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Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 data set while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures, at a computational cost for the gradient evaluation that is comparable to Hartree-Fock theory or hybrid DFT.

Molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different data sets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T data set (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this data set with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a data set comprised of thirteen heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone-backbone interaction data set to an accuracy of 0.28 kcal/mol.

Semiempirical molecular orbital (SEMO) models based on the neglect of diatomic differential overlap (NDDO) approximation efficiently solve the self-consistent field equations by rather drastic approximations. The computational efficiency comes at the cost of an error in the electron-electron repulsion integrals. The error may be compensated by the introduction of parametric expressions to evaluate the electron-electron repulsion integrals, the one-electron integrals, and the core-core repulsion. We review the resulting formalisms of popular NDDO-SEMO models (such as the MNDO(/d), AM1, PMx, and OMx models) in a concise and self-contained manner. We discuss the approaches to implicitly and explicitly describe electron correlation effects within NDDO-SEMO models and we dissect strengths and weaknesses of the different approaches in a detailed analysis. For this purpose, we consider the results of recent benchmark studies. Furthermore, we apply bootstrapping to perform a sensitivity analysis for a selection of parameters in the MNDO model. We also identify systematic limitations of NDDO-SEMO models by drawing on an analogy to Kohn--Sham density functional theory., Comment: 117 pages, 21 figures, 11 tables

Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of these semiempirical molecular orbital models and to develop further improvements on them. The NDDO approximation provides a recipe to approximate electron-electron repulsion integrals (ERIs) in a symmetrically orthogonalized basis based on a far smaller number of ERIs in a locally orthogonalized basis. We first analyze the NDDO approximation by comparing ERIs in both bases for a selection of molecules and for a selection of basis sets. We find that the errors in Hartree-Fock and second-order Moller-Plesset perturbation theory energies grow roughly linearly with the number of basis functions. We then examine different approaches to correct for the errors caused by the NDDO approximation and propose a strategy to directly correct for them in the two-electron matrices that enter the Fock operator., Comment: 35 pages, 10 figures

Despite the importance of ligand dissociation energies for computational chemistry, obtaining accurate ab initio reference data is difficult and density-functional methods of uncertain reliability are chosen for feasibility reasons. Here, we consider advanced coupled-cluster and multi-configurational approaches to reinvestigate our WCCR10 set of ten gas-phase ligand dissociation energies. We assess the potential multi-configurational character of all molecules involved in these reactions in order to determine where single-reference coupled-cluster approaches can be applied. For some reactions of the WCCR10 set, large deviations from density-functional results including semiclassical dispersion corrections from experimental reference data had been observed. We tackle the issue (i) by comparing to ab initio data that comprise dispersion effects on a rigorous first-principles footing and (ii) by a comparison of density-functional approaches that model dispersion interactions in various ways. Only for two reactions, species exhibiting nonnegligible static electron correlation were identified, and hence, we may choose standard single-reference coupled-cluster approaches to compare with density-functional methods for the other eight reactions. For WCCR10, the Minnesota M06-L functional yielded the smallest mean absolute deviation without additional dispersion corrections in comparison to the coupled-cluster results and the PBE0-D3 functional produced the overall smallest mean absolute deviation. The agreement of density-functional results with coupled-cluster data increases significantly upon inclusion of any type of dispersion correction. It is important to emphasize that different density-functional schemes available for this purpose perform equally well. The coupled-cluster dissociation energies, however, deviate significantly from experimental results., Comment: 38 pages, 4 figures, 3 tables

Computational screening of battery electrolyte components is an extremely challenging task because very complex features like solidelectrolyte-interphase (SEI) formation and graphite exfoliation need to be taken into account at least at the final screening stage. We present estimators for both SEI formation and graphite exfoliation based on a combinatorial approach with quantum chemistry calculations on model system reactions, which can be applied automatically for a large number of compounds and thus allows for a systematic first assessment of the relevant properties within screening approaches. Thermodynamic effects are assessed with quantum mechanical calculations, a more heuristic approach is used to estimate kinetic effects., Comment: Supplementary information available from martin.korth@uni-ulm.de

The Li-Air battery is a very promising candidate for powering future mobility, but finding a suitable electrolyte solvent for this technology turned out to be a major problem. We present a systematic computational investigation of the known chemical space for possible Li-Air electrolyte solvents. It is shown that the problem of finding better Li-Air electrolyte solvents is not only - as previously suggested - about maximizing Li+ and O2- solubilities, but about finding the optimal balance of these solubilities with the viscosity of the solvent. As our results also show that trial-and-error experiments on known chemicals are unlikely to succeed, full chemical sub-spaces for the most promising compound classes are investigated, and suggestions are made for further experiments. The proposed screening approach is transferable and robust and can readily be applied to optimize electrolytes for other electrochemical devices. It goes beyond the current state-of-the-art both in width (considering the number of compounds screened and the way they are selected), as well as depth (considering the number and complexity of properties included)., Comment: Supporting Information available from martin.korth@uni-ulm.de