Highly correlated configuration interaction (CI)
wavefunctions going beyond the simple singles and doubles
(CISD) model space can provide very reliable potential
energy surfaces, describe electronic excited states, and
yield benchmark energies and molecular properties for use
in calibrating more approximate methods. Unfortunately,
such wavefunctions are also notoriously difficult to
evaluate due to their extreme computational demands. The
dimension of a full CI procedure, which represents the
exact solution of the electronic Schroedinger equation for
a fixed one-particle basis set, grows factorially with the
number of electrons and basis functions. For very large
configuration spaces, the number of CI coupling
coefficients becomes prohibitively large to store on disk;
these coefficients must be evaluated as needed in a
so-called direct CI procedure. Work done by several groups
since 1980 has focused on using Slater determinants rather
than spin (S^{2}) eigenfunctions because coupling
coefficients are easier to compute with the former. We
review the fundamentals of the configuration interaction
method and discuss various determinant-based CI algorithms.
Additionally, we consider some applications of highly
correlated CI methods.