# Evaluation of Computational Chemistry Methods for Predicting Redox Potentials of Quinone-Based Cathodes for Li-Ion Batteries

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Choice of Descriptors

^{2}) and root-mean-square error (RMSE) of the linear regression (LR) between the computational data and the measured redox potentials. To facilitate the comparison between models with different scales, we used the normalized RMSE (NRMSE) [24], which is defined as the RMSE for any given dataset divided by the range of redox potentials spanned by that dataset:

#### 2.2. Experimental Data for Validation

^{+}, as this value is similar to errors in DFT calculations [29]; (3) the redox potentials of compounds that involve a two-electron lithiation process should be clearly specified rather than be presented as a range of values [28]; (4) the lithiation sites on the molecules should be limited to the carbonyl groups that are directly attached to the rings of quinones, as opposed to the chemical functional groups of the molecules; and (5) molecules with more than four rings should be ignored because it is known that the π-π stacking interaction between quinones rapidly increases with the number of aromatic rings [30] and the intermolecular interactions consequently increase, which is likely to result in errors within the gas phase approximation [20]. In addition to these criteria, fluorinated 2, 2′-bis-p-benzoquinone (F

_{2}-BBQ) [21] from dataset No. 5 was removed because of its fast decomposition (12% capacity retained after 20th cycle) and therefore lack of discharge voltage data. As a result, a total of 39 compounds divided into seven sets were identified for the validation of the descriptors and computational models. The two-dimensional (2D) structures of these compounds are shown in Figure 1.

_{3}, –CF

_{3}, –C

_{4}F

_{9}, –C

_{6}F

_{13}, –Cl, –COOH, –NH

_{2}, –CH

_{3}, –Br, –C

_{4}H

_{9}, –CH(CH

_{3})

_{2}, –C(CH

_{3})

_{3}, –OCH

_{3}, –COOLi, and –COOCH

_{3}. The measured values of redox potentials were obtained by two different experimental techniques: galvanostatic cycling and cyclic voltammetry. Further details on the electrolytes, discharge rates, and type of data source that was used to obtain the measured redox potentials are summarized in Table 1, and the operation voltage and charge/discharge windows for the seven datasets are tabulated in Table S9.

#### 2.3. Computational Scheme

- (1)
- The three-dimensional (3D) molecular geometries were initially created by using the Maestro editor in the Schrödinger Materials Science Suite (version 2019-3) [31].
- (2)
- A search for the lowest energy conformer was performed for all the compounds using the OPLS3e [32] force field.
- (3)
- The lowest energy conformers were further optimized in the gas phase with various SEQM, DFTB, and DFT methods that are described below. As an additional step, single point energy (SPE) calculations using two representative DFT methods were performed on frozen atom coordinates obtained from the SEQM or DFTB optimizations. Altogether, these optimizations yielded descriptor data that were obtained at three levels of approximation: SEQM or DFTB, DFT, and a hybrid of the two.
- (4)
- To explore the possible contributions of solvation effects (as explored in previous studies [18,33]), SPE calculations were performed again in an implicit solvation environment within the standard Poisson–Boltzmann Formalism (PBF) [34], in which the parameters for the solvent phase were set according to the experimental conditions from each dataset.

^{++}** [42] basis set with polarization and diffuse functions was used for the DFT calculations. For DFT optimization calculations, we used grids with medium point density, whereas for DFT SPE calculations, we used finer grids. The hybrid scheme, i.e., the DFT calculated SPE on the SEQM- or DFTB-optimized coordinates, was performed without the dispersion corrections, as they showed no significant advantage when using the full DFT-based calculation scheme. The dielectric constant, molecular weight, and density of the electrolyte solvent used for the SPE calculations involving the implicit solvation effect are provided in Supporting Information Table S1. The values for binary solvents were calculated based on their molar ratios in the mixtures.

## 3. Results and Discussions

^{2}and RMSE data are shown in Supporting Information Figure S1, Tables S5–S7 and S11–S13. We begin with a discussion of the performance of the three descriptors at the highest level of theory considered in this work; the DFT calculated results as shown in Figure 2a–c. Firstly, when using HOMO energy as the descriptor, there was considerable spread in NRMSE values for the various DFT methods for all datasets (Figure 2c). Secondly, when using $\mathrm{\Delta}{E}_{r}$ (Figure 2a), the NRMSE spread was ~10%, except for dataset No. 2, for which the NRMSE ranged from 3.82% to 29.78%. Thirdly, when the reactant molecule’s LUMO energy was used as the descriptor (Figure 2b), all DFT methods showed quite similar performance for each dataset, with an NRMSE spread of approximately 5%. A consensus between the various DFT methods applied in the current study reveals problems with the optimized structures and the corresponding energies of the lithiated molecules. In addition, when considering DFT methods without implicit solvation, LUMO energy was found to be the best descriptor for predicting the redox potentials not only because of the high consistency between various DFT methods on NRMSE but also because of its lowest prediction error among three descriptors.

^{3}times faster to compute. As shown in Figure 2e, the prediction accuracies of the SEQM methods were almost as good as the DFT simulations for datasets No. 1, 2, and 5, but they were slightly worse for datasets No. 3, 4, 6, and 7. The average NRMSE values for GFN1-xTB and SCC-DFTB were 15.85 and 19.60%, respectively. The DFTB methods showed similar prediction accuracies to DFT for datasets No. 1, 2, 4, and 5, though they were comparably worse for datasets No. 3 and 6.

^{2}, and RMSE of hybrid calculations for three descriptors are shown in Figure 3 and Supporting Information Figure S2, Tables S2–S7 and S11–S13. Two SEQM (AM1 and PM7) and two DFTB (GFN1-xTB and SCC-DFTB) methods were used for the geometry optimizations, and these were followed by SPE calculations using the B3LYP functional. Yet again, the relative behavior of the three descriptors remained unchanged across all seven datasets, and LUMO clearly emerged as the most accurate descriptor with the lowest NRMSE. Remarkably, when using LUMO as the descriptor, the performance of the hybrid scheme was just as good as the DFT calculations across the seven datasets (Figure 3b,e). Within the gas phase approximation, the notable similarities between the hybrid scheme and DFT results suggest that the differences between the bare low-level calculations and the full DFT calculations originated from the prediction of energies rather than the difference in geometries. It can be observed that inclusion of implicit solvation led to a miniscule effect on the prediction accuracy when using the LUMO descriptor, which was the same as the case of the full DFT calculations. The average NRMSE of the hybrid scheme PM7/B3LYP

_{g}(11.46%) was slightly less than that of AM1/B3LYP

_{g}(13.83%), which was different than the performance of the bare SEQM calculations. A similar conclusion was reached for the hybrid scheme of DFTB and DFT, for which the SCC-DFTB/B3LYP

_{g}(12.01%) slightly outperformed GFN1-xTB/B3LYP

_{g}(13.11%), and the bare GFN1-xTB results had smaller average NRMSE values than the bare SCC-DFTB results. According to these findings, the PM7 and SCC-DFTB methods are efficient for geometry optimization, and the AM1 and GFN1-xTB methods are better at predicting energies. In summary, when LUMO energy is used as the descriptor for the prediction of measured redox potentials, the hybrid scheme PM7/B3LYP

_{g}is the best choice.

## 4. Conclusions

## Supplementary Materials

^{2}of three descriptors: $\mathrm{\Delta}{E}_{r}$, LUMO energy, and HOMO energy. The computational data were calculated by using (a–c) DFT, (d–f) SEQM, and (g–i) DFTB methods for the seven experimental datasets. PBE

_{g}and PBE

_{s}represent single point calculations in gas (g) and solvent (s) phases, respectively. The shaded vertical bars in (b,e,h) show the fully B3LYP

_{g}calculated data; Figure S2: R

^{2}of three descriptors: $\mathrm{\Delta}{E}_{r}$, LUMO energy, and HOMO energy. The computational data were calculated by using (a–c) hybrid SEQM/DFT scheme and (d,e) hybrid DFTB/DFT scheme for the seven experimental datasets. Accordingly, AM1/B3LYP

_{g}and AM1/B3LYP

_{s}suggest that the molecules were optimized only with AM1 and their energies were calculated by using B3LYP functional either without or with solvation effect, respectively. The shaded vertical bars in (b,e,h) show the fully B3LYP

_{g}calculated data; Table S2: NRMSE of $\mathrm{\Delta}{E}_{r}$ as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S3: NRMSE of LUMO energy of the reactant molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S4: NRMSE of HOMO energy of the product molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S5: R

^{2}of $\mathrm{\Delta}{E}_{r}$ as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S6: R

^{2}of LUMO energy of the reactant molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S7: R

^{2}of HOMO energy of the product molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S8: Average NRMSE of the seven datasets for LUMO descriptor as calculated with B3LYP, SEQM, DFTB, and the hybrid schemes of SEQM (or DFTB) and B3LYP; Table S9: Summary of operation voltage and charge/discharge windows for the seven datasets; Table S10: The 2D structures of seven quinones, the zero-point energy (𝑍𝑃𝐸) of quinone reactants and lithiated products, and their difference in 𝑍𝑃𝐸 with the functional of PBE and B3LYP in gas phase; Table S11: RMSE of $\mathrm{\Delta}{E}_{r}$ as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S12: RMSE of LUMO energy of the reactant molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets; Table S13: RMSE of HOMO energy of the product molecules as computed with DFT, SEQM, DFTB, and hybrid schemes of SEQM (or DFTB) and DFT methods for the seven datasets.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**2D structures of the molecules that were used for the calibration of computational methods. A total of seven different experimental datasets were considered in the current study.

**Figure 2.**NRMSE of three descriptors—$\mathrm{\Delta}{E}_{r}$, LUMO energy, and HOMO energy—calculated with (

**a**–

**c**) DFT functionals, (

**d**–

**f**) SEQM methods, and (

**g**–

**i**) DFTB methods for the seven datasets. PBE

_{g}and PBE

_{s}represent the calculation of single point energy in the gas (g) and solvent phases (s), respectively. The shaded vertical bars in (

**b**,

**e**,

**h**) show the fully B3LYP

_{g}calculated data.

**Figure 3.**NRMSE of three descriptors: $\mathrm{\Delta}{E}_{r}$, LUMO energy, and HOMO energy. The hybrid schemes of SEQM/DFT (

**a**–

**c**) and DFTB/DFT (

**d**–

**f**) were used for the seven datasets. Accordingly, AM1/B3LYP

_{g}and AM1/B3LYP

_{s}suggest that the molecules were optimized only with AM1, and their energies were calculated by using B3LYP functional either without or with solvation effect, respectively. The shaded vertical bars in (

**b**,

**e**) show the fully B3LYP

_{g}calculated data.

Dataset | Electrolyte | Number of Molecules | Discharge Condition | Range of Redox Potential (vs. Li/Li ^{+}) | Data Source * |
---|---|---|---|---|---|

1 | 1 M LiPF_{6}-EC + DEC (v/v = 3:7) | 4 | 0.1 mA | 0.60 V | Table |

2 | 1 M LiPF_{6}-EC + DMC (w/w = 1:1) | 4 | 1 Li per 5 h | 0.44 V | Text |

3 | 1 M LiPF_{6}-EC + DMC (w/w = 1:1) | 5 | 1 Li per 5 h | 0.66 V | Table |

4 | 1 M LiPF_{6}-EC + DMC (v/v = 3:7) | 6 | 1 mV/s | 1.55 V | Text |

5 | 2.75 M LiTFSI-Tetraglyme | 8 | 40 mA/g | 0.30 V | Table |

6 | 1 M LiTFSI-Tetraglyme | 5 | 40 mA/g | 1.00 V | Table |

7 | 1 M LiPF_{6}-PC | 7 | 1 Li per 10 h | 0.82 V | Text |

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**MDPI and ACS Style**

Zhou, X.; Khetan, A.; Er, S. Evaluation of Computational Chemistry Methods for Predicting Redox Potentials of Quinone-Based Cathodes for Li-Ion Batteries. *Batteries* **2021**, *7*, 71.
https://doi.org/10.3390/batteries7040071

**AMA Style**

Zhou X, Khetan A, Er S. Evaluation of Computational Chemistry Methods for Predicting Redox Potentials of Quinone-Based Cathodes for Li-Ion Batteries. *Batteries*. 2021; 7(4):71.
https://doi.org/10.3390/batteries7040071

**Chicago/Turabian Style**

Zhou, Xuan, Abhishek Khetan, and Süleyman Er. 2021. "Evaluation of Computational Chemistry Methods for Predicting Redox Potentials of Quinone-Based Cathodes for Li-Ion Batteries" *Batteries* 7, no. 4: 71.
https://doi.org/10.3390/batteries7040071