Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the infinitely flexible complete basis set) to the electronic time-independent, non-relativistic

Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

Explanation

It is a special case of the

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 ...

method in which ''all''

Slater determinant In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two fermion ...

s (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

eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

s of the electronic molecular Hamiltonian within the basis set of the above-mentioned configuration state functions. 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. This is because exact solution of the full CI determinant is

NP-complete In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any ...

, so the existence of a polynomial time algorithm is unlikely. The Davidson correction is a simple correction which allows one to estimate the value of the full CI energy from a limited

expansion result. 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,

multireference configuration interaction In quantum chemistry, the multireference configuration interaction (MRCI) method consists of a configuration interaction expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinants which correspond to exci ...

, finite-order Møller–Plesset perturbation theory, and

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 ...

theory. Although fewer ''N''-electron functions are required if one employs a basis of spin-adapted functions (''Ŝ''² 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 C. Handy in 1980. In the 1980s and 1990s, full CI programs were adapted to provide arbitrary-order Møller–Plesset perturbation theory wave functions, and in the 2000s they have been adapted to provide

wave functions to arbitrary orders, greatly simplifying the task of programming these complex methods.

References

{{DEFAULTSORT:Full Configuration Interaction Quantum chemistry Theoretical chemistry Computational chemistry