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.

We have obtained uniform frequency scaling factors λ(harm) (for harmonic frequencies), λ(fund) (for fundamentals), and λ(ZPVE) (for zero-point vibrational energies (ZPVEs)) for the Weigend-Ahlrichs and other selected basis sets for MP2, SCS-MP2, and a variety of DFT functionals including double hybrids. For selected levels of theory, we have also obtained scaling factors for true anharmonic fundamentals and ZPVEs obtained from quartic force fields. For harmonic frequencies, the double hybrids B2PLYP, B2GP-PLYP, and DSD-PBEP86 clearly yield the best performance at RMSD = 10-12 cm(-1) for def2-TZVP and larger basis sets, compared to 5 cm(-1) at the CCSD(T) basis set limit. For ZPVEs, again, the double hybrids are the best performers, reaching root-mean-square deviations (RMSDs) as low as 0.05 kcal/mol, but even mainstream functionals like B3LYP can get down to 0.10 kcal/mol. Explicitly anharmonic ZPVEs only are marginally more accurate. For fundamentals, however, simple uniform scaling is clearly inadequate.

The S66x8 dataset for noncovalent interactions of biochemical relevance has been re-examined by means of MP2-F12 and CCSD(F12*)(T) methods. We deem our revised benchmark data to be reliable to about 0.05 kcal mol(-1) RMS. Most levels of DFT perform quite poorly in the absence of dispersion corrections: somewhat surprisingly, that is even the case for the double hybrids and for dRPA75. Analysis of optimized D3BJ parameters reveals that the main benefit of dRPA75 and DSD double hybrids alike is the treatment of midrange dispersion. dRPA75-D3BJ is the best performer overall at RMSD = 0.10 kcal mol(-1). The nonlocal VV10 dispersion functional is especially beneficial for the double hybrids, particularly in DSD-PBEP86-NL (RMSD = 0.12 kcal mol(-1)). Other recommended dispersion-corrected functionals with favorable price/performance ratios are ωB97X-V, and, surprisingly, B3LYP-D3BJ and BLYP-D3BJ (RMSDs of 0.23, 0.20 and 0.23 kcal mol(-1), respectively). Without dispersion correction (but parametrized for midrange interactions) M06-2X has the lead (RMSD = 0.45 kcal mol(-1)). A collection of three energy-based diagnostics yields similar information to an SAPT analysis about the nature of the noncovalent interaction. Two of those are the percentages of Hartree-Fock and of post-MP2 correlation effects in the interaction energy; the third, CSPI = [IE - IE]/[IE + IE] or its derived quantity DEBC = CSPI/(1 + CSPI(2))(1/2), describes the character of the MP2 correlation contribution, ranging from 0 (purely dispersion) to 1 (purely other effects). In addition, we propose an improved, parameter-free scaling for the (T) contribution based on the Ecorr[CCSD-F12b]/Ecorr[CCSD] and Ecorr[CCSD(F12*)]/Ecorr[CCSD] ratios. For Hartree-Fock and conventional DFT calculations, full counterpoise generally yields the fastest basis set convergence, while for double hybrids, half-counterpoise yields faster convergence, as previously established for correlated ab initio methods.

Noncovalent interactions between molecules are key for many biological processes. Necessarily, when molecules interact, the electronic charge in each of them is redistributed. Here, we show experimentally that, in chiral molecules, charge redistribution is accompanied by spin polarization. We describe how this spin polarization adds an enantioselective term to the forces, so that homochiral interaction energies differ from heterochiral ones. The spin polarization was measured by using a modified Hall effect device. An electric field that is applied along the molecules causes charge redistribution, and for chiral molecules, a Hall voltage is measured that indicates the spin polarization. Based on this observation, we conjecture that the spin polarization enforces symmetry constraints on the biorecognition process between two chiral molecules, and we describe how these constraints can lead to selectivity in the interaction between enantiomers based on their handedness. Model quantum chemistry calculations that rigorously enforce these constraints show that the interaction energy for methyl groups on homochiral molecules differs significantly from that found for heterochiral molecules at van der Waals contact and shorter (i.e., ∼0.5 kcal/mol at 0.26 nm).spin | chirality | enantioselectivity | biorecognition | exchange interaction T he wealth of information on protein structure has led to a much better understanding of the relation between structure and function in biomolecular processes and biological machines (1); however, basic phenomena remain unexplained in terms of structure-function relationships. Biorecognition, which is based on noncovalent interactions between molecules, retains mysteries, and its calculation evades first principles theory (2, 3). This failure suggests that some essential features are not included in our current description of these interactions (4,5). In this study, we show that charge polarization, which occurs in any biorecognition event, is accompanied by spin polarization for chiral molecules, an effect that is missing in most treatments. The subsequent magnetic interaction energies are small and therefore, play no significant role in the interactions; however, the spin polarization constrains the symmetry of the wave function(s) involved with the intermolecular interaction, so that significant differences in energy emerge for interactions between molecules of the same chirality and those of opposite chirality. Thus, this phenomenon may impact quantitative modeling of biorecognition events and contribute to our understanding of enantiorecognition in nature (6).Nucleotides, amino acids, and sugars are chiral; namely, they do not possess mirror plane symmetry but have symmetry like a "hand" (cheir in Greek). Force field models for the interaction between biomolecules do not account for spin polarization or include terms with chiral symmetry. Noncovalent interactions between biomolecules are commonly described classically by way of force fields, which are constructed from their geometrie...

Benchmark ab initio energies for BEGDB and WATER27 data sets have been re-examined at the MP2 and CCSD(T) levels with both conventional and explicitly correlated (F12) approaches. The basis set convergence of both conventional and explicitly correlated methods has been investigated in detail, both with and without counterpoise corrections. For the MP2 and CCSD-MP2 contributions, rapid basis set convergence observed with explicitly correlated methods is compared to conventional methods. However, conventional, orbital-based calculations are preferred for the calculation of the (T) term, since it does not benefit from F12. CCSD(F12*) converges somewhat faster with the basis set than CCSD-F12b for the CCSD-MP2 term. The performance of various DFT methods is also evaluated for the BEGDB data set, and results show that Head-Gordon's ωB97X-V and ωB97M-V functionals outperform all other DFT functionals. Counterpoise-corrected DSD-PBEP86 and raw DSD-PBEPBE-NL also perform well and are close to MP2 results. In the WATER27 data set, the anionic (deprotonated) water clusters exhibit unacceptably slow basis set convergence with the regular cc-pVnZ-F12 basis sets, which have only diffuse s and p functions. To overcome this, we have constructed modified basis sets, denoted aug-cc-pVnZ-F12 or aVnZ-F12, which have been augmented with diffuse functions on the higher angular momenta. The calculated final dissociation energies of BEGDB and WATER27 data sets are available in the Supporting Information. Our best calculated dissociation energies can be reproduced through n-body expansion, provided one pushes to the basis set and electron correlation limit for the two-body term; for the three-body term, post-MP2 contributions (particularly CCSD-MP2) are important for capturing the three-body dispersion effects. Terms beyond four-body can be adequately captured at the MP2-F12 level.