Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

Abstract

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

Non‐covalent Interactions and Charge Transfer between Propene and Neutral Yttrium‐Doped and Pure Gold Clusters

“…The (75,302) integration grid, as it is implemented in the Q‐Chem software, was applied in all cases. The method was tested by reference CCSD(T)/DEF2‐TZVPPD calculations for Au 4 , Au 6 and Au 5 Y clusters using the MRCC program . Furthermore, single point CAM‐B3LYP/DEF2‐TZVP calculations were carried out on the optimized geometries for all sizes.…”

“…The method was tested by reference CCSD(T)/DEF2-TZVPPD calculations [57] for Au 4 ,A u 6 and Au 5 Yc lusters using the MRCC program. [58][59][60] Furthermore, single point CAM-B3LYP/DEF2-TZVP [61] calculations were carried out on the optimized geometries for all sizes. The initial cluster-propene geometries were systematically generated in p and di-s bonding modes and subsequently optimized using DFT calculations.…”

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

“…Thus, the (T0) approximation does not provide a sufficiently robust computational model. The off‐diagonal couplings can be included by either solving the local (T) equations iteratively or through the Laplace transformation technique . The former approach requires the storage of the (T) amplitudes, while the latter requires performing (T0)‐like calculations for several (typically 3–4) quadrature points.…”

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)]

“…[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). 29 Their new scheme is capable to compute very accurate CCSD(T) correlation energies for systems with more than ten thousand basis functions.…”

“…17,19,[27][28][29] Most recently, Nagy and Kállay combined their LNO approach with LT CCSD(T). 29 Their new scheme is capable to compute very accurate CCSD(T) correlation energies for systems with more than ten thousand basis functions. By calculating all intermediates on the fly, there is no storage bottleneck anymore in their new method.…”