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Configuration interaction: Difference between revisions

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* [[Post Hartree-Fock]]
* [[Post Hartree-Fock]]
* [[Electron correlation]]
* [[Electron correlation]]
* [[Multi reference configuration interaction]]
* [[Multireference configuration interaction]]


[[Category:Quantum chemistry]]
[[Category:Quantum chemistry]]

Revision as of 09:33, 18 July 2005

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. Two meanings are connected to the term configuration interaction in this context. Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), interaction means the mixing (interaction) of different electronic configurations (states). Due to the long CPU time and immense hardware required for CI calculations, the method is limited to relatively small systems.

In contrast to the Hartree-Fock method, in order to account for electron correlation, CI uses a variational wave function that is a linear combination of determinant built from spin orbitals (denoted by the superscript SD),

where Ψ is usually the electronic ground state of the system. When solving the CI equations, approximations to excited states are also obtained, which differ in the values of their coefficients cI.

Two meanings are connected to the term configuration interaction in this context. Mathematically, configuration simply describes the linear combination used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), interaction means the mixing (interaction) of different electronic configurations (states).

The CI procedure leads to a general matrix eigenvalue equation:

where c is the coefficient vector, e is the eigenvalue matrix, and the elements of the hamiltonian and overlap matrices are, respectively,

,
.

Slater determinants are constructed from sets of orthonormal spin orbitals, so that , making the identity matrix and simplifying the above matrix equation.

See also