Perturbative Solution to the Coupled-Cluster Equations

scribe here how Eq. (4.19) may be solved in a manner that shows the connection between the CC and the MBPT approaches. We solve 

Inserting this value of into the CC expression for the total energy as given in Eq. (4.16) yields 

This expression is nothing but the result obtained in second-order perturbation theory, which is written explicitly in Eq. (3.38). 

The iterative process carried out when determining the cluster amplitudes from Eq. (4.19) may be continued by inserting the cluster amplitudes from one iteration into the right-hand side of Eq. (4.19) to obtain the new ampli- 

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