Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning.

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.

Predicting Density Functional Theory-Quality Nuclear Magnetic Resonance Chemical Shifts via Δ-Machine Learning.

First-principles prediction of nuclear magnetic resonance chemical shifts plays an increasingly important role in the interpretation of experimental spectra, but the required density functional theory (DFT) calculations can be computationally expensive. Promising machine learning models for predicting chemical shieldings in general organic molecules have been developed previously, though the accuracy of those models remains below that of DFT. The present study demonstrates how much higher accuracy chemical shieldings can be obtained via the Δ-machine learning approach, with the result that the errors introduced by the machine learning model are only one-half to one-third the errors expected for DFT chemical shifts relative to experiment. Specifically, an ensemble of neural networks is trained to correct PBE0/6-31G chemical shieldings up to the target level of PBE0/6-311+G(2d,p). It can predict 1H, 13C, 15N, and 17O chemical shieldings with root-mean-square errors of 0.11, 0.70, 1.69, and 2.47 ppm, respectively. At the same time, the Δ-machine learning approach is 1-2 orders of magnitude faster than the target large-basis calculations. It is also demonstrated that the machine learning model predicts experimental solution-phase NMR chemical shifts in drug molecules with only modestly worse accuracy than the target DFT model. Finally, the ability to estimate the uncertainty in the predicted shieldings based on variations within the ensemble of neural network models is also assessed.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems.

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.