An efficient linear-scaling CCSD(T) method based on local natural orbitals

Abstract

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.

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

“…In our fragmentation-based local correlation approach, 47,51,54 which is related to the cluster-in-molecule 55,56 and the incremental schemes, 42,57,58 the MOs are localized, and a domain of LMOs, E i , is constructed for each occupied LMO i. The approximate contribution of LMO i to the correlation energy, hereafter denoted by δE i (E i ), is evaluated in this domain.…”

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction

“…Another quite impressive area is the family of local correlation methods, 19,20 which have recently managed to produce CCSD(T)-quality results on systems as large as proteins. 21,22 The combination of THC and local correlation methodology lies outside the focus of the present study, but is certainly an important future development. Additionally, we will use a generalized Einstein summation convention in which repeated indices are asserted to be summed over.…”

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)]

“…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.…”

“…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).…”