At the moment we will place this section into an appendix, although later we will include it in a section on realtionships with other methods. The equations given here are the standard approach to the relationship between CI and CC theory, but I have never found them to be particularly satisfying or enlightening.
The configuration interaction (CI) expansion may be written using a linear ansatz[44]
where
Since both CI and CC must give the exact answer in the limit,
If we expand the CI equations (B.2) and equate these with the CC equations (to orders of excitations) we find:
and
In general,
where the 
summations are over positive intgers. That is, all CI
excitation (even higher order excitations) include low-order cluster
operators. 
serves as an example. Even if the cluster operator
were truncated at 
, contributions to
all possible CI excitation operators would still be included. It should
be understood that although a non-linear ansatz is used to construct the
cluster operators, the resulting wavefunction is still a linear combination
of Slater determinants, just as in the CI method.
