This method is equivalent to computing the eigenvalues of the electronic molecular Hamiltonian within the basis set of the above-mentioned configuration state functions.
This is because exact solution of the full CI determinant is NP-complete[citation needed], so the existence of a polynomial time algorithm is unlikely.
Because full CI results are exact within the space spanned by the orbital basis set, they are invaluable in benchmarking approximate quantum chemical methods.
[citation needed] Although fewer N-electron functions are required if one employs a basis of spin-adapted functions (Ŝ2 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 coupled cluster wave functions to arbitrary orders, greatly simplifying the task of programming these complex methods.