Hybrid Machine Learning Approach to Predict the Site Selectivity of Iridium-Catalyzed Arene Borylation.

The borylation of aryl and heteroaryl C-H bonds is valuable for the site-selective functionalization of C-H bonds in complex molecules. Iridium catalysts ligated by bipyridine ligands catalyze the borylation of the C-H bond that is most acidic and least sterically hindered in an arene, but predicting the site of borylation in molecules containing multiple arenes is difficult. To address this challenge, we report a hybrid computational model that predicts the Site of Borylation (SoBo) in complex molecules. The SoBo model combines density functional theory, semiempirical quantum mechanics, cheminformatics, linear regression, and machine learning to predict site selectivity and to extrapolate these predictions to new chemical space. Experimental validation of SoBo showed that the model predicts the major site of borylation of pharmaceutical intermediates with higher accuracy than prior machine-learning models or human experts, demonstrating that SoBo will be useful to guide experiments for the borylation of specific C(sp2)-H bonds during pharmaceutical development.

Fast calculation of hydrogen-bond strengths and free energy of hydration of small molecules.

Hydrogen bonding is an interaction of great importance in drug discovery and development as it may significantly affect chemical and biological processes including the interaction of small molecules with other molecules, proteins, and membranes. In particular, hydrogen bonding can impact drug-like properties such as target affinity and oral availability which are critical to developing effective pharmaceuticals, and therefore, numerous methods for the calculation of properties such as hydrogen-bond strengths, free energy of hydration, or water solubility have been proposed over time. However, the accessibility to efficient methods for the predictions of such properties is still limited. Here, we present the development of Jazzy, an open-source tool for the prediction of hydrogen-bond strengths and free energies of hydration of small molecules. Jazzy also allows the visualisation of hydrogen-bond strengths with atomistic resolution to support the design of compounds with desired properties and the interpretation of existing data. The tool is described in its implementation, parameter fitting, and validation against two data sets of experimental hydration free energies. Jazzy is also applied against two chemical series of bioactive compounds to show that hydrogen-bond strengths can be used to understand their structure-activity relationships. Results from the validations highlight the strengths and limitations of Jazzy, and suggest its suitability for interactive design, screening, and machine-learning featurisation.

An open-source framework for fast-yet-accurate calculation of quantum mechanical features.

We present the open-source framework kallisto that enables the efficient and robust calculation of quantum mechanical features for atoms and molecules. For a benchmark set of 49 experimental molecular polarizabilities, the predictive power of the presented method competes against second-order perturbation theory in a converged atomic-orbital basis set at a fraction of its computational costs. The calculation of isotropic molecular polarizabilities is robust for a data set of more than 80 000 molecules. We present furthermore a generally applicable van der Waals radius model that is rooted on atomic static polarizabilites. Efficiency tests show that such radii can even be calculated for small- to medium-size proteins where the largest system (SARS-CoV-2 spike protein) has 42 539 atoms. Following the work of Domingo-Alemenara et al. [Domingo-Alemenara et al., Nat. Commun., 2019, 10, 5811], we present computational predictions for retention times for different chromatographic methods and describe how physicochemical features improve the predictive power of machine-learning models that otherwise only rely on two-dimensional features like molecular fingerprints. Additionally, we developed an internal benchmark set of experimental super-critical fluid chromatography retention times. For those methods, improvements of up to 10.6% are obtained when combining molecular fingerprints with physicochemical descriptors. Shapley additive explanation values show furthermore that the physical nature of the applied features can be retained within the final machine-learning models. We generally recommend the kallisto framework as a robust, low-cost, and physically motivated featurizer for upcoming state-of-the-art machine-learning studies.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions.

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

Extension and evaluation of the D4 London-dispersion model for periodic systems.

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredients are additional reference polarizabilities for highly-coordinated group 1-5 elements derived from pseudo-periodic electrostatically-embedded cluster calculations. To illustrate the performance of the updated method, several test cases are considered, for which we compare D4 to its predecessor D3(BJ), as well as to a comprehensive set of other dispersion-corrected methods. The largest improvements are observed for solid-state polarizabilities of 16 inorganic salts, where the D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides values in good agreement with experimental and/or high-level references. These results suggest the application of the proposed D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.

A generally applicable atomic-charge dependent London dispersion correction.

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

Understanding and Quantifying London Dispersion Effects in Organometallic Complexes.

Quantum chemical methods are nowadays able to determine properties of larger chemical systems with high accuracy and Kohn-Sham density functional theory (DFT) in particular has proven to be robust and suitable for everyday applications of electronic structure theory. A clear disadvantage of many established standard density functional approximations like B3LYP is their inability to describe long-range electron correlation effects. The inclusion of such effects, also termed London dispersion, into DFT has been extensively researched in recent years, resulting in some efficient and routinely used correction schemes. The well-established D3 method has demonstrated its efficiency and accuracy in numerous applications since 2010. Recently, it was improved by developing the successor (termed D4) which additionally includes atomic partial charge information for the generation of pairwise dispersion coefficients. These coefficients determine the leading-order (two-body) and higher-order (three- or many-body) terms of the D4 dispersion energy which is simply added to a standard DFT energy. With its excellent accuracy-to-cost ratio, the DFT-D4 method is well suited for the determination of structures and chemical properties for molecules of most kinds. While dispersion effects in organic molecules are nowadays well studied, much less is known for organometallic complexes. For such systems, there has been a growing interest in designing dispersion-controlled reactions especially in the field of homogeneous catalysis. Here, efficient electronic structure methods are necessary for screening of promising model complexes and quantifying dispersion effects. In this Account, we describe the quality of calculated structural and thermodynamic properties in gas-phase obtained with DFT-D4 corrected methods, specifically for organometallic complexes. The physical effects leading to London dispersion interactions are briefly discussed in the picture of second-order perturbation theory. Subsequently, basic theoretical aspects of the D4 method are introduced followed by selected case studies. Several chemical examples are presented starting with the analysis of transition metal thermochemistry and noncovalent interactions for small, heavy element containing main group compounds. Computed reaction energies can only match highly accurate reference values when all energy contributions are included in the DFT treatment, thus highlighting the major role of dispersion interactions for the accurate description of thermochemistry in gas-phase. Furthermore, the correlation between structural and catalytic properties is emphasized where the accessibility of high quality structures is essential for reaction planning and catalyst design. We present calculations for aggregates of organometallic systems with intrinsically large repulsive electrostatic interactions which can be stabilized by London dispersion effects. The newly introduced inclusion of atomic charge information in the DFT-D4 model robustly leads to quantitatively improved dispersion energies in particular for metallic systems. By construction it yields results which are easily understandable due to a clear separation into hybridization and charge (oxidation) state and two- and many-body effects, respectively. Due to its high computational efficiency, the D4 dispersion model is even applicable to low-cost classical and semiempirical theoretical methods.

Simplified DFT methods for consistent structures and energies of large systems.

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

A general intermolecular force field based on tight-binding quantum chemical calculations.

A black-box type procedure is presented for the generation of a molecule-specific, intermolecular potential energy function. The method uses quantum chemical (QC) information from our recently published extended tight-binding semi-empirical scheme (GFN-xTB) and can treat non-covalently bound complexes and aggregates with almost arbitrary chemical structure. The necessary QC information consists of the equilibrium structure, Mulliken atomic charges, charge centers of localized molecular orbitals, and also of frontier orbitals and orbital energies. The molecular pair potential includes model density dependent Pauli repulsion, penetration, as well as point charge electrostatics, the newly developed D4 dispersion energy model, Drude oscillators for polarization, and a charge-transfer term. Only one element-specific and about 20 global empirical parameters are needed to cover systems with nuclear charges up to radon (Z = 86). The method is tested for standard small molecule interaction energy benchmark sets where it provides accurate intermolecular energies and equilibrium distances. Examples for structures with a few hundred atoms including charged systems demonstrate the versatility of the approach. The method is implemented in a stand-alone computer code which enables rigid-body, global minimum energy searches for molecular aggregation or alignment.

Extension of the D3 dispersion coefficient model.

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities α(iω). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.

London Dispersion Enables the Shortest Intermolecular Hydrocarbon H···H Contact.

Neutron diffraction of tri(3,5-tert-butylphenyl)methane at 20 K reveals an intermolecular C-H···H-C distance of only 1.566(5) Å, which is the shortest reported to date. The compound crystallizes as a C3-symmetric dimer in an unusual head-to-head fashion. Quantum chemical computations of the solid state at the HSE-3c level of theory reproduce the structure and the close contact well (1.555 Å at 0 K) and emphasize the significance of packing effects; the gas-phase dimer structure at the same level shows a 1.634 Å C-H···H-C distance. Intermolecular London dispersion interactions between contacting tert-butyl substituents surrounding the central contact deliver the decisive energetic contributions to enable this remarkable bonding situation.

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies.

We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.