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. It is a special case of the configuration interaction method in which all Slater determinants (or configuration state functions, CSFs) of the proper symmetry are included in the variational procedure (i.e. all Slater determinants obtained by exciting all possible electrons to all possible virtual orbitals, orbitals which are unoccupied in the electronic ground state configuration). This method is equivalent to computing the eigenvalues of the electronic molecular Hamiltonian within the basis set of the above mentioned configuration state functions. The variational method is, in quantum mechanics, one way of finding approximations to the lowest energy eigenstate or ground state. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... Configuration interaction (CI) is a variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a multi-electron system. ... 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 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. ... The electronic Hamiltonian for a multi-electron molecule in atomic units is: where is the vector position of electron with vector components in Bohr radii, is the charge of fixed nucleus a in units of the elementary charge, is the vector position of nucleus with vector components in Bohr radii. ...

In a minimal basis set a full CI computation is very easy. But in larger basis sets this is usually just a limiting case which is not often attained. The Davidson correction is a simple correction which allows one to estimate the value of the full-CI energy from a limited configuration interaction expansion result. In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... Configuration interaction (CI) is a variational method for solving the nonrelativistic Schrödinger equation within the Born-Oppenheimer approximation for a multi-electron system. ...

Because the number of determinants required in the full-CI expansion grows factorially with the number of electrons and orbitals, full CI is only possible for atoms or very small molecules with about a dozen or fewer electrons. Full CI problems including several million up to a few billion determinants are possible using current algorithms. Because full CI results are exact within the space spanned by the orbital basis set, they are invaluable in benchmarking approximate quantum chemical methods. This is particularly important in cases such as bond-breaking reactions, diradicals, and first-row transition metals, where electronic near-degeneracies can invalidate the approximations inherent in many standard methods such as Hartree-Fock theory, finite-order Møller-Plesset perturbation theory, and coupled cluster theory. 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. ... Møller-Plesset perturbation theory is an implementation of perturbation theory in quantum chemistry, which provides a method for adding excitations to the Hartree-Fock wavefunction and therefore including the effect of electron correlation. ... Coupled cluster method is a technique used for description of the many-body systems. ...

Although fewer N-electron functions are required if one employs a basis of spin-adapted functions ( eigenfunctions), the most efficient full CI programs employ a Slater determinant basis because this allows for the very rapid evaluation of coupling coefficients using string-based techniques advanced by Nicholas Handy in 1980. In the 1980's and 1990's, full CI programs were adapted to provide arbitrary-order Møller-Plesset perturbation theory wave functions, and in the 2000's they have been adapted to provide coupled cluster wave functions to arbitrary orders, greatly simplifying the task of programming these complex methods. Møller-Plesset perturbation theory is an implementation of perturbation theory in quantum chemistry, which provides a method for adding excitations to the Hartree-Fock wavefunction and therefore including the effect of electron correlation. ... Coupled cluster method is a technique used for description of the many-body systems. ...