Hartree-Fock method
From apm
Revision as of 13:07, 7 June 2023 by Apm (Talk | contribs) (related section and link to Wikipedia page about Density functional theory)
(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)
Related
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:
