In this paper we derive basic properties of the Green's-function matrix elements stemming from the exponential coupled-cluster (CC) parametrization of the ground-state wave function. We demonstrate that all intermediates used to express the retarded (or, equivalently, ionized) part of the Green's function in the $\omega$ representation can be expressed only through connected diagrams. Similar properties are also shared by the first-order $\omega$ derivative of the retarded part of the CC Green's function. Moreover, the first-order $\omega$ derivative of the CC Green's function can be evaluated analytically. This result can be generalized to any order of $\omega$ derivatives. Through the Dyson equation, derivatives of the corresponding CC self-energy operator can be evaluated analytically. In analogy to the CC Green's function, the corresponding CC self-energy operator can be represented by connected terms. Our analysis can easily be generalized to the advanced part of the CC Green's function.

• Received 18 October 2016
• Revised 21 November 2016

DOI:https://doi.org/10.1103/PhysRevA.94.062512