Prediction of Exchange-Correlation Energy of Graphene Sheets from Reverse Degree-Based Molecular Descriptors with Applications
Abstract
:1. Introduction
2. Relationship between the Exchange-Correlation Energy and the Reverse General Inverse Sum Indeg Descriptor of Graphene Sheets
Graphene Sheets | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
C6 | 12 | 6 | 6 | 4.2426 | 6 | 24 | 6 | 6 | 3 | 12 | 12 |
C10 | 38 | 33 | 6.8284 | 6.0165 | 6.6667 | 136 | 10.771 | 11.243 | 9.1667 | 14 | 122 |
C13 | 48 | 39 | 10.243 | 8.5855 | 10 | 162 | 14.657 | 15.364 | 11.5 | 21 | 138 |
C16 | 58 | 45 | 13.657 | 11.154 | 13.333 | 188 | 18.542 | 19.485 | 13.833 | 28 | 154 |
C19 | 68 | 51 | 17.071 | 13.723 | 16.667 | 214 | 22.428 | 23.606 | 16.167 | 35 | 170 |
C22 | 79 | 60 | 20.364 | 16.267 | 20 | 249 | 26.485 | 27.546 | 19 | 41.5 | 202 |
C24 | 84 | 60 | 23.485 | 18.414 | 23 | 252 | 29.314 | 30.728 | 20 | 48 | 192 |
C28 | 98 | 71 | 27.485 | 21.534 | 27 | 296 | 34.314 | 35.728 | 23.5 | 56 | 230 |
C30 | 104 | 73 | 30.399 | 24.104 | 30.33 | 306 | 37.199 | 38.849 | 24.833 | 62 | 230 |
C32 | 110 | 75 | 33.314 | 25.673 | 32.667 | 316 | 40.97 | 41.97 | 26.167 | 68 | 230 |
3. Reverse General Inverse Sum Indeg Descriptor of Graphene
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4. Conclusions
- The regression models (Table 4) derived from reverse topological descriptors in the present article were extremely accurate for predicting the exchange-correlation energies in the graphene sheets.
- The reverse sum−connectivity descriptor with was the best predictor among the 11 studied descriptors. Meanwhile, the reverse redefined first Zagreb descriptor performed poorly.
- The density functional theory (DFT) calculations of the electronic structure, such as the exchange-correlation energies of the graphene sheets, were precise; however, they were computationally expensive while the reverse topological descriptors models presented herein required minimal computations and provided high levels of accuracy.
- Analytical expressions of the reverse first and second Zagreb descriptor, reverse Randić descriptor, reverse sum−connectivity descriptor, reverse harmonic descriptor, reverse hyper Zagreb descriptor, reverse geometric−arithmetic descriptor, reverse inverse sum indeg descriptor, and reverse redefined first and third Zagreb descriptors have been obtained for graphene structures.
- Researchers who are trying to better understand the behaviour of graphene are likely to find the numerical values and graphical representations presented in this article helpful.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Corresponding Reverse Topological Descriptors | ||
---|---|---|
Reverse first Zagreb descriptor | ||
Reverse second Zagreb descriptor | ||
Reverse Randić descriptor | ||
Reverse sum−connectivity descriptor | ||
Reverse harmonic descriptor | ||
Reverse hyper Zagreb descriptor | ||
Reverse geometric−arithmetic descriptor | ||
Reverse arithmetic−geometric descriptor | ||
Reverse inverse sum indeg descriptor | ||
Reverse redefined first Zagreb descriptor | ||
Reverse redefined third Zagreb descriptor |
Graphene Sheets | EC Energy | |
---|---|---|
278.3728274 | ||
582.3543 | ||
870.9878 | ||
1165.387066 | ||
1512.946726 | ||
1868.115158 | ||
2129.987845 | ||
2698.081041 | ||
2951.482056 | ||
3253.425639 |
Regression Equation | r | SE | F |
---|---|---|---|
) | 0.980475724 | 213.8003228 | 198.893 |
) | 0.945489731 | 354.0705116 | 67.437 |
) | 0.997953668 | 69.52114251 | 1948.719 |
0.998617364 | 57.15508183 | 2887.026 | |
0.997778424 | 72.43364998 | 1794.526 | |
0.947685472 | 347.0617000 | 70.514 | |
0.997280715 | 80.12777418 | 1464.977 | |
0.980655201 | 95.36092088 | 1031.971 | |
0.980655201 | 212.8250165 | 200.793 | |
) | 0.998037144 | 68.08980614 | 2031.849 |
) | 0.896497248 | 481.7127938 | 32.755 |
24 | 23 | 2.9142 | 2.9476 | 2.8333 | 94 | 5.8856 | 6.1213 | 5.8333 | 6 | 90 | |
58 | 45 | 13.657 | 11.154 | 13.333 | 188 | 18.542 | 19.485 | 13.833 | 28 | 154 | |
104 | 73 | 30.339 | 23.604 | 27.833 | 306 | 37.199 | 38.849 | 24.833 | 62 | 230 | |
162 | 107 | 53.142 | 40.295 | 52.333 | 448 | 61.856 | 64.213 | 38.833 | 108 | 318 | |
232 | 147 | 81.885 | 61.231 | 80.833 | 614 | 92.512 | 95.577 | 55.833 | 166 | 418 | |
314 | 193 | 116.63 | 86.408 | 115.33 | 804 | 129.17 | 132.94 | 75.833 | 236 | 530 | |
408 | 245 | 157.11 | 115.83 | 155.83 | 1018 | 171.83 | 176.30 | 98.833 | 318 | 654 | |
514 | 303 | 204.11 | 149.50 | 202.83 | 1256 | 220.48 | 225.67 | 124.83 | 412 | 790 | |
632 | 367 | 256.86 | 187.40 | 254.83 | 1518 | 275.14 | 281.03 | 153.83 | 518 | 938 | |
762 | 437 | 315.60 | 229.54 | 313.33 | 1804 | 335.80 | 342.40 | 185.83 | 636 | 1098 |
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Albadrani, M.; Ali, P.; El-Garaihy, W.H.; Abd El-Hafez, H. Prediction of Exchange-Correlation Energy of Graphene Sheets from Reverse Degree-Based Molecular Descriptors with Applications. Materials 2022, 15, 2889. https://doi.org/10.3390/ma15082889
Albadrani M, Ali P, El-Garaihy WH, Abd El-Hafez H. Prediction of Exchange-Correlation Energy of Graphene Sheets from Reverse Degree-Based Molecular Descriptors with Applications. Materials. 2022; 15(8):2889. https://doi.org/10.3390/ma15082889
Chicago/Turabian StyleAlbadrani, Mohammed, Parvez Ali, Waleed H. El-Garaihy, and Hassan Abd El-Hafez. 2022. "Prediction of Exchange-Correlation Energy of Graphene Sheets from Reverse Degree-Based Molecular Descriptors with Applications" Materials 15, no. 8: 2889. https://doi.org/10.3390/ma15082889