Green’s function coupled cluster formulations utilizing extended inner excitations

Abstract

In this paper we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potentials and electron affinities effects in the N −1 and N +1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N -electron system. Furthermore, we reveal the so-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 function matrix elements, the excitation level of inner auxiliary operators Xp(ω) and Yq(ω) cannot exceed n+1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e. the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. In comparison with the GFCCSD results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions. arXiv:1809.06884v3 [cond-mat.str-el]

Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction

“…Note that, in Fig. 4c (and its inset), by extrapolating the six-frequency model from the regime of [-304.77, -293.89] eV to [-326.57, -293.89] eV, three significant satellites, which were not reported in the previous GFCC-i (2,3) calculations, [66] are identified at -320.85, -315.41, and -308.88 eV, respectively (a weaker shoulder peak can also be seen at ∼-316.77 eV). The configuration analysis shows that these satellites are mainly attributed to the 1π −1 2σ −1 1π * two-electron process (classified as the so-called direct shake-up states), and are consistent with the configuration analysis of the satellites obtained from GFCCSD/GFCCSD-MOR To further test the efficiency of the proposed GFCC-MOR method, we examine its application to some larger systems.…”

“…Note that, due to stronger many-body effect in the inner valence regime, it usually requires much more effort for the linear solver to converge the GFCC linear system for the X p 's in that domain than it does for the X p 's in the outer valence regime. [65,66] Therefore, in comparison to the model in Fig. 1b, the model in Fig.…”

“…As discusseded in our previous work on this subject [51,[62][63][64][65][66], the practical calculation of GFCCSD matrix employing the above method involves the solution of the conventional To address this issue, in the context of high performance computing, one can divide the full computational task posed by the GFCC method into several smaller tasks according to the number of orbitals and frequencies desired. In so doing, one can distribute these smaller tasks over the available processors to execute them concurrently.…”

Coupled Cluster Green's function formulations based on the effective Hamiltonians

“…Moreover, we also assumed that Λ int = T † int (the efficiency of this approximation was discussed in Refs. [55]). (1)int , Q N −1…”

“…We demonstrated that the GFCCi(2,3) approximation can significantly improve the location of satellite peaks compared to the GFCCSD formalism. [55] For this reason we decided to combine the GFCC-i(2,3) approach with the DUCC effective Hamiltonians (DUCC-GFCC-i(2,3) approach).…”