Coupled cluster

About: Coupled cluster is a research topic. Over the lifetime, 6280 publications have been published within this topic receiving 301055 citations.

The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei

Abstract: We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell- model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies

Abstract: The contributions from various excitation levels to excitation energies calculated within a coupled cluster framework are analyzed in terms of order in the fluctuation potential. In particular, the role of triple excitations is considered, focusing on their importance for describing excitations of single and double replacement dominated character. Several noniterative triples corrections to the coupled cluster singles and doubles (CCSD) excitation energies are proposed. In the CCSDR(3) approach, which is a noniterative analog to the recently proposed iterative CC3 model, single replacement dominated excitations are correct through third order in the fluctuation potential, and double replacement dominated excitations are correct through second order. The performance of CCSDR(3) is compared to other noniterative and iterative triples models in benchmark calculations on CH+, Ne, BH, and CH2.

A short-range gradient-corrected density functional in long-range coupled-cluster calculations for rare gas dimers

Abstract: A previously proposed scheme for coupling short-range (sr) density functionals with wavefunction-based long-range (lr) ab initio methods has been extended by (a) developing a new gradient-corrected sr functional of the Perdew–Burke–Ernzerhof (PBE) type and (b) introducing coupled-cluster (CC) approaches (CC with single and double excitations (CCSD), and with additional perturbative triples (CCSD(T))) at the ab initio side. The results show that mixing-in of lr-ab initio correlation helps to remove deficiencies of currently used density functionals for the treatment of van-der-Waals interactions. Compared to full ab initio calculations, the basis set dependence is weaker so that the accuracy of the mixed results surpasses that of the ab initio ones for basis sets of triple-zeta quality.

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory

Abstract: The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.