Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes.

The titular domain-based local pair natural orbital (DLPNO) approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with ≲10 heavy atoms, but for larger systems, the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions; these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory.

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost.

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory.

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn-Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. As in other contexts, correct asymptotic behavior can be enforced via "optimal tuning" based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with "extended" (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

Mechanism of Cobalt-Catalyzed Heterodimerization of Acrylates and 1,3-Dienes. A Potential Role of Cationic Cobalt(I) Intermediates.

Coupling reactions of feedstock alkenes are promising, but few of these reactions are practiced industrially. Even though recent advances in the synthetic methodology have led to excellent regio- and enantioselectivies in the dimerization reactions between 1,3-dienes and acrylates, the efficiency as measured by the turnover numbers (TON) in the catalyst has remained modest. Through a combination of reaction progress kinetic analysis (RPKA) of a prototypical dimerization reaction, characterization of isolated low-valent cobalt catalyst precursors involved, several important details of the mechanism of this reaction have emerged. (i) The prototypical reaction has an induction period that requires at least two hours of stir time to generate the competent catalyst. (ii) Reduction of a Co(II) complex to a Co(I) complex, and subsequent generation of a cationic [Co(I)]+ species are responsible for this delay. (iii) Through RPKA using in situ IR spectroscopy, same excess experiments reveal inhibition by the product towards the end of the reaction and no catalyst deactivation is observed as long as diene is present in the medium. The low TON observed is most likely the result of the inherent instability of the putative cationic Co(I)-species that catalyzes the reaction. (iv) Different excess experiments suggest that the reaction is first order in the diene and zero order in the acrylate. (v) Catalyst loading experiments show that the catalyst is first order. The orders in the various regents were further confirmed by Variable Time Normalization Analysis (VTNA). (vi) A mechanism based on oxidative dimerization [via Co(I)/Co(III)-cycle] is proposed. Based on the results of this study, it is possible to increase the TON by a factor of 10 by conducting the reaction at an increased concentration of the starting materials, especially, the diene, which seems to stabilize the catalytic species.

Extending admixture mapping to nuclear pedigrees: application to sarcoidosis.

We describe statistical methods that extend the application of admixture mapping from unrelated individuals to nuclear pedigrees, allowing existing pedigree-based collections to be fully exploited. Computational challenges have been overcome by developing a fast algorithm that exploits the factorial structure of the underlying model of ancestry transitions. This has been implemented as an extension of the program ADMIXMAP. We demonstrate the application of the method to a study of sarcoidosis in African Americans that has previously been analyzed only as an admixture mapping study restricted to unrelated individuals. Although the ancestry signals detected in this pedigree analysis are generally similar to those detected in the earlier analysis of unrelated cases, we are able to extract more information and this yields a much sharper exclusion map; using the classical criterion of an LOD score of minus 2, the pedigree analysis is able to exclude a risk ratio of 2 or more associated with African ancestry over 96% of the genome, compared with only 83% in the earlier analysis of unrelated individuals only. Although the pedigree extension of ADMIXMAP can use ancestry-informative markers only at relatively low density, it can use imputed ancestry states from programs such as WINPOP or HAPMIX that use dense SNP marker genotypes for admixture mapping. This extends both the efficiency and the range of application of this powerful gene mapping method.