Accurate three-body noncovalent interactions: the insights from energy decomposition.

An impressive collection of accurate two-body interaction energies for small complexes has been assembled into benchmark databases and used to improve the performance of multiple density functional, semiempirical, and machine learning methods. Similar benchmark data on nonadditive three-body energies in molecular trimers are comparatively scarce, and the existing ones are practically limited to homotrimers. In this work, we present a benchmark dataset of 20 equilibrium noncovalent interaction energies for a small but diverse selection of 10 heteromolecular trimers. The new 3BHET dataset presents complexes that combine different interactions including π-π, anion-π, cation-π, and various motifs of hydrogen and halogen bonding in each trimer. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition of the two- and three-body interaction energies shows that 3BHET consists of electrostatics- and dispersion-dominated complexes. The nonadditive three-body contribution is dominated by induction, but its influence on the overall bonding type in the complex (as exemplified by its position on the ternary diagram) is quite small. We also tested the extended SAPT (XSAPT) approach which is capable of including some nonadditive interactions in clusters of any size. The resulting three-body dispersion term (obtained from the many-body dispersion formalism) is mostly in good agreement with the supermolecular CCSD(T)-MP2 values and the nonadditive induction term is similar to the three-body SAPT(DFT) data, but the overall three-body XSAPT energies are not very accurate as they are missing the first-order exchange terms.

Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory.

Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.

Extension of an Atom-Atom Dispersion Function to Halogen Bonds and Its Use for Rational Design of Drugs and Biocatalysts.

A dispersion function Das in the form of a damped atom-atom asymptotic expansion fitted to ab initio dispersion energies from symmetry-adapted perturbation theory was improved and extended to systems containing heavier halogen atoms. To illustrate its performance, the revised Das function was implemented in the multipole first-order electrostatic and second-order dispersion (MED) scoring model. The extension has allowed applications to a much larger set of biocomplexes than it was possible with the original Das. A reasonable correlation between MED and experimentally determined inhibitory activities was achieved in a number of test cases, including structures featuring nonphysically shortened intermonomer distances, which constitute a particular challenge for binding strength predictions. Since the MED model is also computationally efficient, it can be used for reliable and rapid assessment of the ligand affinity or multidimensional scanning of amino acid side-chain conformations in the process of rational design of novel drugs or biocatalysts.

Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies.

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), Edisp(20) and Eexch-disp(20), suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, Edisp(20)-F12 and Eexch-disp(20)-F12, have been proposed recently. However, the original formalism (M., Kodrycka , J. Chem. Theory Comput. 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVXZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the Edisp(20)-F12 and Eexch-disp(20)-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged Edisp(20)-F12 and Eexch-disp(20)-F12 numbers can be substituted for conventional Edisp(20) and Eexch-disp(20) ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.

Nonapproximated third-order exchange induction energy in symmetry-adapted perturbation theory.

The exchange terms in symmetry-adapted perturbation theory (SAPT) are normally calculated within the so-called S2 or single exchange approximation, which approximates the all-electron antisymmetrizer by interchanges of at most one electron pair between the interacting molecules. This approximation is typically very accurate at the van der Waals minimum separation and at larger intermolecular distances but begins to deteriorate at short range. Nonapproximated expressions for the second-order SAPT exchange corrections have been derived some time ago by Schäffer and Jansen [Mol. Phys. 111, 2570 (2013)]. In this work, we extend Schäffer and Jansen's formalism to derive and implement a nonapproximated expression for the third-order exchange-induction correction. Numerical tests on several representative noncovalent databases show that the S2 approximation underestimates the exchange-induction contributions in both second and third orders. This underestimation is very similar in relative terms, but the larger absolute values of the third-order exchange-induction effects, and their near complete cancellation with the corresponding induction energies, make the third-order errors more severe. In the worst-case scenario of interactions involving ions, the breakdown of the S2 approximation can result in a qualitatively wrong, attractive character of SAPT total energies at short range {as first observed by Lao and Herbert [J. Phys. Chem. A 116, 3042 (2012)]}. As expected, the inclusion of the full third-order exchange-induction energy in place of its S2-approximated counterpart restores the correct, repulsive short-range behavior of the SAPT potential energy curves computed through the third order.

Ab Initio Study of Chiral Discrimination in the Glycidol Dimer.

Chiral discrimination, the ability of a chiral molecule to exhibit different weak intermolecular interactions than its mirror image, is investigated for dimers of oxiranemethanol (glycidol). In this regard, high-level ab initio calculations were performed to study the chiral recognition effects in the homochiral and heterochiral dimers of glycidol. Fourteen dimer structures, seven homochiral and seven heterochiral, were studied: they all feature two intermolecular O-H···O hydrogen bonds. These structures have been determined with the second-order Møller-Plesset perturbation theory (MP2) using the aug-cc-pVTZ basis set and verified to pertain to actual local minima. The benchmark interaction energy values were computed using MP2 extrapolated from the aug-cc-pVQZ and aug-cc-pV5Z bases with a higher-level correction from a coupled-cluster calculation in the aug-cc-pVTZ basis. The global minimum structure is a homochiral one, with the two hydrogen bonds forming a part of a ring with eight heavy atoms. A similar heterochiral structure has a binding energy smaller by about 0.6 kcal/mol. The largest diastereomeric energy difference is about 1.0 kcal/mol. Further insight into the origins of chiral discrimination was provided by symmetry-adapted perturbation theory (SAPT) and a functional-group SAPT (F-SAPT) difference analysis to investigate the direct and indirect effects of two -H/-CH2OH substitutions leading from an achiral ethylene oxide dimer to the chiral glycidol dimer. Last but not least, harmonic frequency shifts relative to a noninteracting glycidol molecule were calculated and analyzed for all conformations to get insight into the origins of chiral discrimination. It is found that the largest frequency shifts are related to the effect of hydrogen bonding on the O-H stretch mode, the stability of the ring involving both hydrogen bonds, and the transition between two nonequivalent minima of the glycidol molecule.

Interactions of CO2 with cluster models of metal-organic frameworks.

The interactions between carbon dioxide and cluster models of coordinatively unsaturated metal-organic frameworks (MOFs) were studied using a variety of ab initio methods. Three metal species and three organic linkers in four structures were considered in these models as a representation of the tunable nature of MOFs and the potential multireference character of such systems. Common single-reference methods, such as MP2 and CCSD(T), were compared with multireference methods based on complete active space self-consistent field theory, going as far as multireference configuration interaction with single and double excitations (MRCISD). Special consideration is taken to avoid issues of size inconsistency in the CI results, where an alternate reference is used in the interaction energy definition. The benchmark values are used to judge the adequacy of a selection of density functionals for the current systems. Symmetry-adapted perturbation theory (SAPT) decomposition was performed to elucidate the important effects that comprise the binding interactions. The systems proved to have very limited multireference character, and MP2 values were closer to the CCSD(T) benchmark than the more difficult MRCISD results. Though the SAPT total energies prove to be relatively poor approximations to the benchmark interaction energies, they reveal (in most cases) the correct trends with respect to the choice of the metal. The SAPT energy decompositions indicate that the CO2 binding is primarily driven by electrostatics, but induction and dispersion also provide sizable, and quite similar, attractive contributions. Importantly, the small diformate model provides a faithful representation of complexes with large aromatic linkers, both in terms of the total interaction energy and the SAPT decomposition.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

Chiral Self Recognition: Interactions in Propylene Oxide Complexes.

We elucidate the subtle energetic effects that give rise to chiral recognition in the propylene oxide dimer. Specifically, we investigate six homochiral (RRx) and six heterochiral (RSx) structures of this complex, with the RRn-RSn pair sharing the same pattern of weak O···H-C hydrogen bonds but subtly differing in energy due to chiral effects. The interaction energies for the 12 structures are computed at various levels of electronic structure theory and basis set up to the complete basis set limit of the coupled-cluster approach with single, double, and perturbative triple excitations (CCSD(T)). These benchmark interaction energies are compared to the results of various approximate approaches, both density functional theory-based and wave function-based. We find that while the RRn-RSn diastereomeric energy differences exhibit a great deal of error cancellation between the individual interaction energies, most approximate methods have a hard time even reproducing the correct signs of these differences consistently. The origins of the RRn-RSn differences are elucidated by several symmetry-adapted perturbation theory (SAPT) analyses ranging from ordinary intermolecular SAPT to a functional-group SAPT (F-SAPT) decomposition of direct and indirect H → CH3 substitution effects leading from achiral ethylene oxide complexes to chiral propylene oxide ones. It is shown that the largest diastereomeric energy differences are correlated to the variations in the electrostatic and dispersion SAPT contributions. Finally, the effect of chiral interactions on the vibrational frequencies of a propylene oxide molecule is investigated, showing that the interaction results in largest frequency shifts, splittings, and chiral discrimination effects in the lowest, torsional vibrational mode of the noninteracting monomer.

Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory.

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell Edisp(20)-F12 and Eexch-disp(20)-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [ J. Chem. Theory Comput. 2018 , 14 , 5105 - 5117 ] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of Edisp(20)-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of Edisp(20)-F12 and Eexch-disp(20)-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for Edisp(20) and Eexch-disp(20) computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for Edisp(20) and either (X + 1) or (X + 2) for Eexch-disp(20). While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller-Plesset perturbation theory, SAPT-F12(MP2) [ Frey , J. A. ; Chem. Rev. 2016 , 116 , 5614 - 5641 ] and observed that it is also quite successful in speeding up the basis set convergence of conventional Edisp(20) + Eexch-disp(20), albeit with some outliers.

Platinum, gold, and silver standards of intermolecular interaction energy calculations.

High-accuracy noncovalent interaction energies are indispensable as data points for potential energy surfaces and as benchmark values for improving and testing more approximate approaches. The preferred algorithm (the gold standard) for computing these energies has been the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)] converged to the complete basis set (CBS) limit. However, gold-standard calculations are expensive as correlated interaction energies converge slowly with the basis set size, and establishing the CBS limit to better than 0.05 kcal/mol typically requires a CCSD(T) calculation in a basis set of at least triple-zeta quality. If an even higher accuracy is required (for example, for the assignment of complicated high-resolution spectra), establishing a superior platinum standard requires both a precisely converged CCSD(T)/CBS limit and the corrections for the core correlation, relativistic effects, and higher-order coupled-cluster terms at least through the perturbative quadruple excitations. On the other hand, if a triple-zeta CCSD(T) calculation is not feasible but a double-zeta one is, it is worthwhile to look for a silver standard that provides the most accurate and consistent approximation to the gold standard at a reduced computational cost. We review the recent developments aimed at (i) increasing the breadth and diversity of the available collection of gold-standard benchmark interaction energies, (ii) evaluating the best computational strategies for platinum-standard calculations and producing beyond-CCSD(T) potential energy surfaces for spectroscopic and scattering applications of the highest precision, and (iii) improving the accuracy of the silver-standard, double-zeta-level CCSD(T)/CBS estimates through the use of explicit correlation and midbond basis functions. We also outline the remaining challenges in the accurate ab initio calculations of noncovalent interaction energies.

Spin splittings from first-order symmetry-adapted perturbation theory without single-exchange approximation.

The recently proposed spin-flip symmetry-adapted perturbation theory (SF-SAPT) first-order exchange energy [Patkowski et al., J. Chem. Phys. 148, 164110 (2018)] enables the standard open-shell SAPT approach to treat arbitrary spin states of the weakly interacting complex. Here, we further extend first-order SF-SAPT beyond the single-exchange approximation to a complete treatment of the exchanges of electrons between monomers. This new form of the exchange correction replaces the single-exchange approximation with a more moderate single-spin-flip approximation. The newly developed expressions are applied to a number of small test systems to elucidate the quality of both approximations. They are also applied to the singlet-triplet splittings in pancake bonded dimers. The accuracy of the single-exchange approximation deteriorates at short intermolecular separations, especially for systems with few electrons and for the high-spin state of the complex. In contrast, the single-spin-flip approximation is exact for interactions involving a doublet molecule and remains highly accurate for any number of unpaired electrons. Because the single-exchange approximation affects the high-spin and low-spin states of pancake bonded complexes evenly, the resulting splitting values are of similar accuracy to those produced by the formally more accurate single-spin-flip approximation.

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development.

Psi4NumPy demonstrates the use of efficient computational kernels from the open-source Psi4 program through the popular NumPy library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Furthermore, several reference codes have been integrated into Jupyter notebooks, allowing background, underlying theory, and formula information to be associated with the implementation. Psi4NumPy tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

First-order symmetry-adapted perturbation theory for multiplet splittings.

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Improving "Silver-Standard" Benchmark Interaction Energies with Bond Functions.

We investigate the effect of adding midbond basis functions on the performance of various conventional and explicitly correlated (F12) estimates of complete basis set limit coupled-cluster (CCSD(T)/CBS) noncovalent interaction energies. In particular, we search for an improved "silver standard" of interaction energy calculations for systems where the CCSD(T) computation is feasible in a double-ζ basis but not in a triple-ζ one. We follow a recent study ( Sirianni J. Chem. Theory Comput. 2017 , 13 , 86 ) of different CCSD(T)-F12 variants in midbondless bases over the A24 and S22 benchmark interaction energy databases, and extend Dunning's correlation-consistent basis sets with three different midbond sets. The addition of bond functions is highly beneficial for conventional CCSD(T) and most CCSD(T)-F12 variants, improving both the CCSD part and the unscaled triples contribution. However, the commonly used scaling of triples by the ratio of the MP2-F12 and MP2 correlation energies usually overshoots: as a result, the scaled triples term gets worse upon the addition of bond functions. In contrast, a milder triples scaling by the ratio of the CCSD-F12b and CCSD correlation energies ( Brauer , Phys. Chem. Chem. Phys. 2016 , 18 , 20905 ) leads to the most accurate estimates of this term as long as bond functions are included. The combination of the triples term scaled in this way with the CCSD-F12b interaction energy leads to the CCSD(Tbb)-F12b approach that provides consistent high accuracy when a (3 s3 p2 d2 f) set of midbond functions is added to the aug-cc-pVDZ atom-centered basis set. The combination of midbond functions and the composite MP2/CBS+δ(CCSD(T)) treatment is able to make up for the deficiencies in the atom-centered part of the basis set, in particular, for a partial (or even complete) lack of diffuse functions. Considering both the A24 and S22 accuracy and the computational efficiency, we propose several new "silver standard" approaches improving upon the currently established midbondless levels of theory, ranging from the most consistent CCSD(Tbb)-F12b/aug-cc-pVDZ+(3 s3 p2 d2 f) variant (with mean unsigned errors of 0.010 and 0.042 kcal/mol for the A24 and S22 databases, respectively) to the significantly cheaper MP2/CBS+δ(CCSD(T))/cc-pVDZ+(3 s3 p2 d2 f) approach (mean unsigned errors of 0.039 and 0.096 kcal/mol for A24 and S22, respectively).

Accurate virial coefficients of gaseous krypton from state-of-the-art ab initio potential and polarizability of the krypton dimer.

We have developed a new krypton-krypton interaction-induced isotropic dipole polarizability curve based on high-level ab initio methods. The determination was carried out using the coupled-cluster singles and doubles plus perturbative triples method with very large basis sets up to augmented correlation-consistent sextuple zeta as well as the corrections for core-core and core-valence correlation and relativistic effects. The analytical function of polarizability and our recently constructed reference interatomic potential [J. M. Waldrop et al., J. Chem. Phys. 142, 204307 (2015)] were used to predict the thermophysical and electromagnetic properties of krypton gas. The second pressure, acoustic, and dielectric virial coefficients were computed for the temperature range of 116 K-5000 K using classical statistical mechanics supplemented with high-order quantum corrections. The virial coefficients calculated were compared with the generally less precise available experimental data as well as with values computed from other potentials in the literature {in particular, the recent highly accurate potential of Jäger et al. [J. Chem. Phys. 144, 114304 (2016)]}. The detailed examination in this work suggests that the present theoretical prediction can be applied as reference values in disciplines involving thermophysical and electromagnetic properties of krypton gas.

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability.

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory.

Since the original fitting of Grimme's DFT-D3 damping parameters, the number and quality of benchmark interaction energies has increased significantly. Here, conventional benchmark sets, which focus on minimum-orientation radial curves at the expense of angular diversity, are augmented by new databases such as side chain-side chain interactions (SSI), which are composed of interactions gleaned from crystal data and contain no such minima-focused bias. Moreover, some existing databases such as S22×5 are extended to shorter intermolecular separations. This improved DFT-D3 training set provides a balanced description of distances, covers the entire range of interaction types, and at 1526 data points is far larger than the original training set of 130. The results are validated against a new collection of 6773 data points and demonstrate that the effect of refitting the damping parameters ranges from no change in accuracy (LC-ωPBE-D3) to an almost 2-fold decrease in average error (PBE-D3).

An accurate benchmark description of the interactions between carbon dioxide and polyheterocyclic aromatic compounds containing nitrogen.

We assessed the performance of a large variety of modern density functional theory approaches for the adsorption of carbon dioxide on molecular models of pyridinic N-doped graphene. Specifically, we selected eight polyheterocyclic aromatic compounds ranging from pyridine and pyrazine to 1,6-diazacoronene and investigated their complexes with CO2 for a large range of intermolecular distances and including both in-plane and stacked orientations. The benchmark interaction energies were computed at the complete-basis-set limit MP2 level plus a CCSD(T) coupled-cluster correction in a moderate but carefully selected basis set. Using a set of 96 benchmark CCSD(T)-level interaction energies as a reference, we investigated the accuracy of DFT-based approaches as a function of the density functional, the dispersion correction, the basis set, and the counterpoise correction or lack thereof. While virtually all DFT variants exhibit some deterioration of accuracy for distances slightly shorter than the van der Waals minima, we were able to identify several schemes such as B2PLYP-D3 and M05-2X-D3 whose average errors on the entire benchmark data set are in the 5-10% range. The top DFT performers were subsequently used to investigate the energy profile for a carbon dioxide transition through model N-doped graphene pores. All investigated methods confirmed that the largest, N4H4 pore allows for a barrierless CO2 transition to the other side of a graphene sheet.