Analytical gradients for molecular-orbital-based machine learning.

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 dataset 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 a density-corrected density functional theory calculation.

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states.

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. The application of Nesbet's theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. 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 datasets 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 dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 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 the 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 dataset to an accuracy of 0.28 kcal/mol.

Molecular Recognition and Cocrystallization of Methylated and Halogenated Fragments of Danicalipin A by Enantiopure Alleno-Acetylenic Cage Receptors.

Enantiopure (P)4- and (M)4-configured alleno-acetylenic cage (AAC) receptors offer a highly defined interior for the complexation and structure elucidation of small molecule fragments of the stereochemically complex chlorosulfolipid danicalipin A. Solution (NMR), solid state (X-ray), and theoretical investigations of the formed host-guest complexes provide insight into the conformational preferences of 14 achiral and chiral derivatives of the danicalipin A chlorohydrin core in a confined, mostly hydrophobic environment, extending previously reported studies in polar solvents. The conserved binding mode of the guests permits deciphering the effect of functional group replacements on Gibbs binding energies ΔG. A strong contribution of conformational energies toward the binding affinities is revealed, which explains why the denser packing of larger apolar domains of the guests does not necessarily lead to higher association. Enantioselective binding of chiral guests, with energetic differences ΔΔG293 K up to 0.7 kcal mol-1 between diastereoisomeric complexes, is explained by hydrogen- and halogen-bonding, as well as dispersion interactions. Calorimetric studies (ITC) show that the stronger binding of one enantiomer is accompanied by an increased gain in enthalpy ΔH but at the cost of a larger entropic penalty TΔS stemming from tighter binding.

Hydrogen-Bonded Networks: Molecular Recognition of Cyclic Alcohols in Enantiopure Alleno-Acetylenic Cage Receptors.

Enantiopure (P)4 - and (M)4 -alleno-acetylenic cage (AAC) receptors form circular fourfold hydrogen-bonding networks in their closed cage conformation. Theoretical studies reveal a preferential clockwise (cw) orientation of the H-bonding array for (P)4 -configured and counterclockwise (ccw) for (M)4 -configured receptors (ΔEcw-ccw =-2.6 to -3.1 kcal mol-1 ). Solution and solid-state studies show how the H-bonding network of the receptor is expanded upon encapsulation of alcohol-containing guests. Topologies reminiscent of those found in isolated water clusters are observed: circular fourfold & docking, pentagonal, linear fivefold, and hexagonal boat-shaped. Expansion of the H-bonding network together with optimal space occupancy yields very high ligand affinities (ΔG293 K =-9.0 kcal mol-1 for endo-tropine). The H-bonding network in the complexes also contributes substantially to the enantioselective complexation of chiral diols, such as (R,R)- and (S,S)-trans-cyclohexane-1,2-diol.

Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation.

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 Møller-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.

Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes.

The accurate calculation of ligand dissociation (or equivalently, ligand binding) energies is crucial for computational coordination chemistry. Despite its importance, 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 multiconfigurational approaches to reinvestigate our WCCR10 set of 10 gas-phase ligand dissociation energies [ J. Chem. Theory Comput. 2014, 10, 3092]. We assess the potential multiconfigurational character of all molecules involved in these reactions with a multireference diagnostic [ Mol. Phys. 2017, 115, 2110] in order to determine where single-reference coupled-cluster approaches can be applied. For some reactions of the WCCR10 set, large deviations of density-functional results including semiclassical dispersion corrections from experimental reference data had been observed. This puzzling observation deserves special attention here, and 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. For two reactions, species exhibiting nonnegligible static electron correlation were identified. These two reactions represent hard problems for electronic structure methods and also for multireference perturbation theories. However, most of the ligand dissociation reactions in WCCR10 do not exhibit static electron correlation effects, and hence, we may choose standard single-reference coupled-cluster approaches to compare with density-functional methods. For WCCR10, the Minnesota M06-L functional yielded the smallest mean absolute deviation of 13.2 kJ mol-1 out of all density functionals considered (PBE, BP86, BLYP, TPSS, M06-L, PBE0, B3LYP, TPSSh, and M06-2X) without additional dispersion corrections in comparison to the coupled-cluster results, and the PBE0-D3 functional produced the overall smallest mean absolute deviation of 4.3 kJ mol-1. 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 from experimental results on average by 30.3 kJ mol-1. Possible reasons for these deviations are discussed.

Dispersion and Halogen-Bonding Interactions: Binding of the Axial Conformers of Monohalo- and (±)-trans-1,2-Dihalocyclohexanes in Enantiopure Alleno-Acetylenic Cages.

Enantiopure alleno-acetylenic cage (AAC) receptors with a resorcin[4]arene scaffold, from which four homochiral alleno-acetylenes converge to shape a cavity closed by a four-fold OH-hydrogen-bonding array, form a highly ordered porous network in the solid state. They enable the complexation and co-crystallization of otherwise non-crystalline small molecules. This paper analyzes the axial conformers of monohalo- and (±)-trans-1,2-dihalocyclohexanes, bound in the interior cavity of the AACs, on the atomic level in the solid state and in solution, accompanied by accurate calculations. The dihedral angles ϑa,a (X-C(1)-C(2)-X/H) of the axial/diaxial conformers deviate substantially from 180°, down to 144°, accompanied by strong flattening of the ring dihedral angles. Structure optimization of the isolated guest molecules demonstrates that the non-covalent interactions with the host hardly affect the dihedral angles, validating that the host is an ideal means to study the elusive axial/diaxial conformers. X-ray co-crystal structures of AACs further allowed for a detailed investigation, both experimentally and theoretically, on the interplay between space occupancy, guest conformation, and chiral recognition based purely on dispersion forces and weak C-X···π (X = Cl, Br, I) and C-X···||| (acetylene) contacts (X = Cl, Br). The theoretical analysis of the non-covalent interactions between host and guest confirmed the high shape complementarity with fully enveloping dispersive interactions between the binding partners, rationalizing the high degree of enantioselectivity in the previously communicated complexation of (±)-trans-1,2-dimethylcyclohexane. This study also showed that (±)-trans-1,2-dihalocyclohexanes (X = Cl, Br) engage in significant halogen bonding (XB) interactions C-X···||| with the hosts. Slow host-guest exchange on the NMR time scale enabled the characterization of the encapsulated guests in solution, demonstrating that the complexes have identical geometries to those seen in the solid state, with the guests bound in axial/diaxial conformations.

Uncertainty quantification for quantum chemical models of complex reaction networks.

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

Alternative Single-Solvent Electrolytes Based on Cyanoesters for Safer Lithium-Ion Batteries.

To identify alternative single-solvent-based electrolytes for application in lithium-ion batteries (LIBs), adequate computational methods were applied to screen specified physicochemical and electrochemical properties of new cyanoester-based compounds. Out of 2747 possible target compounds, two promising candidates and two structurally equivalent components were chosen. A constructive selection process including evaluation of basic physicochemical properties as well assessing the compatibility towards graphitic anodes was initiated to identify the most promising candidates. With addition of a film-forming additive in a low concentration, the most promising candidate showed an adequate long-term cycling stability with LiNi1/3 Mn1/3 Co1/3 O2 [NMC(111)] in a full-cell setup using graphite as anode material. The main advantages of the new electrolyte formulation are related to its good thermal behavior, especially with regard to safety in combination with satisfying electrochemical performance.

How to estimate solid-electrolyte-interphase features when screening electrolyte materials.

Computational screening of battery electrolyte components is an extremely challenging task because very complex features like solid-electrolyte-interphase (SEI) formation and graphite exfoliation need to be taken into account at least in the final screening stage. We present estimators for both SEI formation and graphite exfoliation based on a combinatorial approach using quantum chemistry calculations on model system reactions, which can be applied automatically for a large number of compounds and thus allows for the systematic first assessment of the relevant properties using screening approaches. The thermodynamic effects are assessed using quantum mechanical calculations, while a more heuristic approach is used to estimate the kinetic effects.

Charting the known chemical space for non-aqueous lithium-air battery electrolyte solvents.

Li-air batteries are very promising candidates 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 also 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).

Large-scale virtual high-throughput screening for the identification of new battery electrolyte solvents: computing infrastructure and collective properties.

A volunteer computing approach is presented for the purpose of screening a large number of molecular structures with respect to their suitability as new battery electrolyte solvents. Collective properties like melting, boiling and flash points are evaluated using COSMOtherm and quantitative structure-property relationship (QSPR) based methods, while electronic structure theory methods are used for the computation of electrochemical stability window estimators. Two application examples are presented: first, the results of a previous large-scale screening test (PCCP, 2014, 16, 7919) are re-evaluated with respect to the mentioned collective properties. As a second application example, all reasonable nitrile solvents up to 12 heavy atoms are generated and used to illustrate a suitable filter protocol for picking Pareto-optimal candidates.