Coupled-cluster studies. II. The role of localization in correlation calculations on extended systems

Förner, Wolfgang; Ladik, J.; Otto, P.; Čı́žek, J.

doi:10.1016/0301-0104(85)87035-x

Cited by 127 publications

(63 citation statements)

References 22 publications

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“…tion, the integrals, intermediates, and wave function parameters connecting orbitals localized far from each other give negligible contributions and can be neglected. [6][7][8][9][10][11] One of the pioneers of the local correlation methods is Pulay, 6 who used an orthogonal set of localized orbitals [12][13][14] as the occupied one-particle subspace and a non-orthogonal redundant set of atomic orbitals (AOs) projected onto the complement of the occupied space [projected atomic orbitals (PAOs)] to describe the virtual space. To reduce the dimension of the interacting configuration space and, at the same time, the computation cost, for all the occupied orbital pairs a restricted set of virtual orbitals were chosen to define the allowed configurations.…”

Section: Introductionmentioning

confidence: 99%

“…This general strategy is followed in the old papers of Förner and co-workers, 7,8 in the incremental method proposed by Stoll and studied by many others, [30][31][32][33][34][35] in the CC method based on the fragment molecular-orbital method, 36 in particular, in the divide-andconquer methods such as the one published by Li and Li,37 and more recently by Ziółkowski et al 38 In other local correlation methods, the correlation energy is expressed as a simple sum of the local contributions without the need for the explicit treatment of interactions of the fragments. The divide-and-conquer CC method recently published by Kobayashi and Nakai 39 applies a buffer region for each fragment to incorporate the effect of the fragmentfragment interactions at the calculation of fragment energies.…”

Section: Introductionmentioning

confidence: 99%

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A general-order local coupled-cluster method based on the cluster-in-molecule approach

Rolik

Kállay

2011

The Journal of Chemical Physics

187

167

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A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems. Our method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with the frozen natural orbital (NO) techniques widely used for the cost reduction of correlation methods. The occupied molecular orbitals (MOs) are localized, and for each occupied MO a local subspace of occupied and virtual orbitals is constructed using approximate Møller-Plesset NOs. The CC equations are solved and the correlation energies are calculated in the local subspace for each occupied MO, while the total correlation energy is evaluated as the sum of the individual contributions. The size of the local subspaces and the accuracy of the results can be controlled by varying only one parameter, the threshold for the occupation number of NOs which are included in the subspaces. Though our local CC method in its present form scales as the fifth power of the system size, our benchmark calculations show that it is still competitive for the CC singles and doubles (CCSD) and the CCSD with perturbative triples [CCSD(T)] approaches. For higher order CC methods, the reduction in computation time is more pronounced, and the new method enables calculations for considerably bigger molecules than before with a reasonable loss in accuracy. We also demonstrate that the independent calculation of the correlation contributions allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A general-order local coupled-cluster method based on the cluster-in-molecule approach

Rolik

Kállay

2011

The Journal of Chemical Physics

187

167

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“…A plausible choice for this purpose is the use of local correlation models, which are these days serious competitors to DFT methods concerning both accuracy and speed. Since the pioneering studies in the eighties, [36][37][38] a number of local correlation approaches have been developed (see, e.g., Refs. 39-47 for representative examples).…”

Section: -2mentioning

confidence: 99%

Exact density functional and wave function embedding schemes based on orbital localization

Hégely

Nagy

Ferenczy

et al. 2016

The Journal of Chemical Physics

148

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Articles you may be interested in (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed. Published by AIP Publishing.[http://dx

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“…The latter problem was thoroughly studied by Subotnik and Head-Gordon, who gave a constructive solution [36,37]. Li, Piecuch, and co-workers [38][39][40][41] resurrected the cluster-inmolecule (CIM) approach [42,43], accenting the possibility of a 'black-box' definition of orbital interaction domains. Recently Rolik and Kallay added higher excitations in the CIM-CC method [44].…”

Section: Introductionmentioning

confidence: 99%

A remark on the disconnected nature of Lagrange equations in the context of a linear-scaling implementation of the coupled-cluster energy gradients

Lyakh

Bartlett

2012

Molecular Physics

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It is known that the Ã-tensor (an array of Lagrange multipliers), necessary for evaluating analytic energy gradients in the coupled-cluster theory, is diagrammatically disconnected in general. This means that the number of non-negligible elements in the Ã-tensor grows faster than linearly with the number of calculated particles. At a formal level, when evaluating the gradients of the coupled-cluster energy, this could prevent obtaining a linear scaling of the operational cost with respect to the number of correlated particles. It is shown that in ground/ excited-state coupled-cluster calculations, based on localized orbitals, the disconnected part of the Ã-tensor, as well as the disconnected part of the left-hand excited-state eigenvector, can be ignored, thus justifying the use of standard screening techniques employed in linear-scaling schemes.

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Coupled-cluster studies. II. The role of localization in correlation calculations on extended systems

Cited by 127 publications

References 22 publications

A general-order local coupled-cluster method based on the cluster-in-molecule approach

A general-order local coupled-cluster method based on the cluster-in-molecule approach

Exact density functional and wave function embedding schemes based on orbital localization

A remark on the disconnected nature of Lagrange equations in the context of a linear-scaling implementation of the coupled-cluster energy gradients

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