What is the Hartree-Fock model?

Hartree-Fock theory is fundamental to much of electronic structure theory. It is the basis of molecular orbital (MO) theory, which posits that each electron’s motion can be described by a single-particle function (orbital) which does not depend explicitly on the instantaneous motions of the other electrons.

Why is Hartree-Fock self consistent?

Due to the nonlinearities introduced by the Hartree–Fock approximation, the equations are solved using a nonlinear method such as iteration, which gives rise to the name “self-consistent field method”.

What is the Hartree-Fock limit?

This limiting energy is the lowest that can be obtained with a single determinant wavefunction. This limit is called the Hartree-Fock limit, the energy is the Hartree-Fock energy, the molecular orbitals producing this limit are called Hartree-Fock orbitals, and the determinant is the Hartree-Fock wavefunction.

What is the Hartree potential?

The Hartree potential is defined as the electrostatic potential from the electron charge density and must be calculated from the Poisson equation: ∇2VH[n](r)=−4πn(r). ∇ 2 V H [ n ] ( r ) = − 4 π n ( r ) .

What is the application of the jellium model in physics?

Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as screening, plasmons, Wigner crystallization and Friedel oscillations.

What is the physics of the zero-temperature phase behavior of jellium?

The physics of the zero-temperature phase behavior of jellium is driven by competition between the kinetic energy of the electrons and the electron-electron interaction energy. The kinetic-energy operator in the Hamiltonian scales as

Why does jellium form a Wigner crystal?

As a result, jellium at zero temperature at a sufficiently low density will form a so-called Wigner crystal, in which the single-particle orbitals are of approximately Gaussian form centered on crystal lattice sites.