Linear scaling coupled cluster method with correlation energy based error control

Ziółkowski, Marcin; Jansı́k, Branislav; Kjærgaard, Thomas; Jørgensen, Poul

doi:10.1063/1.3456535

Cited by 162 publications

(172 citation statements)

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“…An implementation using the QUAMBO approach to localised orbitals also exists [259]. The divide and conquer approach has also been applied to quantum chemistry (up to the CCSD level) [260,261], and implementation of exact exchange interactions has been described [262] (where the accuracy is very dependent on the size of the buffer region). An assessment of the computational time required for different systems [179] with divide and conquer has been made, and relates the time needed to the required accuracy, as well as physical attributes of the system.…”

Section: Divide and Conquermentioning

confidence: 99%

\mathcal{O}(N) methods in electronic structure calculations

2012

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Abstract. Linear scaling methods, or O(N ) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N , in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.

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Section: Divide and Conquermentioning

confidence: 99%

\mathcal{O}(N) methods in electronic structure calculations

2012

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“…26 This is based on tensor factorizations of the MP2 amplitudes. 27 There are also many other methods that exploit the locality of electron correlation, [28][29][30][31][32][33][34][35][36][37][38][39][40] but a review of all these methods is beyond the scope of the current article.…”

Section: Introductionmentioning

confidence: 99%

An efficient local coupled cluster method for accurate thermochemistry of large systems

Werner

Schütz

2011

The Journal of Chemical Physics

268

302

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An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Møller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.

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“…7 Many groups have worked on new developments in order to be able to apply the CCSD(T) method to medium-and large-sized systems. [8][9][10][11][12][13][14][15][16][17][18][19][20] The large and fast growing literature about low order or linear scaling CCSD algorithms has been extensively reviewed in earlier publications. [11][12][13] In this communication, we only a) Author to whom correspondence should be addressed: Frank.Neese@ cec.mpg.de discuss the studies that are focused on the (T) correction.…”

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confidence: 99%

“…10 Besides the above mentioned direct local correlation methods, fragment-based local CCSD(T) method development is a very active area of research. [14][15][16][17][18][19][20] Popular approaches include the cluster-in-molecule (CIM), 15 the natural linear-scaled coupled cluster, 16 the divide-expandconsolidate (DEC), 20 the incremental, 14 and the local natural orbital (LNO) 18 methods, all of which have led to low-order or linear scaling CCSD(T) methods. 17,19,[27][28][29] Most recently, Nagy and Kállay combined their LNO approach with LT CCSD(T).…”

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confidence: 99%