Introduction

Materials that undergo reversible oxidation-reduction reactions (redox-active materials) play a crucial role in numerous research fields and applications, such as energy storage and conversion1,2,3,4,5, photoredox catalysis6,7,8,9, electrochemical sensing10,11,12, and molecular electronics13,14,15, for instance. Redox potentials represent one of the most basic properties of redox-active materials because they display the relative stability of distinct oxidation states, and therefore provide valuable information regarding the direction and feasibility of redox reactions. The knowledge of redox potentials is thus essential in the design of new materials and electrochemical systems. Redox potentials measured by commonly used experimental methods (i.e. potentiometry or cyclic voltametry) are available for a large number of inorganic, organometallic, and organic compounds, mostly in aqueous solutions, and they are usually reported in the form of standard reduction potentials (Eo), or as midpoint potentials at given pH (Em), if prototropic equilibria are involved16,17,18,19,20. These compilations are, however, from multiple sources and they contain data with varying levels of accuracy. Obtaining accurate redox potential data from electrochemical measurements pose several challenges that include the involvement of protonation processes, irreversibility, stability issues, slow reaction kinetics, just to name a few limitations.

The identification of new redox-active compounds and related developments in various applications of redox chemistry can be greatly accelerated via computational screening tools21,22. This approach has been recently well exploited in search for new organic redox couples as potential candidates for next-generation redox flow batteries (RFBs), which are considered as a viable solution to large-scale storage of renewable energy23,24,25,26,27,28,29,30,31. Density functional theory (DFT) calculations provide reasonably accurate redox potentials32,33,34,35,36,37,38,39,40,41,42,43, and the obtained data are often used to analyze structure-property correlations44,45,46,47,48,49, or to build extended databases for virtual screening50,51,52,53,54,55,56,57,58,59,60. Computational screening becomes particularly efficient when quantum chemical (QC) methods are combined with machine learning (ML) techniques61,62,63,64,65,66. Generating molecular databases using DFT or other QC calculations followed by regression or neural network ML analysis has been successfully used to predict redox potentials of various reduction processes relevant to RFB developments67,68,69,70,71,72,73,74,75,76,77,78,79. ML models trained on extended databases and employing molecular-input line-entry system (SMILES) strings80,81,82 as molecular representations provide sound predictions orders of magnitude faster than pure DFT calculations. ML techniques also allow for simultaneous optimization of other targeted properties (i.e. solubility, stability, synthesizability) along with redox potentials. The utilization of multiobjective ML tools in the optimization of desired properties redox-active materials is a promising concept in discovering feasible candidate redox pairs for new RFBs. 67,69,72

We have recently proposed a cost-effective computational protocol that combines semiempirical (GFN2-xTB) and DFT (M06-2X) quantum chemical methods to predict 1e− standard reduction potentials for an enlarged set of organic molecules83. This composite computational approach has been validated via benchmark studies showing satisfactory correlations with experimental data and also with those obtained from more demanding full DFT calculations. The proposed protocol has been applied to generate a molecular database of N-functionalized pyridinium derivatives, and the analysis of substituent effects on the reduction potentials served as a starting point in the exploration of vitamin B6-based redox-active benzoyl pyridinium salts as possible electrolytes in aqueous organic redox flow batteries (AO-RFBs)84. In our present work, we used a very similar computational protocol to construct a diverse database of organic molecules and we applied various deep learning models85 with the aim of developing an easy-to-use predictive tool for 1e− standard reduction potentials in aqueous phase. This tool is made available as an open-access web application, which is introduced and described herein.

Results

Molecular database RP-ChEMBL

Molecules from the ChEMBL molecular library86 were selected to build a database (referred to as RP-ChEMBL) that contains the 3D structures of \({\rm{A}}/{{\rm{A}}\cdot }^{-}\) redox pairs and the computed 1e− standard reduction potentials of the organic species A. ChEMBL is a publicly available large-scale database that provides information on bioactive molecules and proteins with emphasis on drug discovery. This database is not specifically related to redox chemistry, but it encompasses a wide array of already synthesized organic compounds that span a broad chemical space, therefore we think it is appropriate to build a diverse molecular database for screening purposes87,88,89,90. As an initial proof of concept, we focused on relatively small organic molecules. Namely, we have downloaded all molecules with molecular weight (M) less than 200 g/mol and number of heavy atoms greater than 6 from the available ChEMBL compound entries. From these ~38,000 molecules, we selected approximately 8000 molecules with the goal of maintaining high chemical diversity within the selected dataset. The pairwise Tanimoto similarity index91 was used for that purpose. We used the maxmin and sphere-exclusion algorithms92 for dissimilarity-based selection as implemented in Canvas93. Most of the selected compounds are neutral, but some of them are charged species because they are derived from salts. In these latter cases, the counterions were omitted in the subsequent calculations. For species, where the protonation state is not evident (e.g. for tautomeric pairs or anions), the Epik module of the Schrödinger package94 was used to estimate the protonation sites corresponding to pH = 7 in aqueous phase. The Open Babel toolbox [https://openbabel.org/] was used to convert the downloaded SDF structures of the molecules into SMILES codes, which were standardized by using the RDKit package95.

As noted in our previous work83, the semiempirical GFN2-xTB method does not always provide reliable structures during geometry optimizations, and these uncertainties were taken into account when constructing the RP-ChEMBL database as well. Our earlier benchmark calculations revealed that structural transformations—such as bond dissociation, full or partial intramolecular ring closure, and tautomerization—observed during geometry optimizations were typically artifacts of the GFN2-xTB method. It should be noted, however, that structural transformations occurring during the reduction process can also be chemically plausible. Nonetheless, assigning 1e− standard reduction potentials to such molecules is not straightforward, either experimentally or computationally. The analysis of electrochemically induced reactivity, which is certainly an important aspect of redox chemistry, was beyond the scope of the present work. In this study, structural changes occurring upon 1e− reduction were identified through connectivity analysis of the original and reduced states, and the affected molecules were excluded from the database. The final RP-ChEMBL database includes 8033 molecular entries involving heavy atoms C, N, O, F, P, S, Cl, and Br, and the molecular weight of these compounds varies in the range of 78–200 g/mol. The computed 1e− standard reduction potentials span a potential range between –4.3 and +0.8 V versus SHE. The distribution of molecules with respect to the computed potentials is plotted in Fig. 1. It is important to note that the potential window compatible with the practical electrochemical stability of aqueous electrolytes (from –1 V to more positive values) is less populated as a result of diversity requirement, but this potential region is considerably covered as well. All information relevant to the RP-ChEMBL molecular database (computed potentials and structural data) are provided in the Supporting Information (section S1).

Fig. 1: Histogram of computed reduction potentials in dataset RP-ChEMBL.
Fig. 1: Histogram of computed reduction potentials in dataset RP-ChEMBL.The alternative text for this image may have been generated using AI.
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Distribution of one-electron (1e−) standard reduction potentials computed for molecules in the RP-ChEMBL database, showing the overall range of redox values across the dataset.

DeepChem models and their performance

Deep learning models, as implemented in the open-source Python-based DeepChem framework [https://deepchem.io/] 96 (version 2.8.0), were used in our present work to train predictive models on the RP-ChEMBL molecular database. We applied five different deep learning architectures, namely the graph convolutional network models GCN and Graph Conv, graph attention network models GAT and Attentive FP, and the directed acyclic graph model DAG. These models were specifically developed for graph property predictions, therefore, they are expected to be suitable for handling larger datasets of organic molecules.

The primary inputs for all these models were the standardized SMILES codes of the molecules included in RP-ChEMBL, but the SMILES representations were converted to graph structures using the built-in featurizers (for details, see the Supporting Information, section S2). For model training and monitoring the performance, we followed the conventional randomized splitting with the ratio of 0.8:0.1:0.1 to divide the dataset into training, validation and test sets. The basic metrics used to validate the performance of the trainings are the mean absolute error (MAE), the root mean squared error (RMSE), and the determination coefficient of the least squares linear fitting (R2), as referenced to the potentials computed with the GFN2-xTB/M06-2X protocol. The default hyperparameters specific for the neural network of models used in DeepChem proved to perform well for the present purposes; however, some additional parameters regarding the model training and validation were optimized as described in the Supporting Information (sections S2 and S3).

The performance of the trained models is compared in Table 1. All the applied deep learning methods perform remarkably well in terms of the basic metrics. For instance, the MAE values of predictions on the test dataset are smaller than 0.2 V, the RMSE values are between 0.20–0.25 V, and there is a reasonably good correlation between the predicted and the computed potentials as indicated by the R2 data (≥0.9). The level of uncertainty of predictions is actually comparable to that of the GFN2-xTB/M06-2X computational protocol83.

Table 1 Performance metrics of deep learning models trained on the RP-ChEMBL molecular database
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Of the five deep learning models, we find the Attentive FP model to give the best performance with impressive statistical metrics on all three datasets. The parity plot displaying the correlation between the predicted and computed data for this particular model is shown in Fig. 2; the analogous plots obtained for the other models are reported in the Supporting Information (section S4).

Fig. 2: Parity plot of 1e− standard reduction potentials.
Fig. 2: Parity plot of 1e− standard reduction potentials.The alternative text for this image may have been generated using AI.
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Comparison of predicted one-electron (1e−) standard reduction potentials obtained using the Attentive FP model with computed reference values from GFN2-xTB/M06-2X calculations, illustrating the correlation between predicted and calculated data. Red, orange and green circles represent data from training, validation and test sets.

Despite the small MAE value obtained for the Test dataset with the Attentive FP model (MAE = 0.14 V), it is apparent from Fig. 2 that the deviation of the predicted potentials from the computed values covers a much broader energy range. The distribution of signed errors (Fig. 3) shows that the uncertainty of predictions is within ±0.25 V for the majority of the molecules. There are only a few outliers with notable discrepancies (>0.6 V), and the analysis of these cases reveals that some of these deviations originate from the uncertainties of the GFN2-xTB method. Although the RP-ChEMBL database was built by being aware of the limitations of this semiempirical QC method, for a few particular structural units of molecules involved in RP-ChEMBL the geometry optimization gave inaccurate structures resulting in somewhat flawed reduction potentials with the GFN2-xTB/M06-2X protocol. Some of the exceptional deviations could also be related to limited capacity of deep learning method to generalize across the diverse set of molecular structures. A detailed analysis of the origin of the outlier data is presented in the Supporting Information (section S5). Nevertheless, the overall performance of the Attentive FP model is quite acceptable, definitely sufficient for computational screening purposes, and the predictability of the other deep learning models is satisfying as well (see details in the Supporting Information, section S6).

Fig. 3: Signed error distributions for Attentive FP predictions.
Fig. 3: Signed error distributions for Attentive FP predictions.The alternative text for this image may have been generated using AI.
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Distribution of signed errors for predictions using the AttentiveFPModel method, with bars colored by data split (train, valid and test). Overlaid kernel density estimate curves provide a smoothed view of the error distribution for each set. Percentage value indicates the fraction of test molecules with errors within the –0.25 to 0.25 V range.

PredPotS web tool

The trained deep learning models provided the foundation for developing a predictive tool for the estimations of 1e− standard reduction potentials of small or medium-sized organic molecules in aqueous phase. This tool was implemented as an interactive web application accessible through any web browser. The web tool PredPotS (Predicting reduction potentials from SMILES codes) is hosted on a webserver at https://predpots.ttk.hu/. A detailed description of the usage of PredPotS is available in the Supporting Information (section S7), and also under the Help tab of the application. Herein, we only summarize the basic features of the web tool.

Potential predictions in PredPotS are made by entering or uploading the SMILES codes of molecules, and the results are displayed in a table that lists the predictions of all five deep learning models. Model predictions that deviate significantly from the average of these data are treated as outliers and are excluded from the calculation of the mean prediction, which is also displayed in the table. A confidence interval is calculated from the predictions of the individual models and a corresponding confidence rating (1–5) is assigned based on the interval width and the number of contributing predictions. This measure, referred to as prediction confidence, is also shown in the table. This filtering is controlled by a built-in z-score based threshold (for details, see the Supporting Information, section S7). This option can be switched off, but we suggest using it to enhance the confidence level of potential predictions.

The Similarity feature of the web application identifies the molecule included in the RP-ChEMBL database that is structurally most similar to the entered species in terms of molecular fingerprints. The similarity is measured by means of Tanimoto coefficients obtained by using RDKit. The similarity scores and the reduction potentials of the most similar molecules are displayed as a result of similarity search.

The performance metrics of the five deep learning models trained on the RP-ChEMBL molecular database and the corresponding parity plots are available under the Performance tab of the application. The parity plots embody detailed information about the molecules involved in the database (computed and predicted potentials, Lewis structure, etc.), which can be accessed interactively as described in the Help menu. All datasets discussed in the paper are available under the Datasets tab.

Illustrative examples

To illustrate the applicability of PredPotS, we first present the predictions for a few redox-active organic compounds considered recently as potential anolytes for AO-RFBs (Scheme 1). Benzoyl-pyridinium 1+ was shown to undergo reversible one-electron redox process in aqueous solutions, albeit the second redox event was found to be irreversible97. Several substituted variants of this framework have been synthesized and electrochemically characterized recently84, from which we selected 2+ as a representative. Methyl-viologen 32+ is the simplest member of the bipyridinium-based compounds, which are most commonly used active species for anolytes98,99,100,101,102,103,104,105. Extending the π-conjugation of the bipyridinium framework by incorporating a spacer between two pyridinium rings, such as in 44+, is a successful strategy to achieve a two-electron storage anolyte100,106.

Scheme 1: Pyridinium derivatives.
Scheme 1: Pyridinium derivatives.The alternative text for this image may have been generated using AI.
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Illustrative examples for the applicability of PredPotS.

The experimentally determined 1e− reduction potentials of these pyridinium derivatives (as referenced to SHE) are compiled in Table 2 along with the predictions provided by PredPotS. None of these species are involved in the RP-ChEMBL database, but similar pyridinium ions are present as demonstrated by similarity analysis (see the Supporting Information, Fig. S12). The mean predictions are fairly accurate for species 1+ and 2+, but they are reasonable for species 32+ and 44+ as well, and this seems to correlate with the level of confidence of predictions. On the other hand, the order of experimental potentials (i.e. the trend along this series of structurally related species) is not reproduced by most of the models (except Attentive FP). However, such a high level of accuracy cannot be expected for models that were trained over a much broader potential range (between –4.3 and +0.8 V versus SHE) than that covered by the potentials of the four pyridinium compounds (between –0.76 and –0.45 V). Reduction potentials computed with the GFN2-xTB/M06-2X protocol are also reported in Table 2 (last column, and they are indeed more consistent with the experimental data.

Table 2 Potential predictions for pyridinium species listed in Scheme 1a
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One-electron couples from Wardman compilation

For further illustration of the applicability of the PredPotS tool, we consider a larger set of compounds, for which experimental data are available in aqueous solutions. Namely, we have used the Wardman compilation of experimental reduction potentials of one-electron couples17 as a reference and analyzed the quality of PredPotS predictions. The reduction potentials reported in ref. 17 are midpoint potentials of (\({\rm{A}}/{{\rm{A}}\cdot }^{-}\)) couples, which in many cases can be considered as good estimates for 1e− standard reduction potentials. This actually depends on whether prototropic equilibria are coupled or not with reduction processes, but no pH dependence is noted for the compiled reduction potentials. The majority of experimental data refer to pH = 7, but for some entries other pH conditions are given, or even not specified. In the Wardman compilation, the organic species include various quinone, nitroaryl, bipyridinium compounds, as well as some other organic molecules, and the potentials are given versus the SHE.

Molecules with M < 300 g/mol molecular weight, altogether 313 molecules, were selected from the Wardman compilation, and potential predictions were obtained via the PredPotS tool. Although the RP-ChEMBL training database includes molecules with M < 200 g/mol, herein we extended the molecular weight range to assess the applicability of PredPotS tool for larger molecules. Radical oxidant species were not considered in our analysis, as the RP-ChEMBL database involves only closed-shell molecules. The SMILES codes of this molecular set were collected in a csv text file format and uploaded in the online application. The potential predictions were ready within 11 s after the submission. The related database is available under the Datasets tab of PredPotS.

The parity plot showing the correlation between the mean predictions and the experimental 1e− reduction potentials is displayed in Fig. 4. The level of correlation as measured by the R2 metrics is clearly reduced compared to the overall performance of the deep learning methods, but the MAE = 0.21 V value is still reasonably small. The reduced performance is partially due to the significantly narrowed range of potentials of these oxidants as compared to that of the entire RP-ChEMBL database (–1.2 to +0.2 V versus –4.3 to +0.8 V, respectively), but it is also related to the fact that larger molecules (with M > 200) were also included in the present analysis. This latter argument is apparent in Fig. 4, which shows a larger scatter of predictions for M > 200 molecules (highlighted in light blue), and also from the improved metrics found for the M < 200 set in dark blue (R2 = 0.74, MAE = 0.13 V). The parity plot for the M < 200 set of compounds is depicted in Fig. 5, where we highlighted a few classes of compounds, such as quinones, nitrobenzenes, and bipyridimium ions. These compounds form distinct groups along the trendline of the plot providing further support for the reliability of predictions.

Fig. 4: Parity plot of predicted (mean) vs. experimental 1e− reduction potentials for the selected set of Wardman compilation.
Fig. 4: Parity plot of predicted (mean) vs. experimental 1e− reduction potentials for the selected set of Wardman compilation.The alternative text for this image may have been generated using AI.
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Data corresponding to M < 200 molecules are higlighted in dark blue.

Fig. 5: Parity plot of predicted (mean) vs. experimental 1e− reduction potentials for the M < 200 set of Wardman compilation.
Fig. 5: Parity plot of predicted (mean) vs. experimental 1e− reduction potentials for the M < 200 set of Wardman compilation.The alternative text for this image may have been generated using AI.
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Selected classes of compounds are highligted by color codes.

The performance of the five deep learning models regarding their predictions for the M < 200 molecules of the Wardman set is illustrated in Table 3 in terms of the basic metrics. The Attentive FP model shows again the best overall performance with statistical metrics very similar to those of the averaged predictions (for details, see the Supporting Information, section S8).

Table 3 Performance metrics of various deep learning models for predictions of 1e− reduction potentials for the M <200 set of Wardman compilation
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Predictions for larger molecules

The results obtained for the Wardman compilation of one-electron couples imply that the applicability of the PredPotS tool might be extended to larger molecules than those involved in the RP-ChEMBL training set. To evaluate this hypothesis, we selected additional molecules from the ChEMBL database with molecular weight from the 200 < M < 300 range, and computed the 1e− standard reduction potentials using the composite GFN2-xTB/M06-2X protocol (1719 molecules; for details, see the Supporting Information, section S9). The parity plot of mean predicted versus computed data is presented in Fig. 6 and demonstrates a satisfactory correlation for this new set of molecules. The performance metrics found for the mean predictions are indeed encouraging (R2 = 0.89, MAE = 0.18 V), but the uncertainty of these predictions is clearly higher as illustrated by a relatively large number of outliers, as well as by the error distribution diagram shown in Fig. 7. This latter diagram reveals that the discrepancies between the mean predictions and computed data are within ±0.25 V for 74.9% of molecules, whereas this ratio is notably higher (84.1%) for the Test dataset of the original RP-ChEMBL database (see the Supporting Information, section S9).

Fig. 6: Parity plot of predicted (mean) vs. computed (GFN2-xTB/M06-2X) 1e− standard reduction potentials of compounds with molecular weight 200 < M > 300 g/mol.
Fig. 6: Parity plot of predicted (mean) vs. computed (GFN2-xTB/M06-2X) 1e− standard reduction potentials of compounds with molecular weight 200 < M > 300 g/mol.The alternative text for this image may have been generated using AI.
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Outlier data with discrepancies larger than 0.6 V are highlighted in orange.

Fig. 7: Signed error distribution for predictions of molecules with 200–300 g mol⁻¹.
Fig. 7: Signed error distribution for predictions of molecules with 200–300 g mol⁻¹.The alternative text for this image may have been generated using AI.
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An overlaid kernel density estimate (KDE) curve provides a smoothed view of the error distribution, and the percentage value indicates the fraction of molecules with errors within the –0.25 to 0.25 V range.

Based on our analysis, we think that the PredPotS tool could provide informative predictions for larger molecules as well, but the increased level of uncertainty should be taken into account when predictions are made for molecules with M > 200.

Discussion

Our present work builds upon a concept initially formulated within the CompBat project107, which focused on the development of machine learning–assisted high-throughput screening tools for the identification of promising electrolyte materials for aqueous organic redox flow batteries (AO-RFBs). In this context, we have proposed a composite computational approach, specifically the GFN2-xTB/M06-2X protocol, to construct redox potential databases suitable for training various machine learning models. Herein, we developed the RP-ChEMBL database, which comprises one-electron standard reduction potentials of 8033 organic molecules selected from the publicly available ChEMBL molecular library. In constructing our database, we incorporated a structurally diverse set of compounds with molecular weights (M) up to 200 g/mol. While we recognize that this range is below the typical target for balanced AO-RFB design, it still encompasses a diversity of core molecular frameworks that could be suitable for reversible one-electron uptake.

Five graph-based deep learning models were trained and validated on the RP-ChEMBL database, all of which demonstrated remarkable predictive performance. The Attentive FP model was found to be particularly efficient among these architectures. The analysis of error distributions and cases with significant discrepancies between computed and predicted reduction potentials highlighted uncertainties associated with the GFN2-xTB method, though these are limited only to a few and very specific structural motifs. Overall, the trained models demonstrated sufficient reliability for predictive applications, which led to the development of an interactive web-based tool. The resulting platform, PredPotS, requires only the SMILES representation of a molecule as input and provides rapid, reliable predictions of 1e− standard reduction potentials for organic compounds in aqueous solution assuming no chemical transformation in the reduced states of molecules. The predictions are obtained within seconds, which is only a fraction of time needed to compute the potentials with the GFN2-xTB/M06-2X protocol.

The practical utility of the PredPotS tool was evaluated using a set of organic redox couples with experimentally reported reduction potentials available in the literature. The predicted values consistently fell within the potential range compatible with the electrochemical stability window of aqueous electrolytes, and showed a reasonable correlation with experimental data, even for compounds with molecular weights exceeding those represented in the training set. This finding was further supported by an analysis on a subset of molecules from the ChEMBL database with molecular weights in the range of 200–300 g/mol, for which the model yielded predictions with only slightly increased uncertainty.

In conclusion, this study presented the methodology and implementation of a predictive tool intended for the preliminary screening of organic compounds in aqueous solution, based on their one-electron reduction potentials. We recommend the use of this tool for obtaining rapid yet reasonable estimates, particularly for molecules of relatively small size, a limitation that can be addressed through further expansion of the underlying database. Prediction accuracy may also be enhanced by incorporating full DFT-based computational methods in future database developments. Efforts in this direction are currently underway within our research group.

Methods

Computational protocol

The composite GFN2-xTB/M06-2X computational protocol has previously been described in details83, but for the sake of clarity, we outline the main features here as well.

The semiempirical extended tight-binding GFN2-xTB method108,109 as implemented in the xtb program package (version 6.4)110 was used to preoptimize the initial geometries of molecules in aqueous phase. We applied the same method to perform conformational search for both oxidation states of the molecules, which was carried out via the crest program111. The most stable conformer based on the aqueous-phase Gibbs free energies was selected for each species to calculate the reduction potential. The solvent effects were incorporated implicitly via the generalized Born model with surface area contributions (GBSA) as implemented in xtb. The rigid-rotor harmonic-oscillator (RRHO) approximation was used to estimate the thermal and entropic contributions to Gibbs free energies at T = 298 K. The structures optimized at GFN2-xTB level were used to carry out single-point DFT electronic energy calculations using the M06-2X functional112 along with the 6-311 + G(d,p) basis set, wherein the solvation effects were estimated via the SMD implicit solvation model using water as a solvent113. The DFT calculations were performed using Gaussian 16114.

The 1e− standard reduction potentials of the organic species comprising our present molecular database were computed according to the Nernst equation:

$${E}_{{\rm{o}}}^{\mathrm{comp}}=-\frac{{G}^{o}\left({{\rm{A}}\cdot }^{-}\right)-\,{G}^{o}\left({\rm{A}}\right)}{F}-\Delta {E}^{{ref}}$$
(1)

where \({G}^{o}\left({\rm{A}}\right)\) and \({G}^{o}\left({{\rm{A}}\cdot }^{-}\right)\) denote the aqueous phase Gibbs free energies of the original and the reduced forms of organic electron acceptor A, F is the Faraday constant, and \({\varDelta E}^{{ref}}\) is the absolute potential of the reference standard hydrogen electrode (SHE) (4.281 V)115. The Gibbs free energies were computed via a composite manner:

$${G}^{o}\left({\rm{A}}/{{\rm{A}}\cdot }^{-}\right)={E}^{{DFT}}\left({\rm{A}}/{{\rm{A}}\cdot }^{-}\right)\,+\,{\Delta G}^{{xTB}}\left({\rm{A}}/{{\rm{A}}\cdot }^{-}\right)$$
(2)

where \({E}^{{DFT}}\left({\rm{A}}/{{\rm{A}}\cdot }^{-}\right)\) refers to the electronic energy term with the inclusion of solvation free energy computed at the DFT level, and \({\Delta G}^{{xTB}}\left({\rm{A}}/{{\rm{A}}\cdot }^{-}\right)\) involves all finite temperature contributions estimated with the GFN2-xTB method. Test calculations on a database of experimental half-peak potentials of a variety of organic potentials, as well as benchmark calculations with respect to full DFT computations demonstrate that this composite protocol is suitable to predict redox potentials for a large set of molecules with an accuracy close to that obtained at full DFT level83.