Difference between revisions of "Hartree-Fock method"
From apm
(just a start for now) |
m (→External links) |
||
| Line 38: | Line 38: | ||
To go beyond "mean field approximation" and beyond representability by slater detierminants there is: | To go beyond "mean field approximation" and beyond representability by slater detierminants there is: | ||
* [https://en.wikipedia.org/wiki/Post%E2%80%93Hartree%E2%80%93Fock Post–Hartree–Fock] | * [https://en.wikipedia.org/wiki/Post%E2%80%93Hartree%E2%80%93Fock Post–Hartree–Fock] | ||
| + | ---- | ||
| + | Completely different methods: | ||
| + | * [https://en.wikipedia.org/wiki/Category:Electronic_structure_methods Category:Electronic_structure_methods] | ||
Revision as of 12:27, 16 June 2021
(wiki-TODO: Extend on this)
The following is basically taken from wikipedia and reformulated in an hopefully more readable way.
Assumptions:
- the exact N-body wave function of the system can be approximated by a single Slater determinant
- the wave function is a single configuration state function with well-defined quantum numbers
- a quantum many-body system in a stationary state BUT the energy level is not necessarily the ground state
- Restricted Hartree–Fock method: The atom or molecule is a closed-shell system with all orbitals doubly occupied.
Approximations:
- atomic cores as static point particles: Born–Oppenheimer approximation
- nonrelativistic (classical momentum operator)
- all energy eigenfunctions are describable by Slater-determinants. One Slater-determinant per eigenfunction.
- An electron "sees" all other electrons as an averaged out density cloud.
This is the mean field approximation
=> Coulomb correlation part of electron correlation is not accounted for
=> The Hartree–Fock cannot capture London dispersion
Accounted for:
- Fermi correlation part of electron correlation (which is an effect of electron exchange)
External links
- Hartree-Fock method
- Hartree–Fock algorithm
- Roothaan–Hall equations – representation of the Hartree–Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type
- Gaussian orbital & Slater-type orbital
- Linear combination of atomic orbitals
- Slater determinant for fermions (or "Slater permanent" for bosons)
- Configuration state function
- Fock operator / Fock matrix
More advanced metods for when there are unpaired electrons:
To go beyond "mean field approximation" and beyond representability by slater detierminants there is:
Completely different methods:
