An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation.

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Strategies for the Design of PEDOT Analogues Unraveled: the Use of Chalcogen Bonds and σ-Holes.

In this theoretical study, we set out to demonstrate the substitution effect of PEDOT analogues on planarity as an intrinsic indicator for electronic performance. We perform a quantum mechanical (DFT) study of PEDOT and analogous model systems and demonstrate the usefulness of the ωB97X-V functional to simulate chalcogen bonds and other noncovalent interactions. We confirm that the chalcogen bond stabilizes the planar conformation and further visualize its presence via the electrostatic potential surface. In comparison to the prevalent B3LYP, we gain 4-fold savings in computational time and simulate model systems of up to a dodecamer. Implications for design of conductive polymers can be drawn from the results, and an example for self-doped polymers is presented where modulation of the strength of the chalcogen bond plays a significant role.

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.

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.

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.

Chalcogen Bonding in Protein-Ligand Complexes: PDB Survey and Quantum Mechanical Calculations.

A chalcogen bond is a nonclassical noncovalent interaction which can stabilise small-molecule crystals as well as protein structures. Here, we systematically explore the stabilising potential of chalcogen bonding in protein-ligand complexes in the Protein Data Bank (PDB). We have found that a large fraction (23 %) of complexes with a S/Se-containing ligand feature close S/Se⋅⋅⋅O/N/S contacts. Eleven non-redundant representative potential S/Se⋅⋅⋅O chalcogen-bond motifs were selected and truncated to model systems and seven more model systems were prepared by S-to-Se substitution. These systems were then subjected to analysis by quantum chemical (QM) methods-electrostatic potential, geometry optimisation or interaction energy calculations, including solvent effects. The QM calculations indicate that chalcogen bonding does indeed play a dominant role in stabilising some of the interaction motifs studied. We thus advocate further exploration of chalcogen bonding with the aim of potential future use in structure-based drug design.

Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases.

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as (12(σi3+σj3))1/3 and one for the well-depth ϵij as (12(ϵi-2+ϵj-2))-1/2. The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

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.