The CI methods converge very slowly to the exact result. This is related to
the fact that they do not contain arbitrary high substitution levels. Of course,
considering arbitrary high levels one would end up with full CI.
However, the coefficients of the individual substitution levels show a certain
structure: Coefficients of higher substitution levels may be approximately
expressed by coefficients of lower substitution levels. Consider two
coinciding substitutions. If these two coinciding
substitutions are statistically independent (non-interacting fragments) the
coefficient is given exactly by the product of the individual substitutions. If the
two fragments do interact the product form is no longer exact but it is
usually still
a very good approximation. Exactly this product form of the coefficients of the
wavefunction expansion is assembled by coupled cluster methods. In other words:
CI spends a lot of effort on calculating the coefficients of higher substitution levels
while coupled cluster incorporates a very good guess for the coefficients
of the higher substitution levels by means of the product form. One may say
that coupled cluster collects "pure" correlation effects at each substitution level
while CI additionally has to collect a lot of redundancy. Since the "pure" correlation effects
at high substitution levels usually decrease rapidly the coupled cluster ansatz
turns out to be very efficient at describing dynamical correlation effects.
However, there is a price one has to pay: The generalization of the
coupled cluster method to include static correlation (multi-refence ansatz)
is no longer trivial as for the CI methods.