Efficient Computational Methods for Accurately Predicting Reduction Potentials of Organic Molecules

First and Second Reductions in an Aprotic Solvent: Comparing Computational and Experimental One-Electron Reduction Potentials for 345 Quinones

Using reference reduction potentials of quinones recently measured relative to the saturated calomel electrode (SCE) in N,N-dimethylformamide (DMF), we benchmark absolute one-electron reduction potentials computed for 345 Q/Q•- and 265 Q•-/Q2- half-reactions using adiabatic electron affinities computed with density functional theory and solvation energies computed with four continuum solvation models: IEF-PCM, C-PCM, COSMO, and SM12. Regression analyses indicate a strong linear correlation between experimental and absolute computed Q/Q•- reduction potentials with Pearson's correlation coefficient (r) between 0.95 and 0.96 and the mean absolute error (MAE) relative to the linear fit between 83.29 and 89.51 mV for different solvation methods when the slope of the regression is constrained to 1. The same analysis for Q•-/Q2- gave a linear regression with r between 0.74 and 0.90 and MAE between 95.87 and 144.53 mV, respectively. The y-intercept values obtained from the linear regressions are in good agreement with the range of absolute reduction potentials reported in the literature for the SCE but reveal several sources of systematic error. The y-intercepts from Q•-/Q2- calculations are lower than those from Q/Q•- by around 320-410 mV for IEF-PCM, C-PCM, and SM12 compared to 210 mV for COSMO. Systematic errors also arise between molecules having different ring sizes (benzoquinones, naphthoquinones, and anthraquinones) and different substituents (titratable vs nontitratable). SCF convergence issues were found to be a source of random error that was slightly reduced by directly optimizing the solute structure in the continuum solvent reaction field. While SM12 MAEs were lower than those of the other solvation models for Q/Q•-, SM12 had larger MAEs for Q•-/Q2- pointing to a larger error when describing multiply charged anions in DMF. Altogether, the results highlight the advantages of, and further need for, testing computational methods using a large experimental data set that is not skewed (e.g., having more titratable than nontitratable substituents on different parent groups or vice versa) to help further distinguish between sources of random and systematic errors in the calculations.

Full theoretical protocol for the design of metal-free organic electron donor-spacer-acceptor systems

A user-friendly (time-dependent) density functional theory based algorithm is proposed to design new donor-spacer-acceptor systems for electron transfer reactions. This algorithm is focused on metal-free organic compounds, most of which contain aromatic or alkene moieties. The oxidation and reduction potentials are calculated, together with the excited-state energy difference including the zero-point energy and the structural properties required to calculate an electron transfer Gibbs free energy change. The proposed algorithm has been tested on well-known systems, while two new compounds are suggested for photoinduced intramolecular electron transfer reactions using this scheme. The methodology here presented is intended to be a tool for synthetic physical-chemists, allowing them to evaluate the properties of hypothetical systems before the synthesis, enabling the study of limitless combinations of donor-spacer-acceptor arrangements.

Unlocking the Potential: Predicting Redox Behavior of Organic Molecules, from Linear Fits to Neural Networks

Redox-active organic molecules, i.e., molecules that can relatively easily accept and/or donate electrons, are ubiquitous in biology, chemical synthesis, and electronic and spintronic devices, such as solar cells and rechargeable batteries, etc. Choosing the best candidates from an essentially infinite chemical space for experimental testing in a target application requires efficient screening approaches. In this Review, we discuss modern in silico techniques for predicting reduction and oxidation potentials of organic molecules that go beyond conventional first-principles computations and thermodynamic cycles. Approaches ranging from simple linear fits based on molecular orbital energy approximation and energy difference approximation to advanced regression and neural network machine learning algorithms employing complex descriptors of molecular compositions, geometries, and electronic structures are examined in conjunction with relevant literature examples. We discuss the interplay between ab initio data and machine learning (ML), i.e., whether it is better to base predictions on low-level quantum-chemical results corrected with ML or to bypass first-principles computations entirely and instead rely on elaborate deep learning architectures. Finally, we list currently available data sets of redox-active organic molecules and their experimental and/or computed properties to facilitate the development of screening platforms and rational design of redox-active organic molecules.

Optimization of G-Quadruplex Ligands through a SAR Study Combining Parallel Synthesis and Screening of Cationic Bis(acylhydrazones)

G-quadruplexes (G4s), secondary structures adopted by guanine-rich DNA and RNA sequences, are implicated in numerous biological processes and have been suggested as potential drug targets. Accordingly, there is an increasing interest in developing high-throughput methods that allow the generation of congeneric series of G4-targeting molecules ("ligands") and investigating their interactions with the targets. We have developed an operationally simple method of parallel synthesis to generate "ready-to-screen" libraries of cationic acylhydrazones, a motif that we have previously identified as a promising scaffold for potent, biologically active G4 ligands. Combined with well-established screening techniques, such as fluorescence melting, this method enables the rapid synthesis and screening of combinatorial libraries of potential G4 ligands. Following this protocol, we synthesized a combinatorial library of 90 bis(acylhydrazones) and screened it against five different nucleic acid structures. This way, we were able to analyze the structure-activity relationships within this series of G4 ligands, and identified three novel promising ligands whose interactions with G4-DNAs of different topologies were studied in detail by a combination of several biophysical techniques, including native mass spectrometry, and molecular modeling.

Linear correlation models for the redox potential of organic molecules in aqueous solutions

In this study, we use the molecular orbital energy approximation (MOEA) and the energy difference approximation (EDA) to build linear correlation models for the redox potentials of 53 organic compounds in aqueous solutions. The molecules evaluated include nitroxides, phenols, and amines. Both the MOEA and EDA methods yield similar correlation models, however, the MOEA method is less computationally expensive. Correlation coefficients (R²) below 0.3 and mean absolute errors above 0.25 V were found for correlation models built without solvent effects. When explicit water molecules and a continuum solvent model are added to the calculations, correlation coefficients close to 0.8 are reached, and mean absolute errors below 0.18 V are obtained. The incorporation of solvent effects is necessary for good correlation models, particularly for redox processes of charged molecules in aqueous solutions. A comparison of the correlation models from different methodologies is provided. Graphical abstract.

Stereoelectronic and Resonance Effects on the Rate of Ring Opening of N-Cyclopropyl-Based Single Electron Transfer Probes

N-Cyclopropyl-N-methylaniline (5) is a poor probe for single electron transfer (SET) because the corresponding radical cation undergoes cyclopropane ring opening with a rate constant of only 4.1 × 10⁴ s^-1, too slow to compete with other processes such as radical cation deprotonation. The sluggish rate of ring opening can be attributed to either (i) a resonance effect in which the spin and charge of the radical cation in the ring-closed form is delocalized into the phenyl ring, and/or (ii) the lowest energy conformation of the SET product (5^•+) does not meet the stereoelectronic requirements for cyclopropane ring opening. To resolve this issue, a new series of N-cyclopropylanilines were designed to lock the cyclopropyl group into the required bisected conformation for ring opening. The results reveal that the rate constant for ring opening of radical cations derived from 1'-methyl-3',4'-dihydro-1'H-spiro[cyclopropane-1,2'-quinoline] (6) and 6'-chloro-1'-methyl-3',4'-dihydro-1'H-spiro[cyclopropane-1,2'-quinoline] (7) are 3.5 × 10² s^-1 and 4.1 × 10² s^-1, effectively ruling out the stereoelectronic argument. In contrast, the radical cation derived from 4-chloro-N-methyl-N-(2-phenylcyclopropyl)aniline (8) undergoes cyclopropane ring opening with a rate constant of 1.7 × 10⁸ s^-1, demonstrating that loss of the resonance energy associated with the ring-closed form of these N-cyclopropylanilines can be amply compensated by incorporation of a radical-stabilizing phenyl substituent on the cyclopropyl group. Product studies were performed, including a unique application of EC-ESI/MS (Electrochemistry/ElectroSpray Ionization Mass Spectrometry) in the presence of ¹⁸O₂ and H₂¹⁸O to elucidate the mechanism of ring opening of 7^•+ and trapping of the resulting distonic radical cation.

In search of the best DFT functional for dealing with organic anionic species

“And the winner is…” This work assesses the ability of different Density Functional Theory (DFT) functionals for a proper treatment of organic anionic species.

Electron spin changes during general anesthesia in Drosophila

We show that the general anesthetics xenon, sulfur hexafluoride, nitrous oxide, and chloroform cause rapid increases of different magnitude and time course in the electron spin content of Drosophila. With the exception of CHCl3, these changes are reversible. Anesthetic-resistant mutant strains of Drosophila exhibit a different pattern of spin responses to anesthetic. In two such mutants, the spin response to CHCl3 is absent. We propose that these spin changes are caused by perturbation of the electronic structure of proteins by general anesthetics. Using density functional theory, we show that general anesthetics perturb and extend the highest occupied molecular orbital of a nine-residue α-helix. The calculated perturbations are qualitatively in accord with the Meyer-Overton relationship and some of its exceptions. We conclude that there may be a connection between spin, electron currents in cells, and the functioning of the nervous system.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Exploring the biological promiscuity of high-throughput screening hits through DFT calculations

The goal of this study is the understanding of biologically promiscuous compounds (frequent hitters) in HTS outcomes through their chemical behavior estimated via reactivity descriptors. Chemical reactivity is often an undesirable property due to the lack in biological selectivity of compounds comprised in HTS libraries. In this study the reactivity indexes have been computed within the DFT formalism, at different levels of theory, for two classes of representative compounds compiled from PubChem database, one comprising frequent hitters and the second one comprising rare hitters (biologically more selective compounds). We found that frequent hitters exert increased reactivity, mainly due to their electrophilic character, compared to the more selective class of compounds.

Formal redox potentials of organic molecules in ionic liquids on the basis of quaternary nitrogen cations as adiabatic electron affinities

Formal redox potentials E°' involving neutral species R and radical anions R(•-) in ionic liquids (ILs) composed of ammonium, pyridinium, and imidazolium cations are discussed from the point of view of the adiabatic electron affinity as a molecular property. The dependence of the 1,4-benzoquinone (BQ)/BQ(•-) redox process in CH2Cl2 and CH3CN is primarily investigated over a wide concentration range of ILs as the supporting electrolyte. A logarithmic relationship involving a positive shift of E°' with increasing concentration is obtained when the concentration is changed from 0.01 to 1.0 M. The relationship of E°' at IL concentrations greater than 1.0 M gradually reaches a plateau and remains there even for the neat ILs. It is found that the E°' values in the neat ILs are not influenced by the measurement conditions, and that they remain considerably dependent on the nature and concentration of the electrolyte when measured using the traditional method involving molecular solvents combined with a supporting electrolyte (0.1-0.5 M). The difference in the E°' values observed in the ammonium and pyridinium ILs is only several millivolts. In addition, ESR and self-consistent isodensity polarized continuum model calculation results reveal that the potential shift toward positive values upon the transition from molecular solvents containing ILs to neat ILs is adequately accounted for by changes in the electrostatic interaction of R(•-) taken into the cavity composed of the solvent and IL. On the other hand, the first reduction waves of quinones, electron-accepting molecules, and polynuclear aromatic hydrocarbons are reversibly or quasi-reversibly observed in the ILs. The electrochemical stability of the ILs is exploited in the facile measurement of these quasi-reversible waves at quite negative potentials, such as for the naphthalene (NP)/NP(•-) couple. Notably, the E°' values obtained in the ammonium ILs correlate well with the calculated standard redox potentials and are linearly fitted with high correlation over all classes of compounds using a single regression equation based on Koopmans' theorem.

Simple and accurate correlation of experimental redox potentials and DFT-calculated HOMO/LUMO energies of polycyclic aromatic hydrocarbons

The ability to accurately predict the oxidation and reduction potentials of molecules is very useful in various fields and applications. Quantum mechanical calculations can be used to access this information, yet sometimes the usefulness of these calculations can be limited because of the computational requirements for large systems. Methodologies that yield strong linear correlations between calculations and experimental data have been reported, however the balance between accuracy and computational cost is always a major issue. In this work, linear correlations (with an R(2) value of up to 0.9990) between DFT-calculated HOMO/LUMO energies and 70 redox potentials from a series of 51 polycyclic aromatic hydrocarbons (obtained from the literature) are presented. The results are compared to previously reported linear correlations that were obtained with a more expensive computational methodology based on a Born-Haber thermodynamic cycle. It is shown in this article that similar or better correlations can be obtained with a simple and cheaper calculation.

Arene trifluoromethylation: an effective strategy to obtain air-stable n-type organic semiconductors with tunable optoelectronic and electron transfer properties

Modulation of organic semiconductor band gap, electron affinities (EA), ionization potentials (IP), and reorganization energies (λ) associated with charge transfer is critical for its applications. We report here that trifluoromethylation not only increases both IP and EA significantly as expected but also narrows the HOMO-LUMO band gaps and increases considerably the air-stability of arene-based n-type organic semiconductors. The increased air-stability results from relatively high EA energies and a change in oxidation mechanism. Calculated EAs and IPs show that trifluoromethylated arenes are excellent candidates for n-type semiconductor materials; though a moderate increase of inner-sphere reorganization energy (λi) associated with charge transfer is the penalty for the improved performance of the trifluoromethylated compounds. However, since λi decreases as the π conjugation increases, a rational design to produce air-stable n-type semiconductor materials with reasonably small λi is simply to prepare trifluoromethylated arenes with extended π conjugation. Furthermore, we found that structural isomerization can fine-tune the optoelectronic and electronic transfer properties of the corresponding aromatics.