Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion.

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller-Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod-Teller-Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol-1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol-1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is -54.01 kJ mol-1, compared to an estimated experimental value of -55.3 ± 2.2 kJ mol-1.

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Optimized damping parameters for empirical dispersion corrections to symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) has become an invaluable tool for studying the fundamental nature of non-covalent interactions by directly computing the electrostatics, exchange (steric) repulsion, induction (polarization), and London dispersion contributions to the interaction energy using quantum mechanics. Further application of SAPT is primarily limited by its computational expense, where even its most affordable variant (SAPT0) scales as the fifth power of system size [O(N5)] due to the dispersion terms. The algorithmic scaling of SAPT0 is reduced from O(N5)→O(N4) by replacing these terms with the empirical D3 dispersion correction of Grimme and co-workers, forming a method that may be termed SAPT0-D3. Here, we optimize the damping parameters for the -D3 terms in SAPT0-D3 using a much larger training set than has previously been considered, namely, 8299 interaction energies computed at the complete-basis-set limit of coupled cluster through perturbative triples [CCSD(T)/CBS]. Perhaps surprisingly, with only three fitted parameters, SAPT0-D3 improves on the accuracy of SAPT0, reducing mean absolute errors from 0.61 to 0.49 kcal mol-1 over the full set of complexes. Additionally, SAPT0-D3 exhibits a nearly 2.5× speedup over conventional SAPT0 for systems with ∼300 atoms and is applied here to systems with up to 459 atoms. Finally, we have also implemented a functional group partitioning of the approach (F-SAPT0-D3) and applied it to determine important contacts in the binding of salbutamol to G-protein coupled ß1-adrenergic receptor in both active and inactive forms. SAPT0-D3 capabilities have been added to the open-source Psi4 software.

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.

Efficient and automated computation of accurate molecular geometries using focal-point approximations to large-basis coupled-cluster theory.

The focal-point approach, combining several quantum chemistry computations to estimate a more accurate computation at a lower expense, is effective and commonly used for energies. However, it has not yet been widely adopted for properties such as geometries. Here, we examine several focal-point methods combining Møller-Plesset perturbation theory (MP2 and MP2.5) with coupled-cluster theory through perturbative triples [CCSD(T)] for their effectiveness in geometry optimizations using a new driver for the Psi4 electronic structure program that efficiently automates the computation of composite-energy gradients. The test set consists of 94 closed-shell molecules containing first- and/or second-row elements. The focal-point methods utilized combinations of correlation-consistent basis sets cc-pV(X+d)Z and heavy-aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6). Focal-point geometries were compared to those from conventional CCSD(T) using basis sets up to heavy-aug-cc-pV5Z and to geometries from explicitly correlated CCSD(T)-F12 using the cc-pVXZ-F12 (X = D, T) basis sets. All results were compared to reference geometries reported by Karton et al. [J. Chem. Phys. 145, 104101 (2016)] at the CCSD(T)/heavy-aug-cc-pV6Z level of theory. In general, focal-point methods based on an estimate of the MP2 complete-basis-set limit, with a coupled-cluster correction evaluated in a (heavy-aug-)cc-pVXZ basis, are of superior quality to conventional CCSD(T)/(heavy-aug-)cc-pV(X+1)Z and sometimes approach the errors of CCSD(T)/(heavy-aug-)cc-pV(X+2)Z. However, the focal-point methods are much faster computationally. For the benzene molecule, the gradient of such a focal-point approach requires only 4.5% of the computation time of a conventional CCSD(T)/cc-pVTZ gradient and only 0.4% of the time of a CCSD(T)/cc-pVQZ gradient.

CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism.

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.

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.

The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions.

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation.

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.

Comparison of Explicitly Correlated Methods for Computing High-Accuracy Benchmark Energies for Noncovalent Interactions.

The reliability of explicitly correlated methods for providing benchmark-quality noncovalent interaction energies was tested at various levels of theory and compared to estimates of the complete basis set (CBS) limit. For all systems of the A24 test set, computations were performed using both aug-cc-pVXZ (aXZ; X = D, T, Q, 5) basis sets and specialized cc-pVXZ-F12 (XZ-F12; X = D, T, Q, 5) basis sets paired with explicitly correlated coupled cluster singles and doubles [CCSD-F12n (n = a, b, c)] with triple excitations treated by the canonical perturbative method and scaled to compensate for their lack of explicit correlation [(T**)]. Results show that aXZ basis sets produce smaller errors versus the CBS limit than XZ-F12 basis sets. The F12b ansatz results in the lowest average errors for aTZ and larger basis sets, while F12a is best for double-ζ basis sets. When using aXZ basis sets (X ≥ 3), convergence is achieved from above for F12b and F12c ansatzë and from below for F12a. The CCSD(T**)-F12b/aXZ approach converges quicker with respect to basis than any other combination, although the performance of CCSD(T**)-F12c/aXZ is very similar. Both CCSD(T**)-F12b/aTZ and focal point schemes employing density-fitted, frozen natural orbital [DF-FNO] CCSD(T)/aTZ exhibit similar accuracy and computational cost, and both are much more computationally efficient than large-basis conventional CCSD(T) computations of similar accuracy.

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).

Counterion and substrate effects on barrier heights of the hydrolytic kinetic resolution of terminal epoxides catalyzed by Co(III)-salen.

Density functional theory (DFT) has been applied to the proposed rate-limiting step of the hydrolytic kinetic resolution (HKR) of terminal epoxides as catalyzed by Co-salen-X (X = counterion) in order to resolve questions surrounding the mechanism. The present results indicate that the bimetallic mechanism proposed by Jacobsen shows nonadditive, cooperative catalysis with a larger reduction in barrier height than the sum of the barrier height reductions from the two monometallic reaction pathways. We computed barrier heights for the reaction using several counterions (chloride, acetate, tosylate, and hydroxide). For the three counterions that are experimentally active (chloride, acetate, and tosylate) the barrier heights are 35, 38, and 34 kJ mol(-1), respectively, while for hydroxide it is 48 kJ mol(-1). The similarity of the barrier heights for chloride, acetate, and tosylate is in agreement with their similar peak reaction rates. The finding that Co-salen-X with these counterions leads to rather different overall reaction profiles suggests that they have quite different rates of reaction with epoxide to form the activated Co-salen-OH required for the bimetallic mechanism. Co-salen-OH is inactive as the sole catalyst for HKR, and this inactivity is ascribed to its larger barrier height for the ring-opening step, rather than to any inability to activate epoxide. Barrier heights were also computed using propylene oxide, 1-hexene oxide, and epichlorohydrin; propylene oxide and 1-hexene oxide have similar barrier heights, 35.5 and 33.2 kJ mol(-1), respectively, and epichlorohydrin has a significantly lower barrier height of 18.8 kJ mol(-1), which is qualitatively consistent with experiments showing faster reactions for epicholorohydrin than propylene oxide when catalyzed by Co-salen-OAc.

Appointing silver and bronze standards for noncovalent interactions: a comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches.

A systematic examination of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-standard quality benchmarks available for 345 interaction energies of 49 bimolecular complexes. Quantum chemical techniques examined include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examination of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissociation curves. Moreover, when benchmarking accuracy is desirable but gold-standard computations are unaffordable, this work recommends silver-standard [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-standard [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, respectively. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014)] and density functional theory [L. A. Burns, Á. Vázquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys. 134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance.

Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies.

A systematic examination of the computational expense and accuracy of Symmetry-Adapted Perturbation Theory (SAPT) for the prediction of non-covalent interaction energies is provided with respect to both method [SAPT0, DFT-SAPT, SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3; with and without CCD dispersion for the last three] and basis set [Dunning cc-pVDZ through aug-cc-pV5Z wherever computationally tractable, including truncations of diffuse basis functions]. To improve accuracy for hydrogen-bonded systems, we also include two corrections based on exchange-scaling (sSAPT0) and the supermolecular MP2 interaction energy (δMP2). When considering the best error performance relative to computational effort, we recommend as the gold, silver, and bronze standard of SAPT: SAPT2+(3)δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ. Their respective mean absolute errors in interaction energy across the S22, HBC6, NBC10, and HSG databases are 0.15 (62.9), 0.30 (4.4), and 0.49 kcal mol(-1) (0.03 h for adenine·thymine complex).

Redox-linked conformational control of proton-coupled electron transfer: Y122 in the ribonucleotide reductase ß2 subunit.

Tyrosyl radicals play essential roles in biological proton-coupled electron transfer (PCET) reactions. Ribonucleotide reductase (RNR) catalyzes the reduction of ribonucleotides and is vital in DNA replication in all organisms. Class Ia RNRs consist of α2 and ß2 homodimeric subunits. In class Ia RNR, such as the E. coli enzyme, an essential tyrosyl radical (Y122O(•))-diferric cofactor is located in ß2. Although Y122O(•) is extremely stable in free ß2, Y122O(•) is highly reactive in the quaternary substrate-α2ß2 complex and serves as a radical initiator in catalytic PCET between ß2 and α2. In this report, we investigate the structural interactions that control the reactivity of Y122O(•) in a model system, isolated E. coli ß2. Y122O(•) was reduced with hydroxyurea (HU), a radical scavenger that quenches the radical in a clinically relevant reaction. In the difference FT-IR spectrum, associated with this PCET reaction, amide I (CO) and amide II (CN/NH) bands were observed. Specific (13)C-labeling of the tyrosine C1 carbon assigned a component of these bands to the Y122-T123 amide bond. Comparison to density functional calculations on a model dipeptide, tyrosine-threonine, and structural modeling demonstrated that PCET is associated with a Y122 rotation and a 7.2 Å translation of the Y122 phenolic oxygen. To test for the functional consequences of this structural change, a proton inventory defined the origin of the large solvent isotope effect (SIE = 16.7 ± 1.0 at 25 °C) on this reaction. These data suggest that the one-electron, HU-mediated reduction of Y122O(•) is associated with two, rate-limiting (full or partial) proton transfer reactions. One is attributable to HU oxidation (SIE = 11.9, net H atom transfer), and the other is attributable to coupled, hydrogen-bonding changes in the Y122O(•)-diferric cofactor (SIE = 1.4). These results illustrate the importance of redox-linked changes to backbone and ring dihedral angles in high potential PCET and provide evidence for rate-limiting, redox-linked hydrogen-bonding interactions between Y122O(•) and the iron cluster.

Buckyplates and buckybowls: examining the effects of curvature on π-π interactions.

π-π interactions are integral to many areas of chemistry, biochemistry, and materials science. Here we use electronic structure theory to analyze how π-π interactions change as the π-systems are curved in model complexes based on coronene and corannulene dimers. Curvature redistributes electronic charge in the π-cloud and creates a dipole moment in these systems, leading to enhanced intermolecular electrostatic interactions in the concave-convex (nested) geometries that are the focus of this work. Curvature of both monomers also has a geometric effect on the interaction by decreasing the average C-C distance between monomers and by increasing the magnitude of both favorable London dispersion interactions and unfavorable exchange-repulsion interactions. Overall, increasing curvature in nested π-π interactions leads to more favorable interaction energies regardless of the native state of the monomers, except at short distances where the most highly curved systems are less favorable as exchange repulsion terms begin to dominate the interaction.

Basis set convergence of the coupled-cluster correction, δ(MP2)(CCSD(T)): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases.

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δ(MP2)(CCSD(T)), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(T(*))-F12) correction, yielding a mean absolute deviation of 0.11 kcal mol(-1) for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(T)) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol(-1), respectively.

Density-functional approaches to noncovalent interactions: a comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals.

A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 - 0.38 kcal/mol.

Assessment of the Performance of DFT and DFT-D Methods for Describing Distance Dependence of Hydrogen-Bonded Interactions.

Noncovalent interactions such as hydrogen bonds, van der Waals forces, and π-π interactions play important roles influencing the structure, stability, and dynamic properties of biomolecules including DNA and RNA base pairs. In an effort to better understand the fundamental physics of hydrogen bonding (H-bonding), we investigate the distance dependence of interaction energies in the prototype bimolecular complexes of formic acid, formamide, and formamidine. Potential energy curves along the H-bonding dissociation coordinate are examined both by establishing reference CCSD(T) interaction energies extrapolated to the complete basis set limit and by assessing the performance of the density functional methods B3LYP, PBE, PBE0, B970, PB86, M05-2X, and M06-2X and empirical dispersion corrected methods B3LYP-D3, PBE-D3, PBE0-D3, B970-D2, BP86-D3, and ωB97X-D, with basis sets 6-311++G(3df,3pd), aug-cc-pVDZ, and aug-cc-pVTZ. Although H-bonding interactions are dominated by electrostatics, it is necessary to properly account for dispersion interactions to obtain accurate energetics. In order to quantitatively probe the nature of hydrogen bonding interactions as a function of distance, we decompose the interaction energy curves into physically meaningful components with symmetry-adapted perturbation theory (SAPT). The SAPT results confirm that the contribution of dispersion and induction are significant at and near equilibrium, although electrostatics dominate. Among the DFT/DFT-D techniques, the best overall results are obtained utilizing counterpoise-corrected ωB97X-D with the aug-cc-pVDZ basis set.