated electrons in a realistic chemical system.

Conclusions:

  • The developed numerical methods provide a viable approach for studying strongly correlated electrons in DFT.
  • The SCE framework, extended to non-radial densities, is a promising avenue for future quantum chemistry research.
  • This work lays the foundation for applying SCE methods to more complex systems.