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Abstract The Hohenberg-Kohn theorem of density-functional theory establishes the existence of a bijection between the ground-state electron density and the external potential of a many-body system. This guarantees a one-to-one map from the electron density to all observables of interest including electronic excited-state energies. Time-Dependent Density-Functional Theory (TDDFT) provides one framework to resolve this map; however, the approximations inherent in practical TDDFT calculations, together with their computational expense, motivate finding a cheaper, more direct map for electronic excitations. Here, we show that determining density and energy functionals via machine learning allows the equations of TDDFT to be bypassed. The framework we introduce is used to perform the first excited-state molecular dynamics simulations with a machine-learned functional on malonaldehyde and correctly capture the kinetics of its excited-state intramolecular proton transfer, allowing insight into how mechanical constraints can be used to control the proton transfer reaction in this molecule. This development opens the door to using machine-learned functionals for highly efficient excited-state dynamics simulations. 

Abstract Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol⁻¹with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol⁻¹) on test data. Moreover, density-basedΔ-learning (learning only the correction to a standard DFT calculation, termedΔ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness ofΔ-DFT  is highlighted by correcting “on the fly” DFT-based molecular dynamics (MD) simulations of resorcinol (C₆H₄(OH)₂) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, thatΔ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails. 

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.