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

Abstract

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.

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

“…The explicit form of the resulting equations can be found in Appendix B of Ref. 15. So far, there is no advantage of these transformations.…”

“…It is then possible to achieve linear scaling of the computational effort with molecular size. 15,40,43,51 We discuss pair approximations further in Sec. II H. The important point is that the convergence of the correlation energy and other molecular properties as a function of domain sizes depends crucially on the choice of the transformation matrices Q ij .…”

“…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.…”

“…16,17,38,39 One way to avoid this is to use local pair approximations, as first introduced by Pulay [16][17][18][19][20] and used in many later PAO methods. 12,15,[40][41][42][43][44][45][46] Local pair approximations provide a simple way to reach linear scaling and to extend OSV-LCCSD to large systems. However, as pointed out in previous work, 15,46,47 the application of local approximations requires a careful balancing of errors (e.g., local pair error versus domain error) and in the current work we reconsider these issues in the context of the OSV method.…”

Range-separated double-hybrid density-functional theory applied to periodic systems

“…This technique was initially proposed by Pulay in the 1980s, 32,33 and extended by Werner, Schütz, and coworkers to high-level correlated methods for molecules. [34][35][36][37][38][39][40][41][42][43][44][45] The adaptation of the local MP2 method to periodic systems has been done in the last decade, 18,46,47 and over the years has been successfully applied to quite a rich variety of systems. [48][49][50][51][52][53][54][55][56][57][58][59][60] The paper is structured as follows.…”