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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 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. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...
The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons (i. ...
Linus Pauling, as a pioneer of the valence bond theory, is one of the first quantum chemists. ...
A Slater determinant (named after the physicist John C. Slater) is an expression in quantum mechanics for the wavefunction of a many-fermion system, which by construction satisfies the Pauli principle. ...
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 SO), In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...
Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ...
 where Ψ is usually the electronic ground state of the system. If the expansion includes all possible Slater determinants 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. The first term in the above expansion is normally the Hartree-Fock determinant. The other determinants can be characterised by the number of spin orbitals that are different from those in the Hartree-Fock determinant. If only one spin orbital differs, we describe this as a single excitation determinant. If two spin orbitals differ it is a double excitation determiant and so on. This is used to limit the number of determinants in the expansion. For example, the method CID is limited to double excitations only. The method CISD is limited to single and double excitations. Single excitations on their own do not mix with the Hartree-Fock determinant. These methods, CID and CISD, are in many standard programs. When solving the CI equations, approximations to excited states are also obtained, which differ in the values of their coefficients cI. Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the given one-particle basis set) to the electronic Schrödinger equation. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...
In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...
The CI procedure leads to a general matrix eigenvalue equation: In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ...
 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.
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