Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory

Abstract

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.

Generalized Prediction of Enthalpies of Formation Using DLPNO‐CCSD(T) Ab Initio Calculations for Molecules Containing the Elements H, C, N, O, F, S, Cl, Br

“…In contrast, Paulechka and Kazakov have used verytightscf and tightPNO settings which are expected to provide higher accuracy. However, especially, the tightPNO settings lead to a significant increase in the computational time required by a factor of up to four . As Table shows, the use of larger basis sets leads to a reduction in the error within the same method, in this case BP86.…”

“…Local pair natural orbital (LPNO) and domain‐based local pair natural orbital (DLPNO) methods offer an attractive solution to the problem, by providing an efficient approximation scheme through which the ideal CCSD(T)) solution is approached in an efficient manner . A key advantage of the DLPNO‐CCSD(T) method is the use of a single method for the calculation of the electronic energy, which thus avoids the issue of requiring empirical weighing of the numerical results, as applied in compound methods such as, for example, the popular G4 method . In addition, the computational cost of DLPNO‐CCSD(T) methods is extremely competitive which makes it suitable for larger scale studies, both larger molecules or large numbers of smaller molecules …”

Hydrogen Bonding of N‐Heterocyclic Carbenes in Solution: Mechanisms of Solvent Reorganization

“…Single‐point energies were calculated using the DLPNO‐CCSD(T) method, with tight settings for the localization, as defined by Neese and Liakos. The single‐point energies obtained with the def2‐TZVPP and def2‐QZVPP basis sets were extrapolated to the complete basis set limit …”

Tuning the Carbon Dioxide Absorption in Amino Acid Ionic Liquids

“…Therefore, we used the domain-based local pair natural orbitals approximation of the CCSD(T), DLPNO-CCSD(T), [61] which scales as O(N 2.30 ), that is, close to O(N 2.27 ) for the B3LYP method, and provides the energies within an error of 1 kJ mol À1 from CCSD(T). [62] In the third step, we conducted zero-point vibrational energy and StatTD calculations of the thermal corrections to the finite-temperature (T = 298.15 K) from the DFT geometries and frequencies according to the approach described in Ref. [63].…”