We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 106 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.
Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) calculations without sacrificing accuracy is a crucial prerequisite for widespread simulation of solution-phase dynamical processes. In this work, we demonstrate the use of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dynamics (MD) simulations to examine polyolefin catalysts in solution. We show that employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, thereby increasing the accessible simulation time-scales. We find that EMFT reproduces DFT-computed binding energies and optimized bond lengths to within chemical accuracy, as well as consistently ranking conformer stability. Furthermore, solution-phase EMFT/MM simulations provide insight into the interaction strength of strongly coordinating and bulky counterions.
NMR-based crystallography approaches involving the combination of crystal structure prediction methods, ab initio calculated chemical shifts and solid-state NMR experiments are powerful methods for crystal structure determination of microcrystalline powders. However, currently structural information obtained from solid-state NMR is usually included only after a set of candidate crystal structures has already been independently generated, starting from a set of single-molecule conformations. Here, we show with the case of ampicillin that this can lead to failure of structure determination. We propose a crystal structure determination method that includes experimental constraints during conformer selection. In order to overcome the problem that experimental measurements on the crystalline samples are not obviously translatable to restrict the single-molecule conformational space, we propose constraints based on the analysis of absent cross-peaks in solid-state NMR correlation experiments. We show that these absences provide unambiguous structural constraints on both the crystal structure and the gas-phase conformations, and therefore can be used for unambiguous selection. The approach is parametrized on the crystal structure determination of flutamide, flufenamic acid, and cocaine, where we reduce the computational cost by around 50%. Most importantly, the method is then shown to correctly determine the crystal structure of ampicillin, which would have failed using current methods because it adopts a high-energy conformer in its crystal structure. The average positional RMSE on the NMR powder structure is ⟨rav⟩ = 0.176 Å, which corresponds to an average equivalent displacement parameter Ueq = 0.0103 Å2.
An approach is presented for the structure determination of clathrates using NMR spectroscopy of enclathrated xenon to select from a set of predicted crystal structures. Crystal structure prediction methods have been used to generate an ensemble of putative structures of o- and m-fluorophenol, whose previously unknown clathrate structures have been studied by 129 Xe NMR spectroscopy. The high sensitivity of the 129 Xe chemical shift tensor to the chemical environment and shape of the crystalline cavity makes it ideal as a probe for porous materials. The experimental powder NMR spectra can be used to directly confirm or reject hypothetical crystal structures generated by computational prediction, whose chemical shift tensors have been simulated using density functional theory. For each fluorophenol isomer one predicted crystal structure was found, whose measured and computed chemical shift tensors agree within experimental and computational error margins and these are thus proposed as the true fluorophenol xenon clathrate structures.
The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.
Structures of the α and ß phases of resorcinol, a major commodity chemical in the pharmaceutical, agrichemical, and polymer industries, were the first polymorphic pair of molecular crystals solved by X-ray analysis. It was recently stated that "no additional phases can be found under atmospheric conditions" (Druzbicki, K. et al. J. Phys. Chem. B 2015, 119, 1681). Herein is described the growth and structure of a new ambient pressure phase, ε, through a combination of optical and X-ray crystallography and by computational crystal structure prediction algorithms. α-Resorcinol has long been a model for mechanistic crystal growth studies from both solution and vapor because prisms extended along the polar axis grow much faster in one direction than in the opposite direction. Research has focused on identifying the absolute sense of the fast direction-the so-called "resorcinol riddle"-with the aim of identifying how solvent controls crystal growth. Here, the growth velocity dissymmetry in the melt is analyzed for the ß phase. The ε phase only grows from the melt, concomitant with the ß phase, as polycrystalline, radially growing spherulites. If the radii are polar, then the sense of the polar axis is an essential feature of the form. Here, this determination is made for spherulites of ß resorcinol (ε, point symmetry 222, does not have a polar axis) with additives that stereoselectively modify growth velocities. Both ß and ε have the additional feature that individual radial lamellae may adopt helicoidal morphologies. We correlate the appearance of twisting in ß and ε with the symmetry of twist-inducing additives.
Generating sets of trial structures that sample the configurational space of crystal packing possibilities is an essential step in the process of ab initio crystal structure prediction (CSP). One effective methodology for performing such a search relies on low-discrepancy, quasi-random sampling, and our implementation of such a search for molecular crystals is described in this paper. Herein we restrict ourselves to rigid organic molecules and, by considering their geometric properties, build trial crystal packings as starting points for local lattice energy minimization. We also describe a method to match instances of the same structure, which we use to measure the convergence of our packing search toward completeness. The use of these tools is demonstrated for a set of molecules with diverse molecular characteristics and as representative of areas of application where CSP has been applied. An important finding is that the lowest energy crystal structures are typically located early and frequently during a quasi-random search of phase space. It is usually the complete sampling of higher energy structures that requires extended sampling. We show how the procedure can first be refined, through targetting the volume of the generated crystal structures, and then extended across a range of space groups to make a full CSP search and locate experimentally observed and lists of hypothetical polymorphs. As the described method has also been created to lie at the base of more involved approaches to CSP, which are being developed within the Global Lattice Energy Explorer (Glee) software, a few of these extensions are briefly discussed.
The ability of computational methods to predict the structures and energetics that determine the equilibrium of solid state mechanochemical reactions has been assessed. Two previously characterised base-catalysed metathesis reactions between aromatic disulfides are studied using crystal structure prediction methods and lattice energy calculations that combine molecular electronic structure methods with anisotropic atom-atom potentials. We find that lattice energy searches locate three of the six crystal structures as global minima on their respective crystal energy landscapes. The remaining structures are less successfully predicted, due to problems modelling relative conformational energies due to limitations of the density functional theory method for calculating intramolecular energies. Prediction of the overall reaction energies proves challenging for current methods, but the results show promise as a base on which to build more accurate and reliable approaches.
We show that the quality of density functional theory (DFT) predictions for the relative stabilities of polymorphs of crystalline para-diiodobenzene (PDIB) is dramatically improved through a simple two-body correction using wavefunction-based electronic structure theory. PDIB has two stable polymorphs under ambient conditions, and like Hongo et al. [J. Phys. Chem. Lett., 1, 1789 (2010)] we find that DFT makes wildly variable predictions of the relative stabilities, depending on the approximate functional used. The two-body corrected scheme, using Grimme's spin-scaled variant of second-order Møller-Plesset perturbation theory and any of the tested density functionals, predicts the α-polymorph to be more stable, consistent with experiment, and produces a relative stability that agrees with the benchmark quantum Monte-Carlo results of Hongo et al. within statistical uncertainty.
