A位阳离子对二维钙钛矿光电特性的调控机理研究

doi:10.6023/A26050151

摘要/Abstract

采用第一性原理计算研究了二维(2D)卤化物钙钛矿(PA)₂APb₂I₇ [PA=[CH₃(CH₂)₄NH₃]^＋; A=[C(NH₂)₃]^＋ (Gua), [C₂H₃(NH₂)₂]^＋ (Ace)]的晶体结构、电子结构、缺陷性质和光学性质. 结果表明, (PA)₂GuaPb₂I₇表现出更明显的Pb-I-Pb角度畸变和面外褶皱, 而(PA)₂AcePb₂I₇具有更接近线性的面内Pb-I-Pb连接方式. 二者属于直接带隙, 带边态主要由Pb-I无机骨架贡献; (PA)₂AcePb₂I₇带隙较小, 面内有效质量更低, 说明其载流子输运更有利. 缺陷计算显示, (PA)₂GuaPb₂I₇中多个缺陷引入较深能级, 而(PA)₂AcePb₂I₇的低形成能缺陷以浅能级为主, 其深能级I_i表现出较高的形成能和迁移势垒. 光学计算表明, (PA)₂AcePb₂I₇的吸收边红移, 最高光谱极限最大效率(SLME)为22.79%. 结果说明, Ace阳离子有利于改善缺陷能级分布、光吸收响应和本征光伏潜力.

关键词: 二维钙钛矿, 第一性原理, 电子结构, 缺陷性质

To elucidate the influence of A-site cations on the photovoltaic properties of two-dimensional Ruddlesden-Popper-type lead iodide perovskites, this work investigates (PA)₂APb₂I₇ using first-principles calculations, where PA denotes n-pentylammonium cation ([CH₃(CH₂)₄NH₃]^＋, PA) and A denotes guanidinium ([C(NH₂)₃]^＋, Gua) or acetamidinium ([C₂H₃(NH₂)₂]^＋, Ace). The calculations were performed using the projector augmented-wave method and the Perdew-Burke-Ernzerhof exchange-correlation functional, and included geometry optimization, structural distortion analysis, electronic structure analysis, defect property calculations, and optical absorption analysis. The results show that the A-site organic cations mainly alter the local Pb-I framework structure through N—H…I hydrogen bonds, while contributing little to the band edge electronic states. In the Gua-based material, the Pb-I-Pb angle distortion is more pronounced, whereas the Ace-based material maintains a more linear in-plane Pb-I-Pb connection, which is beneficial for Pb/I orbital coupling within the inorganic layer. Both materials are direct band gap semiconductors. The valence band maximum is mainly derived from antibonding hybridization between I-5p and Pb-6s orbitals, while the conduction band minimum primarily originates from Pb-6p orbitals. Compared to Gua-based material, the Ace cation-regulated system exhibits a narrower band-gap, lower in-plane effective masses, and more pronounced band edge localization, which favors efficient carrier transport within the inorganic layer. In the Gua-based material, the Gua vacancy (V_Gua), Pb vacancy (V_Pb), and interstitial defects introduce deep transition levels, which may act as carrier trapping or recombination centers. In contrast, low-formation-energy defects in the Ace-based material generally show shallow-level characteristics. For the interstitial iodine defect (I_i), which appears as a deep-level defect in both systems, the Ace-based material shows a higher formation energy and migration barrier than the Gua-based material. Both materials exhibit strong absorption in the visible and near-ultraviolet regions, with absorption coefficients on the order of 10⁵ cm^－1. The Ace-based material shows a red-shift absorption edge and reaches a maximum spectroscopic limited maximum efficiency (SLME) of 22.79%. In summary, A-site cation regulation alters the Pb-I framework connectivity and defect characteristics. Compared with the Gua-based material, the Ace-based material shows advantages in carrier transport, defect tolerance, and theoretical photovoltaic performance.

Key words: two-dimensional perovskite, first-principle, electronic structure, defect property

引用此文

刘佳冬, 刘研博, 张照胜. A位阳离子对二维钙钛矿光电特性的调控机理研究[J]. 化学学报, 2026, 84(10): 1591-1600.

Jiadong Liu, Yanbo Liu, Zhaosheng Zhang. Mechanism of Modulating the Photovoltaic Properties of Two-Dimensional Perovskites via A-Site Cations[J]. Acta Chimica Sinica, 2026, 84(10): 1591-1600.

导出引用 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

分享此文

图/表 10

图1. (PA)2APb2I7 (A=Gua, Ace)优化后的晶体结构

Figure 1. Crystal structures of (PA)2APb2I7 (A=Gua, Ace) after optimization

	Lattice constant/nm			V/nm³	α=γ/(°)	β/(°)	d_Pb-I/nm
	a	b	c	V/nm³	α=γ/(°)	β/(°)	axial	equatorial	average
(PA)₂GuaPb₂I₇	4.124*	0.911*	0.898*	3.363*	90*	93.79*	0.321*	0.322*	0.321*
(PA)₂GuaPb₂I₇	3.986	0.909	0.844	3.059	90	91.09	0.318	0.317	0.318
(PA)₂AcePb₂I₇	4.159*	0.914*	0.895*	3.392*	90*	94.83*	0.323*	0.322*	0.322*
(PA)₂AcePb₂I₇	4.071	0.911	0.843	3.126	90	92.03	0.321	0.316	0.317

表1. 优化后(PA)2APb2I7 (A=Gua, Ace)的结构参数

Table 1. Structural parameters of (PA)2APb2I7 (A=Gua, Ace) after optimization

	D	λ_oct	δ/nm	σ²
(PA)₂GuaPb₂I₇	0.015	1.019	0.011	62
(PA)₂AcePb₂I₇	0.018	1.013	0.057	41

表2. (PA)2APb2I7 (A=Gua, Ace)的畸变参数

Table 2. Distortion parameters of (PA)2APb2I7 (A=Gua, Ace)

	Bonds	ICOHP	Angles/(°)	d_N—H…I/nm
(PA)₂GuaPb₂I₇	H(12)—I(1)	－0.35	153.3	0.268
	H(10)—I(1)	－0.35	153.3	0.268
	H(2)—I(13)	－0.26	152.8	0.276
	H(18)—I(13)	－0.28	154.7	0.275
(PA)₂AcePb₂I₇	H(1)—I(25)	－0.41	152.2	0.263
	H(36)—I(25)	－0.39	151.0	0.265
	H(37)—I(13)	－0.24	155.8	0.283

表3. (PA)2APb2I7 (A=Gua, Ace)氢键的ICOHP、角度和键长

Table 3. ICOHP, angles, and bond lengths of hydrogen bonds in (PA)2APb2I7 (A=Gua, Ace)

图2. (PA)2APb2I7 (A=Gua, Ace)氢键位置: (a) (PA)2GuaPb2I7; (b) (PA)2AcePb2I7

Figure 2. Hydrogen bonding sites in (PA)2APb2I7 (A=Gua, Ace): (a) (PA)2GuaPb2I7; (b) (PA)2AcePb2I7

图3. (PA)2APb2I7 (A=Gua, Ace)电子结构性质: (a) (PA)2GuaPb2I7的PDOS; (b) (PA)2GuaPb2I7的能带结构; (c) (PA)2GuaPb2I7中轴向Pb—I键的COHP; (d) (PA)2GuaPb2I7中赤道Pb—I键的COHP; (e) (PA)2AcePb2I7的PDOS; (f) (PA)2AcePb2I7的能带结构; (g) (PA)2AcePb2I7中轴向Pb—I键的COHP; (h) (PA)2AcePb2I7中赤道Pb—I键的COHP(费米能级位于0 eV处)

Figure 3. Electronic structure properties of (PA)2APb2I7 (A=Gua, Ace): (a) PDOS of (PA)2GuaPb2I7; (b) band structure of (PA)2GuaPb2I7; (c) COHP of the axial bond Pb—I in (PA)2GuaPb2I7; (d) COHP of the equatorial bond Pb—I in (PA)2GuaPb2I7; (e) PDOS of (PA)2AcePb2I7; (f) band structure of (PA)2AcePb2I7; (g) COHP of the axial bond Pb—I in (PA)2AcePb2I7; (h) COHP of the equatorial bond Pb—I in (PA)2AcePb2I7 (The Fermi level is set at 0 eV)

图4. (PA)2APb2I7 (A=Gua, Ace) x轴(面外方向)投影的电荷密度: (a) (PA)2GuaPb2I7的CBM; (b) (PA)2AcePb2I7的CBM; (c) (PA)2GuaPb2I7的VBM; (d) (PA)2AcePb2I7的VBM

Figure 4. Projected charge density along the x-axis (out-of-plane direction) for (PA)2APb2I7 (A=Gua, Ace): (a) CBM of (PA)2GuaPb2I7; (b) CBM of (PA)2AcePb2I7; (c) VBM of (PA)2GuaPb2I7; (d) VBM of (PA)2AcePb2I7

图5. (PA)2APb2I7 (A=Gua, Ace)本征点缺陷的跃迁能级和缺陷形成能: (a) (PA)2GuaPb2I7的空位缺陷; (b) (PA)2GuaPb2I7的间隙缺陷; (c) (PA)2AcePb2I7的空位缺陷; (d) (PA)2AcePb2I7的间隙缺陷

Figure 5. Transition energy levels and defect formation energies of intrinsic point defects in (PA)2APb2I7 (A=Gua, Ace): (a) vacancy defects in (PA)2GuaPb2I7; (b) interstitial defects in (PA)2GuaPb2I7; (c) vacancy defects in (PA)2AcePb2I7; (d) interstitial defects in (PA)2AcePb2I7

图6. (PA)2APb2I7 (A=Gua, Ace)迁移能垒图: (a) (PA)2GuaPb2I7的Ii缺陷迁移能垒; (b) (PA)2AcePb2I7的Ii缺陷迁移能垒; (c) Ii在无机笼中的迁移路径(初态对应x=0, 末态对应x=1)

Figure 6. Defect migration barrier of (PA)2APb2I7 (A=Gua, Ace): (a) defect migration barrier of the Ii defect in (PA)2GuaPb2I7; (b) defect migration barrier of the Ii defect in (PA)2AcePb2I7; (c) migration pathway of Ii within the inorganic framework (x=0 and x=1 correspond to the initial and final states, respectively)

图7. (PA)2APb2I7 (A=Gua, Ace): (a)光吸收谱; (b) SLME

Figure 7. (PA)2APb2I7 (A=Gua, Ace): (a) optical absorption spectra and; (b) SLME

参考文献 75

[1]	Peng, Y.; Zhao, Y.; Yang, J.; Zhang, X.; Cheng, J. Acta Chim. Sinica 2024, 82, 879 (in Chinese).
	(彭亚晶, 赵雨新, 杨金辉, 仉昕昕, 程佳玲, 化学学报, 2024, 82, 879.)
[2]	Liu, X.; Li, B.; Han, M.; Zhang, X.; Chen, J.; Dai, S. Acta Chim. Sinica 2024, 82, 348 (in Chinese).
	(刘雪朋, 李博桐, 韩明远, 张先付, 陈建林, 戴松元, 化学学报, 2024, 82, 348.)
[3]	Xiao, S.; Xu, X. Acta Chim. Sinica 2024, 82, 1031 (in Chinese).
	(肖圣宗, 许雄文, 化学学报, 2024, 82, 1031.)
[4]	Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. J. Am. Chem. Soc. 2009, 131, 6050.
[5]	Green, M. A.; Dunlop, E. D.; Yoshita, M.; Kopidakis, N.; Bothe, K.; Siefer, G.; Hinken, D.; Rauer, M.; Hohl‐Ebinger, J.; Hao, X. Prog. Photovolt.: Res. Appl. 2024, 32, 425.
[6]	Chen, Y.; Zheng, D.; Wang, N.; Liu, J.; Yu, F.; Wu, S.; Liu, S.; Li, Z. Acta Chim. Sinica 2024, 82, 987 (in Chinese).
	(陈宇波, 郑德旭, 王楠, 刘吉双, 于凤阳, 吴飒建, 刘生忠, 李智鹏, 化学学报, 2024, 82, 987.)
[7]	Rodkey, N.; Zanoni, K. P. S.; Piot, M.; Dreessen, C.; Grote, R.; Carroy, P.; Sebastian Alonso, J. E.; Paliwal, A.; Muñoz, D.; Bolink, H. J. Adv. Energy Mater. 2024, 14, 2400058.
[8]	Varshney, A.; Chauhan, S.; Herrera, O. R.; Sharma, S. ACS Omega 2026, 11, 6883.
[9]	Wang, J.; Guo, H.; Yin, X.; Zhang, Y.; Wang, W.; Zhao, C.; Chen, J.; Wen, J.; Sun, W. Acta Chim. Sinica 2026, 84, 231 (in Chinese).
	(汪佳艳, 郭焕焕, 殷逍遥, 张昀照, 王威, 赵晨瑞, 陈洁, 文洁, 孙伟海, 化学学报, 2026, 84, 231.)
[10]	Gao, L.; Jiang, D.; Xu, Y.; Yao, Q.; Liu, F.; Sun, W.; Du, Z.; Sun, L.; Wu, J.; Lan, Z. Acta Chim. Sinica 2026, 84, 223 (in Chinese).
	(高林, 江东彬, 徐源, 姚青, 刘冯立, 孙伟海, 杜振波, 孙留学, 吴季怀, 兰章, 化学学报, 2026, 84, 223.)
[11]	Zhu, W.; Wang, Y.; Li, H.; Wang, Y.; Zheng, S.; Wang, Z.; Chen, S.; Sun, W.; Zhao, X. Acta Chim. Sinica 2025, 83, 616 (in Chinese).
	(朱文昊, 汪玉杰, 李浩, 汪杨, 郑松志, 王则远, 陈劭添, 孙伟海, 赵小敏, 化学学报, 2025, 83, 616.)
[12]	Guo, Z.; Zhou, H. Acta Chim. Sinica 2021, 79, 223 (in Chinese).
	(郭镇域, 周欢萍, 化学学报, 2021, 79, 223.)
[13]	Ben Abdelhadi, A.; Gutiérrez, M.; Cohen, B.; Lezama, L.; Lachkar, M.; Douhal, A. J. Mater. Chem. C 2024, 12, 286.
[14]	Guo, X.; Zhang, F.; Liu, K.; Kong, M.; Liu, Y.; Chen, P.; Zhang, Y. Mater. Res. Bull. 2025, 184, 113254.
[15]	Li, Q.; Liu, M. Appl. Phys. 2021, 11, 461 (in Chinese).
	(李庆宇, 刘铭, 应用物理, 2021, 11, 461.)
[16]	Kumar, A.; Chang, D. W.; Baek, J.-B. Energy Fuels 2023, 37, 17782.
[17]	Zhang, L.; Zhang, H.; Zhu, C.; Guo, X.; Yang, Y. Acta Chim. Sinica 2024, 82, 971 (in Chinese).
	(张林, 张慧, 朱从潭, 郭学益, 杨英, 化学学报, 2024, 82, 971.)
[18]	Frost, J. M.; Walsh, A. Acc. Chem. Res. 2016, 49, 528.
[19]	Wu, H.; Chen, J.; Chai, X.; Gan, Y.; Jiang, Q.; Ma, T.; Xu, C. Clean Coal Technol. 2025, 31, 132 (in Chinese).
	(吴海峰, 陈佳叶, 柴小菲, 甘雅瑄, 蒋琼琼, 马涛, 徐超, 洁净煤技术, 2025, 31, 132.)
[20]	Ren, J.; Geng, X.; Liu, S.; Liu, Q.; Ren, T. ACS Appl. Electron. Mater. 2026, 8, 2725.
[21]	Dolzhenko, Y. I.; Inabe, T.; Maruyama, Y. Bull. Chem. Soc. Jpn. 1986, 59, 563.
[22]	Mitzi, D. B.; Feild, C. A.; Harrison, W. T. A.; Guloy, A. M. Nature 1994, 369, 467.
[23]	Smith, I. C.; Hoke, E. T.; Solis‐Ibarra, D.; McGehee, M. D.; Karunadasa, H. I. Angew. Chem., Int. Ed. 2014, 53, 11232.
[24]	Stoumpos, C. C.; Cao, D. H.; Clark, D. J.; Young, J.; Rondinelli, J. M.; Jang, J. I.; Hupp, J. T.; Kanatzidis, M. G. Chem. Mater. 2016, 28, 2852.
[25]	Kareem, M.; Salih, E. Y.; Sampangi Rama Reddy, B. R.; Nayak, P. P.; Sundharam, S.; Kumar, S. Energy Adv. 2026, 5, 419.
[26]	Xia, L.; Liu, H.; Zhang, K.; Pei, Y. Acta Mater. 2026, 309, 122059.
[27]	Bibi, B.; Karimi, Z.; Shah, S. H.; Shen, F.; Sama, N. U.; Guan, L.; Zhang, J.; Lin, J.; Liu, Z. Inorganics 2026, 14, 73.
[28]	Xu, X.; Pan, Y.; Zhong, Y.; Ran, R.; Shao, Z. Mater. Horiz. 2020, 7, 2519.
[29]	Peksa, P.; Maufort, A.; Baranowski, M.; Surrente, A.; Lutsen, L.; Płochocka, P.; Van Gompel, W. T. M.; Dyksik, M. J. Phys. Chem. C 2024, 128, 17984.
[30]	Ma, Y.; Wang, Y.; Fang, Y.; Jiang, Y.; Dai, Z.; Miao, J. Adv. Opt. Mater. 2024, 12, 2401367.
[31]	Fu, Y.; Hautzinger, M. P.; Luo, Z.; Wang, F.; Pan, D.; Aristov, M. M.; Guzei, I.A.; Pan, A.; Zhu, X.; Jin, S. ACS Cent. Sci. 2019, 5, 1377.
[32]	Hautzinger, M. P.; Pan, D.; Pigg, A. K.; Fu, Y.; Morrow, D.J.; Leng, M.; Kuo, M.-Y.; Spitha, N.; Lafayette, D. P.; Kohler, D. D.; Wright, J. C.; Jin, S. ACS Energy Lett. 2020, 5, 1430.
[33]	Li, X.; Fu, Y.; Pedesseau, L.; Guo, P.; Cuthriell, S.; Hadar, I.; Even, J.; Katan, C.; Stoumpos, C. C.; Schaller, R. D.; Harel, E.; Kanatzidis, M. G. J. Am. Chem. Soc. 2020, 142, 11486.
[34]	Mihalyi-Koch, W.; Guo, S.; Dai, Z.; Pan, D.; Lafayette, D. P.; Scheeler, J. M.; Sanders, K. M.; Teat, S. J.; Wright, J. C.; Lü X.; Rappe, A. M.; Jin, S. Chem 2024, 10, 2180.
[35]	Hautzinger, M. P.; Mihalyi-Koch, W.; Jin, S. Chem. Mater. 2024, 36, 10408.
[36]	Jiang, Y.; He, X.; Liu, T.; Zhao, N.; Qin, M.; Liu, J.; Jiang, F.; Qin, F.; Sun, L.; Lu, X.; Jin, S.; Xiao, Z.; Kamiya, T.; Zhou, Y. ACS Energy Lett. 2019, 4, 1216.
[37]	Chen, E.; Monserrat, B. J. Phys. Chem. C 2024, 128, 12194.
[38]	Yan, J.; Zhang, W.; Geng, S.; Qiu, C.; Chu, Y.; Meng, R.; Zeng, P.; Liu, M.; Xiao, Z.; Hu, Y. Chem. Mater. 2023, 35, 289.
[39]	Robinson, K.; Gibbs, G. V.; Ribbe, P. H. Science 1971, 172, 567.
[40]	Baur, W. H. Acta Crystallogr., ect. B 1974, 30, 1195.
[41]	Garrote-Márquez, A.; Lodeiro, L.; Suresh, R.; Cruz Hernández, N.; Grau-Crespo, R.; Menéndez-Proupin, E. J. Phys. Chem. C 2023, 127, 15901.
[42]	Lin, L.; Jones, T. W.; Yang, T. C.-J.; Li, X.; Wu, C.; Xiao, Z.; Li, H.; Li, J.; Qian, J.; Lin, L.; Shi, J. Q.; Stranks, S. D.; Wilson, G. J.; Wang, X. Matter 2024, 7, 38.
[43]	Jeffrey, G. A. An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997.
[44]	Jiang, J.; Liu, F.; Tranca, I.; Shen, Q.; Tao, S. ACS Appl. Energy Mater. 2020, 3, 11548.
[45]	Xie, Y.; Koknat, G.; Weadock, N. J.; Wang, X.; Song, R.; Toney, M. F.; Blum, V.; Mitzi, D. B. J. Am. Chem. Soc. 2024, 146, 22509.
[46]	Pienia̧żek, A.; Dybała, F.; Polak, M. P.; Przypis, Ł.; Herman, A. P.; Kopaczek, J.; Kudrawiec, R. J. Phys. Chem. Lett. 2023, 14, 6470.
[47]	Zhao, Z.; Niu, Y.; Zhao, Y.; Song, Q.; Xin, L.; Lu, X. Acta Chim. Sinica 2016, 74, 689 (in Chinese).
	(赵梓, 牛玉, 赵阳, 宋琦, 辛璐, 陆熙, 化学学报, 2016, 74, 689.)
[48]	Ghosh, D.; Acharya, D.; Pedesseau, L.; Katan, C.; Even, J.; Tretiak, S.; Neukirch, A. J. J. Mater. Chem. A 2020, 8, 22009.
[49]	Febriansyah, B.; Lekina, Y.; Ghosh, B.; Harikesh, P. C.; Koh, T. M.; Li, Y.; Shen, Z.; Mathews, N.; England, J. ChemSusChem 2020, 13, 2693.
[50]	Marchenko, E. I.; Korolev, V. V.; Fateev, S. A.; Mitrofanov, A.; Eremin, N. N.; Goodilin, E. A.; Tarasov, A. B. Chem. Mater. 2021, 33, 7518.
[51]	Sze, S. M.; Ng, K. K. Physics of Semiconductor Devices, 3rd ed., Wiley-Interscience, Hoboken, 2007.
[52]	Dronskowski, R.; Blöechl, P. E. J. Phys. Chem. 1993, 97, 8617.
[53]	Steinberg, S.; Dronskowski, R. Crystals 2018, 8, 225.
[54]	Ghosh, D.; Acharya, D.; Zhou, L.; Nie, W.; Prezhdo, O. V.; Tretiak, S.; Neukirch, A. J. J. Phys. Chem. Lett. 2019, 10, 5000.
[55]	Zhang, Z.; Liu, Y.; Xiong, Q. J. Chem. Phys. 2025, 163, 024126.
[56]	Lax, M. J. Chem. Phys. 1952, 20, 1752.
[57]	Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van De Walle, C. G. Rev. Mod. Phys. 2014, 86, 253.
[58]	Kumagai, Y.; Oba, F. Phys. Rev. B 2014, 89, 195205.
[59]	Xue, H.; Chen, Z.; Tao, S.; Brocks, G. ACS Energy Lett. 2024, 9, 2343.
[60]	Yin, W.-J.; Shi, T.; Yan, Y. Appl. Phys. Lett. 2014, 104, 063903.
[61]	Zhang, X.; Turiansky, M. E.; Van De Walle, C. G. J. Phys. Chem. C 2020, 124, 6022.
[62]	Mathew, P.; Cho, J.; Kamat, P. V. ACS Energy Lett. 2024, 9, 1103.
[63]	Yantara, N.; Mathews, N. Joule 2024, 8, 1239.
[64]	Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901.
[65]	Hu, J.; Wen, X.; Li, D. Front. Phys. 2023, 18, 33602.
[66]	Wang, V.; Xu, N.; Liu, J. C.; Tang, G.; Geng, W. Comput. Phys. Commun. 2021, 267, 108033.
[67]	Mahal, E.; Mandal, S. C.; Pathak, B. Mater. Adv. 2022, 3, 2464.
[68]	Bi, F.; Zheng, X.; Yam, C. Acta Phys.-Chim. Sin. 2019, 35, 69 (in Chinese).
	(毕富珍, 郑晓, 任志勇, 物理化学学报, 2019, 35, 69.)
[69]	Yu, L.; Zunger, A. Phys. Rev. Lett. 2012, 108, 068701.
[70]	Wang, Z.; Ganose, A. M.; Niu, C.; Scanlon, D. O. J. Mater. Chem. A 2018, 6, 5652.
[71]	Yu, L.; Kokenyesi, R. S.; Keszler, D. A.; Zunger, A. Adv. Energy Mater. 2013, 3, 43.
[72]	Orio, M.; Pantazis, D. A.; Neese, F. Photosynth. Res. 2009, 102, 443.
[73]	Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169.
[74]	Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.
[75]	Blöchl, P. E. Phys. Rev. B 1994, 50, 17953.