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

Abstract

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.

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

“…In both cases, trivial embedding theories can be defined if the fragments or domains are treated at different levels. This possibility has already been explored by several authors, [48][49][50][51] but the arising WFT-in-WFT embedding theories have not yet been compared to the corresponding WFT-in-DFT schemes.…”

“…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.…”

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

“…the adiabatic correction. We calculated this correction with help of the Cfour [94] and mrcc [95,96] program packages at both all-electron and frozen-core CCSD and CCSDT levels of theory [97]. GTOs basis set which were previously used for computation of the two-electron relativistic corrections were utilised.…”

The orbital-specific-virtual local coupled cluster singles and doubles method

“…Matrix factorizations, such as the Cholesky decomposition, and density fitting (DF) [some-times also called resolution of the identity] (Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15] are obvious examples, but methods which define new occupied and virtual orbital sets, such as the projected atomic orbital (PAO), [16][17][18][19][20] frozen natural orbital, [21][22][23][24][25] and pair natural orbital (PNO) (Refs. [26][27][28][29][30][31][32][33] methods, can also be understood in this mathematical language.…”