# A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Protocol and Results

^{+}is one of the reagents. ${U}^{0}$ is defined in the thermodynamic standard state where [H

^{+}] = 1 M or pH = 0. Redox potentials at other pH values, i.e., at conditions different from the standard state, are described by the Nernst equation [18]. The pH of the solution also determines the protonation state of the reactants and products, and therefore affects their energies and the number of protons exchanged in the redox reaction. The redox potential depends essentially on the reaction-free energy in the solution (see Equations (1) and (2)). In principle, the redox potential at any pH could be calculated from the free energies at the protonation state most abundant at that pH. However, at high pH, most OH groups tend to be deprotonated so that the major species of hydroxylated reduced quinones can have several negative charges (up to 6 in the set considered here). Such multiple anions can be challenging for the convergence of electronic structure methods since the additional electrons may not be sufficiently stabilized [16]. Moreover, the accuracy of implicit solvation models is known to deteriorate when increasing the charge of the solute [19]. For these reasons, it is preferable to compute the redox potential at pH = 0 and then transform it to higher pH values [20,21] using expressions based on the Nernst equation, such as Equation (5).

#### 2.1. Initial Guess: Protonation State and Conformer

_{a}calculator of the cheminformatics software package ChemAxon [22]. The resulting SMILES string of the pH = 0 structure is then converted to a 3D structure using Open Babel, [23,24] and its lowest energy conformation is determined using a conformer search script, part of the AMS software suite [25], which is based on RDKit [26] and was locally modified by us to use the MMFF94 force field [27] instead of UFF. This modification was necessary because UFF does not correctly identify the lowest energy conformers with intramolecular hydrogen bonds, while MMFF94 does. This is due to a different treatment of electrostatic interactions (the main component of hydrogen bonding) in the two force fields [28,29]. The relationship between intramolecular hydrogen bonding and stability has been reported before [10,30].

#### 2.2. Calculation of the Redox Potential at pH 0

#### 2.2.1. Choice of Standard Method

#### 2.2.2. Solvation and Thermal Contributions to Free Energy

#### 2.2.3. Comparing Electronic Structure Methods

#### 2.2.4. Limits of Implicit Solvation Models

_{2}O). $\Delta {G}_{\mathrm{s}}\left(\left[\mathrm{A}{\left({\mathrm{H}}_{2}\mathrm{O}\right)}_{n}\right]\right)$ is the solvation free energy of the cluster, i.e., the difference between its gas-phase and COSMO energies (both optimized in the respective phase). The last term is the vaporization free energy

_{2}O in water) to 1 M, and the third is the free-energy change of one mole of an ideal gas from 1 atm to 1 M. The latter two corrections ensure that all reactants and products in gas phase and in solution are in the same 1 M standard state, as explained in ref. [47]. The free energies ${G}_{\mathrm{sol}}^{0}\left(\mathrm{Red},\mathrm{Ox}\right)$ in Equation (2) are then obtained as ${G}_{\mathrm{sol}}^{0}\left(\mathrm{A}\right)={G}_{\mathrm{gas}}^{0}\left(\mathrm{A}\right)+\Delta {G}_{\mathrm{s}}^{\mathrm{cc}}\left(\mathrm{A}\right)$ where ${G}_{\mathrm{gas}}^{0}\left(\mathrm{A}\right)$ is the sum of the B3LYP gas-phase energy and the BLYP thermal contribution.

#### 2.3. Transformation to Higher pH Values

## 3. Summary and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Scheme 1.**Structures and abbreviations of the molecules considered in this study in their oxidized form and most prevalent protonation state at pH = 0.

**Figure 1.**Computed vs. experimental redox potentials at pH = 0: role of solvation and thermal contributions to the free energy. All energies computed with B3LYP functional and ADZP basis set. (

**a**) Starting from gas-phase electronic energies, the effect of adding solvation (COSMO) and thermal contribution (from BLYP gas-phase frequencies). (

**b**) Comparison between thermal contribution computed in gas or solution. (

**c**) Comparison between COSMO and SM12 solvation models. SM12 calculated as a single point at COSMO geometries. The systematic error of SM12 was corrected by −MSE. (

**d**) Comparison between COSMO and COSMO-RS solvation models. The systematic error of COSMO-RS was corrected by −MSE.

**Figure 2.**Computed vs. experimental redox potentials at pH = 0. Comparison between B3LYP and other methods. Systematic errors are corrected by subtracting MSE from all data points. All potentials include BLYP thermal correction except (

**b**). (

**a**) BLYP/ADZP optimized in COSMO. (

**b**) M06-2X-D3(0)/6-31G(2df,p) optimized in COSMO with thermal correction obtained at the same level of theory in gas. (

**c**) rev-DOD-BLYP-D4/TZ2P in COSMO (single point at B3LYP geometries). (

**d**) G4MP2 gas-phase energies + B3LYP/COSMO solvation free energies.

**Figure 3.**Left vertical axis: Solvation free energies of the Ox and Red forms of AQTH14 obtained from the cluster–continuum model as a function of the number n of explicit water molecules. Large empty symbols are the Boltzmann average over a few cluster conformations (small filled symbols). Right vertical axis: resulting standard redox potential expressed as the distance from the experimental value (0.200 V).

**Figure 4.**Computed vs. experimental redox potentials at different pH values. In the (

**left panel**), the transformation from pH 0 to 7 and 13 was carried out with Equation (5) using the number of protons at pH = 0. In the (

**right panel**), the transformation is done with Equation (6) where the number of protons and hence the slope of the Pourbaix diagram was updated at every ${\mathrm{pK}}_{\mathrm{a}}$.

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**MDPI and ACS Style**

Fornari, R.P.; de Silva, P.
A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials. *Molecules* **2021**, *26*, 3978.
https://doi.org/10.3390/molecules26133978

**AMA Style**

Fornari RP, de Silva P.
A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials. *Molecules*. 2021; 26(13):3978.
https://doi.org/10.3390/molecules26133978

**Chicago/Turabian Style**

Fornari, Rocco Peter, and Piotr de Silva.
2021. "A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials" *Molecules* 26, no. 13: 3978.
https://doi.org/10.3390/molecules26133978