Spherical densities and potentials in exactly solvable model molecules

Article Mathematics, Interdisciplinary Applications

Spherical Subspace Potential Functional Theory

Agnes Nagy

Summary: The recent version of density functional theory faces a challenge called 'set-representability problem' when using spherically symmetric densities. It is uncertain whether there exists a density for a given set of spherically symmetric densities. However, this problem can be solved by using potentials instead of densities as fundamental variables. Thus, the spherical subspace potential functional theory is developed.

COMPUTATION (2023)

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Article Physics, Mathematical

Orbital-free spherical density functional theory

Agnes Nagy

Summary: Recently, it has been proven that a set of spherically symmetric densities can uniquely determine the Coulomb external potential. Utilizing this theorem, a previous method has been extended to construct an orbital-free density functional theory. By defining spherical generating functions and generalized Pauli potentials, the Euler equations can be solved.

LETTERS IN MATHEMATICAL PHYSICS (2022)

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Article Chemistry, Physical

Spherical potential functional theory

A. Nagy

Summary: According to Theophilou's recent theorem, a set of spherically symmetric densities uniquely determines the external potential in molecules and solids, leading to a new formulation of density functional theory. However, the problem of representability arises: does a density exist for a given set of spherically symmetric densities? This problem has now been solved by using the potential instead of the density as a basic variable.

JOURNAL OF CHEMICAL PHYSICS (2021)

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Article Chemistry, Physical

Subspace theory with spherically symmetric densities

A. Nagy

Summary: Recently, it has been shown that a set of spherically symmetric non-degenerate densities can uniquely determine the Coulomb external potential. This theory has been extended to degenerate states, where Euler equations and Kohn-Sham equations are derived, and a new form of the virial theorem is presented. It is highlighted that degenerate states of atoms can be treated rigorously as spherically symmetric when a subspace density with equal weighting factors is used.

JOURNAL OF CHEMICAL PHYSICS (2021)

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Article Chemistry, Physical