Difference between revisions of "Hartree-Fock method"

Revision as of 16:56, 14 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

• Hartree equation
• Fock space
• Fock state

More advanced metods for when there are unpaired electrons:

• Restricted open-shell Hartree–Fock (ROHF)
• Unrestricted Hartree–Fock (UHF)

To go beyond "mean field approximation" and beyond representability by slater detierminants there is:

• Post–Hartree–Fock