Peter Rudolf Tentscher

Ionization energies (IEs) of organic compounds come in different forms—adiabatic, vertical, as electrode potentials, or as orbital eigenvalues via Koopmans’ theorem. They have been linked to the reactivity towards electrophiles and have been used to quantitatively describe electron transfer processes. The de novo prediction of IEs is only meaningful when an estimate of the prediction's uncertainty is included. Pulsed-field ionization (PFI) experiments have quantified adiabatic IEs with unprecedented precision. In this work, a new set of PFI-derived IEs is compiled from the literature as a benchmark for prediction methods. This set includes many common functional groups, a size range from diatomics to two aromatic rings, and IEs between 7 and 14 eV. The first-principles CCSD(T)/CBS protocol presently used reproduces these values within 0.05 eV. For adiabatic IEs and vertical IEs/orbital eigenvalues predicted using approximate density functional theory (DFT), linear regression models are proposed, so that IEs calculated using different methods can be directly compared on a physical scale. This elimination of systematic errors improves the error statistics and allows the performance of predicted IEs to be evaluated if used in quantitative structure–property or –activity relationships, as the latter implicitly correct a descriptor's bias. Owing to the structural scope of the test set, the minimum and maximum deviations from experiment should correspond to those expected for common organic molecules. Deviations from reference values found for orbital eigenvalues but also for IEs calculated explicitly with HF or semi-empirical MO methods were as large as 0.5 eV to 2.0 eV. Such large errors could also propagate into quantitative structure–property models, as shown in illustrative examples of oxidation rate constants in solution.

Five-membered nitrogen-containing heterocyclic compounds (azoles) belong to potential moieties in complex structures where transformations during ozonation can occur. This study focused on the azole-ozone chemistry of pyrrole, imidazole, and pyrazole as model compounds. Reaction kinetics and ozonation products were determined by kinetic and analytical methods including NMR, LC-HRMS/MS, HPLC-UV, and IC-MS. Analyses of reactive oxygen species (¹O₂, ^•OH, H₂O₂), quantum chemical computations (Gibbs energies), and kinetic simulations were used to further support the proposed reaction mechanisms. The species-specific second-order rate constants for the reactions of ozone with pyrrole and imidazole were (1.4 ± 1.1) × 10⁶ M^-1 s^-1 and (2.3 ± 0.1) × 10⁵ M^-1 s^-1, respectively. Pyrazole reacted more slowly with ozone at pH 7 (k_app = (5.6 ± 0.9) × 10¹ M^-1 s^-1). Maleimide was an identified product of pyrrole with a 34% yield. Together with other products, formate, formamide, and glyoxal, C and N mass balances of ~50% were achieved. Imidazole reacted with ozone to cyanate, formamide, and formate (~100% yields per transformed imidazole, respectively) with a closed mass balance. For pyrazole, a high ozone:pyrazole molar stoichiometry of 4.6 was found, suggesting the transformation products contributed to the over-stoichiometric consumption of ozone (e.g., hydroxypyrazoles). Glyoxal and formate were the only identified transformation products (C mass balance: 65%). Overall, the identified major products are suspected to hydrolyze and/or be biodegraded and thereby abated by a biological post-treatment typically following ozonation. However, as sub-structures of more complex compounds (e.g., micropollutants), they might be more persistent during the biological post-treatment.

The abatement of organic micropollutants during oxidation processes has become an emerging issue for various urban water systems such as drinking water, wastewater, and water reuse. Reaction kinetics and mechanisms play an important role in terms of efficiency of these processes and the formation of transformation products, which are controlled by functional groups in the micropollutants and the applied oxidants. So far, the kinetic and mechanistic information on the underlying reactions was obtained by experimental studies; additionally, predictive quantitative structure–activity relationships (QSARs) were applied to determine reaction kinetics for the oxidation of emerging compounds. Since this experimental approach is very laborious and there are tens of thousands potential contaminants, alternative strategies need to be developed to predict the fate of micropollutants during oxidative water treatment. Due to significant developments in quantum chemical (QC) computations in recent years and increased computational capacity, QC-based methods have become an alternative or a supplement to the current experimental approach. This Account provides a critical assessment of the current state-of-the-art of QC-based methods for the assessment of oxidation of micropollutants. Starting from a given input structure, QC computations need to locate energetic minima on the potential energy surface (PES). Then, useful thermodynamic and kinetic information can be estimated by different approaches: Experimentally determined reaction mechanisms can be validated by identification of transition structures on the PES, which can be obtained for addition reactions, heavy atom transfer (Cl⁺, Br⁺, O·) and H atom transfer (simultaneous proton and electron transfer) reactions. However, transition structures in the PES cannot be obtained for e^–-transfer reactions. Second-order rate constants k for the reactions of micropollutants with chemical oxidants can be obtained by ab initio calculations or by QSARs with various QC descriptors. It has been demonstrated that second-order rate constants from ab initio calculations are within factors 3–750 of the measured values, whereas QSAR-based methods can achieve factors 2–4 compared to the experimental data. The orbital eigenvalue of the highest occupied molecular orbital (E_HOMO) is the most commonly used descriptor for QSAR-based computations of k-values. In combination with results from experimental studies, QC computations can also be applied to investigate reaction mechanisms for verification/understanding of oxidative mechanisms, calculation of branching ratios or regioselectivity, evaluation of the experimental product distribution and assessment of substitution effects. Furthermore, other important physical-chemical constants such as unknown equilibria for species, which are not measurable due to low concentrations, or pK_a values of reactive transient species can be estimated. With further development of QC-based methods, it will become possible to implement kinetic and mechanistic information from such computations in in silico models to predict oxidative transformation of micropollutants. Such predictions can then be complemented by tailored experimental studies to confirm/falsify the computations.

Reactions with ozone transform organic and inorganic molecules in water treatment systems as well as in atmospheric chemistry, either in the aqueous phase, at gas/particle interfaces, or in the gas phase. Computed thermokinetic data can be used to estimate the reactivities of molecules toward ozone in cases where no experimental data are available. Although the gas-phase reactivity of olefins with ozone has been characterized extensively in the literature, this is not the case for the richer chemistry of ozone with polar molecules, which occurs in the aqueous phase or in microhydrated environments. Here, we selected a number of model reactions with small molecules (ethene, ethyne, hydrogen cyanide, hydrogen chloride, ammonia, bromide, and trimethylamine) to study the accuracy of different quantum chemical methods for describing the reactivities of these molecules with ozone. We calculated benchmark electronic energies of gas-phase reactions of these systems with single-reference coupled cluster (CC) theory. These benchmark results for the binding energy in the van der Waals complex, the energy of the transition structure, and the reaction energy were estimated to be accurate within 1–2 kcal mol^–1. Singlet oxygen (¹O₂) is a common product of ozone reactions. Coupled cluster calculations with up to perturbative quadruples (CCSDT(Q)) were needed to obtain reaction energies accurate within 1 kcal mol^–1 when this species was involved. In (micro)hydrated environments or at interfaces, coupled cluster methods are prohibitively expensive in most cases. We tested the suitability of some contemporary density functional theory (DFT) methods to reproduce the benchmark electronic energy differences. Range-separated functionals were found to be promising candidates to estimate forward barrier heights, with LC-ωPBE rivaling the accuracy of CCSD(T). For energies of reaction, however, DFT methods exhibited large systematic errors, depending on their fraction of orbital exchange. This was found to worsen when ¹O₂ is a product, and no safe recommendation can be given for DFT reaction energies in such cases.

Phenolic moieties are common functional groups in organic micropollutants and in dissolved organic matter, and are exposed to ozone during drinking water and wastewater ozonation. Although unsubstituted phenol is known to yield potentially genotoxic p-benzoquinone during ozonation, little is known about the effects of substitution of the phenol ring on transformation product formation. With batch experiments employing differing ozone/target compound ratios, it is shown that para-substituted phenols (p-alkyl, p-halo, p-cyano, p-methoxy, p-formyl, p-carboxy) yield p-benzoquinones, p-substituted catechols, and 4-hydroxy-4-alkyl-cyclohexadien-1-ones as common ozonation products. Only in a few cases did para-substitution prevent the formation of these potentially harmful products. Quantum chemical calculations showed that different reaction mechanisms lead to p-benzoquinone, and that cyclohexadienone can be expected to form if no such pathway is possible. These products can thus be expected from most phenolic moieties. Kinetic considerations showed that substitution of the phenolic ring results in rather small changes of the apparent second order rate constants for phenol–ozone reactions at pH 7. Thus, in mixtures, most phenolic structures can be expected to react with ozone. However, redox cross-reactions between different transformation products, as well as hydrolysis, can be expected to further alter product distributions under realistic treatment scenarios.

First principles simulations were used to predict aqueous one-electron oxidation potentials (E_ox) and associated half-cell reorganization energies (λ_aq) for aniline, phenol, methoxybenzene, imidazole, and dimethylsulfide. We employed quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations of the oxidized and reduced species in an explicit aqueous solvent, followed by EOM-IP-CCSD computations with effective fragment potentials for diabatic energy gaps of solvated clusters, and finally thermodynamic integration of the non-linear solvent response contribution using classical MD. A priori predicted E_ox and λ_aq values exhibit mean absolute errors of 0.17 V and 0.06 eV, respectively, compared to experiment. We also disaggregate E_ox into several well-defined free energy properties, including the gas phase adiabatic free energy of ionization (7.73 to 8.82 eV), the solvent-induced shift in the free energy of ionization due to linear solvent response (−2.01 to −2.73 eV), and the contribution from non-linear solvent response (−0.07 to −0.14 eV). The linear solvent response component is further apportioned into contributions from the solvent-induced shift in vertical ionization energy of the reduced species (ΔVIE_aq) and the solvent-induced shift in negative vertical electron affinity of the ionized species (ΔNVEA_aq). The simulated ΔVIE_aq and ΔNVEA_aq are found to contribute the principal sources of uncertainty in computational estimates of E_ox and λ_aq. Trends in the magnitudes of disaggregated solvation properties are found to correlate with trends in structural and electronic features of the solute. Finally, conflicting approaches for evaluating the aqueous reorganization energy are contrasted and discussed, and concluding recommendations are given.

To study the influence of aqueous solvent on the electronic energy levels of dissolved organic molecules, we conducted liquid microjet photoelectron spectroscopy (PES) measurements of the aqueous vertical ionization energies (VIE_aq) of aniline (7.49 eV), veratrole alcohol (7.68 eV), and imidazole (8.51 eV). We also reanalyzed previously reported experimental PES data for phenol, phenolate, thymidine, and protonated imidazolium cation. We then simulated PE spectra by means of QM/MM molecular dynamics and EOM-IP-CCSD calculations with effective fragment potentials, used to describe the aqueous vertical ionization energies for six molecules, including aniline, phenol, veratrole alcohol, imidazole, methoxybenzene, and dimethylsulfide. Experimental and computational data enable us to decompose the VIE_aq into elementary processes. For neutral compounds, the shift in VIE upon solvation, ΔVIE_aq, was found to range from ≈−0.5 to −0.91 eV. The ΔVIE_aq was further explained in terms of the influence of deforming the gas phase solute into its solution phase conformation, the influence of solute hydrogen-bond donor and acceptor interactions with proximate solvent molecules, and the polarization of about 3000 outerlying solvent molecules. Among the neutral compounds, variability in ΔVIE_aq appeared largely controlled by differences in solute–solvent hydrogen-bonding interactions. Detailed computational analysis of the flexible molecule veratrole alcohol reveals that the VIE is strongly dependent on molecular conformation in both gas and aqueous phases. Finally, aqueous reorganization energies of the oxidation half-cell ionization reaction were determined from experimental data or estimated from simulation for the six compounds aniline, phenol, phenolate, veratrole alcohol, dimethylsulfide, and methoxybenzene, revealing a surprising constancy of 2.06 to 2.35 eV.

Solvated radicals play an important role in many areas of chemistry, but to date, the nature of their interactions with polar solvent molecules lacks chemical interpretation. We present a computational quantum chemical analysis of the binding motives of binary complexes involving electron-poor and electron-rich radicals bound to water and hydrogen fluoride, considered here as model polar solvent molecules. By comparing the binding strengths of several open-shell and closed-shell complexes, in combination with natural localized molecular orbital analysis, we show that open-shell complexes can exhibit additional donor–acceptor interactions relative to analogous closed-shell systems. This may explain the unexpectedly large binding energies observed in some open-shell complexes. These exploratory results show that specific interactions in open-shell systems deserve more attention, and they imply that the quantum mechanical description of explicit solvent molecules needs to be considered carefully when designing simulation protocols for solvated radicals.