人工光合作用已被普遍應用於產製氫氣或碳燃料(CO, CH4, HCOOH…)，然而高能量密度碳燃料，如甲醇(CH3OH)，卻因反應步驟繁多，難以找到適合的催化劑而鮮少成功產製。此外，目前的光催化劑大都只能吸收紫外線和可見光，故只能在白天進行反應，限制了產物的產量。為此，本論文提出了可吸收近紅外線之光電化學電池完整設計以進行人工光合作用產製甲醇和氫氣，即使在夜間仍可進行反應。本論文從第一原理計算出發，設計新石墨烯量子點(graphene quantum dot, GQD)基底之陽極電催化劑進行產氧反應，以及陰極光催化劑吸收紅外線進行產氫反應和甲醇產製反應。
在計算上，本論文先建立陽極電催化劑「釕-嵌入式非金屬摻雜石墨烯量子點Ru-X4-GQD (X=B, C, N, Si, P)」和陰極光催化劑「氮摻雜石墨烯量子點(NGQD)」之模型。在NGQD光學性質計算上，以含時密度泛函理論(TDDFT)搭配PBE交換相關勢能，計算吸收光譜和電子躍遷，並以此為基礎設計出最適合的NGQD結構以進行紅外線光催化產製甲醇研究。接著，在產製氧氣、氫氣、甲醇之反應步驟模擬上，以密度泛函理論(DFT)搭配 B3LYP 交換相關勢能計算最穩定結構，並考量溶劑效應，深入瞭解新設計之Ru-X4-GQD和NGQD進行氧氣、氫氣、甲醇之產製反應的結構穩定性和可行性。
在陽極產氧研究中，反應過電位大小順序為Ru-N4-GQD < Ru-P4-GQD < Ru-B4-GQD < Ru-C4-GQD < Ru-Si4-GQD，故Ru-N4-GQD為最適合之產氧催化劑，其過電位為1.16 eV，其次是過電位是1.22 eV 的Ru-P4-GQD。此外，在結構穩定性研究中，發現Ru-P4-GQD穩定性最佳，Ru-B4-GQD則可能產生Ru-B斷鍵，穩定性最差。在NGQD紅外線吸收的研究中，證實中心位置氮摻雜(center-site N-doping)可有效降低HOMO-LUMO能隙，增加紅外線吸收的範圍和強度，其中石墨氮摻雜結構(graphitic-N doping)和中心位置胺基氮摻雜結構(amino-N doping at center)對於紅外線吸收能力為最佳。在光陰極產氫氣和甲醇的研究中，證實本研究設計之C24_amino_ct NGQD光催化劑可穩定產製氫氣和甲醇，產氫能障為0.86 eV。在產製甲醇研究中，發現N-C鍵結反應路徑的最大能障為2.11 eV，低於N-O鍵結反應路徑的最大能障2.64 eV，故N-C鍵結是較適合之路徑。

Artificial photosynthesis has been widely used to produce hydrogen or carbon fuels (CO, CH4, HCOOH…). However, high energy density carbon fuels, such as methanol (CH3OH), are difficult to produce successfully due to the many reaction steps, and it is challenging to find suitable catalysts. In addition, most photocatalysts can only absorb ultraviolet and visible light. This means they only work during the day, limiting the yield of products. In an attempt to address the aforementioned challenges, a complete photochemical cell design is proposed to absorb near-infrared (NIR) for producing methanol and hydrogen through artificial photosynthesis, which could still work at night. Through the first principles calculations, the newly designed graphene quantum dot (GQD)-based electrocatalysts for oxygen evolution reaction (OER) as well as NIR-absorbing photocatalysts for hydrogen evolution reaction (HER) and methanol production reaction (MPR) are systematically studied.
In the calculations, firstly, the models of several Ru-embedded nonmetal-doped GQD (Ru-X4-GQD; X=B, C, N, Si) electrocatalysts and nitrogen-doped GQD (NGQD) photocatalysts are constructed. In the optical properties of the NGQDs, the time-dependent density functional theory (TDDFT) and PBE XC-functional are used to calculate the optical absorption spectra and electronic transitions. Based on this, the most suitable NGQD structure is designed for the NIR-photocatalysis of methanol. Then, the density functional theory (DFT), B3LYP XC-functional, and the conductor-like screening model (COSMO) are employed to optimize the structures. Finally, the structural stability and feasibility of the newly designed Ru-X4-GQD and NGQD for producing oxygen, hydrogen, and methanol are further investigated.
In the OER at the anode, the order of overpotential is Ru-N4-GQD < Ru-P4-GQD < Ru-B4-GQD < Ru-C4-GQD < Ru-Si4-GQD. Thus, Ru-N4-GQD is the most suitable catalyst with an overpotential of 1.16 eV followed by Ru-P4-GQD at 1.22 eV. In addition, the structural stability study indicates that Ru-P4-GQD has the best stability, while Ru-B4-GQD has the worst stability because there could be Ru-B bond breakage. Then, the calculated optical properties of the NGQDs confirm that center-site N-doping can effectively reduce the HOMO-LUMO gap and increase the range as well as intensity of the IR absorption. Furthermore, the graphitic-N doping structure and the amino-N doping at center are the best for IR absorption. In the HER and MPR at the photocathode, it is confirmed that the newly designed C24_amino_ct NGQD photocatalyst proposed in this thesis is good at producing hydrogen and methanol stably. For the HER, the calculated potential barrier is 0.86 eV. For the MPR, the maximum potential barrier of the N-C bonding reaction path is 2.11 eV, which is lower than that of the N-O bonding reaction path of 2.64 eV, so N-C bonding is a preferable path.

[1] G. Ciamician, “The photochemistsy of the future,” Science, 36, pp. 385-394, 1912.
[2] A. Fujishima and K. Honda, “Electrochemical photolysis of water at a semiconductor electrode,” Nature, 238, pp. 37-38, 1972.
[3] “Scientists Developing ‘Artificial’ Plants - ScienceDaily.” https://www.sciencedaily.com/releases/2000/11/001127224712.htm
[4] S. Nahar, M. Zain, A. Kadhum, H. Hasan, and M. Hasan, “Advances in Photocatalytic CO2 Reduction with Water: A Review,” Materials (Basel)., 10, No. 629, 2017.
[5] S. Xie, Q. Zhang, G. Liu, and Y. Wang, “Photocatalytic and photoelectrocatalytic reduction of CO2 using heterogeneous catalysts with controlled nanostructures,” Chem. Commun., 52, pp. 35-59, 2016.
[6] K. Park, Y. J. Kim, T. Yoon, S. David, and Y. M. Song, “A methodological review on material growth and synthesis of solar-driven water splitting photoelectrochemical cells,” RSC Adv., 9, pp. 30112-30124, 2019.
[7] R. Matheu and M. Z. Ertem, “The Behavior of the Ru-bda Water Oxidation Catalysts at Low Oxidation States,” Chem. Eur. J., 24, pp. 12838-12847, 2018.
[8] Y. H. Budnikova, “Recent Advances in Metal-Organic Frameworks for Electrocatalytic Hydrogen Evolution and Overall Water Splitting Reactions,” Dalton Trans., 49, pp. 12483-12502, 2020.
[9] A. Radwan, H. Jin, D. He, and S. Mu, “Design Engineering, Synthesis Protocols, and Energy Applications of MOF-Derived Electrocatalysts” Nano-Micro Lett., 13, No. 132, 2021.
[10] K. M. Yam, N. Guo, Z. Jiang, S. Li, and C. Zhang, “Graphene-Based Heterogeneous Catalysis: Role of Graphene,” Catalysts., 10, No. 53, 2020.
[11] Y. Jiao, Y. Zheng, K. Davey, and S. Z. Qiao, “Activity origin and catalyst design principles for electrocatalytic hydrogen evolution on heteroatom-doped graphene,” Nat. Energy, 1, No. 16130, 2016.
[12] M. Khalid, P. A. Bhardwaj, A. M. B. Honorato, and H. Varel, “Metallic single-atoms confined in carbon nanomaterials for the electrocatalysis of oxygen reduction, oxygen evolution, and hydrogen evolution reactions,” Catal. Sci. Technol., 10, pp. 6420-6448, 2020.
[13] D. Chen H. Zhang, Y. Liua, and J. Li, “Graphene and its derivatives for the development of solar cells, photoelectrochemical, and photocatalytic applications,” Energy Environ. Sci., 6, pp. 1362-1387, 2013.
[14] Y. Yan, J. Gong, J. Chen, Z. Zeng, W. Huang, K. Pu, J. Liu, and P. Chen, “Recent Advances on Graphene Quantum Dots: From Chemistry and Physics to Applications,” Adv. Mater., 31, No. 1808283, 2019.
[15] B. Qiao, A. Wang, X. Yang, L. F. Allard, Z. Jiang, Y. Cui, J. Liu, J. Li, and T. Zhang, “Single-atom catalysis of CO oxidation using Pt1/FeOx,” Nature Chem., 3, pp. 634-641, 2011.
[16] X. F. Yang, A. Wang, B. Qiao, J. Li, J. Liu, and T. Zhang, “Single-Atom Catalysts: A New Frontier in Heterogeneous Catalysis,” Acc. Chem. Res., 46, pp. 1740-1748, 2013.
[17] L. Zhang, Y. Ren, W. Liu, A. Wang, and T. Zhang, “Single-atom catalyst: a rising star for green synthesis of fine chemicals,” Natl. Sci. Rev., 5, pp. 653-672, 2018.
[18] Y. Tang, W. Chen, Z. Liu, X. Wang, S. Chang, and X. Dai, “Geometric, electronic, magnetic and catalytic properties of carbon deposited on metal embedded graphene,” Comp. Mater. Sci., 126, pp. 74-81, 2017.
[19] Y. H. Lu, M. Zhou, C. Zhang, and Y. P. Feng, “Metal-Embedded Graphene: A Possible Catalyst with High Activity,” J. Phys. Chem. C, 113, pp. 20156-20160, 2009.
[20] Q. Gao, “A DFT study of the ORR on M–N3 (M = Mn, Fe, Co, Ni, or Cu) co-doped graphene with moiety-patched defects,” Ionics, 26, pp. 2453-2465, 2020.
[21] L. L. Liu, C. P. Chen, L. S. Zhao, Y. Wang, and X. C. Wang, “Metal-embedded nitrogen-doped graphene for H2O molecule dissociation,” Carbon, 115, pp. 773-780, 2017.
[22] T. Kropp, M. Rebarchik, and M. Mavrikakis, “On the active site for electrocatalytic water splitting on late transition metals embedded in graphene,” Catal. Sci. Technol., 9, pp. 6793-6799, 2019.
[23] M. Yang, L. Wang, M. Li, T. Hou, and Y. Li, “Structural stability and O2 dissociation on nitrogen-doped graphene with transition metal atoms embedded: A first-principles study,” AIP Adv., 5, No. 067136, 2015.
[24] W. Ju, A. Bagger, G. P. Hao, A. S. Varela, I. Sinev, V. Bon, B. R. Cuenya, S. Kaskel, J. Rossmeisl, and P. Strasser, “Understanding activity and selectivity of metal-nitrogen-doped carbon catalysts for electrochemical reduction of CO2,” Nat. Commun., 8, No. 944, 2017.
[25] M. Luo, C. Liu, S. G. Peera, T. Liang, “Atomic level N-coordinated Fe dual-metal embedded in graphene: An efficient double atoms catalyst for CO oxidation,” Colliod Surface A, 621, No. 126575, 2021.
[26] S. Wang, L. Shi, X. Bai, Q. Li, C. Ling, and J. Wang, “Highly Efficient Photo-/Electrocatalytic Reduction of Nitrogen into Ammonia by Dual-Metal Sites,” ACS Cent. Sci., 6, pp. 1762-1771, 2020.
[27] C. Zhang, J. Sha, H. Fei, M. Liu, S. Yazdi, J. Zhang, Q. Zhong, X. Zou, N. Zhao, H. Yu, Z. Jiang, E. Ringe, B. I. Yakobson, J. Dong, D. Chen, and J. M. Tour, “Single-Atomic Ruthenium Catalytic Sites on Nitrogen-Doped Graphene for Oxygen Reduction Reaction in Acidic Medium,” ACS Nano, 11, pp. 6930-6941, 2017.
[28] J. Zhang, P. Liu, G. Wang, P. P. Zhang, X. D. Zhuang, M. W. Chen, I. M. Weidinger, and X. L. Feng, “Ruthenium/nitrogen-doped carbon as an electrocatalyst for efficient hydrogen evolution in alkaline solution,” J. Mater. Chem. A, 5, pp. 25314-25318, 2017.
[29] L. Cao, Q. Luo, J. Chen, L. Wang, Y. Lin, H. Wang, X. Liu, X. Shen, W. Zhang, W. Liu, Z. Qi, Z. Jiang, J. Yang and T. Yao, “Dynamic oxygen adsorption on single-atomic Ruthenium catalyst with high performance for acidic oxygen evolution reaction,” Nat. Commun., 10, No. 4849, 2019.
[30] D. H. Kweon, M. S. Okyay, S. J. Kim, J. P. Jeon, H. J. Noh, N. Park, J. Mahmood, and J. B. Baek, “Ruthenium anchored on carbon nanotube electrocatalyst for hydrogen production with enhanced Faradaic efficiency,” Nat. Commun., 11, No. 1278, 2020.
[31] J. Cored, A. G. Ortiz, S. Iborra, M. J. Climent, L. Liu, C. H. Chuang, T. S. Chan, C. Escudero, P. Concepción, and A. Corma, “Hydrothermal Synthesis of Ruthenium Nanoparticles with a Metallic Core and a Ruthenium Carbide Shell for Low-Temperature Activation of CO2 to Methane,” J. Am. Chem. Soc., 141, pp. 19304-19311, 2019.
[32] L. Wu, J. Song, B. Zhou, T. Wu, T. Jiang, and B. Han, “Preparation of Ru/Graphene using Glucose as Carbon Source and Hydrogenation of Levulinic Acid to γ-Valerolactone,” Chem. Asian J., 11, pp. 2792-2796, 2016.
[33] L. Zhu, Q. Cai, F. Liao, M. Sheng, B. Wu, and M. Shao, “Ru-modified silicon nanowires as electrocatalysts for hydrogen evolution reaction,” Electrochem. Commun., 52, pp. 29-33, 2015.
[34] P. G. O’Brien, A. Sandhel, T. E. Wood, A. A. Jelle, L. B. Hoch, D. D. Perovic, C. A. Mims, and G. A. Ozin, “Photomethanation of Gaseous CO2 over Ru/Silicon Nanowire Catalysts with Visible and Near-Infrared Photons,” Adv. Sci., 1, No. 1400001, 2014.
[35] M. Pinzón, A. Romero, A. de Lucas Consuegra, A.R. de la Osa, and P. Sánchez, “Hydrogen production by ammonia decomposition over ruthenium supported on SiC catalyst,” J. Ind. Eng. Chem., 94, pp. 326-335, 2021.
[36] Y. Qiao, P. Yuan, C. W. Pao, Y. Cheng, Z. Pu, Q. Xu, S. Mu, and J. Zhang, “Boron-rich environment boosting ruthenium boride on B, N doped carbon outperforms platinum for hydrogen evolution reaction in a universal pH range,” Nano Energy, 75, No. 104881, 2020.
[37] M. Fan, J. D. Jimenez, S. N. Shirodkar, J. Wu, S. Chen, L. Song, M. M. Royko, J. Zhang, H. Guo, J. Cui, K. Zuo, W. Wang, C. Zhang, F. Yuan, R. Vajtai, J. Qian, J. Yang, B. I. Yakobson, J. M. Tour, J. Lauterbach, D. Sun, and P. M. Ajayan, “Atomic Ru Immobilized on Porous h-BN through Simple Vacuum Filtration for Highly Active and Selective CO2 Methanation,” ACS Catal., 9, pp. 10077-10086, 2019.
[38] Y. Li, F. Chu, Y. Bu, Y. Kong, Y. Tao, X. Zhou, H. Yu, J. Yu, L. Tanga, and Y. Qin, “Controllable fabrication of uniform ruthenium phosphide nanocrystals for the hydrogen evolution reaction,” Chem. Commun., 55, pp. 7828-7831, 2019.
[39] C. Li, Z. Chen, Y. Ni, F. Kong, A. Kong, and Y. Shan, “Coordination compound-derived ordered mesoporous N-free Fe–Px–C material for efficient oxygen electroreduction,” J. Mater. Chem. A, 4, pp. 14291-14297, 2016.
[40] L. Feng, Y. Liu, and J. Zhao, “Fe– and Co–P4-embedded graphenes as electrocatalysts for the oxygen reduction reaction: theoretical insights,” Phys. Chem. Chem. Phys., 17, pp. 30687-30694, 2015.
[41] R. Song, J. Yang, M. Wang, Z. Shi, X. Zhu, X. Zhang, M. He, G. Liu, G. Qiao, and Z. Xu, “Theoretical Study on P‑coordinated Metal Atoms Embedded in Arsenene for the Conversion of Nitrogen to Ammonia,” ACS Omega, 6, pp. 8662-8671, 2021.
[42] X. Guo, S. Liu, and S. Huang, “Single Ru atom supported on defective graphene for water splitting: DFT and microkinetic investigation,” Int. J. Hydrogen Energ., 43, pp. 4880-4892, 2018.
[43] M. Moriya, R. Takahama, K. Kamoi, J. Ohyama, S. Kawashima, R. Kojima, M. Okada, T. Hayakawa, and Y. Nabae, “Fourteen-Membered Macrocyclic Fe Complexes Inspired by FeN4‑Center-Embedded Graphene for Oxygen Reduction Catalysis,” J. Phys. Chem. C, 124, pp. 20730-20735, 2020.
[44] R. Shang, S. N. Steinmann, B. Q. Xu, and P. Sautet, “Mononuclear Fe in N-doped carbon: computational elucidation of active sites for electrochemical oxygen reduction and oxygen evolution reactions,” Catal. Sci. Technol., 10, pp. 1006-1014, 2020.
[45] E. Zhang, T. Wang, K. Yu, J. Liu, W. Chen, A. Li, H. Rong, R. Lin, S. Ji, X. Zheng, Y. Wang, L. Zheng, C. Chen, D. Wang, J. Zhang, and Y. Li, “Bismuth Single Atoms Resulting from Transformation of Metal-Organic Frameworks and Their Use as Electrocatalysts for CO2 Reduction,” J. Am. Chem. Soc., 141, pp. 16569-16573, 2019.
[46] Y. Liu, J. Zhao, and Q. Cai, “Pyrrolic-nitrogen doped graphene: a metal-free electrocatalyst with high efficiency and selectivity for the reduction of carbon dioxide to formic acid: a computational study,” Phys. Chem. Chem. Phys., 18, pp. 5491-5498, 2016.
[47] J. Wu, M. Liu, P. P. Sharma, R. M. Yadav, L. Ma, Y. Yang, X. Zou, X. D. Zhou, R. Vajtai, B. I. Yakobson, J. Lou, and P. M. Ajayan, “Incorporation of Nitrogen Defects for Efficient Reduction of CO2 via Two-Electron Pathway on Three-Dimensional Graphene Foam,” Nano Lett., 16, pp. 466-470, 2016.
[48] Z. Shu, G. Ye, J. Wang, S. Liu, Z. He, W. Zhu, B. Liu, and M. Liu, “Nitrogen-doped carbon with high graphitic-N exposure for electroreduction of CO2 to CO,” Ionics, 27, pp. 3089-3098, 2021.
[49] H. Begum, M. S. Ahmed, and Y. B. Kim, “Nitrogen‑rich graphitic‑carbon @ graphene as a metal‑free electrocatalyst for oxygen reduction reaction,” Sci. Rep., 10, No. 12431, 2020.
[50] W. A. Saidi, “Oxygen Reduction Electrocatalysis Using N‑Doped Graphene Quantum-Dots,” J. Phys. Chem. Lett., 4, pp. 4160-4165, 2013.
[51] M. S. Xie, B. Y. Xia, Y. Li, Y. Yan, Y. Yang, Q. Sun, S. H. Chan, A. Fishere, and X. Wang, “Amino acid modified copper electrodes for the enhanced selective electroreduction of carbon dioxide towards hydrocarbons,” Energy Environ. Sci., 9, pp. 1687-1695, 2016.
[52] Z. Chen, X. Zhang, W. Liu, M. Jiao, K. Mou, X. Zhang, and L. Liu, “Amination strategy to boost the CO2 electroreduction current density of M–N/C single-atom catalysts to the industrial application level,” Energy Environ. Sci., 14, pp. 2349-2356, 2021.
[53] M. Li, W. Wu, W. Ren, H. M. Cheng, N. Tang, W. Zhong, and Y. Du, “Synthesis and upconversion luminescence of N-doped graphene quantum dots,” Appl. Phys. Lett., 101, No. 103107, 2012.
[54] H. Yang, P. Wang, D. Wang, Y. Zhu, K. Xie, X. Zhao, J. Yang, and X. Wang, “New Understanding on Photocatalytic Mechanism of Nitrogen-Doped Graphene Quantum Dots-Decorated BiVO4 Nanojunction Photocatalysts,” ACS Omega, 2, pp. 3766-3773, 2017.
[55] C. Wu, R. Chen, C. Ma, R. Cheng, X. Gao, T. Wang, Y. Liu, P. Huo, and Y. Yan, “Construction of upconversion nitrogen doped graphene quantum dots modified BiVO4 photocatalyst with enhanced visible-light photocatalytic activity,” Ceram. Int., 45, pp. 2088-2096, 2019.
[56] Y. Deng, L. Tang, C. Feng, G. Zeng, J. Wang, Y. Lu, Y. Liu, J. Yu, S. Chen, and Y. Zhou, “Construction of Plasmonic Ag and Nitrogen-Doped Graphene Quantum Dots Codecorated Ultrathin Graphitic Carbon Nitride Nanosheet Composites with Enhanced Photocatalytic Activity: Full-Spectrum Response Ability and Mechanism Insight,” ACS Appl. Mater. Interfaces, 9, pp. 42816-42828, 2017.
[57] H. Liu, H. Wang, Y. Qian, J. Zhuang, L. Hu, Q. Chen, and S. Zhou, “Nitrogen-Doped Graphene Quantum Dots as Metal-Free Photocatalysts for Near-Infrared Enhanced Reduction of 4‑Nitrophenol,” ACS Appl. Nano Mater., 2, pp. 7043-7050, 2019.
[58] M. Born and R. Oppenheimer, “Zur Quantentheorie der Molekeln,” Ann. Phys., 389, pp. 457-484, 1927.
[59] P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev., 136, p. B864, 1964.
[60] W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev., 140, p. A1133, 1965.
[61] D. R. Hartree, “The Wave Mechanics of an Atom with a Non-Coulomb Central Field Part II Some Results and Discussion,” Math. Proc. Cambridge Philos. Soc., 24, pp. 111-132, 1928.
[62] V. Fock, “Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems,” Z. Phys., 62, pp. 126-148, 1930.
[63] D. C. Langreth and M. J. Mehl, “Beyond the local-density approximation in calculations of ground-state electronic properties,” Phys. Rev. B, 28, pp. 1809-1834, 1983.
[64] J. P. Perdew and W. Yue, “Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation,” Phys. Rev. B, 33, pp. 8800-8802, 1986.
[65] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, “Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation,” Phys. Rev. B, 46, pp. 6671-6687, 1992.
[66] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett., 77, pp. 3865-3868, 1996.
[67] A. D. Becke, “Density-functional exchange-energy approximation with correct asymptotic behavior,” Phys. Rev. A, 38, pp. 3098-3100, 1988.
[68] C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Phys. Rev. B, 37, pp. 785-789, 1988.
[69] H. Hellmann, “A new approximation method in the problem of many electrons,” The Journal of Chemical Physics, 3, p. 61, 1935.
[70] “Effective Core Potential,” https://en.wikipedia.org/wiki/Pseudopotential
[71] D. R. Hamann, M. Schlüter, and C. Chiang, “Norm-Conserving Pseudopotentials,” Phys. Rev. Lett., 43, pp. 1494-1497, 1979.
[72] D. Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Phys. Rev. B, 41, pp. 7892-7895, 1990.
[73] A. D. Becke, “A new mixing of Hartree-Fock and local density-functional theories,” J. Chem. Phys., 98, pp. 1372-1377, 1993.
[74] A. D. Becke, “Density-functional thermochemistry. III. The role of exact exchange,” J. Chem. Phys., 98, pp. 5648-5652, 1993.
[75] S. H. Vosko, L. Wilk, and M. Nusair, “Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis,” Can. J. Phys., 58, pp. 1200-1211, 1980.
[76] S. Grimme, “Accurate description of van der Waals complexes by density functional theory including empirical corrections,” J. Comput. Chem., 25, pp. 1463-1473, 2004.
[77] S. Grimme, “Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction,” J. Comput. Chem., 27, pp. 1787-1799, 2006.
[78] P. Jurecka, J. cerný, P. Hobza, and D. R. Salahub, “Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations,” J. Comput. Chem., 28, pp. 555-569, 2007.
[79] A. Tkatchenko and M. Scheffler, “Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data,” Phys. Rev. Lett., 102, No. 073005, 2009.
[80] E. R. McNellis, J. Meyer, and K. Reuter, “Azobenzene at coinage metal surfaces: Role of dispersive van der Waals interactions,” Phys. Rev. B, 80, No. 205414, 2009.
[81] A. Klamt and G. Schüürmann, “COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient,” J. Chem. Soc., Perkin Trans., 2, pp. 799-805, 1993
[82] J. Andzelm, C. Kölmel, and A. Klamt, “Incorporation of solvent effects into density functional calculations of molecular energies and geometries,” J. Chem. Phys., 103, pp. 9312-9320, 1995.
[83] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science, 220, pp. 671-680, 1983.
[84] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21, pp. 1087-1092, 1953.
[85] E. Runge and E. K. U.Gross, “Density-functional theory for time-dependent systems,” Phys. Rev. Lett., 52, pp. 997-1000, 1984.
[86] G. Vignale, “Mapping from current densities to vector potentials in time-dependent current density functional theory,” Phys. Rev. B - Condens. Matter Mater. Phys., 70, No. 201102, 2004.
[87] M. A. L. Marques and E. K. U. Gross, “Time-dependent density functional theory,” Annu. Rev. Phys. Chem., 55, pp. 427-455, 2004.
[88] M. Petersilka, U. J. Gossmann, and E. K. U. Gross, “Excitation Energies from Time-Dependent Density-Functional Theory,” Phys. Rev. Lett., 76, pp. 1212-1215, 1996.
[89] J. Franck, “Elementary processes of photochemical reactions,” Trans. Faraday Soc., 21, pp. 536-542, 1926.
[90] E. Condon, “A Theory of Intensity Distribution in Band Systems,” Phys. Rev., 28, pp. 11182-1201, 1926.
[91] “Vibrational Spectra - Adrea’s Notebook and Journal.” http://adreasnow.com/Notes/Undergrad Notes/Sem 5. Comp Chemistry/10. Vibrational Spectra/
[92] B. Delley, “An all-electron numerical method for solving the local density functional for polyatomic molecules,” J. Chem. Phys., 92, pp. 508-517, 1990.
[93] B. Delley, “From molecules to solids with the DMol3 approach,” J. Chem. Phys., 113, pp. 7756-7764, 2000.
[94] B. Delley, “Hardness conserving semilocal pseudopotentials,” Phys. Rev. B, 66, No. 155125, 2002.
[95] J. C. Slater, “Atomic Radii in Crystals,” J. Chem. Phys., 41, pp. 3199-3204, 1964.
[96] P. Pyykkö and M. Atsumi, “Molecular Single-Bond Covalent Radii for Elements 1–118,” Chem. Eur. J., 15, pp.186-197, 2009.
[97] Á. Valdés, Z. W. Qu, G. J. Kroes, J. Rossmeisl, and J. K. Nørskov, “Oxidation and Photo-Oxidation of Water on TiO2 Surface,” J. Phys. Chem. C, 112, 26, pp. 9872-9879, 2008.
[98] D. R. Cooper, B. D’Anjou, N. Ghattamaneni, B. Harack, M. Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E. Whiteway, and V. Yu, “Experimental Review of Graphene,” ISRN Condens. Matter Phys., 2012, No. 501686, 2012.
[99] J. L. Bredas, “Mind the gap!,” Mater. Horiz., 1, pp. 17-19, 2014.
[100] C. N. Yeh, C. Wu, H. Su, and J. D. Chai, “Electronic properties of the coronene series from thermally-assisted-occupation density functional theory,” RSC Adv., 8, pp. 34350-34358, 2018.
[101] T. Koopmans, “Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms,” Physica, 1, pp. 104-113, 1934.
[102] A. Szabo and N. S. Ostlund, “Modern Quantum Chemistry,” Dover Publications, p 127, 1982.
[103] G. W. Ejuh, F. Tchangnwa Nya, N. Djongyang, and J. M. B. Ndjaka, “Theoretical study on the electronic, optoelectronic, linear and non linear optical properties and UV–Vis Spectrum of Coronene and Coronene substituted with Chlorine,” SN Appl. Sci., 2, No. 1247, 2020.
[104] K. Ida, H. Sakai, K. Ohkubo, Y. Araki, T. Wada, T. Sakanoue, T. Takenobu, S. Fukuzumi, and T. Hasobe, “Electron-Transfer Reduction Properties and Excited-State Dynamics of Benzo[ghi]peryleneimide and Coroneneimide Derivatives,” J. Phys. Chem. C, 118, pp. 7710-7720, 2014.
[105] S. Tobita, S. Leach, H. W. Jochims, E. Rühl, E. Illenberger, and H. Baumgärtel, “Single- and double-ionization potentials of polycyclic aromatic hydrocarbons and fullerenes by photon and electron impact,” Can. J. Phys., 72, pp. 1060-1069, 1994.
[106] M. A. Duncan, A. M. Knight, Y. Negishi, S. Nagao, Y. Nakamura, A. Kato, A. Nakajima, and K. Kaya, “Production of jet-cooled coronene and coronene cluster anions and their study with photoelectron spectroscopy,” Chem. Phys. Lett., 309, pp. 49-54, 1999.
[107] R. Abouaf and S. Diaz-Tendero, “Electron energy loss spectroscopy and anion formation in gas phase coronene,” Phys. Chem. Chem. Phys., 11, pp. 5686-5694, 2009.
[108] E. Clar, J. M. Robertson, R. Schloegl, and W. Schmidt, “Photoelectron spectra of polynuclear aromatics. 6. Applications to structural elucidation: ‘circumanthracene,’” J. Am. Chem. Soc., 103, pp. 1320-1328, 1981.
[109] G. Chen, R. G. Cookscor, E. Corpuz, and L. T. Scott, “Estimation of the electron affinities of C60, corannulene, and coronene by using the kinetic method,” J. Am. Soc. Mass Spectrom., 7, pp. 619-627, 1996.
[110] A. Menon, J. A. H. Dreyer, J. W. Martin, J. Akroyd, J. Robertson, and M. Kraft, “Optical band gap of cross-linked, curved, and radical polyaromatic hydrocarbons,” Phys. Chem. Chem. Phys., 21, pp. 16240-16251, 2019.
[111] M. F. Budyka, “Semiempirical study on the absorption spectra of the coronene-like molecular models of graphene quantum dots,” Spectrochimi. Acta Part A, 207, pp. 1-5, 2019.
[112] F. Abu-Awwad and P. Politzer, “Variation of parameters in Becke-3 hybrid exchange-correlation functional,” J. Comp. Chem., 21, pp. 227-238, 2000.
[113] B. Shi, D. Nachtigallová, A. J. A. Aquino, F. B. C. Machado, and H. Lischka, “High-level theoretical benchmark investigations of the UV-vis absorption spectra of paradigmatic polycyclic aromatic hydrocarbons as models for graphene quantum dots,” J. Chem. Phys., 150, No. 124302, 2019.
[114] P. Błoński, J. Tuček, Z. Sofer, V. Mazánek, M. Petr, M. Pumera, M. Otyepka, and R. Zbořil, “Doping with Graphitic Nitrogen Triggers Ferromagnetism in Graphene,” J. Am. Chem. Soc., 139, pp. 3171-3180, 2017.
[115] E. C. Stoner, “Collective electron ferromagnetism,” Proc. R. Soc. Lond. A, 165, pp. 372-414, 1938.
[116] H. González-Herrero, J. M. Gómez-Rodríguez, P. Mallet, M. Moaied, J. J. Palacios, C. Salgado, M. M. Ugeda, J. Y. Veuillen, F. Yndurain, and I. Brihuega, “Atomic-scale control of graphene magnetism by using hydrogen atoms,” Science, 352, pp. 437-441, 2016.
[117] T. Tang, L. Wu, S. Gao, F. He, M. Li, J. Wen, X. Li, and F. Liu, “Universal Effectiveness of Inducing Magnetic Moments in Graphene by Amino-Type sp3-Defects,” Materials, 11, No. 616, 2018.
[118] E. H. Lieb, “Two Theorems on the Hubbard Model,” Phys. Rev. Lett., 62, pp. 1201-1204, 1989.
[119] R. Babar and M. Kabir, “Ferromagnetism in nitrogen-doped graphene,” Phys. Rev. B, 99, No. 115442, 2019.