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.
Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function.
Due to the long CPU time and large memory 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 configuration state functions (CSFs) built from spin orbitals (denoted by the superscript SO), where Ψ is usually the electronic ground state of the system.
If the expansion includes all possible CSFs of the appropriate symmetry, then this is a full configuration interaction procedure which exactly solves the electronic Schrödinger equation within the space spanned by the one-particle basis set.
If only one spin orbital differs, we describe this as a single excitation determinant.
An important problem of truncated CI methods is their size-inconsistency which means the energy of two infinitely separated particles is not double the energy of the single particle[clarification needed].
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
MRCI also gives better correlation of the ground state which is important if it has more than one dominant determinant.