A fast and user-friendly computational for predicting the regioselectivity of electrophilic aromatic substitution reactions of heteroaromatic systems is presented.

We present new dispersion and hydrogen bond corrections to the PM6 method, PM6-D3H+, and its implementation in the GAMESS program. The method combines the DFT-D3 dispersion correction by Grimme et al. with a modified version of the H+ hydrogen bond correction by Korth. Overall, the interaction energy of PM6-D3H+ is very similar to PM6-DH2 and PM6-DH+, with RMSD and MAD values within 0.02 kcal/mol of one another. The main difference is that the geometry optimizations of 88 complexes result in 82, 6, 0, and 0 geometries with 0, 1, 2, and 3 or more imaginary frequencies using PM6-D3H+ implemented in GAMESS, while the corresponding numbers for PM6-DH+ implemented in MOPAC are 54, 17, 15, and 2. The PM6-D3H+ method as implemented in GAMESS offers an attractive alternative to PM6-DH+ in MOPAC in cases where the LBFGS optimizer must be used and a vibrational analysis is needed, e.g., when computing vibrational free energies. While the GAMESS implementation is up to 10 times slower for geometry optimizations of proteins in bulk solvent, compared to MOPAC, it is sufficiently fast to make geometry optimizations of small proteins practically feasible.

The PM6 implementation in the GAMESS program is extended to elements requiring -integrals and interfaced with the conducter-like polarized continuum model of solvation, including gradients. The accuracy of aqueous solvation energies computed using AM1, PM3, PM6, and DFT tight binding (DFTB) and the Solvation Model Density (SMD) continuum solvation model is tested using the Minnesota Solvation Database data set. The errors in SMD solvation energies predicted using Neglect of Diatomic Differential Overlap (NDDO)-based methods are considerably larger than when using density functional theory (DFT) and HF, with root mean square error (RMSE) values of 3.4-5.9 (neutrals) and 6-15 kcal/mol (ions) compared to 2.4 and ∼5 kcal/mol for HF/6-31G(d). For the NDDO-based methods, the errors are especially large for cations and considerably higher than the corresponding conductor-like screening model results, which suggests that the NDDO/SMD results can be improved by re-parameterizing the SMD parameters focusing on ions. We found that the best results are obtained by changing only the radii for hydrogen, carbon, oxygen, nitrogen, and sulfur, and this leads to RMSE values for PM3 (neutrals: 2.8/ions: ∼5 kcal/mol), PM6 (4.7/∼5 kcal/mol), and DFTB (3.9/∼5 kcal/mol) that are more comparable to HF/6-31G(d) (2.4/∼5 kcal/mol). Although the radii are optimized to reproduce aqueous solvation energies, they also lead more accurate predictions for other polar solvents such as dimethyl sulfoxide, acetonitrile, and methanol, while the improvements for non-polar solvents are negligible.

We have collected computed barrier heights and reaction energies (and associated model structures) for five enzymes from studies published by Himo and co-workers. Using this data, obtained at the B3LYP/6- 311+G(2d,2p)[LANL2DZ]//B3LYP/6-31G(d,p) level of theory, we then benchmark PM6, PM7, PM7-TS, and DFTB3 and discuss the influence of system size, bulk solvation, and geometry re-optimization on the error. The mean absolute differences (MADs) observed for these five enzyme model systems are similar to those observed for PM6 and PM7 for smaller systems (10–15 kcal/mol), while DFTB results in a MAD that is significantly lower (6 kcal/mol). The MADs for PMx and DFTB3 are each dominated by large errors for a single system and if the system is disregarded the MADs fall to 4–5 kcal/mol. Overall, results for the condensed phase are neither more or less accurate relative to B3LYP than those in the gas phase. With the exception of PM7-TS, the MAD for small and large structural models are very similar, with a maximum deviation of 3 kcal/mol for PM6. Geometry optimization with PM6 shows that for one system this method predicts a different mechanism compared to B3LYP/6-31G(d,p). For the remaining systems, geometry optimization of the large structural model increases the MAD relative to single points, by 2.5 and 1.8 kcal/mol for barriers and reaction energies. For the small structural model, the corresponding MADs decrease by 0.4 and 1.2 kcal/mol, respectively. However, despite these small changes, significant changes in the structures are observed for some systems, such as proton transfer and hydrogen bonding rearrangements. The paper represents the first step in the process of creating a benchmark set of barriers computed for systems that are relatively large and representative of enzymatic reactions, a considerable challenge for any one research group but possible through a concerted effort by the community. We end by outlining steps needed to expand and improve the data set and how other researchers can contribute to the process.

A new Web application called The Molecule Calculator (MolCalc) is described. The entry page is a molecular editor (JSmol) for interactive molecule building. The resulting structure can then be used to estimate molecular properties such as heats of formation and other thermodynamic properties, vibrational frequencies and vibrational modes, and molecular orbitals and orbital energies. These properties are computed using the GAMESS program at either the RHF/STO-3G (orbitals and orbital energies) or PM3 level of theory (all other properties) in a matter of seconds or minutes depending on the size of the molecule. The results, though approximate, can help students develop a chemical intuition about how molecular structure affects molecular properties, without performing the underlying calculations by hand, a nearly impossible task for all but the simplest chemical systems.

The PM6 semiempirical method and the dispersion and hydrogen bond-corrected PM6-D3H+ method are used together with the SMD and COSMO continuum solvation models to predict pKa values of pyridines, alcohols, phenols, benzoic acids, carboxylic acids, and phenols using isodesmic reactions and compared to published ab initio results. The pKa values of pyridines, alcohols, phenols, and benzoic acids considered in this study can generally be predicted with PM6 and ab initio methods to within the same overall accuracy, with average mean absolute differences (MADs) of 0.6–0.7 pH units. For carboxylic acids, the accuracy (0.7–1.0 pH units) is also comparable to ab initio results if a single outlier is removed. For primary, secondary, and tertiary amines the accuracy is, respectively, similar (0.5–0.6), slightly worse (0.5–1.0), and worse (1.0–2.5), provided that di- and tri-ethylamine are used as reference molecules for secondary and tertiary amines. When applied to a drug-like molecule where an empirical pKa predictor exhibits a large (4.9 pH unit) error, we find that the errors for PM6-based predictions are roughly the same in magnitude but opposite in sign. As a result, most of the PM6-based methods predict the correct protonation state at physiological pH, while the empirical predictor does not. The computational cost is around 2–5 min per conformer per core processor, making PM6-based pKa prediction computationally efficient enough to be used for high-throughput screening using on the order of 100 core processors.

Lipophilicity, as measured by the partition coefficient between octanol and water (log P), is a key parameter in early drug discovery research. However, measuring log P experimentally is difficult for specific compounds and log P ranges. The resulting lack of reliable experimental data impedes development of accurate in silico models for such compounds. In certain discovery projects at Novartis focused on such compounds, a quantum mechanics (QM)-based tool for log P estimation has emerged as a valuable supplement to experimental measurements and as a preferred alternative to existing empirical models. However, this QM-based approach incurs a substantial computational cost, limiting its applicability to small series and prohibiting quick, interactive ideation. This work explores a set of machine learning models (Random Forest, Lasso, XGBoost, Chemprop, and Chemprop3D) to learn calculated log P values on both a public data set and an in-house data set to obtain a computationally affordable, QM-based estimation of drug lipophilicity. The message-passing neural network model Chemprop emerged as the best performing model with mean absolute errors of 0.44 and 0.34 log units for scaffold split test sets of the public and in-house data sets, respectively. Analysis of learning curves suggests that a further decrease in the test set error can be achieved by increasing the training set size. While models directly trained on experimental data perform better at approximating experimentally determined log P values than models trained on calculated values, we discuss the potential advantages of using calculated log P values going beyond the limits of experimental quantitation. We analyze the impact of the data set splitting strategy and gain insights into model failure modes. Potential use cases for the presented models include pre-screening of large compound collections and prioritization of compounds for full QM calculations.

We present new dispersion and hydrogen bond corrections to the PM6 method, PM6-D3H+, and its implementation in the GAMESS program. The method combines the DFT-D3 dispersion correction by Grimme et al with a modified version of the H+ hydrogen bond correction by Korth. Overall, the interaction energy of PM6-D3H+ is very similar to PM6-DH2 and PM6-DH+, with RMSD and MAD values within 0.02 kcal/mol of one another. The main difference is that the geometry optimizations of 88 complexes result in 82, 6, 0, and 0 geometries with 0, 1, 2, and $\ge$ 3 imaginary frequencies using PM6-D3H+ implemented in GAMESS, while the corresponding numbers for PM6-DH+ implemented in MOPAC are 54, 17, 15, and 2. The PM6-D3H+ method as implemented in GAMESS offers an attractive alternative to PM6-DH+ in MOPAC in cases where the LBFGS optimizer must be used and a vibrational analysis is needed, e.g. when computing vibrational free energies. While the GAMESS implementation is up to 10 times slower for geometry optimizations of proteins in bulk solvent, compared to MOPAC, it is sufficiently fast to make geometry optimizations of small proteins practically feasible.