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 linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

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. Mathematical ...

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 elect ...

s (or

configuration state function In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration. In general, one configuration gives rise to several CSFs; all have the same ...

s, 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 of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

s of the

electronic molecular Hamiltonian In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation p ...

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, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by tryi ...

, 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 excita ...

, 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 in ...

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