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In this paper we analyze new approximations of the Green's function coupledcluster (GFCC) method where locations of poles are improved by extending theexcitation level of inner auxiliary operators. These new GFCC approximationscan be categorized as GFCC-i($n,m$) method, where the excitation level of theinner auxiliary operators ($m$) used to describe the ionization potentials andelectron affinities effects in the $N$$-$1 and $N$+1 particle spaces is higherthan the excitation level ($n$) used to correlate the ground-state coupledcluster wave function for the $N$-electron system. Furthermore, we reveal theso-called "$n$+1" rule in this category (or the GFCC-i($n$,$n$+1) method),which states that in order to maintain size-extensivity of the Green's functionmatrix elements, the excitation level of inner auxiliary operators$X_p(\omega)$ and $Y_q(\omega)$ cannot exceed $n$+1. We also discuss the roleof the moments of coupled cluster equations that in a natural way assures theseproperties. Our implementation in the present study is focused on the firstapproximation in this GFCC category, i.e. the GFCC-i(2,3) method. As our firstpractice, we use the GFCC-i(2,3) method to compute the spectral functions forthe N$_2$ and CO molecules in the inner and outer valence regimes. Incomparison with the GFCCSD results, the computed spectral functions from theGFCC-i(2,3) method exhibit better agreement with the experimental results andother theoretical results, particularly in terms of providing higher resolutionof satellite peaks and more accurate relative positions of these satellitepeaks with respect to the main peak positions.

Green's function coupled cluster formulations utilizing extended inner excitations