What is the Difference Between Hartree and Hartree-Fock Method?

The Hartree and Hartree-Fock methods are both self-consistent field methods used in computational physics and chemistry to approximate the values of energy and wavefunctions of a system. However, there are key differences between the two methods:

1. Wavefunction Type: The Hartree method uses a bosonic wave function, which is symmetric with respect to the interchange of particles. On the other hand, the Hartree-Fock method uses a fermionic wave function, specifically a Slater determinant, which takes into account the anti-symmetry property of the wavefunction.
2. Electron Correlation: Both methods account for electron-electron interactions in an average way. However, the Hartree-Fock method is considered more accurate than the Hartree method because it uses antisymmetrized wavefunctions, which provide a better description of the electronic structure.
3. Self-Consistent Field Method: Both methods involve a self-consistent field method, but the Hartree-Fock method is an improvement over the Hartree method due to its use of a more appropriate wavefunction.

In summary, the main difference between the Hartree and Hartree-Fock methods is the type of wavefunction used, with the Hartree-Fock method being more accurate due to its use of antisymmetrized wavefunctions.

Comparative Table: Hartree vs Hartree-Fock Method

The Hartree method and the Hartree-Fock method are both computational methods for approximating the solution of many-body electron problems in atoms, molecules, and solids. Here is a table summarizing the differences between the two methods:

The Hartree method is an earlier approach that ignores electron-electron interactions and uses single-electron orbitals to describe atomic systems as hydrogen-like atoms. It is not an approximation but rather an exact solution for specific cases. On the other hand, the Hartree-Fock method is an improved method that combines Hartree's work with Fock's, accounting for electron-electron interactions and using orbitals for multiple electrons, including spin orbitals. The Hartree-Fock method often assumes that the exact N-body wave function can be expressed as a Slater determinant, which is a determinant of one-particle orbitals first used by Heisenberg and Dirac in 1926.