N/F掺杂及N-F共掺杂TiO_2(101)表面特性的第一性原理研究
|
摘要
为提高TiO_2对太阳光的吸收率，增强其在可见光范围的光催化能力，人们对TiO_2进行了一系列改性研究，近来最为有效的进展是N、F等阴离子掺杂TiO_2的改性及其光催化活性研究，实验表明N、F掺杂可以增强TiO_2在可见光下的光催化活性，但理论上对其可见光响应机制的讨论仍然存在争议。原因之一可能是模拟计算采用的模型与实验室制备的材料存在较大差异。比如，大多数模拟计算采用的模型是体相TiO_2结构，而材料的表面特性对光催化反应的影响更大。此外，在关于TiO_2掺杂改性的研究中，研究者们对杂质元素替位掺杂的情况讨论得较多，而较少考虑填隙及吸附等其它有可能在材料制备中出现的杂质类型。
为了对N／F掺杂和N-F共掺杂TiO_2的可见光响应机制有一个更深入的认识，本文采用密度泛函理论(DFT)平面波赝势方法计算了N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构。计算采用广义梯度近似(GGA)的方法处理电子与电子间的交换关联能，由于该方法对过渡金属氧化物带隙能的计算结果总是与实际值存在严重偏离，本文亦采用GGA+U(Hubbard系数)方法对模型的电子结构进行了计算。本文的工作包括以下几个部分：
首先，通过对表面能和空位形成能的分析建立合适的锐钛矿相TiO_2(101)表面晶胞模型，并采用GGA及GGA+u的方法讨论清洁表面和存在氧空位的缺陷表面的电子结构。GGA的计算表明氧空位对TiO_2带隙能的减小影响极小，而GGA+U的计算表明氧空位能够显著降低TiO_2的带隙能。
其次，分别采用GGA及GGA+U的方法计算N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构。为了了解不同杂质类型对TiO_2表面电予结构的影响，除了N／F替位掺杂的情况外，N／F填隙掺杂及N／F在TiO_2表面吸附的情况也进行了讨论。由于研究证实N／F替位掺杂能够降低氧空位的形成能，也就是说N／F替位掺杂对氧空位的形成有促进作用，本文在讨论N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构的同时，也讨论了存在氧空位的N／F掺杂和N-F共掺杂缺陷表面的电子结构。
GGA的计算表明F掺杂对材料的电子结构没有明显的影响，而N杂质轨道的引入导致TiO_2价带的展宽，对带隙能的降低起到促进作用。GGA+U的计算却给出不同的结论：N掺杂只是在带隙中引入一个孤立的杂质能级，并没有导致带隙能的降低：反而F掺杂带来明显的带隙能的降低。通过比较，GGA+U的计算与一些实验测量结果能够较好地符合。此外，GGA和GGA+U的计算都表明N的吸附和填隙掺杂会在价带与导带之间形成若干新的能态，而吸附F原子对TiO_2的能态分布没有影响。
最后，我们对一个孤立氧分子在锐钛矿相TiO_2(101)表面的不同氧空位上的吸附形态进行了研究。对最容易实现的吸附形态的电子结构进行了计算，结果表明吸附氧分子在价带顶附近引入新的能态，可以改善TiO_2表面对可见光的响应特性。
In order to enhance the visible light (VIS) sensitivity of TiO_2 photocatalyst materials,people have made many efforts including introducing anionic species for doping. Recently,the research on nitrogen(N)/fluorin(F)-doped and N-F-codoped TiO_2 has made effectiveprogress. Some groups confirmed that N/F-doping and N-F-codoping can enhance thephotocatalysis of TiO_2 under VIS radiation experimentally. However the mechanism of theVIS sensitivity for N/F-doping and N-F-codoping is still a controversial question fortheoretic researchers. One of the reasons may be the differences between the models usedin simulation calculations with the material synthesized in lab. For example, most ofsimulation calculations were performed on TiO_2 bulk structure, whereas the surfaceproperties play an important role on photocatalytic reactions. Moreover, many theoreticworks considered substitutional doping only, neglecting the situation of interstitial dopingas well as adsorption.
In our present work, the electronic structures of N/F-doped and N-F-codoped TiO_2anatase (101) surfaces have been investigated by density functional theory (DFT)plane-wave pseudopotential method in order to give a further insight on the mechanism ofthe VIS sensitivity for N/F-doped and N-F-codoped TiO_2. Because the general gradientapproximation (GGA) which was used to describe the exchange-correlation effects alwaysleads to a severe underestimation of the band gap for the case of transition metal oxide,GGA + U (Hubbard coefficient) method was also adopted to calculate the electronicstructures. Our work includes the following parts:
First, the model of TiO_2 anatase (101) surface used in simulation calculations has beenbuilt by analyzing surface energy and oxygen vacancy formation energy. Both GGA andGGA+U methods were performed to calculate the electronic structure of pure anatase (101)surface as well as the defective surface (the surface with oxygen vacancies). GGAcalculations demonstrated that the introducing of oxygen vacancy takes little effect onband gap narrowing, whereas GGA +U calculations confirmed that oxygen vacancyreduces the band gap effectively.
Second, N/F-doped and N-F-codoped TiO_2 anatase (101) surfaces have beeninvestigated by both GGA and GGA+U methods. Besides the situation of substitutionaldoping, N/F interstitial doping in the surfaces as well as N/F adsorption on the surfaceshas also been taken into account in order to find how different doping styles make effecton the electronic structure of TiO_2. Because it has been confirmed that N/F-doping islikely introducing oxygen vacancies in TiO_2, the N/F-doped TiO_2 anatase (101) defectivesurface has also been analyzed as well as the N-F-codope, d defective surface.
GGA calculations demonstrated that F 2p states take no effect on band gap narrowingand N induced states have a positive effect on band gap narrowing by leading anexpansion of VB. Whereas GGA+U calculations gave different results. There is noobvious expansion of VB neither band gap narrowing observed by N-doping besides someisolated N 2p states lying in the gap. And F-doping was found playing an important roleon band gap narrowing. From the comparison of GGA and GGA+U calculations, wefound GGA+U calculations can give a better explanation for the reported experimentalobservations. Additionally, both GGA and GGA+U calculations for interstitial N-dopingand surface N/F adsorption on TiO_2 showed that N dopant/adsorbate introduces severalnew states between VB and CB of TiO_2, and F adsorbate takes no effect on electronicstructure of TiO_2.
Lastly, we have investigated several possible adsorption configurations for an isolatedO_2 molecule at different surface oxygen vacancy sites on TiO_2 anatase (101) surface. Theelectronic properties of the most energetic adsorption configuration have been discussedand it was found that the appearance of oxygen adsorbate induced states near the edge ofthe VB may attribute to the improvement of visible light sensitivity of TiO_2 surface.
为了对N／F掺杂和N-F共掺杂TiO_2的可见光响应机制有一个更深入的认识，本文采用密度泛函理论(DFT)平面波赝势方法计算了N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构。计算采用广义梯度近似(GGA)的方法处理电子与电子间的交换关联能，由于该方法对过渡金属氧化物带隙能的计算结果总是与实际值存在严重偏离，本文亦采用GGA+U(Hubbard系数)方法对模型的电子结构进行了计算。本文的工作包括以下几个部分：
首先，通过对表面能和空位形成能的分析建立合适的锐钛矿相TiO_2(101)表面晶胞模型，并采用GGA及GGA+u的方法讨论清洁表面和存在氧空位的缺陷表面的电子结构。GGA的计算表明氧空位对TiO_2带隙能的减小影响极小，而GGA+U的计算表明氧空位能够显著降低TiO_2的带隙能。
其次，分别采用GGA及GGA+U的方法计算N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构。为了了解不同杂质类型对TiO_2表面电予结构的影响，除了N／F替位掺杂的情况外，N／F填隙掺杂及N／F在TiO_2表面吸附的情况也进行了讨论。由于研究证实N／F替位掺杂能够降低氧空位的形成能，也就是说N／F替位掺杂对氧空位的形成有促进作用，本文在讨论N／F掺杂和N-F共掺杂锐钛矿相TiO_2(101)表面的电子结构的同时，也讨论了存在氧空位的N／F掺杂和N-F共掺杂缺陷表面的电子结构。
GGA的计算表明F掺杂对材料的电子结构没有明显的影响，而N杂质轨道的引入导致TiO_2价带的展宽，对带隙能的降低起到促进作用。GGA+U的计算却给出不同的结论：N掺杂只是在带隙中引入一个孤立的杂质能级，并没有导致带隙能的降低：反而F掺杂带来明显的带隙能的降低。通过比较，GGA+U的计算与一些实验测量结果能够较好地符合。此外，GGA和GGA+U的计算都表明N的吸附和填隙掺杂会在价带与导带之间形成若干新的能态，而吸附F原子对TiO_2的能态分布没有影响。
最后，我们对一个孤立氧分子在锐钛矿相TiO_2(101)表面的不同氧空位上的吸附形态进行了研究。对最容易实现的吸附形态的电子结构进行了计算，结果表明吸附氧分子在价带顶附近引入新的能态，可以改善TiO_2表面对可见光的响应特性。
In order to enhance the visible light (VIS) sensitivity of TiO_2 photocatalyst materials,people have made many efforts including introducing anionic species for doping. Recently,the research on nitrogen(N)/fluorin(F)-doped and N-F-codoped TiO_2 has made effectiveprogress. Some groups confirmed that N/F-doping and N-F-codoping can enhance thephotocatalysis of TiO_2 under VIS radiation experimentally. However the mechanism of theVIS sensitivity for N/F-doping and N-F-codoping is still a controversial question fortheoretic researchers. One of the reasons may be the differences between the models usedin simulation calculations with the material synthesized in lab. For example, most ofsimulation calculations were performed on TiO_2 bulk structure, whereas the surfaceproperties play an important role on photocatalytic reactions. Moreover, many theoreticworks considered substitutional doping only, neglecting the situation of interstitial dopingas well as adsorption.
In our present work, the electronic structures of N/F-doped and N-F-codoped TiO_2anatase (101) surfaces have been investigated by density functional theory (DFT)plane-wave pseudopotential method in order to give a further insight on the mechanism ofthe VIS sensitivity for N/F-doped and N-F-codoped TiO_2. Because the general gradientapproximation (GGA) which was used to describe the exchange-correlation effects alwaysleads to a severe underestimation of the band gap for the case of transition metal oxide,GGA + U (Hubbard coefficient) method was also adopted to calculate the electronicstructures. Our work includes the following parts:
First, the model of TiO_2 anatase (101) surface used in simulation calculations has beenbuilt by analyzing surface energy and oxygen vacancy formation energy. Both GGA andGGA+U methods were performed to calculate the electronic structure of pure anatase (101)surface as well as the defective surface (the surface with oxygen vacancies). GGAcalculations demonstrated that the introducing of oxygen vacancy takes little effect onband gap narrowing, whereas GGA +U calculations confirmed that oxygen vacancyreduces the band gap effectively.
Second, N/F-doped and N-F-codoped TiO_2 anatase (101) surfaces have beeninvestigated by both GGA and GGA+U methods. Besides the situation of substitutionaldoping, N/F interstitial doping in the surfaces as well as N/F adsorption on the surfaceshas also been taken into account in order to find how different doping styles make effecton the electronic structure of TiO_2. Because it has been confirmed that N/F-doping islikely introducing oxygen vacancies in TiO_2, the N/F-doped TiO_2 anatase (101) defectivesurface has also been analyzed as well as the N-F-codope, d defective surface.
GGA calculations demonstrated that F 2p states take no effect on band gap narrowingand N induced states have a positive effect on band gap narrowing by leading anexpansion of VB. Whereas GGA+U calculations gave different results. There is noobvious expansion of VB neither band gap narrowing observed by N-doping besides someisolated N 2p states lying in the gap. And F-doping was found playing an important roleon band gap narrowing. From the comparison of GGA and GGA+U calculations, wefound GGA+U calculations can give a better explanation for the reported experimentalobservations. Additionally, both GGA and GGA+U calculations for interstitial N-dopingand surface N/F adsorption on TiO_2 showed that N dopant/adsorbate introduces severalnew states between VB and CB of TiO_2, and F adsorbate takes no effect on electronicstructure of TiO_2.
Lastly, we have investigated several possible adsorption configurations for an isolatedO_2 molecule at different surface oxygen vacancy sites on TiO_2 anatase (101) surface. Theelectronic properties of the most energetic adsorption configuration have been discussedand it was found that the appearance of oxygen adsorbate induced states near the edge ofthe VB may attribute to the improvement of visible light sensitivity of TiO_2 surface.
引文
[1] Fujishima A., Honda K., Electrochemical photolysis of water at a semiconductor electrode. Nature, 1972, 238:37-38
[2] 张文彬，谢利群，白元峰．纳米TiO_2光催化机理及改性研究进展．化工科技，2005，13(6)：52-57
[3] 尹荔松，沈辉．二氧化钛光催化研究进展及应用．材料导报，2000，14(12)：23-25
[4] Carey J H, Lawrence J, Tosine H M. Photodechlorination of PCB's in the presence of titanium dioxide in aqueous suspensions. Bull Environ Contain Toxicol, 1976, 16: 697-701
[5] Frank S. N., Bard A. J. Heterogeneous photocatalytic oxidation of cyanide and Sulfite in Aqueous Solution at Semiconductor Powder. J. Phys. Chem., 1977, 81:1484-1495
[6] Yang J. C., Kim Y. C., Shul Y. G., et al., Characterization of photoreduction Pt/TiO_2 and decomposition of dichlorocetic acid over photoreduced Pt/TiO_2 catalysts, Appl. Surf. Sci., 1997, 121:525-529
[7] 李春雷，麦碧娴，潘海祥等．载银TiO_2催化剂上Aroclor1260的光催化降解．中国环境科学，2002，22(2)：123-127
[8] Choi W., Termin A., and Hoffmann M. R. The rolr of metal ion dopants in quantum-sized TiO_2: correlation between photoreactivity and charge carrier recombination dynamics, J. Phys. Chem., 1994, 98:13669-13669
[9] Linsebigler A. L., Lu G. Q., and Yates J. T. Photocatalysis on TiO_2 surfacex: principles mechanisms, and selected results, Chem, Rev., 1995, 95:735
[10] Asahi R., Morikawa T., Ohwaki T., et al., Visible-light photocatalysis in nitrogen-doped titanium oxides, Science, 2001, 293:269-271.
[11] 康华，崔洪亮，李桂春．非金属离子掺杂对TiO_2光催化活性的影响．中国非金属矿工业导刊，2008，70(5)：30-33
[12] Khan S. U. M., A1-Shahry M., Ingler Jr. W. B. Efficient photochemicalwater splitting by a chemically modified n-TiO_2, Science, 2002, 297:2243-2245
[13] Sakthivel S., Kisch H., Daylight photocatalysis by carbon-modified titanium dioxide, Angew. Chem. Int. Ed., 2003,42:4908-4911
[14] Ohno T., Tsubota T., Nishijima K., Miyamoto Z. Degradation of methylcne blue on carbonate species-doped TiO_2 photocatalysts under visible light, Chem. Lett., 2004,33:750-751
[15] Umebayashi T., Yamaki T., Itoh H., Asai K., Band gap narrowing of titanium dioxide by sulfur doping, Appl. Phys. Lett., 2002, 81:454-456
[16] Umebayashi T., Yamaki T., Tanaka S., Asai K., Visible light induced degradation of methylene blue on S-doped TiO_2, Chem. Lett., 2003, 32:330-331
[17] Yamaki T., Sumita T., Yamamoto S. Formation of TiO_(2-x)F_x compounds in fluorine-implanted TiO_2, Mater. Sci. Lett., 2002, 21:33-35
[18] Yamaki T., Umebayashi T., Sumita T., et al., Fluorine-doping in titanium dioxide by implantation technique, Nuclear Instruments and Methods in Phydics Research, 2003, 206: 254-258
[19] Yu J. C, Ho W., Yu J., et al., Efficient visible-light-induced photocatalytic disinfection on sulfurdoped nanocrystalline titania, Environ. Sci. Technol., 2005, 39: 1175-1179
[20] Li D., Haneda H., Hishita S., et al., Visible-light-driven N-F-codoped TiO_2 photocatalysts. 1.Synthesis by spray pyrolysis and surface characterization, Chem.Mater, 2005, 17: 2588-2595
[21] Li D., Haneda H., Hishita S., et al., Visible-light-driven N-F-codoped TiO_2 photocatalysts.2.Optical characterization, photocatalysis and potential application to air purification, Chem.Mater., 2005, 17:2596-2602.
[22] Li D., Haneda H., Hishita S., et al., Visible-light-driven nitrogen-doped TiO_2 photocatalysts: effect of nitrogen precursors on their photocatalysis for decomposition of gas-phase organic pollutants, Materials Science and Engineering, 2005, 117:67-75.
[23] Li D., Ohashi N., Hishita S., et al., Origin of visible-light-driven photocatalysis: A comparative study on N/F-doped and N-F-codoped TiO_2 powders by means of experimental characterizations and theoretical calculations, J. Solid State Chem., 2005, 178:3293-3302
[24] Sato S., Nakamura R., Abe S., Visible-light sensitization of TiO_2 photocatalysts by wet-method N doping, Appl. Cata. A: General, 2005, 284: 131-137
[25] Todorova N., Giannakopoulou T., Romanos G., et al., Preparation of fluorine-doped TiO_2 photocatalysts with controlled crystalline structure, Inter. J. Photoenergy, 2008, 2008:534038
[26] Wu G.S., Chen A.C., Direct growth of F-doped TiO_2 particulate thin films with high photocatalytic activity for environmental applications, J. Photochem. Photobio. A: Chem., 2008, 195:47-53
[27] Xu J.J., Ao Y.H., Fu D.G., Yuan C.W., Low-temperature preparation of F-doped TiO_2 film and its photocatalytic activity under solar light, Appl. Surf. Sci., 2008, 254:3033-3038
[28] Zhou J. K., Lv L., Yu J.Q., et al., Synthesis of self-organized polycrystalline F-doped TiO_2 hollow microspheres and their photocatalytic activity under visible light, J. Phys. Chem. C, 2008,112: 5316-5321
[29] Li D., Haneda H., Labhsetwar N. K., et al., Visible-light-driven photocatalysis on fluorine-doped TiO_2 powders by the creation of surface oxygen vacancies, Chem. Phys. Lett. 2005,401:579-584
[30] Nakano Y, Morikawa T., Ohwaki T., Taga Y, Deep-level optical spectroscopy investigation of N-doped TiO_2 films, Appl. Phys. Lett., 2005, 86:132104
[31] Wang Y, Doren D. J., First-principles calculations on TiO_2 doped by N, Nd, and vacancy, Solid State Commun., 2005, 136:186-189
[32] Batzill M., Morales E. H., Diebold U., Influence of nitrogen doping on the defect formation and surface properties of TiO_2 rutile and anatase, Phys. Rev. Lett., 2006, 96:026103
[33] Lee J. Y, Park J., Cho J. H., Electronic properties of N- and C-doped TiO_2, Appl. Phys. Lett. 2005, 87:011904
[34] Hoffman M. R., Martin S. T., Choi W., et al., Environmental applications of semiconductor photocatalysis. Chem. Rev., 1995, 95: 69-96
[35] Diebold U., The surface science of titanium dioxide, Surf. Sci. Rep., 2003, 48:53-229
[36] Anpo M., Yamashita H., Ichihashi Y., et al., Photocatalytic reduction of CO_2 withH_2O on various titanium oxide catalysts, J. Electroanalytical Chem., 1995, 396:21-26
[37] Mo S. D. and Ching W. Y., Electonic and optical properties of three phases of titanium dioxide: Rutile, anatase, and brookite. Physical Review B, 1995, 51(19):13023-13031
[38] 马新国．锐钛矿型TiO_2表面的理论研究．华中科技大学图书馆，2007
[39] Diebold U., Ruzycki N., Herman G. S., Selloni A., One step towards bridging the materials gap: surface studies of TiO_2 anatase, Catalysis Today, 2003, 85: 93-100
[40] 赵洁，邱克辉，董宏伟．锐钛矿型纳米TiO_2光催化降解与环保应用研究进展．中国非会属矿工业导刊，2006 56(4)：50-55
[41] Hebenstreit W., Ruzycki N., Herman G. S., Gou Y. and Diebold U., Scanning tunneling microscopy investigation of the TiO_2 anatase (101) surface, Phys. Rev. B, 2000, 62:16334-16336
[42] Franchini C., Bayer V., Podloucky R., An efficient two-step technique for nitrogen-doped titanium dioxide synthesizing: visible-light-induced photodecomposition of methylene blue, Phys. Rev. B, 2006, 73:155402
[43] Fox H., Horsfield A. P., Gillan M. J., Density functional calculations of surface free energies, J. Chem. Phys., 2006, 124:134709
[44] Li Y. L., Yao K. L., Liu Z. L., Gao G. Y., First-principles study of the composition structure and stability of the FeO (111) surface, Phys. Rev. B, 2005, 72:155446
[45] Chatterjee A., Niwa S., Mizukami F., Structure and property correlation for Ag deposition on a-Al_2O_3: a first principle study, J. Mole. Graphic and Modeling, 2005, 23: 447-456
[46] Calatayud M., Minot C., Reactivity of the oxygen sites on the V_2O_5/TiO_2 anatase catalyst, J. Phys. Chem. B, 2004, 108:15679-15685
[47] Muscat J., Harrison N. M., First-principles study of potosium adsorption on TiO_2 surface, Phys. Rev. B, 1999, 59:15457
[48] Hohenberg P., Kohn W., Inhomogeneous electron gas, Phys. Rev. B, 1964, 136: 864-871
[49] Kohn W., Sham L. J., Self-consistent equations including exchange and correlation effects, Phys Rev, A, 1965, 140:1133-1138
[50] 谢希德，陆栋．固体能带理论，复旦大学出版社，1998
[51] Born M., Huang K., Dynamical theory of crystal lattices, Oxford University Press, 1951
[52] Thomas L. H., Proc. Cambridge Philos. Soc., 1927, 23542-23547
[53] Wiger E., On the interaction of electrons in metals. Phys. Rev., 1934, 46:1002-1011
[54] Slater J. C., A simplification of the Hartree-Fock method. Phys. Rev., 1951, 81:385-390
[55] Slater J. C., Wilson T. M., Wood J. H., Comparison of several exchange potentials for electrons in the Cu+ ion, Phys. Rev., 1969,179:28-38
[56] Hedin L., Lundqvist B. I., Explicit local exchange-correlation potentials, J. Phys. C: Solid State Phys., 1971, 4(14):2064-2083
[57] Ceperley D. M., Zunger A., Ground state of the electron gas by a stochastic method, Phys. Rev. Lett., 1980, 45:566-569
[58] Perdew T. P., Zunger A., Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B, 1981, 23:5048-5079
[59] Perpew J. P., Wang Y., Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45:13244-13249
[60] Perdew J. P., Chevary J. A., Vosko S. H., Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B, 1993, 46:6671-6687
[61] Becke A. D., Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A, 1988, 38:3098-3100
[62] Perdew J. P., Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B, 1986, 33:8822-8824
[63] Stampfl C., Van de Walle C.G., Density-functional calculations for Ⅲ-Ⅴ nitrides using the local-density approximation and the generalized gradient approximation, Phys. Rev. B, 1999, 59, 5521-5535
[64] Anisimov V. I., Poteryaev A. I., Korotin M. A., et al., First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory, J. Phys.: Condens. Matter, 1997, 9:7359-7367
[65] Terakura K., Oguchi T., Williams A. R., Band theory of insulating transition-metal monoxides:band-structure calculations, Phys. Rev. B, 1984, 30:4734-4747
[66] Dudarev S.L., Botton G. A., Savrasov S.Y., Humphreys C.J. and Sutton A.P. An Electron-energy-loss spectra and the structural stability of nickel oxide: LSDA+U study, Phys. Rev. B, 1998, 57:1505-1509
[67] Bloch F., Quantum mechanics of electrons in crystal lattices, Z. Physik. 1928, 52:555-600
[68] Slater J. C, Koster G. F., Simplified LCAO method for the periodic potential problem. Phys. Rev. 1954, 94:1498-1524
[69] Herring C, Hill A. G, The theoretical constitution of metallic beryllium. Phys. Rev., 1940,58:132-162
[70] Ihm J., Zunger A., Cohen M. L., Momentum-space formalism for the total energy of Solids. J. Phys. C, 1979, 12:4409-4422
[71] Payne M. C, Teter M. P., Ahan D. C.,et al., Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients, Rev. Mod. Phys., 1992, 64:1045-1097
[72] Herman F., Killman S., Atomic Structure Calculation, Prentice-Hall, Englewood Cliffs. N. J. 1963
[73] Korringa J., On the calculation of the energy of a Bloch wave in a metal. Physica, 1917, 13(6-7):392-400
[74] Kohn W., Rostoker N., Solution of the Schrodinger equation in periodic lattices with an application to metallic lithium, Phys. Rev., 1954, 91:1111-1120
[75] Anderson O. K., Linear methods in band theory, Phys. Rev. B, 1975, 12:3060-3083
[76] Skiver H. L, The LMTO method, Ed. by M. Cardona and P. Fulde. Heidelberg. Springer-Verlag, 1984
[77] Hamann D. R., Schluter M., Chiang C, Norm-conserving pseudopotentials, Phys. Rev. Lett., 1979,43:1494-1497
[78] Laasonen K., Car R., Lee C, et al., Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics, Phys. Rev. B, 1991,43:6796-6799
[79] Laasonen K., Pasquarello A., Car R., et al., Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B, 1993,47:10142-10153
[80] Lee C, Vanderbilt D., Laasonen K., Ab initio studies on high pressure phases of ice, Phys. Rev. Lett., 1992, 69:462-465
[81] Pasquarello A., Laasonen K., Car R., et al., Ab initio molecular dynamics for d-electron systems: Liquid copper at 1500 K, Phys. Rev. Lett., 1992, 69:1982-1985
[82] Segall M. D., Lindan P. J. D., Probert M. J., C. J. et al., First-principles simulation: ideas illustrations and the CASTEP code, J. Phys.: Cond. Matt., 2002, 14: 2717-2743
[83] Howard C. J., Sabine T. M., Dickson F., Structural and thermal parameters for rutile and anatase. Acta. Crystallographica, Sec.B: Struct. Sci., 1992,47:462-468
[84] Rodriguez J.A, Hrbek J, Dvorak J, Jirsak T, Maiti A., Interaction of sulfur with TiO_2 (110): Photoemission and density-functional studies Chemical Physics Letters 2001 336 337-384
[85] A. Arya and E. A. Carter, Structure, bonding, and adhesion at the TiC_2(100)/Fe(110) interface from first principles, J. Chem, Phys., 2003,118:8982-8996
[86] Lazzeri M., Vittadini A., Selloni A., Structure and energetics of stoichiometric TiO_2 anatase surfaces, Phys. Rev. B, 2001, 63:155409
[87] Lazzeri M, Vittadini A and Selloni A Erratum: Structure and energetics of stoichiometric TiO_2 anatase surfaces, Phys. Rev. B, 2002, 65:119901
[88] Oviedo J., San Miguel M. A., Sanz J. F., Oxygen vacancies on TiO_2 (110) from first principles calculations, J. Chem. Phys. 2004, 121:7427-7435
[89] Finazzi E., Di Valentin C, Selloni A., Pacchioni G, Fist Principles study of nitrogen doping at the anatase TiO_2 (101) surface, J. Phys. Chem. C, 2007, 111:9275-9282
[90] Xu Y., Chen W. K., Liu S.H., et al., Interaction of photoactive catechol with TiO_2 anatase (101) surface: A periodic density functional theory study, Chem. Phys. 2007, 331:275-282
[91] See A. K., Bartynsky R. A., Inverse photoemission study of the defective TiO_2 (110) surface, J. Vac. Sci. Technol. A, 1992, 10:2591-2600
[92] Gao, G. Y.; Yao, K. L.; Liu, Z.L., Fist Principles study on magnetism and electronic structure of V-doped rutile TiO_2, Phys. Lett. A, 2006, 359:523-527
[93] Perebeinos, V.; Vogt, T., Jahn-Teller transition in TiF_3 investigated using density-functional theory, Phys. Rev. B, 2004, 69:115102
[94] Ihara T., Miyoshia M, Iriyamab Y., et al., Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping, Appl. Cata. B: Environmental, 2003, 42:403-409
[95] Justicia I., Garcia G, V(?)zquez L., et al., Self-doped titanium oxide thin films for efficient visible: An example: Nonylphenol photodegradation, Sensors and Actuators B: Chemical, 2005, 109:52-56.
[96] Wu X. Y., Selloni A., Lazzeri M, S., Nayak K., Oxygen vacancy mediated adsorption and reactions of molecular oxygen on the TiO_2(110) surface, Phys. Rev. B, 2003, 68 (24):241402
[97] Dionysiou D. D., Burbano A. A., Suidan M .T., et al., Effect of oxygen in a thin-film rotating disk photocatalytic reactor, Environ. Sci. Technol, 2002, 36:3834-3836
[2] 张文彬，谢利群，白元峰．纳米TiO_2光催化机理及改性研究进展．化工科技，2005，13(6)：52-57
[3] 尹荔松，沈辉．二氧化钛光催化研究进展及应用．材料导报，2000，14(12)：23-25
[4] Carey J H, Lawrence J, Tosine H M. Photodechlorination of PCB's in the presence of titanium dioxide in aqueous suspensions. Bull Environ Contain Toxicol, 1976, 16: 697-701
[5] Frank S. N., Bard A. J. Heterogeneous photocatalytic oxidation of cyanide and Sulfite in Aqueous Solution at Semiconductor Powder. J. Phys. Chem., 1977, 81:1484-1495
[6] Yang J. C., Kim Y. C., Shul Y. G., et al., Characterization of photoreduction Pt/TiO_2 and decomposition of dichlorocetic acid over photoreduced Pt/TiO_2 catalysts, Appl. Surf. Sci., 1997, 121:525-529
[7] 李春雷，麦碧娴，潘海祥等．载银TiO_2催化剂上Aroclor1260的光催化降解．中国环境科学，2002，22(2)：123-127
[8] Choi W., Termin A., and Hoffmann M. R. The rolr of metal ion dopants in quantum-sized TiO_2: correlation between photoreactivity and charge carrier recombination dynamics, J. Phys. Chem., 1994, 98:13669-13669
[9] Linsebigler A. L., Lu G. Q., and Yates J. T. Photocatalysis on TiO_2 surfacex: principles mechanisms, and selected results, Chem, Rev., 1995, 95:735
[10] Asahi R., Morikawa T., Ohwaki T., et al., Visible-light photocatalysis in nitrogen-doped titanium oxides, Science, 2001, 293:269-271.
[11] 康华，崔洪亮，李桂春．非金属离子掺杂对TiO_2光催化活性的影响．中国非金属矿工业导刊，2008，70(5)：30-33
[12] Khan S. U. M., A1-Shahry M., Ingler Jr. W. B. Efficient photochemicalwater splitting by a chemically modified n-TiO_2, Science, 2002, 297:2243-2245
[13] Sakthivel S., Kisch H., Daylight photocatalysis by carbon-modified titanium dioxide, Angew. Chem. Int. Ed., 2003,42:4908-4911
[14] Ohno T., Tsubota T., Nishijima K., Miyamoto Z. Degradation of methylcne blue on carbonate species-doped TiO_2 photocatalysts under visible light, Chem. Lett., 2004,33:750-751
[15] Umebayashi T., Yamaki T., Itoh H., Asai K., Band gap narrowing of titanium dioxide by sulfur doping, Appl. Phys. Lett., 2002, 81:454-456
[16] Umebayashi T., Yamaki T., Tanaka S., Asai K., Visible light induced degradation of methylene blue on S-doped TiO_2, Chem. Lett., 2003, 32:330-331
[17] Yamaki T., Sumita T., Yamamoto S. Formation of TiO_(2-x)F_x compounds in fluorine-implanted TiO_2, Mater. Sci. Lett., 2002, 21:33-35
[18] Yamaki T., Umebayashi T., Sumita T., et al., Fluorine-doping in titanium dioxide by implantation technique, Nuclear Instruments and Methods in Phydics Research, 2003, 206: 254-258
[19] Yu J. C, Ho W., Yu J., et al., Efficient visible-light-induced photocatalytic disinfection on sulfurdoped nanocrystalline titania, Environ. Sci. Technol., 2005, 39: 1175-1179
[20] Li D., Haneda H., Hishita S., et al., Visible-light-driven N-F-codoped TiO_2 photocatalysts. 1.Synthesis by spray pyrolysis and surface characterization, Chem.Mater, 2005, 17: 2588-2595
[21] Li D., Haneda H., Hishita S., et al., Visible-light-driven N-F-codoped TiO_2 photocatalysts.2.Optical characterization, photocatalysis and potential application to air purification, Chem.Mater., 2005, 17:2596-2602.
[22] Li D., Haneda H., Hishita S., et al., Visible-light-driven nitrogen-doped TiO_2 photocatalysts: effect of nitrogen precursors on their photocatalysis for decomposition of gas-phase organic pollutants, Materials Science and Engineering, 2005, 117:67-75.
[23] Li D., Ohashi N., Hishita S., et al., Origin of visible-light-driven photocatalysis: A comparative study on N/F-doped and N-F-codoped TiO_2 powders by means of experimental characterizations and theoretical calculations, J. Solid State Chem., 2005, 178:3293-3302
[24] Sato S., Nakamura R., Abe S., Visible-light sensitization of TiO_2 photocatalysts by wet-method N doping, Appl. Cata. A: General, 2005, 284: 131-137
[25] Todorova N., Giannakopoulou T., Romanos G., et al., Preparation of fluorine-doped TiO_2 photocatalysts with controlled crystalline structure, Inter. J. Photoenergy, 2008, 2008:534038
[26] Wu G.S., Chen A.C., Direct growth of F-doped TiO_2 particulate thin films with high photocatalytic activity for environmental applications, J. Photochem. Photobio. A: Chem., 2008, 195:47-53
[27] Xu J.J., Ao Y.H., Fu D.G., Yuan C.W., Low-temperature preparation of F-doped TiO_2 film and its photocatalytic activity under solar light, Appl. Surf. Sci., 2008, 254:3033-3038
[28] Zhou J. K., Lv L., Yu J.Q., et al., Synthesis of self-organized polycrystalline F-doped TiO_2 hollow microspheres and their photocatalytic activity under visible light, J. Phys. Chem. C, 2008,112: 5316-5321
[29] Li D., Haneda H., Labhsetwar N. K., et al., Visible-light-driven photocatalysis on fluorine-doped TiO_2 powders by the creation of surface oxygen vacancies, Chem. Phys. Lett. 2005,401:579-584
[30] Nakano Y, Morikawa T., Ohwaki T., Taga Y, Deep-level optical spectroscopy investigation of N-doped TiO_2 films, Appl. Phys. Lett., 2005, 86:132104
[31] Wang Y, Doren D. J., First-principles calculations on TiO_2 doped by N, Nd, and vacancy, Solid State Commun., 2005, 136:186-189
[32] Batzill M., Morales E. H., Diebold U., Influence of nitrogen doping on the defect formation and surface properties of TiO_2 rutile and anatase, Phys. Rev. Lett., 2006, 96:026103
[33] Lee J. Y, Park J., Cho J. H., Electronic properties of N- and C-doped TiO_2, Appl. Phys. Lett. 2005, 87:011904
[34] Hoffman M. R., Martin S. T., Choi W., et al., Environmental applications of semiconductor photocatalysis. Chem. Rev., 1995, 95: 69-96
[35] Diebold U., The surface science of titanium dioxide, Surf. Sci. Rep., 2003, 48:53-229
[36] Anpo M., Yamashita H., Ichihashi Y., et al., Photocatalytic reduction of CO_2 withH_2O on various titanium oxide catalysts, J. Electroanalytical Chem., 1995, 396:21-26
[37] Mo S. D. and Ching W. Y., Electonic and optical properties of three phases of titanium dioxide: Rutile, anatase, and brookite. Physical Review B, 1995, 51(19):13023-13031
[38] 马新国．锐钛矿型TiO_2表面的理论研究．华中科技大学图书馆，2007
[39] Diebold U., Ruzycki N., Herman G. S., Selloni A., One step towards bridging the materials gap: surface studies of TiO_2 anatase, Catalysis Today, 2003, 85: 93-100
[40] 赵洁，邱克辉，董宏伟．锐钛矿型纳米TiO_2光催化降解与环保应用研究进展．中国非会属矿工业导刊，2006 56(4)：50-55
[41] Hebenstreit W., Ruzycki N., Herman G. S., Gou Y. and Diebold U., Scanning tunneling microscopy investigation of the TiO_2 anatase (101) surface, Phys. Rev. B, 2000, 62:16334-16336
[42] Franchini C., Bayer V., Podloucky R., An efficient two-step technique for nitrogen-doped titanium dioxide synthesizing: visible-light-induced photodecomposition of methylene blue, Phys. Rev. B, 2006, 73:155402
[43] Fox H., Horsfield A. P., Gillan M. J., Density functional calculations of surface free energies, J. Chem. Phys., 2006, 124:134709
[44] Li Y. L., Yao K. L., Liu Z. L., Gao G. Y., First-principles study of the composition structure and stability of the FeO (111) surface, Phys. Rev. B, 2005, 72:155446
[45] Chatterjee A., Niwa S., Mizukami F., Structure and property correlation for Ag deposition on a-Al_2O_3: a first principle study, J. Mole. Graphic and Modeling, 2005, 23: 447-456
[46] Calatayud M., Minot C., Reactivity of the oxygen sites on the V_2O_5/TiO_2 anatase catalyst, J. Phys. Chem. B, 2004, 108:15679-15685
[47] Muscat J., Harrison N. M., First-principles study of potosium adsorption on TiO_2 surface, Phys. Rev. B, 1999, 59:15457
[48] Hohenberg P., Kohn W., Inhomogeneous electron gas, Phys. Rev. B, 1964, 136: 864-871
[49] Kohn W., Sham L. J., Self-consistent equations including exchange and correlation effects, Phys Rev, A, 1965, 140:1133-1138
[50] 谢希德，陆栋．固体能带理论，复旦大学出版社，1998
[51] Born M., Huang K., Dynamical theory of crystal lattices, Oxford University Press, 1951
[52] Thomas L. H., Proc. Cambridge Philos. Soc., 1927, 23542-23547
[53] Wiger E., On the interaction of electrons in metals. Phys. Rev., 1934, 46:1002-1011
[54] Slater J. C., A simplification of the Hartree-Fock method. Phys. Rev., 1951, 81:385-390
[55] Slater J. C., Wilson T. M., Wood J. H., Comparison of several exchange potentials for electrons in the Cu+ ion, Phys. Rev., 1969,179:28-38
[56] Hedin L., Lundqvist B. I., Explicit local exchange-correlation potentials, J. Phys. C: Solid State Phys., 1971, 4(14):2064-2083
[57] Ceperley D. M., Zunger A., Ground state of the electron gas by a stochastic method, Phys. Rev. Lett., 1980, 45:566-569
[58] Perdew T. P., Zunger A., Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B, 1981, 23:5048-5079
[59] Perpew J. P., Wang Y., Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45:13244-13249
[60] Perdew J. P., Chevary J. A., Vosko S. H., Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B, 1993, 46:6671-6687
[61] Becke A. D., Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A, 1988, 38:3098-3100
[62] Perdew J. P., Density-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B, 1986, 33:8822-8824
[63] Stampfl C., Van de Walle C.G., Density-functional calculations for Ⅲ-Ⅴ nitrides using the local-density approximation and the generalized gradient approximation, Phys. Rev. B, 1999, 59, 5521-5535
[64] Anisimov V. I., Poteryaev A. I., Korotin M. A., et al., First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory, J. Phys.: Condens. Matter, 1997, 9:7359-7367
[65] Terakura K., Oguchi T., Williams A. R., Band theory of insulating transition-metal monoxides:band-structure calculations, Phys. Rev. B, 1984, 30:4734-4747
[66] Dudarev S.L., Botton G. A., Savrasov S.Y., Humphreys C.J. and Sutton A.P. An Electron-energy-loss spectra and the structural stability of nickel oxide: LSDA+U study, Phys. Rev. B, 1998, 57:1505-1509
[67] Bloch F., Quantum mechanics of electrons in crystal lattices, Z. Physik. 1928, 52:555-600
[68] Slater J. C, Koster G. F., Simplified LCAO method for the periodic potential problem. Phys. Rev. 1954, 94:1498-1524
[69] Herring C, Hill A. G, The theoretical constitution of metallic beryllium. Phys. Rev., 1940,58:132-162
[70] Ihm J., Zunger A., Cohen M. L., Momentum-space formalism for the total energy of Solids. J. Phys. C, 1979, 12:4409-4422
[71] Payne M. C, Teter M. P., Ahan D. C.,et al., Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients, Rev. Mod. Phys., 1992, 64:1045-1097
[72] Herman F., Killman S., Atomic Structure Calculation, Prentice-Hall, Englewood Cliffs. N. J. 1963
[73] Korringa J., On the calculation of the energy of a Bloch wave in a metal. Physica, 1917, 13(6-7):392-400
[74] Kohn W., Rostoker N., Solution of the Schrodinger equation in periodic lattices with an application to metallic lithium, Phys. Rev., 1954, 91:1111-1120
[75] Anderson O. K., Linear methods in band theory, Phys. Rev. B, 1975, 12:3060-3083
[76] Skiver H. L, The LMTO method, Ed. by M. Cardona and P. Fulde. Heidelberg. Springer-Verlag, 1984
[77] Hamann D. R., Schluter M., Chiang C, Norm-conserving pseudopotentials, Phys. Rev. Lett., 1979,43:1494-1497
[78] Laasonen K., Car R., Lee C, et al., Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics, Phys. Rev. B, 1991,43:6796-6799
[79] Laasonen K., Pasquarello A., Car R., et al., Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B, 1993,47:10142-10153
[80] Lee C, Vanderbilt D., Laasonen K., Ab initio studies on high pressure phases of ice, Phys. Rev. Lett., 1992, 69:462-465
[81] Pasquarello A., Laasonen K., Car R., et al., Ab initio molecular dynamics for d-electron systems: Liquid copper at 1500 K, Phys. Rev. Lett., 1992, 69:1982-1985
[82] Segall M. D., Lindan P. J. D., Probert M. J., C. J. et al., First-principles simulation: ideas illustrations and the CASTEP code, J. Phys.: Cond. Matt., 2002, 14: 2717-2743
[83] Howard C. J., Sabine T. M., Dickson F., Structural and thermal parameters for rutile and anatase. Acta. Crystallographica, Sec.B: Struct. Sci., 1992,47:462-468
[84] Rodriguez J.A, Hrbek J, Dvorak J, Jirsak T, Maiti A., Interaction of sulfur with TiO_2 (110): Photoemission and density-functional studies Chemical Physics Letters 2001 336 337-384
[85] A. Arya and E. A. Carter, Structure, bonding, and adhesion at the TiC_2(100)/Fe(110) interface from first principles, J. Chem, Phys., 2003,118:8982-8996
[86] Lazzeri M., Vittadini A., Selloni A., Structure and energetics of stoichiometric TiO_2 anatase surfaces, Phys. Rev. B, 2001, 63:155409
[87] Lazzeri M, Vittadini A and Selloni A Erratum: Structure and energetics of stoichiometric TiO_2 anatase surfaces, Phys. Rev. B, 2002, 65:119901
[88] Oviedo J., San Miguel M. A., Sanz J. F., Oxygen vacancies on TiO_2 (110) from first principles calculations, J. Chem. Phys. 2004, 121:7427-7435
[89] Finazzi E., Di Valentin C, Selloni A., Pacchioni G, Fist Principles study of nitrogen doping at the anatase TiO_2 (101) surface, J. Phys. Chem. C, 2007, 111:9275-9282
[90] Xu Y., Chen W. K., Liu S.H., et al., Interaction of photoactive catechol with TiO_2 anatase (101) surface: A periodic density functional theory study, Chem. Phys. 2007, 331:275-282
[91] See A. K., Bartynsky R. A., Inverse photoemission study of the defective TiO_2 (110) surface, J. Vac. Sci. Technol. A, 1992, 10:2591-2600
[92] Gao, G. Y.; Yao, K. L.; Liu, Z.L., Fist Principles study on magnetism and electronic structure of V-doped rutile TiO_2, Phys. Lett. A, 2006, 359:523-527
[93] Perebeinos, V.; Vogt, T., Jahn-Teller transition in TiF_3 investigated using density-functional theory, Phys. Rev. B, 2004, 69:115102
[94] Ihara T., Miyoshia M, Iriyamab Y., et al., Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping, Appl. Cata. B: Environmental, 2003, 42:403-409
[95] Justicia I., Garcia G, V(?)zquez L., et al., Self-doped titanium oxide thin films for efficient visible: An example: Nonylphenol photodegradation, Sensors and Actuators B: Chemical, 2005, 109:52-56.
[96] Wu X. Y., Selloni A., Lazzeri M, S., Nayak K., Oxygen vacancy mediated adsorption and reactions of molecular oxygen on the TiO_2(110) surface, Phys. Rev. B, 2003, 68 (24):241402
[97] Dionysiou D. D., Burbano A. A., Suidan M .T., et al., Effect of oxygen in a thin-film rotating disk photocatalytic reactor, Environ. Sci. Technol, 2002, 36:3834-3836