The domain based local pair natural orbital coupled cluster method with single-, double-, and perturbative triple excitations (DLPNO–CCSD(T)) is an efficient quantum chemical method that allows for coupled cluster calculations on molecules with hundreds of atoms. Because coupled-cluster theory is the method of choice if high-accuracy is needed, DLPNO–CCSD(T) is very promising for large-scale chemical application. However, the various approximations that have to be introduced in order to reach near linear scaling also introduce limited deviations from the canonical results. In the present work, we investigate how far the accuracy of the DLPNO–CCSD(T) method can be pushed for chemical applications. We also address the question at which additional computational cost improvements, relative to the previously established default scheme, come. To answer these questions, a series of benchmark sets covering a broad range of quantum chemical applications including reaction energies, hydrogen bonds, and other noncovalent interactions, conformer energies, and a prototype organometallic problem were selected. An accuracy of 1 kcal/mol or better can readily be obtained for all data sets using the default truncation scheme, which corresponds to the stated goal of the original implementation. Tightening of the three thresholds that control DLPNO leads to mean absolute errors and standard deviations from the canonical results of less than 0.25 kcal/mol (<1 kJ/mol). The price one has then to pay is an increased computational time by a factor close to 3. The applicability of the method is shown to be independent of the nature of the reaction. On the basis of the careful analysis of the results, three different sets of truncation thresholds (termed “LoosePNO”, “NormalPNO”, and “TightPNO”) have been chosen for “black box” use of DLPNO–CCSD(T). This will allow users of the method to optimally balance performance and accuracy.

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A production level implementation of the closed-shell local quadratic configuration interaction and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals [local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approximation (LNPO-CEPA) method [F. Neese et al., Chem. Phys. 130, 114108 (2009)] and makes extended use of the resolution of the identity (RI) or density fitting (DF) approximation. Two variants of each method are compared. The less accurate approximations (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indices to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (T(CutPNO)) has been studied. Extended numerical tests have been performed on absolute and relative correlation energies as function of basis set size and T(CutPNO) as well as on reaction energies, isomerization energies, and weak intermolecular interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calculations on larger molecules are reported (ranging from 40-86 atoms) and it is shown that for medium sized molecules the total wall clock time required to complete the LPNO-CCSD calculations is only two to four times that of the preceding self-consistent field (SCF). Thus these methods are highly suitable for large-scale computational chemistry applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts.

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.

In this study we examine the accuracy of domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD­(T)) on a large benchmark data set. To this end, we use the recently published GMTKN55 superset of molecules that contains 1505 relative energies and 2462 single-point calculations. To our knowledge this is the most comprehensive benchmark evaluation of any highly correlated wave function based ab initio method to date. In the first part of the study, canonical CCSD­(T) reference calculations were carried out on the entire test set in order to guarantee that the reference data are of uniform quality. Second, DLPNO-CCSD­(T) calculations were carried out under identical conditions. The main finding is that with the exception of two data sets, all data sets have a MAD of 0.4 kcal/mol or less and the majority of sets have a MAD of less than 0.2 kcal/mol. For open shells, the accuracy of the DLPNO calculations was significantly improved through an iterative version of the triples correction.