Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids
Abstract
:1. Introduction
2. Materials and Methods
- Vertical transition of single ions, where the final state preserves the structure of the initial state.
- Adiabatic transition of single ions, where the final state is energetically relaxed to its minimum.
- Vertical or adiabatic transition of neutral ionic couples.
- 4.
- For a reduction reaction where the reagent (initial state) is the chemical specie B with net charge m:
3. Results
3.1. Vertical Transitions Approximation Starting from Ions
- MP2 in vacuum.
- B3LYP in vacuum.
- B3LYP in a simulated polar medium
- B3LYP in a simulated polar medium with the inclusion of empirical dispersion forces.
Anion | Etot(A−) | Etot(A) | Anodic Limit | Etot(A2−) | Cathodic Limit |
trans TFSI | −1823.63092 | −1823.39173 | 4.99 | −1823.34804 | −9.08 |
cis TFSI | −1823.63007 | −1823.39515 | 4.87 | −1823.33703 | −9.36 |
transFSI | −1349.23486 | −1348.99802 | 4.92 | −1348.94736 | −9.21 |
cisFSI | −1349.23324 | −1349.00147 | 4.79 | −1348.94942 | −9.11 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit | Etot(B2+) | Anodic Limit |
N1114 | −331.02025 | −331.04434 | −0.81 | −330.45111 | 13.88 |
N122(2O1) | −445.22449 | −445.22282 | −1.50 | −444.71155 | 12.36 |
EMI | −343.49078 | −343.56614 | 0.57 | −342.96762 | 12.64 |
Anion | Etot(A−) | Etot(A) | Anodic Limit | Etot(A2−) | Cathodic Limit |
trans TFSI | −1827.20535 | −1826.99235 | 4.28 | −1826.95785 | −8.13 |
cis TFSI | −1827.20097 | −1827.00271 | 3.88 | −1826.95553 | −8.07 |
transFSI | −1351.66082 | −1351.43819 | 4.54 | −1351.40995 | −8.22 |
cisFSI | −1351.6592 | −1351.44255 | 4.38 | −1351.41302 | −8.09 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit | Etot(B2+) | Anodic Limit |
N1114 | −332.13521 | −332.18441 | −0.13 | −331.58873 | 13.26 |
N122(2O1) | −446.65622 | −446.68747 | −0.61 | −446.16199 | 11.85 |
EMI | −344.56568 | −344.66596 | 1.25 | −344.04875 | 12.47 |
Anion | Etot(A−) | Etot(A) | Anodic Limit | Etot(A2−) | Cathodic Limit |
trans TFSI | −1827.28312 | −1827.00165 | 6.13 | −1827.24442 | −2.50 |
cis TFSI | −1827.28187 | −1827.00041 | 6.12 | −1827.24039 | −2.58 |
transFSI | −1351.73851 | −1351.44738 | 6.39 | −1351.71605 | −2.07 |
cisFSI | −1351.73742 | −1351.45178 | 6.24 | −1351.71803 | −1.98 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit | Etot(B2+) | Anodic Limit |
N1114 | −332.21925 | −332.18622 | −2.35 | −331.88683 | 7.50 |
N122(2O1) | −446.73390 | −446.69196 | −2.59 | −446.45716 | 6.00 |
EMI | −344.64676 | −344.67272 | −0.76 | −344.36680 | 6.08 |
Anion | Etot(A−) | Etot(A) | Anodic Limit | Etot(A2−) | Cathodic Limit |
trans TFSI | −1827.30034 | −1827.01849 | 6.14 | −1827.25980 | −2.55 |
cis TFSI | −1827.29967 | −1827.01740 | 6.15 | −1827.25726 | −2.60 |
transFSI | −1351.74681 | −1351.45603 | 6.38 | −1351.72454 | −2.06 |
cisFSI | −1351.74565 | −1351.46024 | 6.23 | −1351.72263 | −2.08 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit | Etot(B2+) | Anodic Limit |
N1114 | −332.24174 | −332.20839 | −2.36 | −331.90927 | 7.50 |
N122(2O1) | −446.76405 | −446.72115 | −2.62 | −446.48594 | 6.03 |
EMI | −344.65858 | −344.68410 | −0.77 | −344.37864 | 6.08 |
3.2. Adiabatic Transition Approximation Starting from Ions
3.3. Vertical and Adiabatic Transition Approximations Starting from Ionic Couples
4. Discussion
- MAE: mean absolute error
- MRE: mean relative error
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Anion | Etot(A−) | Etot(A) | Anodic Limit |
trans TFSI | −1823.62028 | −1823.41428 | 4.09 |
cis TFSI | −1823.61928 | −1823.43472 | 3.51 |
transFSI | −1349.23911 | −1349.03932 | 3.92 |
cisFSI | −1349.23863 | −1349.04332 | 3.80 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit |
N1114 | −330.80012 | −330.93418 | 2.15 |
N122(2O1) | −444.97169 | −445.11011 | 2.27 |
EMI | −343.35246 | n.a. | n.a. |
Anion | Etot(A−) | Etot(A) | Anodic Limit |
trans TFSI | −1827.19679 | −1827.01722 | 3.38 |
cis TFSI | −1827.19244 | −1827.02017 | 3.18 |
transFSI | −1351.66633 | −1351.47866 | 3.60 |
cisFSI | −1351.66656 | −1351.47947 | 3.58 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit |
N1114 | −331.92069 | −332.08220 | 2.89 |
N122(2O1) | −446.41160 | n.a. | n.a. |
EMI | −344.43057 | −344.56575 | 2.18 |
Anion | Etot(A−) | Etot(A) | Anodic Limit |
trans TFSI | −1827.27619 | −1827.01489 | 5.58 |
cis TFSI | −1827.27456 | −1827.02984 | 5.13 |
transFSI | −1351.74524 | −1351.48717 | 5.49 |
cisFSI | −1351.74472 | −1351.48705 | 5.48 |
Cation | Etot(B+) | Etot(B) | Cathodic Limit |
N1114 | −332.00411 | −332.08443 | 0.70 |
N122(2O1) | −446.48997 | −446.58365 | 1.06 |
EMI | −344.52342 | −344.57263 | −0.13 |
Couple | Etot(AB) | Etot(AB−) | Etot(AB+) | Cathodic Limit | Anodic Limit |
vertical approximation | |||||
N1114-TFSI | −2159.46931 | −2159.39488 | −2159.14778 | −3.46 | 7.20 |
N122(2O1)-TFSI | −2273.986794 | −2273.89748 | −2273.66706 | −3.87 | 7.16 |
EMI-TFSI | −2171.90189 | −2171.86766 | −2171.57799 | −2.38 | 7.26 |
N1114-FSI | −1683.921127 | −1683.85372 | −1683.57549 | −3.27 | 7.85 |
EMI-FSI | −1696.354203 | −1696.32878 | −1696.01017 | −2.14 | 7.81 |
adiabatic approximation | |||||
N1114-TFSI | −2159.468312 | −2159.49395 | −2159.178994 | −0.77 | 6.34 |
N122(2O1)-TFSI | −2273.986794 | −2273.984858 | −2273.697808 | −1.51 | 6.33 |
EMI-TFSI | −2171.90189 | −2171.906218 | −2171.60822 | −1.34 | 6.45 |
N1114-FSI | −1683.921127 | −1683.95163 | −1683.616591 | −0.64 | 6.75 |
EMI-FSI | −1696.354203 | −1696.363319 | −1696.046943 | −1.21 | 6.82 |
Couple | Etot(AB) | Etot(AB−) | Etot(AB+) | Cathodic Limit | Anodic Limit |
vertical approximation | |||||
N1114-TFSI | −2159.56461 | −2159.53508 | −2159.27601 | −2.26 | 6.32 |
N122(2O1)-TFSI | −2274.08905 | −2274.06063 | −2273.81845 | −2.23 | 5.83 |
EMI-TFSI | −2171.98306 | −2171.99998 | −2171.71060 | −1.01 | 5.88 |
N1114-FSI | −1684.00735 | −1683.99813 | −1683.70824 | −1.71 | 6.60 |
EMI-FSI | −1696.42519 | −1696.44125 | −1696.15003 | −1.03 | 5.95 |
BMIM-Cl | −883.67826 | −883.69723 | −883.43663 | −0.94 | 5.05 |
adiabatic approximation | |||||
N1114-TFSI | −2159.56461 | −2159.64148 | −2159.30582 | 0.61 | 5.51 |
N122(2O1)-TFSI | −2274.08905 | −2274.16691 | −2273.82620 | 0.64 | 5.62 |
EMI-TFSI | −2171.98306 | −2172.02960 | −2171.72324 | −0.21 | 5.54 |
N1114-FSI | −1684.00735 | −1684.10311 | −1683.74163 | 1.12 | 5.70 |
EMI-FSI | −1696.42519 | −1696.47219 | −1696.16292 | −0.19 | 5.61 |
BMIM-Cl | −883.678262 | −883.726384 | −883.446842 | −0.16 | 4.78 |
Computational Method | MP2 in Vacuum | B3LYP in Vacuum | B3LYP in Polar Medium | B3LYP with D in Polar Medium |
---|---|---|---|---|
Vertical transitions from ions | ||||
MAE | −0.07 | −0.71 | 1.30 | 1.30 |
MRE | −1% | −14% | 27% | 27% |
Adiabatic transitions from ions | ||||
MAE | −1.21 | −1.39 | 0.45 | |
MRE | −25% | −28% | 9% | |
Vertical transitions from ionic couples | ||||
MAE | 2.56 | 1.65 | ||
MRE | 53% | 34% | ||
Adiabatic transitions from ionic couples | ||||
MAE | 1.22 | 0.70 | ||
MRE | 25% | 14% |
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Paolone, A.; Brutti, S. Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids. Materials 2021, 14, 3221. https://doi.org/10.3390/ma14123221
Paolone A, Brutti S. Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids. Materials. 2021; 14(12):3221. https://doi.org/10.3390/ma14123221
Chicago/Turabian StylePaolone, Annalisa, and Sergio Brutti. 2021. "Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids" Materials 14, no. 12: 3221. https://doi.org/10.3390/ma14123221