# Properties of the periodic Hartree-Fock minimizer

@article{Ghimenti2008PropertiesOT, title={Properties of the periodic Hartree-Fock minimizer}, author={Marco Ghimenti and Mathieu Lewin}, journal={arXiv: Mathematical Physics}, year={2008} }

We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.

## 2 Citations

### Some mathematical models in quantum chemistry and uncertainty quantification

- Mathematics
- 2012

The contributions of this thesis work are two fold. The first part deals with the study of local defects in crystalline materials. Chapter 1 gives a brief overview of the main models used in quantum…

### Periodic Hartree-Fock Theory

- Physics
- 2012

Die Hartree-Fock-Approximation (HF) ist die am haufigsten verwendete Approximationsmethode fur Viel-Fermionen-Systeme. Wir untersuchen periodische HF-Modelle, die die Elektronen in einem Kristall…

## References

SHOWING 1-10 OF 19 REFERENCES

### A New Approach to the Modeling of Local Defects in Crystals: The Reduced Hartree-Fock Case

- Physics
- 2008

This article is concerned with the derivation and the mathematical study of a new mean-field model for the description of interacting electrons in crystals with local defects. We work with a reduced…

### There are no unfilled shells in unrestricted Hartree-Fock theory.

- PhysicsPhysical review letters
- 1994

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the…

### Generalized Hartree-Fock theory and the Hubbard model

- Physics
- 1993

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices…

### On the convergence of SCF algorithms for the Hartree-Fock equations

- Mathematics
- 2000

The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting…

### Error bound for the Hartree-Fock energy of atoms and molecules

- Physics
- 1992

We estimate the error of the Hartree-Fock energy of atoms and molecules in terms of the one-particle density matrix corresponding to the exact ground state. As an application we show this error to be…

### The Hartree-Fock theory for Coulomb systems

- Mathematics
- 1977

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties…

### Solutions of Hartree-Fock equations for Coulomb systems

- Mathematics
- 1987

This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizäcker equation.

### Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

- Physics
- 1994

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z ∞. In this and a companion work (see [28]) we show that there are five regions…

### Variational principle for many-fermion systems

- Physics
- 1981

If ψ is a determinantal variational trial function for the N-fermion Hamiltonian, H, with one- and two-body terms, then e 0 ⩽ 〈 ψ,Hψ〉= E(K), where e 0 is the ground-state energy, K is the one-body…