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.

SQM2.20: Semiempirical quantum-mechanical scoring function yields DFT-quality protein-ligand binding affinity predictions in minutes.

Accurate estimation of protein-ligand binding affinity is the cornerstone of computer-aided drug design. We present a universal physics-based scoring function, named SQM2.20, addressing key terms of binding free energy using semiempirical quantum-mechanical computational methods. SQM2.20 incorporates the latest methodological advances while remaining computationally efficient even for systems with thousands of atoms. To validate it rigorously, we have compiled and made available the PL-REX benchmark dataset consisting of high-resolution crystal structures and reliable experimental affinities for ten diverse protein targets. Comparative assessments demonstrate that SQM2.20 outperforms other scoring methods and reaches a level of accuracy similar to much more expensive DFT calculations. In the PL-REX dataset, it achieves excellent correlation with experimental data (average R2 = 0.69) and exhibits consistent performance across all targets. In contrast to DFT, SQM2.20 provides affinity predictions in minutes, making it suitable for practical applications in hit identification or lead optimization.

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.

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.

Non-Covalent Interactions Atlas Benchmark Data Sets 3: Repulsive Contacts.

The new R739×5 data set from the Non-Covalent Interactions Atlas series (www.nciatlas.org) focuses on repulsive contacts in molecular complexes, covering organic molecules, sulfur, phosphorus, halogens, and noble gases. Information on the repulsive parts of the potential energy surface is crucial for the development of robust empirically parametrized computational methods. We use the new data set of highly accurate CCSD(T)/CBS interaction energies to test selected density functional theory (DFT) and semiempirical quantum-mechanical methods. The double-hybrid functionals were the best performing, with the revDSD-PBEP86-D3 being the most accurate DFT method, followed by the range-separated ωB97X functionals. Out of semiempirical methods, GFN2-xTB yielded the best results. On the example of the PM6 method, we analyze the source of error and its relation to the difficulties in the description of conformational energies, and we also devise an immediately applicable correction that fixes the most serious uncorrected issues previously encountered in practical calculations.

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.

SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design.

Invited for this month's cover is the group of Prof. Pavel Hobza, Czech Academy of Sciences, Prague. The cover picture shows a powerful automated quantum mechanics based SQM/COSMO approach to protein-ligand scoring. It comprises thorough preparation of ligand structures, extensive generation of binding complexes, fast geometry relaxation and reliable affinity prediction. Read the full text of the Minireview at 10.1002/cplu.202000120.

Non-Covalent Interactions Atlas Benchmark Data Sets 2: Hydrogen Bonding in an Extended Chemical Space.

The Non-Covalent Interactions Atlas (www.nciatlas.org) aims to provide a new generation of benchmark data sets for noncovalent interactions. The HB300SPX data set presented here extends the coverage of hydrogen bonds to phosphorus, sulfur, and halogens up to iodine. It is again complemented by a set of dissociation curves, HB300SPX×10. The new data make it possible to analyze the transferability of the parametrization of, e.g., dispersion corrections for the density functional theory (DFT) from simple organic molecules to a broader chemical space. The HB300SPX×10 has also been used for the extension of the parametrization of hydrogen-bonding corrections in the semiempirical PM6-D3H4X and DFTB3-D3H5 methods to additional elements.

SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design.

Quantum mechanical (QM) methods have been gaining importance in structure-based drug design where a reliable description of protein-ligand interactions is of utmost significance. However, strategies i. e. QM/MM, fragmentation or semiempirical (SQM) methods had to be pursued to overcome the unfavorable scaling of QM methods. Various SQM-based approaches have significantly contributed to the accuracy of docking and improvement of lead compounds. Parametrizations of SQM and implicit solvent methods in our laboratory have been instrumental to obtain a reliable SQM-based scoring function. The experience gained in its application for activity ranking of ligands binding to tens of protein targets resulted in setting up a faster SQM/COSMO scoring approach, which outperforms standard scoring methods in native pose identification for two dozen protein targets with ten thousand poses. Recently, SQM/COSMO was effectively applied in a proof-of-concept study of enrichment in virtual screening. Due to its superior performance, feasibility and chemical generality, we propose the SQM/COSMO approach as an efficient tool in structure-based drug design.

Non-Covalent Interactions Atlas Benchmark Data Sets: Hydrogen Bonding.

The Non-Covalent Interactions Atlas project (www.nciatlas.org) aims to cover a wide range of noncovalent interactions with a new generation of benchmark data sets. This Article presents the first two data sets focused on hydrogen bonding: HB375, featuring neutral systems, and IHB100 for ionic H-bonds. Both data sets are complemented by 10-point dissociation curves (HB375×10, IHB100×10). The interaction energies are extrapolated to the CCSD(T)/CBS limit from calculations in large basis sets. The Article also summarizes the design principles that will be used to construct the subsequent data sets in the series. The testing of DFT-D methods on the HB375 set has revealed interesting, previously unnoticed issues. The application of the new data to the testing and parametrization of semiempirical QM methods is also discussed.

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.

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.

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.

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.

Gating the electron transfer at a monocopper centre through the supramolecular coordination of water molecules within a protein chamber mimic.

Functionality of enzymes is strongly related to water dynamic processes. The control of the redox potential for metallo-enzymes is intimately linked to the mediation of water molecules in the first and second coordination spheres. Here, we report a unique example of supramolecular control of the redox properties of a biomimetic monocopper complex by water molecules. It is shown that the copper complex based on a calix[6]arene covalently capped with a tetradentate [tris(2-methylpyridyl)amine] (tmpa) core, embedding the metal ion in a hydrophobic cavity, can exist in three different states. The first system displays a totally irreversible redox behaviour. It corresponds to the reduction of the 5-coordinate mono-aqua-CuII complex, which is the thermodynamic species in the +II state. The second system is detected at a high redox potential. It is ascribed to an "empty cavity" or "water-free" state, where the CuI ion sits in a 4-coordinate trigonal environment provided by the tmpa cap. This complex is the thermodynamic species in the +I state under "dry conditions". Surprisingly, a third redox system appears as the water concentration is increased. Under water-saturation conditions, it displays a pseudo-reversible behaviour at a low scan rate at the mid-point from the water-free and aqua species. This third system is not observed with the Cu-tmpa complex deprived of a cavity. In the calix[6]cavity environment, it is ascribed to a species where a pair of water molecules is hosted by the calixarene cavity. A molecular mechanism for the CuII/CuI redox process with an interplay of (H2O) x (x = 0, 1, 2) hosting is proposed on the basis of computational studies. Such an unusual behaviour is ascribed to the unexpected stabilization of the CuI state by inclusion of the pair of water molecules. This phenomenon strongly evidences the drastic influence of the interaction between water molecules and a hydrophobic cavity on controlling the thermodynamics and kinetics of the CuII/CuI electron transfer process.