The Configuration Interaction (CI) method is often employed by chemists
when studying atoms or small molecules. In this method
is minimised by searching through all 
which
are linear combinations of N-electron determinants made up from a
total of M basis states (M>>N). This is obviously impractical to do
thoroughly since there are
N-electron determinants and therefore the matrix to be diagonalised
has dimension 
. Hence Configuration Interaction calculations
usually only include determinants close to the Hartree-Fock ground
state determinant. This means ignoring all high energy states, so the
accuracy of these Configuration Interaction calculations is not as
good as results found using Quantum Monte Carlo. Configuration
Interaction calculations are not possible in solids due to the large
number of determinants which would be required, however they can
provide highly accurate results for small systems. In other words, CI
calculations scale very badly with system size.