Representation of the CCSD Amplitude Equations

The leading term of H is just the electronic Hamiltonian itself. For its contribution to the Tj amplitude equation, we must evaluate the matrix elements, (Of l(/]sj + as before. Since these elements contain the reference 

For the contribution of to the T2 amplitude equation, we must evaluate the matrix element, (Of- l( N + Tn)I o)5 which contains the reference deter- 

The contribution of the second term of Eq. [122] to the amplitude equation is only slightly more complicated. This term involves the matrix element, and, as before, we will consider only the con- 

However, the first two of these fragments can connect to the T diagram in only one index—via either a single hole line or particle line—thus leaving an additional line extending below the Tj interaction line in the final diagram, for example, 

Because such diagrams cannot represent matrix elements that have the reference wavefunction on the right, only the third diagram above can contribute to 

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