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.

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 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. 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. Possible reasons for these deviations are discussed.

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 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. K E Y W O R D SNDDO approximation, semi-empirical methods | INTRODUCTIONThe driving force for the development of semiempirical molecular orbital (SEMO) models has always been the desire to accelerate quantum chemical calculations. At the outset of the development of SEMO models in the middle of the last century, [1][2][3][4][5][6][7][8][9][10] the goal was to carry out electronic structure calculations for small molecules, which was not routinely possible with ab initio electronic structure methods at that time. Since then, theoretical chemistry has seen a remarkable development not only in terms of computational resources but also in terms of ab initio methodology. [11] One must not forget that most electronic structure methods which we apply routinely today, such as Kohn-Sham density functional theory (KS-DFT) [12] and coupled cluster theory, [13] were developed concurrently with today's SEMO models. As a consequence of algorithmic and methodological developments, [11] accurate ab initio electronic structure methods have long replaced SEMO models in their original areas of application (electronic structure calculations for small molecules). Nevertheless, SEMO models did not become extinct. Instead, they opened up different areas of application which can broadly be divided into three categories (see also Ref. [14] for a recent review): (1) simulations of very large systems such as proteins [15][16][17][18][19][20][21][22] and those with thousands of small molecules, [23,24] (2) calculations for a large number of isolated and unrelated medium-sized molecules, for example, in virtual high-throughput screening schemes for materials discovery [25,26] and docking-and-scoring of potential drug candidates, [27][28][29][30][31][32] and (3) entirely new applications such as real-time quantum chemistry where ultra-fast SEMO models allow the perception of visual and h...

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.