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Machine learning is becoming increasingly important in the prediction of nuclear magnetic resonance (NMR) chemical shifts and other observable properties. This chapter provides an introduction to the construction of machine learning (ML) models for predicting NMR properties, including the discussion of feature engineering, common ML model types, Δ-ML and transfer learning, and the curation of training and testing data. Then it discusses a number of recent examples of ML models for predicting chemical shifts and spin–spin coupling constants in organic and inorganic species. These examples highlight how the decisions made in constructing the ML model impact its performance, discuss strategies for achieving more accurate ML models, and present some representative case studies showing how ML is transforming the way NMR crystallography is performed. 

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller–Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods findsr²SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost. 

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. The test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset. 

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol⁻¹at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.