Green's function moments

[obackhouse]

I'd like to calculate expressions for the vectors

$$\bar{a}^\dagger_p | 0 \rangle$$

$$\bar{a}_p | 0 \rangle$$

$$\bar{a}^\dagger_p (1 + \Lambda) | 0 \rangle$$

$$\bar{a}_p (1 + \Lambda) | 0 \rangle$$

where $\bar{a}$ are similarity transformed (the rendering of the bars isn't that clear). These are essentially the bra and ket of the 1RDM expressions (they're for computing arbitrary order moments).

The expressions for CCSD should look like those in the appendix of this paper (the $p \neq q$ cases). I haven't managed to get the correct expressions, is this possible?