Post-Hartree-Fock
Encyclopedia
In computational chemistry
, post-Hartree–Fock methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF) method. They add electron correlation
which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.
In general, the SCF procedure makes several assumptions about the nature of the multi-body Schrödinger equation
and its set of solutions:
For the great majority of systems under study, in particular for excited states and processes such as molecular dissociation reactions, the fourth item is by far the most important. As a result, the term post-Hartree–Fock method is typically used for methods of approximating the electron correlation of a system.
Usually, post-Hartree–Fock methods give more accurate results than Hartree–Fock calculations, although the added accuracy comes with the price of added computational cost.
Computational chemistry
Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids...
, post-Hartree–Fock methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF) method. They add electron correlation
Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.- Atomic and molecular systems :...
which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.
In general, the SCF procedure makes several assumptions about the nature of the multi-body Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
and its set of solutions:
- The Born–Oppenheimer approximation is inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei.
- Typically, relativisticSpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
effects are completely neglected. The momentum operatorMomentum operatorIn quantum mechanics, momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once...
is assumed to be completely classicalClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
. - The basis setBasis setBasis set can refer to:* Basis * Basis set...
is composed of a finite number of orthogonal functions. The true wavefunction is a linear combinationLinear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results...
of functions from a completeComplete spaceIn mathematical analysis, a metric space M is called complete if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M....
(infinite) basis set. - The energy eigenfunctions are assumed to be products of one-electron wavefunctions. The effects of electron correlation, beyond that of exchange energy resulting from the anti-symmetrizationFermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
of the wavefunction, are completely neglected.
For the great majority of systems under study, in particular for excited states and processes such as molecular dissociation reactions, the fourth item is by far the most important. As a result, the term post-Hartree–Fock method is typically used for methods of approximating the electron correlation of a system.
Usually, post-Hartree–Fock methods give more accurate results than Hartree–Fock calculations, although the added accuracy comes with the price of added computational cost.
Post-Hartree–Fock methods
- Configuration interactionConfiguration interactionConfiguration interaction is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination...
(CI) - Coupled clusterCoupled clusterCoupled cluster is a numerical technique used for describing many-body systems. Its most common use is as one of several quantum chemical post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry...
(CC) - Møller–Plesset perturbation theory (MP2, MP3, MP4, etc.)
- Quadratic configuration interactionQuadratic configuration interactionQuadratic configuration interaction is an extension of Configuration interaction that corrects for size-consistency errors in the all singles and double excitation CI methods ....
(QCI) - Quantum chemistry composite methodsQuantum chemistry composite methodsQuantum chemistry composite methods are computational chemistry methods that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set with methods that employ lower levels of theory with larger basis sets...
(G2, G3, CBS, T1. etc.)
Related methods
Methods that use more than one determinant are not strictly post-Hartree–Fock methods, as they use a single determinant as reference, but they often use similar perturbation, or configuration interaction methods to improve the description of electron correlation. These methods include:- Multi-configurational self-consistent fieldMulti-configurational self-consistent fieldMulti-configurational self-consistent field is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate...
(MCSCF) - Multireference single and double configuration interactionMultireference configuration interactionIn quantum chemistry, the multireference configuration interaction method consists in a configuration interaction expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinants which correspond to excitations of the ground state electronic configuration but...
(MRDCI) - N-electron valence state perturbation theoryN-Electron Valence state Perturbation TheoryIn quantum chemistry, n-electron valence state perturbation theory is a perturbative treatment applicable to multireference CASCI-type wavefunctions. It can be considered as a generalization of the well-known second-order Møller-Plesset perturbation theory to multireference Complete Active Space...
(NEVPT).