A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C60
Abstract
1. Introduction
2. Materials and Methods
3. Results
3.1. Bond Length, Bond Angle, and Dihedral Angles of Fullerene
3.2. Natural Bond Analysis
3.3. Correlation Energy and HOMO-LUMO Gap of α Electrons of Fullerene C60
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | C1 | C6 | C2 | Minimum | Maximum | Median |
---|---|---|---|---|---|---|
ESP | −0.031000 | 0.009000 | −0.035000 | −0.040000 | 0.040000 | 0.0 |
NBO | −0.000020 | 0.000010 | 0.000010 | −0.000030 | 0.000030 | 0.0 |
Mulliken | 0.000011 | −0.000022 | −0.000022 | −0.000049 | 0.000046 | 0.0 |
Hirshfeld | −0.000020 | 0.000013 | 0.000010 | −0.000022 | 0.000023 | 0.0 |
CM5 | −0.000020 | 0.000013 | 0.000010 | −0.000022 | 0.000023 | 0.0 |
Bond | Line of Center between Two Nuclei | Hybrid 1 | Hybrid 2 | |||||
---|---|---|---|---|---|---|---|---|
Hybrid 1–2 | θ (Theta) | φ (Phi) | θ | φ | Dev | θ | φ | Dev |
Fullerene C60 | ||||||||
C1–C2 (σ) | 129.4 | 264.9 | 140.6 | 255.2 | 13.1 | 62.4 | 91.8 | 13.1 |
C1–C6 (σ) | 47.9 | 167.4 | 58.7 | 154.1 | 15.1 | 140.8 | 5.5 | 15.1 |
C1–C6 (π) | 47.9 | 167.4 | 50.3 | 276.1 | 75.8 | 71.9 | 297.4 | 75.8 |
Benzene | ||||||||
C1–C2 (σ) | 90.0 | 22.7 | 90.0 | 17.9 | 4.1 | 90.0 | 207.6 | 4.1 |
C1–C6 (σ) | 90.0 | 142.7 | 90.0 | 147.6 | 4.1 | 90.0 | 317.9 | 4.1 |
C1–C6 (π) | 90.0 | 142.7 | 0.0 | 0.0 | 90.0 | 0.0 | 0.0 | 90.0 |
Molecule | Bond | Energy (Hartree) | Geminal | Vicinal | Energy (kcal/mol) |
---|---|---|---|---|---|
Fullerene C60 | C1–C2 (σ) | −0.88405 | 4 | 12 | 34.98 |
Total | C1–C2 | 4 | 12 | 34.98 (100% + 38%) | |
C1–C6 (σ) | −0.93273 | 4 | 8 | 26.33 | |
C1–C6 (π) | −0.34383 | 4 | 8 | 110.14 | |
Total | C1–C6 | 8 | 16 | 143.70 (100% + 22%) | |
Benzene | C1–C2 (σ) | −0.90988 | 4 | 6 | 21.74 |
Total | C1–C2 | 4 | 6 | 21.76 (100%) | |
C1–C6 (σ) | −0.91019 | 4 | 6 | 21.76 | |
C1–C6 (π) | −0.29735 | 0 | 4 | 87.66 | |
Total | C1–C6 | 4 | 10 | 111.70 (100%) |
Fullerene C60 | Benzene(MP2/6–31G*/CCSD(T)/aug-cc-pvtz) | ||||||
---|---|---|---|---|---|---|---|
Donor | Type | Acceptor | E (kcal/mol) | Donor | Type | Acceptor | E (kcal/mol) |
C1–C2 (σ) | Rydberg | C3 | 0.8 | C1–C2 (σ) | Rydberg | C3 | 1.36/0.92 |
Rydberg | C3 | 1.64 | Rydberg | C3 | 2.02/1.93 | ||
Rydberg | C6 | 0.8 | Rydberg | C6 | 1.36/0.92 | ||
Rydberg | C6 | 1.64 | Rydberg | C6 | 2.02/1.93 | ||
Rydberg | C7 | 1.31 | Antibond | C1–C6 | 3.24/2.25 | ||
Rydberg | C9 | 1.31 | Antibond | C1–H7 | 1.49/0.91 | ||
Antibond | C1–C6 | 3.91 | Antibond | C2–C3 | 3.24/2.25 | ||
Antibond | C1–C7 | 2.05 | Antibond | C2–H8 | 1.49/0.91 | ||
Antibond | C2–C3 | 3.91 | Antibond | C3–H9 | 2.77/3.15 | ||
Antibond | C2–C9 | 2.05 | Antibond | C6-H12 | 2.77/3.15 | ||
Antibond | C3–C11 | 3.48 | Total | C1–C2 | 10 | 21.76/18.32 | |
Antibond | C6–C17 | 3.48 | C1–C6 (σ) | Rydberg | C2 | 1.36/0.92 | |
Antibond | C7–C19 | 3.8 | Rydberg | C2 | 2.02/1.93 | ||
Antibond | C7–C19 | 0.5 | Rydberg | C5 | 1.36/0.92 | ||
Antibond | C9–C10 | 3.8 | Rydberg | C5 | 2.02/1.93 | ||
Antibond | C9–C10 | 0.5 | Antibond | C1–C2 | 3.24/2.25 | ||
Total | C1–C2 | 16 | 34.98 | Antibond | C1–H7 | 1.50/0.91 | |
C1–C6 (σ) | Rydberg | C2 | 1.61 | Antibond | C2–H8 | 2.77/3.15 | |
Rydberg | C5 | 1.61 | Antibond | C5–C6 | 3.24/2.25 | ||
Rydberg | C7 | 1.61 | Antibond | C5–H11 | 2.77/3.15 | ||
Rydberg | C7 | 1.61 | Antibond | C6–H12 | 1.50/0.91 | ||
Antibond | C1–C2 | 3.68 | Total | 10 | 21.78/18.32 | ||
Antibond | C1–C7 | 3.68 | C1–C6 (π) | Rydberg | C2 | 2.57/1.88 | |
Antibond | C2–C9 | 1.75 | Rydberg | C5 | 2.57/1.88 | ||
Antibond | C5–C6 | 3.68 | Antibond | C2–C3 | 42.39/41.94 | ||
Antibond | C5–C15 | 1.75 | Antibond | C4–C5 | 42.39/41.94 | ||
Antibond | C6–C17 | 3.68 | Total | 4 | 89.92/87.64 | ||
Antibond | C7–C8 | 1.75 | |||||
Antibond | C6–C17 | 1.75 | |||||
Total | 12 | 28.16 | |||||
C1–C6 (π) | Rydberg | C1 | 0.53 | ||||
Rydberg | C2 | 1.75 | |||||
Rydberg | C5 | 1.75 | |||||
Rydberg | C6 | 0.53 | |||||
Rydberg | C7 | 1.75 | |||||
Rydberg | C17 | 1.75 | |||||
Antibond | C1–C2 | 1.2 | |||||
Antibond | C1–C7 | 1.2 | |||||
Antibond | C2–C3 | 25.66 | |||||
Antibond | C4–C5 | 25.66 | |||||
Antibond | C5–C6 | 1.2 | |||||
Antibond | C6–C17 | 1.2 | |||||
Antibond | C7–C19 | 25.66 | |||||
Antibond | C17–C18 | 25.66 | |||||
Total | 14 | 115.54 | |||||
Total | C1–C6 | 26 | 143.70 (122%) | Total | C1–C6 | 14 | 111.70 (100%) |
Total | C1–C2 | 16 | 34.98 (138%) | Total | C1–C2 | 10 | 21.76 (100%) |
Method | MP2 (Hartree) | HF (Hartree) | MP2—HF (kcal/mol) | (MP2—HF)/ (kcal/mol e) |
---|---|---|---|---|
Fullerene C60 | ||||
MP2/3–21G* | −2264.4378913 | −2258.9901941 | −3418.48 | −9.50 |
MP2/6–31G* | −2279.6317630 | −2271.8025400 | −4912.92 | −13.65 |
MP2/def2svp | −2277.8316660 | −2270.0928633 | −4865.21 | −13.49 |
Benzene (The CCSD(T)/aug-cc-pvtz recovered correlation is counted by CCSD(T)-HF) | ||||
MP2/3–21G* | −229.9376703 | −229.4155101 | −327.657 | −7.80 |
MP2/6–31G* | −231.4577321 | −230.7018849 | −474.302 | −11.29 |
MP2/def2svp | −231.3162080 | −230.5345726 | −490.477 | −11.68 |
CCSD(T)/aug-cc-pvtz | −231.8204089 | −230.7804015 | −652.615 | −15.54 |
Method (α Electron) | HOMO H1u (eV) | LUMO T1u (eV) | LUMO + 1 T2u (eV) | H1u to T1u (eV) | H1u to T2u (eV) |
---|---|---|---|---|---|
MP2/3-21G* | −8.19 | −0.92 | 0.75 | −7.27 | −8.94 |
MP2/6–31G* | −7.57 | −0.57 | 1.09 | −7.00 | −8.66 |
Experimental [7] | −4.90 | ||||
B3LYP/Def2svp | −7.63 | −5.95 | −5.01 | −1.68 | −2.62 |
BP86/Def2svp | −5.94 | −4.13 | −3.07 | −1.81 | −2.87 |
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Liu, Y.; Gao, Y.; Altalhi, T.; Liu, D.-J.; Yakobson, B.I. A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C60. Nanomaterials 2024, 14, 1576. https://doi.org/10.3390/nano14191576
Liu Y, Gao Y, Altalhi T, Liu D-J, Yakobson BI. A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C60. Nanomaterials. 2024; 14(19):1576. https://doi.org/10.3390/nano14191576
Chicago/Turabian StyleLiu, Yuemin, Yunxiang Gao, Tariq Altalhi, Di-Jia Liu, and Boris I. Yakobson. 2024. "A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C60" Nanomaterials 14, no. 19: 1576. https://doi.org/10.3390/nano14191576
APA StyleLiu, Y., Gao, Y., Altalhi, T., Liu, D.-J., & Yakobson, B. I. (2024). A Quantum Mechanical MP2 Study of the Electronic Effect of Nonplanarity on the Carbon Pyramidalization of Fullerene C60. Nanomaterials, 14(19), 1576. https://doi.org/10.3390/nano14191576