Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

Kowalski, Karol

doi:10.1103/physreva.94.062512

Cited by 29 publications

(50 citation statements)

References 78 publications

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“…The earliest are from Nooijen and coworkers 22,23 while the most recent ones can be found in Ref. 13,[24][25][26]. These solve for the Green's function using linear equations on the real axis.…”

Section: Introductionmentioning

confidence: 99%

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Shee

Zgid

2019

J. Chem. Theory Comput.

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We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on a non-hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled 1D Hubbard model projected onto a single site impurity problem and a half-filled 2D Hubbard model projected onto a 4-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of the Green's function CCSD solver within the self-energy embedding theory (SEET) with Hartee-Fock (HF) and Green's function second order (GF2) for the treatment of the environment.

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Section: Introductionmentioning

confidence: 99%

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Shee

Zgid

2019

J. Chem. Theory Comput.

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“…This representation can be used to prove/derive basic properties of GFCC including connected character of Green's function matrix elements and their arbitraryorder ω-derivatives. [48,49] The possibility of calculating GFCC matrix and their ω-derivatives, through the Dyson equations, extends in a natural way to the corresponding self-energies. These properties enable one to calculate spectral functions, pole strengths, and other properties using GFCC method.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we further extend the analysis carried out in the previous papers. [ [46][47][48][49][50] In particular, motivated by the accuracy attainable by the GFCC model with singles, doubles, and triples (GFCCSDT) [47] we explore the possibilities of further improving accuracies of calculated pole locations by only increasing excitation level in the auxiliary inner operators X p (ω) and Y q (ω). To this end we discuss the general class of GFCC-i(n, m) approximations, where n is the rank of excitations included in the T and Λ operators, while m designates the excitation level used to define X p (ω) and Y q (ω) operators.…”

Section: Introductionmentioning

confidence: 99%

Green’s function coupled cluster formulations utilizing extended inner excitations

Kowalski

2018

The Journal of Chemical Physics

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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]

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“…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.…”

Section: Methodsmentioning

confidence: 99%

“…Alternatively, the CC Green's function matrix may be obtained directly in its analytic form [25][26][27] through the evaluation of a shifted set of linear systems involving the IP/EA-EOM-CC Hamiltonian at a frequency of interest [51,[62][63][64][65][66]. In the treatment of the GFCC method as a linear system, one is able to bypass the need for the evaluation of the eigenstates of the IP/EA-EOM-CC Hamiltonian explicitly, and in principle efficiently resolve the entire spectrum of the IP/EA-EOM-CC Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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

Beeumen

Williams‐Young

Kowalski

et al. 2019

J. Chem. Theory Comput.

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The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, more robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest which requires high resolution descriptions of spectral function, instead of solving GFCC linear equation of full dimension for every single frequency point of interest, an efficiently-solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematicallyimproved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct, the reduced order model obtained by this method is also found to provide a high quality initial guess which improves the convergence rate for the existing iterative linear solver.

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Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

Cited by 29 publications

References 78 publications

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods

Green’s function coupled cluster formulations utilizing extended inner excitations

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

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