Hartree-Fock method - Revision history

Apm: related section and link to Wikipedia page about Density functional theory

2023-06-07T12:07:26Z

related section and link to Wikipedia page about Density functional theory

← Older revision		Revision as of 14:07, 7 June 2023
Line 16:		Line 16:
	'''Accounted for:'''		'''Accounted for:'''
	* Fermi correlation part of electron correlation (which is an effect of electron exchange)		* Fermi correlation part of electron correlation (which is an effect of electron exchange)

			== Related ==

			* [[Density of states]]
			* [[Density functional theory]]

	== External links ==		== External links ==
Line 41:		Line 46:
	Completely different methods:		Completely different methods:
	* [https://en.wikipedia.org/wiki/Category:Electronic_structure_methods Category:Electronic_structure_methods]		* [https://en.wikipedia.org/wiki/Category:Electronic_structure_methods Category:Electronic_structure_methods]
			* '''[https://en.wikipedia.org/wiki/Density_functional_theory Density functional theory]'''

Apm: /* External links */

2021-06-16T10:27:26Z

External links

← Older revision		Revision as of 12:27, 16 June 2021
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]

Apm: just a start for now

2021-06-14T15:56:08Z

just a start for now

New page

{{stub}}
{{wikitodo|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: [https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation 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. <br>This is the [https://en.wikipedia.org/wiki/Mean-field_theory '''mean field approximation'''] <br>=> Coulomb correlation part of electron correlation is not accounted for <br>=> The Hartree–Fock cannot capture [[London dispersion]]
'''Accounted for:'''
* Fermi correlation part of electron correlation (which is an effect of electron exchange)

== External links ==

* [https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Hartree-Fock method]
* [https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method#Hartree%E2%80%93Fock_algorithm Hartree–Fock algorithm]
* [https://en.wikipedia.org/wiki/Roothaan_equations Roothaan–Hall equations] – representation of the Hartree–Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type
* [https://en.wikipedia.org/wiki/Gaussian_orbital Gaussian orbital] & [https://en.wikipedia.org/wiki/Slater-ype_orbital Slater-type orbital]
* [https://en.wikipedia.org/wiki/Linear_combination_of_atomic_orbitals Linear combination of atomic orbitals]
* [https://en.wikipedia.org/wiki/Slater_determinant Slater determinant] for fermions (or "Slater permanent" for bosons)
* [https://en.wikipedia.org/wiki/Configuration_state_function Configuration state function]
* [https://en.wikipedia.org/wiki/Fock_matrix Fock operator / Fock matrix]
----
* [https://en.wikipedia.org/wiki/Hartree_equation Hartree equation]
* [https://en.wikipedia.org/wiki/Fock_space Fock space]
* [https://en.wikipedia.org/wiki/Fock_state Fock state]
----
More advanced metods for when there are unpaired electrons:
* [https://en.wikipedia.org/wiki/Restricted_open-shell_Hartree%E2%80%93Fock Restricted open-shell Hartree–Fock (ROHF)]
* [https://en.wikipedia.org/wiki/Unrestricted_Hartree%E2%80%93Fock Unrestricted Hartree–Fock (UHF)]
----
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]