Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory.

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Working with benchmark datasets in the Cuby framework.

The development and benchmarking of computational chemistry methods rely on comparison with benchmark data. More and larger benchmark datasets are becoming available, and working efficiently with them is a necessity. The Cuby framework provides rich functionality for working with datasets, comes with many ready-to-use predefined benchmark sets, and interfaces with a wide range of computational chemistry software packages. Here, we review the tools Cuby provides for working with datasets and provide examples of more advanced workflows, such as handling large numbers of computations on high performance computing resources and reusing previously computed data. Cuby has also been extended recently to include two important benchmark databases, NCIAtlas and GMTKN55.

On the Role of Charge Transfer in Many-Body Non-Covalent Interactions.

Charge transfer is one of the mechanisms involved in non-covalent interactions. In molecular dimers, its contribution to pairwise interaction energies has been studied extensively using a variety of interaction energy decomposition schemes. In polar interactions such as hydrogen bonds, it can contribute ten or several tens of percent of the interaction energy. Less is known about its importance in higher-order interactions in many-body systems, mainly because of the lack of methods applicable to this problem. In this work, we extend our method for the quantification of the charge-transfer energy based on constrained DFT to many-body cases and apply it to model trimers extracted from molecular crystals. Our calculations show that charge transfer can account for a large fraction of the total three-body interaction energy. This also has implications for DFT calculations of many-body interactions in general as it is known that many DFT functionals struggle to describe charge-transfer effects correctly.

Non-Covalent Interactions Atlas benchmark data sets 5: London dispersion in an extended chemical space.

The Non-Covalent Interactions Atlas (https://www.nciatlas.org) has been extended with two data sets of benchmark interaction energies in complexes dominated by London dispersion. The D1200 data set of equilibrium geometries provides a thorough sampling of an extended chemical space, while the D442×10 set features dissociation curves for selected complexes. In total, they provide 5178 new CCSD(T)/CBS data points of the highest quality. The new data have been combined with previous NCIA data sets in a comprehensive test of dispersion-corrected DFT methods, identifying the ones that achieve high accuracy in all types of non-covalent interactions in a broad chemical space. Additional tests of dispersion-corrected MP2 and semiempirical QM methods are also reported.

Non-covalent interactions atlas benchmark data sets 4: σ-hole interactions.

The SH250×10 dataset presented here extends the Non-Covalent Interactions Atlas database (https://www.nciatlas.org) to complexes bound by σ-hole interactions - halogen, chalcogen and pnictogen bonds. It comprises 250 complexes where Cl, Br, I, S, Se, P and As interact with diverse electron donors. An accurate CCSD(T)/CBS benchmark is provided for ten points along a dissociation curve of each complex. The SH250×10 set is used in testing a wide variety of DFT functionals and semiempirical quantum-mechanical methods. In DFT calculations, the new data set exposes large errors of some functionals related to exaggerated charge transfer. The size and diversity of the data set have also been exploited in the reparametrization of a halogen-bond correction for the PM6 semiempirical method.

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: a path toward chemical accuracy.

Second-order Møller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeling problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description of van der Waals (London) dispersion interactions and reaction thermochemistry. Here, a spin-component-scaled, dispersion-corrected MP2 model (SCS-MP2D) is proposed that addresses these weaknesses. The dispersion correction, which is based on Grimme's D3 formalism, replaces the uncoupled Hartree-Fock dispersion inherent in MP2 with a more robust coupled Kohn-Sham treatment. The spin-component scaling of the residual MP2 correlation energy then reduces the remaining errors in the model. This two-part correction strategy solves the problem found in earlier spin-component-scaled MP2 models where completely different spin-scaling parameters were needed for describing reaction energies versus intermolecular interactions. Results on 18 benchmark data sets and two challenging potential energy curves demonstrate that SCS-MP2D considerably improves upon the accuracy of MP2 for intermolecular interactions, conformational energies, and reaction energies. Its accuracy and computational cost are competitive with state-of-the-art density functionals such as DSD-BLYP-D3(BJ), revDSD-PBEP86-D3(BJ), ωB97X-V, and ωB97M-V for systems with ∼100 atoms.

Conformational energies and equilibria of cyclic dinucleotides in vacuo and in solution: computational chemistry vs. NMR experiments.

Performance of computational methods in modelling cyclic dinucleotides - an important and challenging class of compounds - has been evaluated by two different benchmarks: (1) gas-phase conformational energies and (2) qualitative agreement with NMR observations of the orientation of the χ-dihedral angle in solvent. In gas-phase benchmarks, where CCSD(T) and DLPNO-CCSD(T) methods have been used as the reference, most of the (dispersion corrected) density functional approximations are accurate enough to justify prioritizing computational cost and compatibility with other modelling options as the criterion of choice. NMR experiments of 3'3'-c-di-AMP, 3'3'-c-GAMP, and 3'3'-c-di-GMP show the overall prevalence of the anti-conformation of purine bases, but some population of syn-conformations is observed for guanines. Implicit solvation models combined with quantum-chemical methods struggle to reproduce this behaviour, probably due to a lack of dynamics and explicitly modelled solvent, leading to structures that are too compact. Molecular dynamics simulations overrepresent the syn-conformation of guanine due to the overestimation of an intramolecular hydrogen bond. Our combination of experimental and computational benchmarks provides "error bars" for modelling cyclic dinucleotides in solvent, where such information is generally difficult to obtain, and should help gauge the interpretability of studies dealing with binding of cyclic dinucleotides to important pharmaceutical targets. At the same time, the presented analysis calls for improvement in both implicit solvation models and force-field parameters.

Benchmark Data Sets of Boron Cluster Dihydrogen Bonding for the Validation of Approximate Computational Methods.

The success of approximate computational methods, such as molecular mechanics, or dispersion-corrected density functional theory, in the description of non-covalent interactions relies on accurate parameterizations. Benchmark data sets are thus required. This area is well developed for organic molecules and biomolecules but practically non-existent for boron clusters, which have been gaining in importance in modern drug as well as material design. To fill this gap, we have introduced two data sets featuring the most common non-covalent interaction of boron clusters, the dihydrogen bond, and calculated reference interaction energies at the "golden standard" CCSD(T)/CBS level. The boron clusters studied interact with formamide, methanol, water and methane at various distances and in two geometrical arrangements. The performance of the tested approximate methods is variable and recommendations for further use are given.

Benchmarking of Semiempirical Quantum-Mechanical Methods on Systems Relevant to Computer-Aided Drug Design.

The semiempirical quantum mechanical (SQM) methods used in drug design are commonly parametrized and tested on data sets of systems that may not be representative models for drug-biomolecule interactions in terms of both size and chemical composition. This is addressed here with a new benchmark data set, PLF547, derived from protein-ligand complexes, consisting of complexes of ligands with protein fragments (such as amino-acid side chains), with interaction energies based on MP2-F12 and DLPNO-CCSD(T) calculations. From these, composite benchmark interaction energies are also built for complexes of the ligand with the complete active site of the protein (PLA15 data set). These data sets are used to test multiple SQM methods with corrections for noncovalent interactions; the role of the solvation model in the calculations is tested as well.

Description of halogen bonding in semiempirical quantum-mechanical and self-consistent charge density-functional tight-binding methods.

This article analyzes the ability of semiempirical quantum-mechanical methods (PM6 and PM7) and self-consistent charge density-functional tight-binding (SCC-DFTB) method DFTB3 to describe halogen bonds. Calculations of the electrostatic potential on the surface of molecules containing halogens show that the σ-hole could be described well in modified neglect of diatomic overlap-based methods. The situation is more complex in the case of DFTB3 where a simpler model is used for the electrostatics, but short-ranged effects are covered in the Hamiltonian. All these methods can thus capture the effects that, for example, define the geometry of halogen bonds. The interaction energies are, however, affected by generally underestimated repulsion, which has been addressed earlier by standalone empirical corrections. Another approach to correcting this issue in DFTB3 is presented here-a modification of the energies of d-orbitals on halogens yields better results than the empirical correction in DFTB3-D3X, although it remains difficult to describe halogen and hydrogen bonds simultaneously. © 2019 Wiley Periodicals, Inc.

Impressive Enrichment of Semiempirical Quantum Mechanics-Based Scoring Function: HSP90 Protein with 4541 Inhibitors and Decoys.

The image shows the ability of SQM-based frame to separate the actives (background: green spheres) from inactives (red spheres) while maintaining a powerful sampling (front: HSP90 crystal complex). Read the full text of the Article at 10.1002/cphc.201900628.

Impressive Enrichment of Semiempirical Quantum Mechanics-Based Scoring Function: HSP90 Protein with 4541 Inhibitors and Decoys.

This paper describes the excellent performance of a newly developed scoring function (SF), based on the semiempirical QM (SQM) PM6-D3H4X method combined with the conductor-like screening implicit solvent model (COSMO). The SQM/COSMO, Amber/GB and nine widely used SFs have been evaluated in terms of ranking power on the HSP90 protein with 72 biologically active compounds and 4469 structurally similar decoys. Among conventional SFs, the highest early and overall enrichment measured by EF1 and AUC% obtained using single-scoring-function ranking has been found for Glide SP and Gold-ASP SFs, respectively (7, 75 % and 3, 76 %). The performance of other standard SFs has not been satisfactory, mostly even decreasing below random values. The SQM/COSMO SF, where P-L structures were optimised at the advanced Amber level, has resulted in a dramatic enrichment increase (47, 98 %), almost reaching the best possible receiver operator characteristic (ROC) curve. The best SQM frame thus inserts about seven times more active compounds into the selected dataset than the best standard SF.

Reparametrization of the COSMO Solvent Model for Semiempirical Methods PM6 and PM7.

An accurate description of solvation effects is of high importance in modeling biomolecular systems. Our main interest is to find an accurate yet efficient solvation model for semiempirical quantum-mechanical methods applicable to large protein-ligand complexes in the context of computer-aided drug design. We present a survey of readily available methods and a new reparametrization of the COSMO solvent model for PM6 and PM7 calculations in MOPAC. We have tested the reparametrized method on validation data sets of small drug-like molecules for which experimental solvation free energies are available as well as on a set of large model systems of the active site of carbonic anhydrase II interacting with a series of ligands for which experimental affinity values are known. In both cases, there is a significant improvement in accuracy after the reparametrization and the addition of a nonpolar term to the COSMO solvent model.

Ranking Power of the SQM/COSMO Scoring Function on Carbonic Anhydrase†II-Inhibitor Complexes.

Accurate prediction of protein-ligand binding affinities is essential for hit-to-lead optimization and virtual screening. The reliability of scoring functions can be improved by including quantum effects. Here, we demonstrate the ranking power of the semiempirical quantum mechanics (SQM)/implicit solvent (COSMO) scoring function by using a challenging set of 10 inhibitors binding to carbonic anhydrase II through Zn2+ in the active site. This new dataset consists of the high-resolution (1.1-1.4 Å) crystal structures and experimentally determined inhibitory constant (Ki ) values. It allows for evaluation of the common approximations, such as representing the solvent implicitly or by using a single target conformation combined with a set of ligand docking poses. SQM/COSMO attained a good correlation of R2 of 0.56-0.77 with the experimental inhibitory activities, benefiting from careful handling of both noncovalent interactions (e.g. charge transfer) and solvation. This proof-of-concept study of SQM/COSMO ranking for metalloprotein-ligand systems demonstrates its potential for hit-to-lead applications.

Macrocycle Conformational Sampling by DFT-D3/COSMO-RS Methodology.

To find and calibrate a robust and reliable computational protocol for mapping conformational space of medium-sized molecules, exhaustive conformational sampling has been carried out for a series of seven macrocyclic compounds of varying ring size and one acyclic analogue. While five of them were taken from the MD/LLMOD/force field study by Shelley and co-workers ( Watts , K. S. ; Dalal , P. ; Tebben , A. J. ; Cheney , D. L. ; Shelley , J. C. Macrocycle Conformational Sampling with MacroModel . J. Chem. Inf. MODEL: 2014 , 54 , 2680 - 2696 ), three represent potential macrocyclic inhibitors of human cyclophilin A. The free energy values (GDFT/COSMO-RS) for all of the conformers of each compound were obtained by a composite protocol based on in vacuo quantum mechanics (DFT-D3 method in a large basis set), standard gas-phase thermodynamics, and the COSMO-RS solvation model. The GDFT/COSMO-RS values were used as the reference for evaluating the performance of conformational sampling algorithms: standard and extended MD/LLMOD search (simulated-annealing molecular dynamics with low-lying eigenvector following algorithms, employing the OPLS2005 force field plus GBSA solvation) available in MacroModel and plain molecular dynamics (MD) sampling at high temperature (1000 K) using the semiempirical quantum mechanics (SQM) potential SQM(PM6-D3H4/COSMO) followed by energy minimization of the snapshots. It has been shown that the former protocol (MD/LLMOD) may provide a more complete set of initial structures that ultimately leads to the identification of a greater number of low-energy conformers (as assessed by GDFT/COSMO-RS) than the latter (i.e., plain SQM MD). The CPU time needed to fully evaluate one medium-sized compound (∼100 atoms, typically resulting in several hundred or a few thousand conformers generated and treated quantum-mechanically) is approximately 1,000-100,000 CPU hours on today's computers, which transforms to 1-7 days on a small-sized computer cluster with a few hundred CPUs. Finally, our data sets based on the rigorous quantum-chemical approach allow us to formulate a composite conformational sampling protocol with multiple checkpoints and truncation of redundant structural data that offers superior insights at affordable computational cost.

Benchmark Calculations of Interaction Energies in Noncovalent Complexes and Their Applications.

Data sets of benchmark interaction energies in noncovalent complexes are an important tool for quantifying the accuracy of computational methods used in this field, as well as for the development of new computational approaches. This review is intended as a guide to conscious use of these data sets. We discuss their construction and accuracy, list the data sets available in the literature, and demonstrate their application to validation and parametrization of quantum-mechanical computational methods. In practical model systems, the benchmark interaction energies are usually obtained using composite CCSD(T)/CBS schemes. To use these results as a benchmark, their accuracy should be estimated first. We analyze the errors of this methodology with respect to both the approximations involved and the basis set size. We list the most prominent data sets covering various aspects of the field, from general ones to sets focusing on specific types of interactions or systems. The benchmark data are then used to validate more efficient computational approaches, including those based on explicitly correlated methods. Special attention is paid to the transition to large systems, where accurate benchmarking is difficult or impossible, and to the importance of nonequilibrium geometries in parametrization of more approximate methods.

Description of non-covalent interactions in SCC-DFTB methods.

We have analyzed the description of non-covalent interactions in multiple variants of the self-consistent charges density functional tight binding (SCC-DFTB) method. While the description of London dispersion can be easily improved by empirical correction, hydrogen bonding poses a much more difficult problem. We have implemented an interaction energy decomposition scheme that allowed us to quantify the error at the level of first-order electrostatic and polarization terms. Both are underestimated because of the monopole approximation used in SCC-DFTB, with the latter being affected also by the use of minimal basis set. Among the methods tested, SCC-DFTB with the empirical D3H4 corrections worked best. To make this correction compatible with the latest development in SCC-DFTB, we have reparameterized it for use with third-order SCC-DFTB with the 3OB parameter set. © 2017 Wiley Periodicals, Inc.

SQM/COSMO Scoring Function at the DFTB3-D3H4 Level: Unique Identification of Native Protein-Ligand Poses.

We have recently introduced the "SQM/COSMO" scoring function which combines a semiempirical quantum mechanical description of noncovalent interactions at the PM6-D3H4X level and the COSMO implicit model of solvation. This approach outperformed standard scoring functions but faced challenges with a metalloprotein featuring a Zn2+···S- interaction. Here, we invoke SCC-DFTB3-D3H4, a higher-level SQM method, and observe improved behavior for the metalloprotein and high-quality results for the other systems. This method holds promise for diverse protein-ligand complexes including metalloproteins.

Non-covalent interactions in anisole-(CO2)n (n = 1, 2) complexes.

Non-covalent interactions are ubiquitous and represent a very important binding motif. The direct experimental measurement of binding energies in complexes has been elusive for a long time despite its importance, for instance, for understanding and predicting the structure of bio-macromolecules. Here, we report a combined experimental and computational analysis on the 1 : 1 and 1 : 2 clusters formed by anisole (methoxybenzene) and carbon dioxide molecules. We have obtained a detailed description of the interaction between CO2 and anisole. This system represents quite a challenging test for the presently available experimental and theoretical methods for the characterization of weakly bound molecular complexes. The results, evaluated in the framework of previous studies on anisole clusters, show a very good agreement between experimental and theoretical data. A comparison of the experimental and computational data enabled the binding energy values of the 1 : 1 and 1 : 2 clusters to be determined in the ground electronic state of the neutral and cation complex and in the first excited singlet state of the neutral complex. In addition, it was possible to adduce the presence of different 1 : 1+ conformers, prepared by direct ionization of the 1 : 1 complex or by dissociative ionization of the 1 : 2 complex.

B-Hπ: a nonclassical hydrogen bond or dispersion contact?

Close B-Hπ contacts have recently been observed in crystallographic structures of Ir-dithiolene-phosphine complexes containing boron hydride cluster. This finding was interpreted using quantum chemical calculations as a new type of electrostatically driven nonclassical hydrogen bonding. However, such an explanation contradicts the wealth of evidence for unique noncovalent interactions of boron hydrides. Moreover, care must be exercised when computational methods are used to interpret new phenomena. Therefore, here, we cautiously examine the B-Hπ interaction by means of advanced quantum chemistry and disprove the claimed attractive electrostatic nature and rather define it as a nonspecific dispersion-driven contact. In summary, we present evidence that the crystallographically observed B-Hπ contacts do not constitute a novel type of hydrogen bonding of boron hydride clusters.