In
computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of mo ...
, 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 is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons.
Ato ...
which is a more accurate way of including the repulsions between electrons than in the
Hartree–Fock method
In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.
The Hartree–Fock method ofte ...
where repulsions are only averaged.
Details
In general, the SCF procedure makes several assumptions about the nature of the multi-body
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
and its set of solutions:
* For molecules, the
Born–Oppenheimer approximation
In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and electro ...
is inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei.
* Typically,
relativistic effects are completely neglected. The
momentum operator
In quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimensio ...
is assumed to be completely nonrelativistic.
* The
basis set is composed of a finite number of
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
functions. The true wavefunction is a
linear combination of functions from a
complete
Complete may refer to:
Logic
* Completeness (logic)
* Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable
Mathematics
* The completeness of the real numbers, which implies ...
(infinite) basis set.
* The
energy eigenfunctions are assumed to be products of one-electron wavefunctions. The effects of
electron correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons.
Ato ...
, beyond that of exchange energy resulting from the
anti-symmetrization 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 interaction
Configuration interaction (CI) 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. Mathemati ...
(CI)
*
Coupled cluster
Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used ...
(CC)
*
Multi-configuration time-dependent Hartree Multi-configuration time-dependent Hartree (MCTDH) is a general algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. MCTDH can thus determine the quantal motio ...
(MCTDH,)
*
Møller–Plesset perturbation theory
Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post–Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation effects by m ...
(MP2, MP3, MP4, etc.)
*
Quadratic configuration interaction Quadratic configuration interaction (QCI) is an extension of configuration interaction that corrects for size-consistency errors in single and double excitation CI methods (CISD).
Size-consistency means that the energy of two non-interacting (i. ...
(QCI)
*
Quantum chemistry composite methods (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 field
Multi-configurational self-consistent field (MCSCF) 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 (e.g., for mole ...
(MCSCF)
*
Multireference single and double configuration interaction (MRCISD)
*
N-electron valence state perturbation theory (NEVPT).
References
Further reading
*
{{DEFAULTSORT:Post-Hartree-Fock
Quantum chemistry
Computational chemistry