# Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem.

@article{Levy1979UniversalVF, title={Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem.}, author={Mel Levy}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={1979}, volume={76 12}, pages={ 6062-5 } }

Universal variational functionals of densities, first-order density matrices, and natural spin-orbitals are explicitly displayed for variational calculations of ground states of interacting electrons in atoms, molecules, and solids. In all cases, the functionals search for constrained minima. In particular, following Percus [Formula: see text] is identified as the universal functional of Hohenberg and Kohn for the sum of the kinetic and electron-electron repulsion energies of an N-representable…

## 1,477 Citations

### Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number.

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The kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and the paper closes with an analogous point-wise property involving the external potential.

### Systematic construction of approximate one-matrix functionals for the electron-electron repulsion energy

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The Legendre transform of an (approximate) expression for the ground-state energy E0(η,g) of an N-electron system yields the one-matrix functional Vee[Γ(x′,x)] for the electron-electron repulsion…

### Assessment of simple exchange-correlation energy functionals of the one-particle density matrix

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An improved density matrix functional (DMF) combining the properties of the “corrected Hartree” (CH) and “corrected Hartree–Fock” (CHF) approximations is proposed. Functionals of the CH/CHF type and…

### Density Functional Theory

- Physics
- 1989

The formalism of density-functional theory for electronic structure is reviewed. Simplified proofs of the Hohenberg-Kohn existence theorems are given for ground states by employing the new…

### Bilinear Constraints Upon the Correlation Contribution to the Electron-Electron Repulsion Energy as a Functional of the One-Electron Reduced Density Matrix.

- MathematicsJournal of chemical theory and computation
- 2019

Perturbative analysis of the functional U[n,ψ] that yields the correlation component U of the electron-electron repulsion energy in terms of the vectors ψ(1) and n of the natural spinorbitals and…

### Orbital-free effective embedding potential: Density-matrix functional theory case

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- 2009

Minimization of the Hohenberg-Kohn total energy functional EHK [] in the presence of the constraint - B 0, where B is some arbitrarily chosen electron density comprising integer number of electrons…

### Exact analytic total energy functional for Hooke's atom generated by local-scaling transformations

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- 2004

An analytic closed form for the total energy density functional for Hooke's atom-an artificial two-electron system with harmonic electron-nuclear and Coulombic electron-electron interaction terms-has…

### The One-Electron Reduced Density Matrix Functional Theory of Spin-Polarized Systems.

- PhysicsJournal of chemical theory and computation
- 2020

Any implementation of DMFT based upon "two-index" 2C is shown to be generally unsuitable for spin-polarized systems (and incapable of yielding the spin-parallel components of U for thespin-unpolarization ones).

### Consequences for exchange energy density functional of exponentially decaying nature of atomic electron densities

- PhysicsJ. Comput. Chem.
- 1999

A simple model is studied for the atomic exchange energy density functional, which is based on the exponential decaying feature of the density and the Fermi–Amaldi model for exchange correlation. The…

### On the formulation of a density matrix functional for Van der Waals interaction of like- and opposite-spin electrons in the helium dimer.

- PhysicsThe Journal of chemical physics
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It is demonstrated that in principle the dispersion energy can be obtained from a density matrix functional, with distinct NO functionals for the different types of correlation that imply that they can be used in conjunction without problems of double counting.