# Natural Orbital Functional for the Many-Electron Problem

@article{Goedecker1998NaturalOF, title={Natural Orbital Functional for the Many-Electron Problem}, author={Stefan Goedecker and C. J. Umrigar}, journal={Physical Review Letters}, year={1998}, volume={81}, pages={866-869} }

The solution of the quantum mechanical many-electron problem is one of the central problems of physics. A great number of schemes that approximate the intractable many-electron Schrodinger equation have been devised to attack this problem. Most of them map the manybody problem to a self-consistent one-particle problem. Probably the most popular method at present is density functional theory (DFT) [1] especially when employed with the generalized gradient approximation (GGA) [2,3] for the…

## Tables from this paper

## 171 Citations

### Local Exchange Potentials in Density Functional Theory

- Physics
- 2014

DFT is a method that deals eciently with the ground state any-electron problem. It replaces the solution of the many-electron Schrodinger's equation with an equation to determine the electronic…

### Uniform Electron Gas from Two-Particle Wavefunctions

- Chemistry, Physics
- 2002

A common approach to the many-electron problem (atoms, molecules and solids) is its transformation into a fewer-particle problem. In Density Functional Theory1,2 (DFT) one rewrites the ground-state…

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

- Mathematics
- 2002

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…

### Natural Orbital Functional Theory

- Computer Science
- 2000

One of the central problems of solid state physics and quantum chemistry is to find an accurate and computationally affordable method for the description of electronic correlation that can be applied to large systems, particularly those with deep core electrons.

### Towards a practical pair density-functional theory for many-electron systems

- Physics
- 2004

In pair density-functional theory, the only unknown piece of the energy is the kinetic energy T as a functional of the pair density P(x{sub 1},x{sub 2}). Although T [P] has a simpler structure than…

### An approximate exchange-correlation hole density as a functional of the natural orbitals

- Physics
- 2002

The Fermi and Coulomb holes that can be used to describe the physics of electron correlation are calculated and analysed for a number of typical cases, ranging from prototype dynamical correlation to…

### Density Functional Theory I

- Physics
- 1996

A short overview is given of fundamentals of the modern Density Functional Theory (DFT), an alternative approach to the quantum many-body problem. Basic theorems of Hohenberg and Kohn (HK) are…

### Natural orbital functional for multiplets

- PhysicsPhysical Review A
- 2019

A natural orbital functional for electronic systems with any value of the spin is proposed. This energy functional is based on a new reconstruction for the two-particle reduced density matrix (2RDM)…

### Geminal functional theory: A synthesis of density and density matrix methods

- Physics
- 2000

The energy of any atom or molecule with an even number N of electrons is shown to be an exact functional of a single geminal where the functionals for both the kinetic energy and the external…

## References

SHOWING 1-10 OF 19 REFERENCES

### Density-functional theory of atoms and molecules

- Chemistry
- 1989

Current studies in density functional theory and density matrix functional theory are reviewed, with special attention to the possible applications within chemistry. Topics discussed include the…

### Phys

- 73, 1344 (1980); 73, 4653
- 1980

### Phys

- Rev. 136, B864
- 1964

### Phys

- Rev. 140, A1133
- 1965

### Phys

- Rev. A 55, 1765
- 1997

### Phys

- Rev. A 38, 3098 (1988); C. Lee, W. Yang and R. G. Parr, Phys. Rev. B 37, 785 (1988); B. Miehlich, A. Savin, H. Stoll and H. Preuss, Chem. Phys. Lett. 157, 200 (1988); J. P. Perdew and Y. Wang, Phys. Rev. B 33, 8800 (1986); J. P. Perdew, Phys. Rev. B 33, 8822 (1986); erratum ibid. 34, 7406
- 1986

### Phys

- 69, 4431 (1978); G. Zumbach and K. Maschke, J. Chem. Phys. 82, 5604
- 1985

### Theor

- Chim. Acta 1, 343
- 1963

### Phys

- Rev. Lett. 60, 1719 (1988); C.J. Umrigar, Phys. Rev. Lett. 71, 408 (1993); C.J. Umrigar, M.P. Nightingale and K.J. Runge, J. Chem. Phys. 99, 2865
- 1993