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Coupled cluster

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


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TL;DR: In this paper, a new implementation of the orthogonally spin-adapted open-shell (OS) coupled-cluster (CC) formalism that is based on the unitary group approach to many-electron correlation problem is described.
Abstract: A new implementation of the orthogonally spin‐adapted open‐shell (OS) coupled‐cluster (CC) formalism that is based on the unitary group approach to many‐electron correlation problem is described. Although the emphasis is on the so‐called state specific single‐reference but multiconfigurational OS CC approach, the developed algorithms as well as the actual codes are also amenable to multireference CC applications of the state‐universal type. A special attention is given to simple OS doublets and OS singlet and triplet cases, the former being applicable to the ground states of radicals and the latter to the excited states of closed shell systems. The encoding of the underlying formalism is fully automated and is based on a convenient decomposition of the Hamiltonian into the effective zero‐, one‐, and two‐orbital contributions as well as on the general strategy that focuses on the excitation operator driven evaluation of individual absolute, linear, quadratic, etc., coupled cluster coefficients, rather than on the standard molecular (spin) orbital driven algorithms. In this way unnecessary duplications are avoided and efficient codes are developed both for the general formula generation and final executable modules. A thorough testing of this procedure on a number of model cases is described and several illustrative applications at the ab initio level are provided.

156 citations

Journal ArticleDOI
TL;DR: The atomization energies of these clusters display much stronger basis set dependence than the clustering energies, which allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustered energies.
Abstract: The (TiO2)n clusters and their anions for n = 1−4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-ζ level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of for...

156 citations

Journal ArticleDOI
TL;DR: The in-medium similarity renormalization group (IM-SRG) for open-shell nuclei is formed using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry, and is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-n nucleon and three-nucleon interactions.
Abstract: We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.

155 citations

Journal ArticleDOI
TL;DR: In this research a program has been written in the C programming language which can efficiently compute the quasivacuum expectation value of a product of creation and annihilation operators and scalar arrays and which has been applied to open-shell coupled cluster theory.
Abstract: Theoretical methods in chemistry frequently involve the tedious solution of complex algebraic equations. Then the solutions, sometimes still quite complex, are usually hand-coded by a programmer into an efficient computer language. During this procedure it is all too easy to make an error which will go undetected. A better approach would be to introduce the computer at an even earlier stage in the development of the theory by programming it to first solve the set of equations and then compile the solution into an efficient computer language. In this research a program has been written in the C programming language which can efficiently compute the quasivacuum expectation value of a product of creation and annihilation operators and scalar arrays. The terms in the resulting expressions are then transformed into a canonical form so that all equivalent terms can be combined. Finally, the equations are compiled into a simple representation which can be rapidly interpreted by a Fortran program. This symbol manipulator has been applied to open-shell coupled cluster theory. Two coupled cluster methods using high-spin open-shell references are presented. In one of these methods, the cluster operator contains the unitary group generators, and products thereof, which generate all single and double excitations with respect to the reference. The other uses a simplified cluster operator which generates equations that must be spin-projected. These methods are compared to other descriptions of electron correlation for the CH2 singlet-triplet splitting and the NH2 potential energy surface.

155 citations

Journal ArticleDOI
TL;DR: A formal analysis shows that the ic-MRCC method is invariant with respect to rotation among active orbitals, and that the orthogonalization procedure used to produce the set of linearly independent excitation operators plays a crucial role in guaranteeing the invariance properties.
Abstract: We have formulated and implemented an internally contracted multireference coupled cluster (ic-MRCC) approach aimed at solving two of the problems encountered in methods based on the Jeziorski–Monkhorst ansatz: (i) the scaling of the computational and memory costs with respect to the number of references, and (ii) the lack of invariance of the energy with respect to rotations among active orbitals. The ic-MRCC approach is based on a straightforward generalization of the single-reference coupled cluster ansatz in which an exponential operator is applied to a multiconfigurational wave function. The ic-MRCC method truncated to single and double excitations (ic-MRCCSD) yields very accurate potential energy curves in benchmark computations on the Be + H2 insertion reaction, the dissociation of hydrogen fluoride, and the symmetric double dissociation of water. Approximations of the ic-MRCC theory in which the Baker–Campbell–Hausdorff expansion is truncated up to a given number of commutators are found to conver...

155 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023163
2022351
2021267
2020344
2019253
2018244