摘要
本论文采用基于密度泛函理论(DFT)的第一性原理计算来研究金属薄膜表面与原子或分子相互作用的微观机制。主要内容包括三部分:一是金属薄膜的量子尺寸效应(QSE)及其对表面力能学量和化学反应的调制;二是金属表面的初始氧化;最后采用DFT+U方法来计算强关联材料PuO_2和Pu_2O_3的基态电子结构。
在第一部分内容中,第三、四章的两个工作分别计算了Cu(001)和Pb(111)薄膜的量子尺寸效应。
第三章中,我们对厚度从1到26个原子单层(ML)的清洁Cu(001)薄膜展开了系统的第一性原理计算。详细讨论了对应于布里渊区内一定极值点的量子阱态,给出了Cu(001)薄膜的电子结构、表面能、电子功函数、层间弛豫等物理量随薄膜厚度变化的量子振荡行为。同时,我们也讨论了Cs原子在Cu(001)表面的吸附性质,给出了吸附能及局域电子态密度随薄膜层厚的变化关系,体现了Cu(001)薄膜的量子尺寸效应。研究发现,由于贵金属费米面特有的“脖子”轨道和“肚子”轨道的量子干涉,使得Cu(001)薄膜表面的表面稳定性、化学活性和化学反应会呈现出长短周期(2.7ML和5.6ML)相耦合的复杂振荡行为。
第四章中,我们计算了清洁和有3d-磁性单原子(Cr、Mn、Fe和Co)吸附的Pb(111)薄膜的力能学量、电子结构和自旋磁矩等性质随薄膜厚度(1-18ML)的变化行为。原子的吸附能随薄膜厚度的增加表现出与清洁薄膜表面能相一致的量子振荡趋势,反映了吸附能的量子尺寸效应。Cr、Mn原子的吸附能比较接近,明显小于Fe和Co的情况。Cr和Mn吸附后,体系总的自旋磁矩展现出与清洁薄膜表面表面能反相的振荡趋势,这源于Pb(111)表面6p传导电子自旋极化程度的量子振荡行为。而Fe和Co吸附后,体系总的磁矩随薄膜厚度增加的变化无规律。根据吸附原子与表面相互作用的强弱和表面传导电子对吸附原子的磁屏蔽效应的振荡行为,我们理论上预言Cr、Mn原子在Pb(111)薄膜上的近藤效应会受到金属薄膜量子尺寸效应的调制。
第二部分内容中,第五、六章的两个工作分别系统研究了两类金属表面Pb(111)和Be(0001)的初始表面氧化。
对于Pb(111)表面的初始氧化,我们强调O_2解离后O原子与金属表面的相互作用,系统研究了从0.11 ML到1ML的覆盖度范围内O原子在Pb(111)表面和次表面的吸附性质;计算出O原子在表面和次表面的扩散能量势垒,以及O原子从表面到次表面渗透势垒。整个覆盖度范围内fcc位和tetra-Ⅱ分别是O在表面和次表面的最佳吸附位置。O原子在最佳吸附位置的结合能均随着覆盖度的增加单调递增,意味着O吸附原子间存在相互吸引的有效相互作用,趋于在Pb(111)表面和次表面形成团簇。在整个覆盖度范围内,O吸附原子在Pb(111)次表面的吸附更加稳定。O原子在Pb(111)表面和次表面的扩散势垒受覆盖度影响明显,随覆盖度的增加而增大。我们发现低覆盖度时O从面上hcp位到次表面tetra-Ⅰ位的渗透势垒仅为0.065 eV。表明O_2在Pb(111)表面分解后,即使在低覆盖度下O也会很容易渗透到次表面与第二层Pb原子耦合成键。我们对O/Pb(111)吸附体系的其它性质进行了细致地计算讨论,包括电荷重新分布、原子结构的层间弛豫、功函数和电子态密度.我们发现在Pb(111)表面氧化过程中O-Pb化学键具有离子-共价性相混合的特征:离子性体现在Pb-6p电子向O-2p轨道的转移;而共价性表现在Pb失掉6p电子后,Pb-6s~2孤对电子与O-2p电子态的杂化。
对于Be(0001)的表面氧化,我们着重来看O_2在Be(0001)表面的吸附性质和分解过程。计算结果区分了O_2的物理和化学吸附态,分别出现在平行表面和垂直表面的通道中。我们分析了最稳定的分子化学吸附态(HH-Z通道)的电子结构,发现O_2反键态分子轨道π_p~*自旋上电子向表面Be原子空态的转移,以及表面Be原子占据态电子对O_2反键态分子轨道π_p~*自旋下空态的反哺,同时O_2与Be(0001)表面原子间存在明显的共价键。通过计算绝热等势能面来确定O_2在Be(0001)表面的解离路径,发现沿T-Y通道是O_2解离的最佳通道,解离能量势垒为0.23 eV。在sp-简单金属表面氧化的研究工作中,我们首次理论上报道了O_2分解时存在绝热势垒。
最后,我们在DFT+U的理论框架下,对PuO_2和β-Pu_2O_3的铁磁、反铁磁和非磁三种结构展开了系统计算。我们发现LDA+U和GGA+U(U=4 eV)都能改进传统的密度泛函理论计算,给出能够和实验结果相吻合的Pu氧化物电子结构,并确认PuO_2和β-Pu_2O_3的基态为反铁磁性质。对U参数的考虑促使Pu-5f电子在费米能级处发生劈裂,从而导致了金属-绝缘体转变,且两种钚氧化物绝缘体能隙随U参数增大而增大。此外,我们计算了β-Pu_2O_3到PuO_2的氧化反应的反应能,结果显示该氧化过程是一个放热过程,与实验上观测到150-200℃Pu的自燃现象对应。
By using first-principles calculations based on the density functional theory(DFT),the dissertation is devoted to the study of the micro-mechanism of the interactions between adatoms/molecules and metal surfaces.The main content includes three parts:(Ⅰ) the quantum size effect(QSE) of metal thin film and its modulation on surface energetics and surface chemical reactivities;(Ⅱ) the incipient oxidation of metal surfaces;(Ⅲ) studying the electronic structure and properties of strongly-correlated materials PuO_2 and Pu_2O_3 with DFT+U approach.
For partⅠ,studies in chapter 3 and chapter 4 systematically calculate the QSE of Cu(001) and Pb(111) thin films,respectively.
In chapter 3,first-principles calculations of Cu(001) free-standing thin films with thickness ranging from 1 monolayer(ML) to 26ML,have been performed to investigate the oscillatory quantum size effects exhibited in surface energy,work function,atomic relaxation.Quantum well states have been identified and clarified at particular k points corresponding to the stationary extrema in the bulk Brillouin zone,and are in good agreement with experimental observations.Furthermore, we have investigated Cs adsorption onto Cu(001) thin films as a function of the film thickness. The calculated surface properties clearly feature quantum oscillations as a function of the film thickness,with oscillation periods characterized by a superposition of long and short length scales, due to the quantum interference between the 'Belly'-and 'Neck' -orbital on the bulk Fermi surface of noble metals.Our systematically calculated results clearly show large-amplitude quantum oscillations in adsorption energetics,which may be used to tailor catalysis,chemical reactions, and other surface processes in nanostructured materials.
In chapter 4,we carry out the first-principles calculations Pb(111) films up to 18 ML to investigate the quantum size effects exhibited in the surface energetics and magnetic properties after the monatomic adsorption of 3d-metal,including Mn,Cr,Fe and Co atom.The oscillatory behavior of adsorption energy as a function of the thickness of Pb(111) thin film is same with that of the surface energy of the clean Pb(111) film,which indicate the prototype of QSE in Pb(111) film.The adsorption energy of Cr or Mn adatom is quantitatively much lower than that of Fe or Co adatom,which show the relatively weak interaction between Cr or Mn adatom and outmost Pb atoms.The oscillation in the total magnetic moment of Cr/Pb(111) or Mn/Pb(111) adsorption systems takes on regular oscillation with a period of two Pb monolayers,and is notably different from Fe/Pb(111) or Co/Pb(111) systems,where the oscillation is irregular.The regular oscillation in the magnetic moment can be attributed to the various spin-polarization of Pb(111)-surface conduction electrons modulated by the QSE of Pb(111).According to the adatom-substrate interaction and the screening effect from the surface conduction electrons,we theoretically predict that the QSE of Pb(111) thin film will modulate the Kondo effect of Cr or Mn adatom.
For partⅡ,studies in chapter 5 and chapter 6 systematically explore the incipient oxidation of Pb(111) and Be(0001) surfaces,respectively.
In chapter 5,we focus on the interaction between atomic oxygen and Pb(111) surface after the molecular dissociation.The atomic and energetic properties of purely on-surface and subsurface oxygen structures at the Pb(111) surface are systematically investigated for a wide range of coverage and adsorption sites.The fcc and tetra-Ⅱsites are found to be energetically preferred for the onsurface and subsurface adsorption,respectively,in the whole range of coverage considered.The on-surface and subsurface oxygen binding energies monotonically increase with the coverage,and the latter is always higher than the former,thus indicating a tendency to the formation of oxygen islands(clusters) and the higher stability of subsurface adsorption.The on-surface and subsurface diffusion path energeties of atomic oxygen,as well as the activation barriers for oxygen penetration from the on-surface to the subsurface sites,are presented at low and high coverage.The activation barrier for the on-surface or the subsurface O diffusion becomes high when increasing the coverage. In particular,we have shown that the activation barrier for the penetration from the on-surface hcp to the subsurface tetra-Ⅰsite is as low as 0.065 eV,which indicates that the oxygen atoms can directly incorporate into the lead below the topmost Pb layer right after on-surface O_2 dissociation at low coverage.The other properties of the O/Pb(111) system,including the charge distribution, the lattice relaxation,the work function,and the electronic density of states,are also studied and discussed in detail.It is pointed out that the O-Pb chemical bonding during surface oxidation displays a mixed ionic/covalent character.Here the ionicity is featured by a charge flow from Pb-6p to O-2p states,while the covalency is featured by the Pb-6s~2 'lone pair' effect,which results from hybridization of Pb 6s and O 2p states.
In chapter 6,the focus of our interest is the adsorption and dissociation of molecular oxygen on the Be(0001) surface.The physisorbed and chemisorbed molecular precursor states are identified to be along the parallel and vertical channels,respectively.It is shown that the vertical channel with O_2 being at the hcp hollow sites of the Be(0001) surface is the most stable channel for the molecular chemisorption.The electronic and magnetic properties of this most stable chemisorbed molecular state are studied,which show that the electrons transfer forth and back between the spinresolved antibondingπ~* molecular orbitais and surface Be sp states.A distinct covalent weight in the molecule-metal bond is also shown.The dissociation of O_2 is determined by calculating the adiabatic potential energy surfaces,wherein the T-Y channel is found to be most stable and favorable for dissociative adsorption of O_2.Remarkably,we predict that unlike other simple sp metal surfaces such as Al(111) and Mg(0001),the adiabatic dissociation process of O_2 at Be(0001) is an activated type with a sizeable energy barrier(0.23 eV).
In the end,the electronic structure and properties of PuO_2 andβ-Pu_2O_3 of different magnetic structures,including ferromagnetism,anti-ferromagnetism and non-magnetism,have been studied from first principles.The LDA+U and the GGA+U formalisms have been used to account for the strong on-site Coulomb repulsion among the localized Pu 5f electrons.We discuss how the properties of PuO_2 and Pu_2O_3 are affected by the choice of U as well as the choice of exchangecorrelation potential.Our results show that by choosing an appropriate U=4 eV,it is promising to correctly and consistently describe atomic structure and anti-ferromagnetic properties of PuO_2 andβ-Pu_2O_3.The inclusion of nonzero U forces the Pu-5f band to split at the Fermi level and,thus, drives the metallic-insulating transition.The insulating band gaps for PuO_2 andβ-Pu_2O_3 have been shown as a function of U.Also,oxidation reaction of Pu_2O_3,leading to formation of PuO_2, and its dependence on U and exchange-correlation potential have been studied.Our results show that the oxidation process of theβ-Pu_2O_3 is an exothermic reaction,which is mostly responsible for the experimentally observed plutonium pyrophoricity at 150-200℃.
引文
[1]张立德,牟季美,著,纳米材料和纳米结构,科学出版社(2001).
[2]W.P.Halperin,Rev.Mod.Phys.58,532(1986);P.Ball,and L.Garwin,Nature 355,761(1992).
[3]M.Haruta,Catal.Today 36,153(1997).
[4]徐亚伯,表面物理导论,中国杭州,浙江大学出版社,1992.
[5]R.M.Martin,electronic structure:basic theory and practical methods,(Cambridge University Press,Cambridge,2004)
[6]T.Ando,Y.Arakawa,K.Furuya,S.Komiyama and H.Nakashima,Mesoscopic Physics and Electronics,(Springer Express 1998).
[7]B.V.Zeghbroeck,Principles of Semiconductor Devices,Colarado University;D.A.B.Miller,Semiconductor Optoelectronics Devices,Stanford University.
[8]T.-C.Chiang,Surf.Sci.Pep.39,181(2000).
[9]M.Mihn,P.Pervan,and D.P.Woodruff,Rep.Prog.Phys.65,99(2002).
[10]P.M.Echenique and J.B.Pendry,J.Phys.C 11,2065(1978).
[11]N.V.Smith,Phys.Rev.B 32,3549(1985).
[12]姜鹏.量子阱态调制金属表面化学活性的STM研究.博士学位论文,北京:中国科学院物理研究所,(2007).
[13]P.Grunberg,R.Schreiber,Y.Pang,et al,Phys.Rev.Lett.57,2442(1986).
[14]S.S.P.Parkin,et al,Phys.Rev.Lett.64,2304(1990);
S.S.P.Parkin,et al,Phys.Rev.Lett.66,2152(1991);
S.S.P.Parkin,Phys.Rev.Lett.67,3598(1991).
[15]S.N.Okuno and K.Inomata,Phys.Rev.Lett.72,1553(1994);
J.Mathon,M.Villeret,R.B.Muniz,J.A.e Castro,and D.M.Edwards,Phys.Rev.Lett.74,3696(1995);
P.Segovia,E.G.Michel,and J.E.Ortega,Phys.Rev.Lett.77,3455(1996);
F.J.Himpsel,J.Phys.Condens.Matter.11,9483(1999);
F.G.Curti,A.Danese,and R.A.Bartynski,Phys.Rev.Lett.80,2213(1998).
[16]R.K.Kawakami,E.Rotenberg,E.J.Eecorcia-Aparicio,H.J.Choi,T.R.Cummins,J.G.Tobin,N.V.Smith,and Z.Q.Qin,Phys.Rev.Lett.80,1754(1998);R.K.Kawakami,E.Rotenberg,E.J.Escorcia-Aparicio,H.J.Choi,J.H.Wolfe,N.V.Smith,and Z.Q.Qiu,Phys.Rev.Lett.82, 4098(1999);R.K.Kawakami,E.Rotenberg,H.J.Choi,E.J.Escorcia-Aparicio,M.O.Bowen,J.H.Wolfe,E.Arenholz,Z.D.Zhang,N.V.Smith,and Z.Q.Qiu,Nature,398,132(1999).
[17]O.O.Brovko,P.A.Ignatiev,et al.,Phys.Rev.Lett.101,036809(2008).
[18]Y.Guo,Y.-F.Zhang,X.-Y.Bao,T.-Z.Han,Z.Tang,L.-X.Zhang,W.-G.Zhu,E.G.Wang,Q.Niu,Z.Q.Qiu,J.-F.Jia,Z.-X.Zhao,and Q.-K.Xue,et al.,Science 306,1915(2004);Y.-F.Zhang,J.-F.Jia,T.-Z.han,Z.Tang,Q.-T.Shen,Y.Guo,Z.Q.Qiu,and Q.-K.Xue,Phys.Rev.Lett.95,096802(2005).
[19]Li-Ying Ma,Lin Tang,Ze-Lei Guan,Ke He,Kang An,Xu-Cun Ma,Jin-Feng Jia,Qi-Kun Xue,Y.Han,Steve Huang,and Feng Liu,Phys.Rev.Lett.97,266102(2006);Xin-Yu Bao,Yan-Feng Zhang,Yupeng Wang,Jin-Feng Jia,Qi-Kun Xue,X.C.Xie,and Zhong-Xian Zhao,Phys.Rev.Lett.95,247005(2005).
[20]Nφskov J K.,Pep.Prog.Phys.53,1253(1990).
[21]杨宇.若干与吸附相关的表面问题的第一原理研究.博士学位论文,北京:清华大学,(2008).
[22]H.Brune,J.Wintterlin,J.Trost,G.Ertl,et al.,J.Chem.Phys.99,2128(1993).
[23]L.(O|¨)sterlund,I.Zoric,and B.Kasemo,Phys.Rev.B 55,15452(1997).
[24]A.Hellman,Phys.Rev.B 72,201403(R)(2005).
[25]L.Aballe,A.Barinov,et al.,Phys.Per.Lett.93,196103(2004).
[26]T.Sasaki and T.Ohno,Phys.Rev.B 60,7824(1999);K.Honkala and K.Laasonen,Phys.Rev.Lett.84,705(2000).
[27]Y.Yourdshahyan,B.Razaznejad,and B.I.Lundqvist,Solid State Commun.117,531(2001).
[28]Y.Yourdshahyan,B.Razaznejad,and B.I.Lundqvist,Phys.Rev.B 65,075416(2002).
[29]J.Behler,B.Delley,S.Lorenz,K.Reuter,and M.Scheffler,Phys.Rev.Lett.94,036104(2005);J.Behler,K.Reuter,and M.Scheffler,Phys.Rev.B 77,115421(2008).
[30]X.L.Fan,W.M.Lan,and Z.F.Liu,Phys.Rev.Lett.96,079801(2006).
[31]K.Th(u|¨)rmer,E.Williams,and J.Reutt-Robey,Science 297,2033(2002).
[32]P.Jiang,X.Ma,L.L.Wang,Y.S.Fu,S.H.Ji,Y.Qi,J.Jia,and Q.-K.Xue,to be published.
[33]X.Ma,P.Jiang,Y.Qi,J.Jia,Y.Yang,W.Duan,W.-X.Li,X.Bao,S.-B.Zhang,and Q.-K.Xue,Proc.Natl.Acad.Sci.U.S.A.104,9204(2007).
[34]P.Jiang,X.Ma,Y.Yang,Y.X.Ning,L.L.Wang,Y.S.Fu,S.H.Ji,Y.Qi,W.Duan,S.-B.Zhang,J.Jia,and Q.-K.Xue,to be published.
[35]王广涛.过渡金属氧化物第一性原理计算研究,博士学位论文,北京:中国科学院物理研究所,(2008).
[36]K.T.Moore,G.Laan,Rev.Mod.Phys.81,000235(2009) and references therein.
[37]李震宇.新材料物性的第一性原理研究,博士学位论文,安徽合肥:中国科学技术大学,(2004).
[38]P.A.M.Dirac,The principles of quantum mechanics(Clarendon Press,Oxford,1958).
[39]E.Schr(o|¨)dinger,Ann.der.Phys.79,36(1926).
[40]W.K.Heisenberg,Z.Phys.33,879(1925)
[41]W.Kohn,Nobel Lecture:Electronic structure of matter-wave functions and density functionals.Rev.Mod.Phys.71,1253(1998).
[42]P.Hohenberg and W.Kohn,Phys.Rev.B 133,864(1964).
[43]W.Kohn and L.J.Sham,Phys.Rev.A 140,1133(1965).
[44]R.M.Dreizler and E.K.U.Gross,Density Functional Theory,(Springer,1990).
[45]R.G.Parr and W.Yang,Density-Functional Theory of Atoms and Molecules,(Oxford university Press,New York,1989).
[46]M.Koch and M.C.Holthausen,A Chemist's Guide to Density Functional Theory,(Wiley-VCH,Weinheim,1990).
[47]谢希德,固体能带理论,中国上海,复旦大学出版社,1998.
[48]M.Born and J.R.Oppenheimer,Ann.Physik 84,457(1927).
[49]M.Born and K.Huang,Dynamical Theory of Crystal Lattice,(Oxfort Uni-versity Press,1954).
[50]D.R.Hartree,Proc.Cam.Phil.Soc 24,89(1928).
[51]V.Fork,Z.Phys 61,209(1930).
[52]H.Thmos,Proc.Camb.phil.Soc.23,542(1927).
[53]E.Fermi,Accad.Naz.Lincei.7,602(1927).
[54]J.Grotendorst,S.BlA(u|¨)gel,and D.Marx,Computational Nanoscience:Do It Yourself! NIC Series 31,48(2006).
[55]D.M.Ceperley and B.J.Alder,Phys.Rev.Lett 45,566(1980).
[56]J.P.Perdew and A.Zunger,Phys.Rev.B 23,5048(1981).
[57]J.P.Perdew and Y.Wang,Phys.Rev.B 45,13244(1992).
[58]S.H.Vosko,et al.,Can.J.Phys 58,1200(1980).
[59]J.P.Perdew,et al.,Phys.Rev.Lett 77,3865(1996).
[60]J.P.Perdew,et al.,Phys.Rev.B 46,6671(1992)
[61]A.D.Becke,Phys.Rev.A as,3098(1988).
[62]C.Lee,et al.,Phys.Rev.B 37,785(1988).
[63]A.E.Mattsson,et al,Modelling Simul.Mater.Sci.Eng.R 13,1(2005).
[64]A.D.Becke J.Chem.Phys 98,5648(1993);P.J.Stephens et al J.Phys.Chem 98,11623(1994).
[65]J.P.Perdew and K.Schmidt,Density Functional Theory and Its Application to Materials vol CP577,ed.V Van Doren et al,(American Institute of Physics,Melville,NY 2001).
[66]J.Tao,et al.,Phys.Rev.Lett 91,146401(2003).
[67]R.Armiento and A.E.Mattsson,Phys.Rev.B 66,74(2002).
[68]Y.Andersson,et al.,Phys.Rev.Left 76,102(1996);E.Hult,et al.,Phys.Rev.Left 77,2029(1996);H.Rydberg,et al.,Phys.Rev.Lett 91,126402(2003);M.Dion,et al.,Phys.Rev.Lett 92,246401(2004).
[69]W.Kohn,et al.,Phys.Rev.Lett 80,4153(1998).
[70]J.F.Dobson and J.Wang,Phys.Rev.Lett 82,2123(1999).
[71]A.E.Mattsson and W.Kohn,J.Chem.Phys 115,3441(2001).
[72]K.Carling,et al.,Phys.Rev.Lett 85,3862(2000).
[73]T.R.Mattsson and A.E.Mattsson,Phys.Rev.B 66,214110(2002).
[74]A.E.Mattsson and D.R.Jennison,Surf.Sci.Lett.L 520,661(2002).
[75]V.N.Staroverov,et al.,J.Chem.Phys 119,12129(2003).
[76]J.P.Perdew and A.Zunger,Phys.Rev.B 23,5048(1981);P.Svane and O.Gunanrsson,Phys.Rev.Lett.65,1148(1990).
[77]K.Burke,et al.,A Guided Tour of Time-Dependent Density Functional Theory in Springer Lecture Notes in Physics,1998.
[78]S.Baroni,et al.,Rev.Mod.Phys.73,515(2001)
[79]V.I.Anisimov,J.Zaanen,and O.K.Andersen,Phys.Rev.B 44,943(1991).
[80]A.Georges,et al.,Rev.Mod.Phys.68,13(1996).
[81]J.C.Slater,Phys.Rev.51,846(1937).
[82]Vanderbilt,Phys.Rev.B,41,7892(1990).
[83]G.Kresse and J.Hafner,Phys.Rev.B 47,558(1993);
[84]G.Kresse and J.Furthm(u|¨)ller,Comput.Mater.Sci.6,15(1996);
[85]G.Kresse and J.Furthm(u|¨)ller,Phys.Rev.B 54,11169(1996).
[86]G.Kresse and D.Joubert,Phys.Rev.B 59,1758(1999).
[87]M.Bockstedte,A.Kley,J.Nengebauer,and M.Scheffler,Comput.Phys.Commun.107,187(1997).
[88]P.S.Bl(o|¨)chl,Phys.Rev.B 50,17953(1994).
[89]P.E.Bl(o|¨)chl,O.Jepsen,and O.K.Andersen,Phys.Rev.B 49,16223(1994).
[90]H.J.Monkhorst and J.D.Pack,Phys.Rev.B 13,5188(1976).
[91]J.P.Perdew,et al.,Phys.Rev.B 46,6671(1992).
[92]M.Weinert and J.W.Davenport,Phys.Rev.B 45,13709(1992).
[93]Princinciples of Surface Physics,edited by F.Bechstedt(Springer,Verlng Berlin Heidelberg,2003).
[94]J.Neugebauer and M.Scheffler,Phys.Rev.B 46,16067(1992).
[95]J.-J.Paggel,T.Miller,and T.-C.Chiang,Science 283,1709(1999).
[96]Z.Tesanovic,M.V.Jaric,and S.Maekawa,Phys.Rev.Lett.57,2760(1986).
[97]A.E.Meyerovich and S.Stepaniants,Phys.Rev.Lett.73 316(1994).
[98]A.Kawabata,J.Phys.Soc.Jpn.62,3988(1993).
[99]M.Hupalo,S.Kremmer,V.Yeh,L.Berbil-Bautista,and M.C.Tringides,Surf.Sci.493,526(2001);M.Hupalo and M.C.Tringides,Phys.Rev.B 65,115406(2002).
[100]W.B.Su,S.h.Chang,W.B.Jian,et al.,Phys.Rev.Lett.86,5116(2001).
[101]R.Otero,A.L.Vazquez de Parga,and R.Miranda,Phys.Rev.B 66,115401(2002).
[102]H.Hong,C.M.Wei,M.Y.Chou,et al.,Phys.Rev.Lett.90,076104(2003).
[103]D.-A.Luh,T.Miller,J.J.Paggel,M.Y.Chou,and T.-C.Chiang,Science 292,1131(2001).
[104]For a review,see Z.Q.Qiu and N.V.Smith,J.Phys.:Condens.Matter 14,R169,and references therein.
[105]M.N.Baibich,J.M.Broto,A.Fert,F.Nguyen Van Dau,F.Petroff,P.Etienne,G.Creuzet,A.Friederich,and J.Chazelas,Phys.Rev.Lett.61,2472(1988).
[106]J.E.Ortega and F.J.Himpsel,Phys.Rev.Lett.69,844(1992).
[107]P.Bruno,J.Magn.Magn.Mater.121,248(1993).
[108]D.M.Edwards,et al.,Phys.Rev.Lett.67,493(1991).
[109]M.Kralj,A.Siber,P.Pervan,M.Milun,T.Valla,P.D.Johnson,and D.P.Woodruff,Phys.Rev.B 64,085411(2001).
[110]See,for example,S.A.Lindgren and L.Wallden,Phys.Rev.Lett.59,3003(1987).
[111]N.V.Smith,N.B.Brookes,Y.Chang,and P.D.Johnson,Phys.Rev.B 49,332(1994).
[112]V.L.Moruzzi,J.F.Janak,and A.R.Williams,Calculated Electronic Properties of Metals(Pergamon,New York,1978).
[113]Y.Wang,Z.-Y.Lu,X.-G.Zhang,and X.F.Han,Phys.Rev.Lett.97,087210(2006).
[114]P.J.Feibelman,Phys.Rev.B 27,1991(1983).
[115]A.Kiejna,J.Peisert,and P.Schraroeh,Surf.Sci.432,54(1999).
[116]S.Ciraci and I.P.Batra,Phys.Rev.B 33,4294(1985);I.P.Batra,S.Ciraci,G.P.Srivastava,J.S.Nelson,and C.Y.Fong,Phys.Rev.B 34,8246(1986).
[117]J.C.Boettger and S.B.Trickey,Phys.Rev.B 45,1363(1992);U.Birkenheuer,J.C.Boettger,and N.R(o|¨)sch,Chem.Phys.Lett.341,103(1995);K.F.Wojciechowski and H.Bogdanow,Surf.Sci.397,53(1998);K.Doll,N.M.harrison,and V.R.Saunders,J.Phys.:Condens.Matter 11,5007(1999).
[118]J.M.Carlsson and B.Hellsing,Phys.Rev.B 61,13 973(2000).
[119]C.M.Wei and M.Y.Chou,Phys.Rev.B 66,233408(2002).
[120]C.M.Wei and M.Y.Chou,Phys.Rev.B 68,125406(2003).
[121]P.Lazic,Z.Crljen,and R.Brako,Phys.Rev.B 71,155402(2005).
[122]D.Yu,M.Scheffler,and M.Persson,Phys.Rev.B 74,113401(2006).
[123]A.Ayuela,E.Ogando,and N.Zabala,Phys.Rev.B 75,153403(2007).
[124]D-J.Huang,P.D.Jhonson,and X.shi,Phys.Rev.B 54,17123(1996).
[125]F.G.Curti,A.Danese,and R.A.Bartynski,Phys.Lett.80,2213(1998)
[126]R.Kl(a|¨)sges,D.Schmitz,C.Carbone,W.Eberhardt,P.Lang,R.Zeller,and P.H.Dederichs,Phys.Rev.B 57,R969(1998).
[127]R.K.Kawakami,E.Rotenberg,and Ernesto J.Escorcia-Aparicio,Phys.Lett.82,4098(1999).
{128]Y.Z.Wu,C.Y.Won,E.Rotenberg,H.W.Zhao,F.Toyoma,N.V.Smith,and Z.Q.Qiu,Phys.Rev.B 66,245418(2002).
[129]A.Danese and R.A.Bartynski,Phys.Rev.B 65,174419(2002).
[130]J.M.An,D.Raczkowski,Y.Z.Wu,C.Y.Won,L.W.Wang,A.Canning,M.A.Van Hove,E.Rotenberg,and Z.Q.Qiu,Phys.Rev.B 68,045419(2003).
[131]Y.Z.Wu,A.K.Schmid,M.S.Altman,X.F.Jin,and Z.Q.Qiu,Phys.Lett.94,027201(2005).
[132]Eli Rotenberg,Y.Z.Wu,J.M.An,M.A.Van Hove,A.Canning,L.W.Wang,and Z.Q.Qiu,Phys.Rev.B 68,075426(2006).
[133]Y.Z.Wu,C.Won,E.Rotenberg,H.W.Zhao,Q.-K.Xue,W.Kim,T.L.Owens,N.V.Smith,and Z.Q.Qiu,Phys.Rev.B 73,125333(2006).
[134]W.L.Ling,Eli Rotenberg,H.J.Choi,J.H.Wolfe,F.Toyama,Silena Paik,N.V.Smith,and Z.Q.Qiu,Phys.Rev.B 65,1134066(2002).
[135]Chiara Baldacchini,Letizia Chiodo,F.Allegretti,Carlo Mariani,Maria Grazia Betti,P.Monachesi,and R.Del Sole,Phys.Rev.B 68,190519(2003).
[136]F.Bisio,M.Nyvlt,J.Franta,H.Petek,and J.Kirschner,Phys.Rev.Lett.96,087601(2006).
[137]M.Bauer,S.Pawlik,and M.Aeschlimann,Phys.Rev.B 55,10040(1997).
[138]S.Ogawa,H.Nagano,and H.Petek,Phys.Rev.Lett.82,1931(1999).
[139]A.G.Borisov,J.P.Gauyacq,A.K.Kazansky,E.V.Chulkov,V.M.Silkin,and P.M.Echenique,Phys.Rev.Lett.86,488(2001).
[140]J.P.Ganyacq,A.G.Borisov,and A.K.Kazansky,Appl.Phys.A 78,141(2004).
[141]C.Corriol,V.M.Silkin,D.Sanchez-Portal,A.Arnau,E.V.Chulkov,P.M.Echenique,T.von Hole,J.Kliewer,J.Kr(o|¨)ger,and R.Berndt,Phys.Rev.Lett.95,176802(2005).
[142]Th.yon Hole,J.Kro|¨)ger,and R.Berndt,cond-mat/0603551.
[143]D.V.Chudinov,S.E.Kul'kova,and I.Yu.Smolin,Physics of the Solid State 45,590(2003).
[144]R.-Q.Wu and D.-S.Wang,Phys.Rev.B 41,12541(1990).
[145]K.Wandelt,in Physics and Chemistry of Alkali Metal Adsorption,edited by H.P.Bonzel,A.M.Bradshaw,and G.Ertl(Elsevier,Amsterdam,1989).
[146]L.Aballe,A.Barinov,A.Locatelli,S.Heun,and M.Kiskinova,Phys.Rev.Lett.93,196103(2004).
[147]Y.Z.Wu,privite communication.
[148]C.Kittel,Introduction to Solid State Physics,5th ed.(Wiley,New York,1976).
[149]R.K.Kawakmi et al.,Phys.Rev.Lett.80,1754(1998).
[150]E.G.McRae and M.L.Kane,Surf.Sci.108,435(1981).
[151]V.Fiorentini and M.Methfessel,J.Phys.:Condens.Matter 8,6525(1996).
[152]Z.Y.Zhang,Q.Niu,and C.K.Shih,Phys.Rev.Lett.80,5381(1998).
[153]Note that the first derivative of the total energy has also been successfully used to study the stability of nanostructures.
[154]H.-R.Tang,W.-N.Wang,and K.-N.Fan,Chem.Phys.Lett.355,410(2002).
[155]J.J.Paggei,C.M.Wei,M.Y.Chou,D.-A.Luh,T.Miller,and T.-C.Chiang,Phys.Rev.B 66,233403(2002).
[156]Juarez L.F.Da Silva,K.Schroeder,and S.Bl(u|¨)gel,Phys.Rev.B 69,245411(2004).
[157]A.G.Danese,F.G.Curti,and R.A.Bartynski,Phys.Rev.B 70,165420(2004).
[158]W.Berndt,D.Weick,C.Stampfl,A.M.Bradshaw,and M.Sche er,Surf.Sci.330,182(1995).
[159]S.Andersson and J.B.Pendry,Solid States Commun.16,563(1975).
[160]J.E.Demuth,D.W.Jepsen,and P.M.Marcus,J.Phys.C(Solid States Phys.) 8,L25(1975).
[161]C.yon Eggeling,G.Schmidt,G.Besold,L.Hammer,K.Heinz,and K.M(u|¨)ller,Surf.Sci.221,11(1989).
[162]S.Aminpirooz,A.Schmalz,L.Becker,N.Pangher,J.Haase,M.M.Nielsen,D.R.Batchelor,E.Bφgh,and D.L.Adams,Phys.Rev.B 46,15594(1992).
[163]U.Muschiol,P.Bayer,K.Heinz,W.Oed,and J.B.Pendry,Surf.Sci.275,185(1992).
[164]S.Mizuno,H.Tochihara,and T.Kawamura,Surf.Sci.293,239(1993).
[165]D.A.Arena,F.G.Curti,and R.A.Bartynski,Phys.Rev.B 56,15404(1997).
[166]E.Wimmer,A.J.Freeman,J.R.Hiskes,and A.M.Karo,Phys.Rev.B 28,3074(1983).
[167]P.Nordlander and J.C.Tully,Phys.Rev.B 42,5564(1990).
[168]H.Ishida,Phys.Rev.B 38,8006(1988);H.Ishida and A.Liebsch,Phys.Rev.B 45,6171(1992).
[169]D.M.Newns,Phys.Rev.178,1123(1969).
[170]J.K.Norskov,Rep.Prog.Phys.53,1253(1990).
[171]M.Kralj,A.Siber,P.Pervan,M.Milun,T.Valla,P.D.Johnson,and D.P.Woodruff,Phys.Rev.B 64,085411(2001).
[172]J.M.Carlsson and B.Hellsing,Phys.Rev.B 61,13 973(2000).
[173]C.M.Wei and M.Y.Chou,Phys.Rev.B 75,195417(2007).
[174]J.Kondo,Prog.Theor.Phys.32,37(1964).
[175]A.C.Hewson,The Kondo Problem to Heavy Fermions(Cambridge University Press,Cambridge,England,1993).
[176]V.Madhavan,W.Chen,T.Jamneala,M.F.Crommie,and N.S.Wingreen,Science 280,567(1998).
[177]P.Wahl,L.Diekhoner,M.A.Schneider,L.Vitali,G.Wittich,and K.Kern,Phys.Rev.Lett.93,176603(2004);N.Quaas,M.Wenderoth,A.Weismann,R.G.Ulbrich,and K.Schonhammer,Phys.Rev.B 69,201103(R)(2004).
[178]J.Li,W.-D.Schneider,R.Berndt,and B.Delley,Phys.Rev.Lett.80,2893(1998).
[179]A.Yazdani,B.A.Jones,C.P.Lutz,M.F.Crommie,and D.M.Eigler,Science 275,1767(1997).
[180]A.J.Heinrich,J.A.Gupta,C.P.Lutz,and D.M.Eigler,Science 306,466(2004)
[181]P.Wahl,L.Diekh(o|¨)ner,G.Wittich,L.Vitali,M.A.Schneider,and K.Kern,Phys.Rev.Lett.95,166601(2005).
[182]A.Zhao et al.,Science 309,1542(2005).
[183]V.Iancu,A.Deshpande,and S.-W.Hla,Nano Lett.6,820(2006).
[184]V.Iancu,A.Deshpande,and S.-W.Hla,Phys.Rev.Lett.97,266603(2006).
[185]L.Gao et al.,Phys.Rev.Lett.99,106402(2007).
[186]P.Czoschke,H.Hong,L.Basile,and T.-C.Chiang,Phys.Rev.Lett.91,226801(2003);P.Czoschke,H.hong,L.Basile,and T.-C.Chiang,Phys.Rev.Lett.93,036103(2004);M.H.Upton,C.M.Wei,M.Y.Chou,T.Miller,and T.-C.Chiang,Phys.Rev.Lett.93,026802(2004);D.A.Ricci,T.Miller,and T.-C.Chiang,Phys.Rev.Lett.93,136801(2004);M.H.Upton,T.Miller,and T.-C.Chiang,Phys.Rev.B 71,033403(2005);P.Czoschke,H.Hong,L.Basile,and T.-C.Chiang,Phys.Rev.B 72,075402(2005).
[187]J.H.Dil,J.W.Kim,S.Gokhale,M.Tallarida,and K.Horn,Phys.Rev.B 70,045405(2004).
[188]Z.Y.Zhang,Q.Niu,and C.K.Shih,Phys.Rev.Lett.80,5381(1998).
[189]T.-L.Chan,C.Z.Wang,M.Hupalo,M.C.Tringides,and K.M.Ho,Phys.Rev.Lett.96,226102(2006).
[190]Mustafa M.(O|¨)zer,Yu Jia,Biao Wu,Zhenyu Zhang,and Hanno H.Weitering,Phys.Rev.B 72,113409(2005).
[191]Y.Jia,B.Wu,H.H.Weltering,and Z.Y.Zhang,Phys.Rev.B 74,035433(2006).
[192]V.Yeh,L.Berbil-Bantista,C.Z.Wang,K.M.Ho,and M.C.Tringides,Phys.Rev.Lett.85,5158(2000).
[193]W.B.Su,S.H.Chang,W.B.Jian,C.S.Chang,L.J.Chen,and T.T.Tsong,Phys.Rev.Lett.86,5116(2001).
[194]Roberto Otero,Amadeo L.Vazquez de Parga,and Rodolfo Miranda,Phys.Rev.B 66,115401(2002).
[195]E.Ogando,N.Zabala,E.V.Chulkov,and M.J.Puska,Phys.Rev.B 69,153410(2004);E.Ogando,N.Zabala,E.V.Chulkov,and M.J.Puska,Phys.Rev.B 71,205401(2005);A.Ayuela,E.Ogando,and N.Zabala,Phys.Rev.B 75,153403(2007).
[196]Giuliana Materzanini,Peter Saalfrank,and Philip J.D.Lindan,Phys.Rev.B 63,235405(2001).
[197]A.A.Shanenko,M.D.Croitoru,and F.M.Peeters,Phys.Rev.B 75,014519(2007).
[198]P.S.Kirchmann,M.Wolf,J.H.Dil,K.Horn,and U.Bovensiepen,Phys.Rev.B 76,075406(2007).
[199]J.H.Dil,T.U.Kampen,B.H(u|¨)sen,T.Seyller,and K.Horn,Phys.Rev.B 75,161401(R)(2007).
[200]C.A.Jeffrey,E.H.Conrad,R.Feng,M.Hupalo,C.Kim,P.J.Ryan,P.F.Miceli,and M.C.Tringides,Phys.Rev.Left.96,106105(2006).
[201]Shao-Chun Li,Xucun Ms,Jin-Feng Jia,Yan-Feng Zhang,Dongmin Chen,Qian Niu,Feng Liu,Paul S.Weiss,and Qi-Kun Xue,Phys.Rev.B 74,075410(2006).
[202]Peng Jiang,Xucun Ma,Yanxiao Ning,Canli Song,Xi Chen,Jin-Feng Jia,and Qi-Kun Xue,JACS 130,7790(2008)
[203]Ying-Shuang Fu,Shuai-Hua Ji,Xi Chen,Rui Wu,Chen-Chen Wang,Wen-Hui Duan,Xiao-Hui Qiu,Bo Sun,Ping Zhang,Jin-Feng Jia,and Qi-Kun Xue,Phys.Rev.Lett.99,256601(2007).
[204]S.H.Ji,T.Zhang,Y.S.Fu,X.Chen,X.C.Ma,J.Li,W.H.Duan,J.F.Jia,Q.K.Xue,Phys.Rev.Lett.100,226801(2008).
[205]Xieqiu Zhang,Aidi Zhao,Kedong Wang,and Xudong Xiao,Phys.Rev.B 78,035431(2008).
[206]W.Chen,T.Jamneala,V.Madhavan,and M.F.Crommie,Phys.Rev.B 60,8529(R)(1999);V.Madhavan,T.Jamneala,K.Nagaoka,W.Chen,Je-Luen Li,Steven G.Louie,and M.F.Crommie,Phys.Rev.B 66,212411(2002);V.S.Stepanyuk,A.N.Baranov,W.Hergert,and P.Bruno,Phys.Rev.B 68,205422(2003);P.Wahl,P.Simon,L.Diekhoner,V.S.Stepanyuk,P.Bruno,M.A.Schneider,and K.Kern,Phys.Rev.Leet.68,056601(2007).
[207]P.W.Anderson,Phys.Rev.124,41(1961).
[208]M.Alatalo,S.Jaatinen,P.Salo and K.Laasonen,Phys.Rev.B 70,245417(2004),and references therein;S.Jaatinen,J.Blomqvist,P.Salo,A.Puisto,M.Alatalo,M.Hirsim(a|¨)ki,M.Ahonen,and M.Valden,Rev.B 715,075402(2007);J.C.Yang,B.Kolasa,J.M.Gibson,and M.Yeadon,Appl.Phys.Lett.73,2841(1998).
[209]Y.Xu and M.Mavrikakis,Surf.Sci.494,131(2001);A.Soon,M.Todorova,B.Delley,and C.Stamplf,Rev.B 73,165424(2006);G.Ertl,Surf.Sci.6,208(1967);J.Haase and H.J.Kuhr,Surf.Sci.203,L695(1988);F.Jensen,F.Besenbacher,E.L(?)sgsard,and I.Stensgaard,Surf.Sci.259,L774(1991);S.M.Johnston,A.Mulligan,V.Dhanak,and M.Kadodwala,Surf.Sci.519,57(2002).
[210]M.Rocca,L.Savio,L.Vattuone,U.Burghaus,V.Palomba,N.Novelli,F.Buatier de Mongeot,and U.Valbusa,Phys.Rev.B 61,213(2000);L.Savio,L.Vattuone,M.Rocca,F.Buatier de Mongeot,G.Comelli,A.Baraldi,S.Lizzit,and G.Paohcci,Surf.Sci.506,213(2002).
[211]M.A.Barteau and R.J.Madix,J.Electron Spectrosc.Relat.Phenom.31,101(1983);C.T.Campbell and M.T.Paffett,Surf.Sci.143,517(1984);V.I.Bukhtiyarov,V.V.Kaichev,and I.P.Prosvirin,J.Chem.Phys.111,2169(1999);C.T.Cambell,Surf.Sci.173,L641(1986),and references therein.
[212]M.-L.Bocquet,A.Michaelides,P.Sautet,and D.A.King,Phys.Rev.B 68,075413(2003);G.Rovida,F.Pratesi,M.Maglietta,and E.Ferroni,Surf.Sci.43,230(1974);C.T.Campbell,Surf.Sci.157,43(1985);C.I.Carlisle,D.A.King,M.L.Bocquet,J.Cerda and P.Sautet,Phys.Rev.Lett.84,3899(2000).
[213]W.-X.Li,C.Stampfl,and M.Scheffler,Phys.Rev.B 65,075407(2002);W.-X.Li,C.Stampfl,and M.Scheffler,Phys.Rev.B 67,045408(2003).
[214]M.V.Ganduglia-Pirovano and M.Scheffler,Phys.Rev.B 59,15533(1999);M.V.Ganduglia-Pirovano,K.Reuter,and M.Scheffler,Phys.Rev.B 65,245426(2002);G.Comelli,V.R.Dhanak,M.Kiskinova,K.C.Prince,and R.Rosei,Surf.Sci.Rep.32,165(1998),and references there in;M.V.Ganduglia-Pirovano and M.Scheffler,Phys.Rev.B 59,15533(1999);J.Wider,T.Greber,E.etli,T.J.Kreutz,P.Schwaller,and J.Osterwalder,Surf.Sci.417,301(1998);432,170(1999).
[215]E.Lundgren,G.Kresse,C.Klein,M.Borg,J.N.Andersen,M.De Santis,Y.Ganthier,C.Konvicka,M.Schmid,and P.Varga,Phys.Rev.Lett 88,246103(2002),and references therein.
[216]G.Zheng and E.I.Altman,Surf.Sci.462,151(2000);A.P.Seitsonen,Y.D.Kim,S.Schwegmann,and H.Over,Surf.Sci.468,176(2000);M.Todorova,K.Reuter,and M.Scheffler,J.Phys.Chem.B 108,14477(2004);M.Todorova,K.Reuter,and M.Scheffler,Phys.Rev.B 71,195403(2005).
[217]W.-X.Li,L.(O|¨)sterlund,E.K.Vestergaard,R.T.Vang,J.Matthiesen,T.M.Pedersen,E.Laegsgaard,B.Hammer,and F.Besenbacher,Phys.Rev.Lett.93,146104(2004).
[218]J.L.Gland,Surf.Sci.93,487(1980);A.Eichler and J.Hafner,Phys.Rev.Lett.79,4481(1997);A.Bogicevic,J.Str(O|¨)mquist,and B.I.Lundqvist,Phys.Rev.B 57,4289(1998);H.Tang,A.V.der Ven,and B.L.Trout,Phys.Rev.B 70,045420(2004).
[219]K.Reuter,M.-V.Ganduglia-Pirovano,C.Stampfl,and M.Scheffler,Phys.Rev.B 65,165403(2002).
[220]C.Stampfl,S.Schwegmann,H.Over,M.Scheffler,and G.Ertl,Phys.Rev.Lett.77,3371(1996).
[221]K.Honkala,and K.Laasonen,Phys.Rev.Lett.84,705(2000).
[222]T.Sasaki,and T.Ohno,Phys.Rev.B 60,7824(1999).
[223]L.C.Ciacchi,and M.C.Payne,Phys.Rev.Lett.92,176104(2004).
[224]J.Bohler,B.Delley,S.Lorenz,K.Reuter,and M.Scheffler,Phys.Rev.Lett.94,036104(2005).
[225]J.Jacobsen,B.Hammer,K.W.Jacobsen,and J.K.Nφrskov,Phys.Rev.B 52,14954(1995).
[226]A.Kiejna and B.I.Lundqvist,Phys.Rev.B 63,085405(2001),and references therein.
[227]A.Kiejna,Phys.Rev.B 68,235405(2003).
[228]A.Hellman,Phys.Rev.B 72,201403(2005).
[229]E.Schr(o|¨)der,R.Fasel,and A.Kiejna,Phys.Rev.B 69,193405(2004).
[230]E.Schr(o|¨)der,R.Fasel,and A.Kiejna,Phys.Rev.B 69,115431(2004),and references therein.
[231]G.W.Watson,S.C.Parker,G.Kresse,Phys.Rev.B 59,8481(1999).
[232]D.J.Payne,a.G.Egdell,G.Paolicelli,F.Offi,G.Panaccione,P.Lacovig,G.Monaco,G.Vanko,A.Walsh,G.W.Watson,J.Guo,G.Beamson,P.-A.Glans,T.Learmonth,and K.E.Smith,Phys.Rev.B 75,153102(2007).
[233]To test the Pb 5d electron effect,the O/Pb(111) system has been calculated by treating Pb 5d electrons as valence electrons at a 0.25 ML coverage.The Pb 5d states are found to be localized in the deep energy levels ranging from about -17 eV to -16 eV,with a weak hybridization with O 2s states.The calculated physical properties including the binding energy,work functuion,and interlayer relaxations show that the consideration of Pb 5d electrons(as valence electrons) does not change the preferred adsorption site for on-surface and subsurface adsorption.The binding energy has a very little increase of about 0.1 eV in quantity due to the consideration of Pb 5d electrons.But the work function,the Pb-O bonding length,and the interlayer relaxations are found to be quite similar to the results without considering the Pb 5d electrons.
[234]D.Yu and M.Scheffler,Phys.Rev.B 70,155417(2004).
[235]A.Mans,J.H.Dil,A.R.H.F.Ettema,and H.H.Weitering,Phys.Rev.B 72,155442(2005).
[236]H.Krakauer,M.Posternak,A.J.Freeman,and D.D.Koelling,Phys.Rev.B 23,38.59(1981).
[237]K.P.Huber and G.Herzberg,Molecular Spectra and Molecular Structure Ⅳ:Constants of Diatomic Molecules(Van Nostrand Reinhold,New York,1979).
[238]D.J.Payns,R.G.Egdell,A.Walsh,G.W.Watson,J.Guo,P.-A.Glans,T.Learmonth,and K.E.Smith,Phys.Rev.Lett.96,157403(2006).
[239]N.D.Lang,Surf.Sci.127,L118(1983).
[240]J.Wintterlin,R.Schuster,and G.Ertl,Phys.Rev.Lett.77,123(1996).
[241]J.Harris and B.Kasemo,Surf.Sci.105,L281(1981).
[242]H.Brune,J.Wintterlin,J.Trost,G.Ertl,J.Wiechers,and R.J.Behm,J.Chem.Phys.99,2128(1993).
[243]G.Mills and H.Jonsson,Phys,Rev.Lett.72,1124(1994).
[244]G.Mills,H.Jonsson,and G.Schenter,Surf.Sci.324,305(1995).
[245]M.Alatalo,S.Jaatinen,P.Salo and K.Laasonen,Phys.Rev.B 70,245417(2004).
[246]G.Darling and S.Holloway,Rep.Prog.Phys.58,1595(1995).
[247]The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis,edited by D.A.King and D.P.Woodruff(Elsevier,Amsterdam,1988).
[248]H.H.Kung,Transition Metal Oxides,Surface Chemistry and Catalysis(Elsevier,Amsterdam,1989);V.E.Henrich and P.A.Cox,The Surface Science of Metal Oxides(Cambridge University Press,Cambridge,1994).
[249]P.Blonski,A.Kiejna and J.Hafner,Phys.Rev.B 77,155424(2008).
[250]S.Yotsuhashi,Y.Yamada,T.Kishi,W.A.Dino,H.Nakanishi and H.Kasai,Phys.Rev.B 77,115413(2008).
[251]H.Nakatsuji and H.Nakai,J.Chem.Phys.98,2423(1993).
[252]P.A.Gravil,D.M.Bird,and J.A.White,Phys.Rev.Lett.77,3933(1996).
[253]A.Eichler and J.Hafner,Phys.Rev.Lett.79,4481(1997).
[254]A.Eichler,F.Mittendorfer,and J.Harrier,Phys.Rev.B 62,4744(2000).
[255]B.Kasemo,Phys.Rev.Lett.32,1114(1974).
[256]B.Kasemo,R.Toernqvist,J.K.Nφrskov,and B.I.Lundqvist,Surf.Sci.89,554(1979).
[257]G.Katz,Y.Zeiri,and R.Kosloff,J.Chem.Phys.120,3931(2004).
[258]A.M.Wodtke,J.C.Tully,and D.J.Auerbach,Int.Rev.Phys.Chem.23,513(2004).
[259]A.Hellman,B.Razaznejad,Y.Yourdshahyan,H.Ternow,I.Zoric,and B.I.Lundqvist,Surf.Sci.532-535,126(2003).
[260]A.Hellman,B.Razaznejad,and B.I.Lundqvist,Phys.Rev.B 71,205424(2005).
[261]S.M.Driver,J.L(u|¨)decke,G.J.Jackson,and D.P.Woodruff,J.Electron Spectrosc.Relat.Phenom.99,235(1999).
[262]S.Zalkind,M.Polak and N.Shamir Surf.Sci.385,318(1997).
[263]S.Zalkind,M.Polak,and N.Shamir,Surf.Sci.513,501(2002).
[264]S.Zalkind,M.Polak and N.Shamir,Phys.Rev.B 71,125413(2005).
[265]C.Linsmeiser and J.Wanner Surf.Sci.454,305(2000).
[266]E.Wachowicz and A.Kiejns,J.Phys.:Condens.Matter 13,10767(2001).
[267]V.M.Amonenko,V.Ye.Ivanov,G.F.Tikhinskij,and V.A.Finkel,Phys.Met.Metallogr.14,47(1962).
[268]M.Lazzeri and S.de Gironcoli Phys.Rev.Lett.81,2096(1998).
[269]K.Pohl,J.-H.Cho,K.Terakura,M.Scheffler,and E.W.Plummer,Phys.Rev.Lett.80,2853(1998);H.L.Davis,J.B.Hannon,K.B.Ray,and E.W.Plummer,ibid.88,2632(1992).
[270]K.P.Huber and G.Herzberg,Molecular Spectra and Molecular Structure Ⅳ:Constants of Diatomic Molecules(Van Ncetrand Reinhold,New York,1979).
[271]A.Eichler,F.Mittendorfer,and J.Hafner Phys.Rev.B 62,4744(2000).
[272]Y.Yang,G.Zhou,J.Wu,W.H.Duan,Q.K.Xue,B.L.Gu,P.Jiang,X.C.Ms,and S.-B.Zhang,J.Chem.Phys.128,164705(2008).
[273]J.M.Haschke,Los Alamos Sci.26,253(2000).
[274]J.M.Haschke,T.H.Allen,and L.A.Morales,Science 287,285(2000).
[275]V.I.Anisimov,J.Zaanen,and O.K.Anderson,Phys.Rev.B 44,943(1991).
[276]V.I.Anisimov,I.V.Solovyev,M.A.Korotin,M.T.Czyzyk,and G.A.Sawatzky,Phys.Rev.B 48,16929(1993).
[277]I.V.Solovyev,P.H.Dederichs,and V.I.Anisimov,Phys.Rev.B 50,16861(1994).
[278]S.Y.Savrasov and G.Kotliar,Phys.Rev.Lett.84,3670(2000).
[279]A.B.Shick,V.Drchal,and L.Havela,Europhys.Lett.69,568(2005).
[280]A.Shick,L.Havela,J.Kolorenc,V.Drchal,T.Gouder,and P.M.Oppeneer,Phys.Rev.B 13,104415(2006).
[281]C.Loschen,J.Carrasco,K.M.Neyman,and F.Illas,Phys.Rev.B 75,035115(2007).
[282]M.Butterfield,T.Durakiewicz,E.Guziewicz,J.Joyce,A.Arko,K.Graham,D.Moore,and L.Morales,Surf.Sci.571,74(2004).
[283]M.T.Butterfield,T.Durakiewicz,I.D.Prodan,G.E.Scuseria,E.Guziewicz,J.A.Sordo,K.N.Kudin,R.L.Martin,J.J.Joyce,A.J.Arko,K.S.Graham,D.P.Moore,and L.A.Morales,Surf.Sci.600,1637(2006).
[284]T.Gouder,A.Seibert,L.Havela,and J.Rebizant,Surf.Sci.601,L77(2007).
[285]I.D.Prodan,G.E.Scuseria,J.A.Sordo,K.N.Kudin,and R.L.Martin,J.Chem.Phys.123,014703(2005).
[286]I.D.Prodan,G.E.Scuseria,and R.L.Martin,Phys.Rev.B 73,045104(2006).
[287]I.D.Prodan,G.E.Scuseria,and R.L.Martin,Phys.Rev.B 76,033101(2007).
[288]D.van der Marel and G.A.Sawatzky,Phys.Rev.B 37,10674(1988);J.F.Herbst,R.E.Watson,and I.Lindgren,ibid.14,3265(1976).
[289]A.B.Shick,A.I.Liechtenstein,and W.E.Pickett,Phys.Rev.B 60,10763(1999).
[290]A.B.Shick,V.Janis,and P.M.Oppeneer,Phys.Rev.Lett.94,016401(2005).
[291]C.E.McNeilly,J.Nucl.Mater.11,53(1964).
[292]P.Santini,R.Lemanski,and P.Erdos,Adv.Phys.48,537(1999);M.Colarieti-Tosti,O.Eriksson,L.Nordstrom,J.Wills,and M.S.S.Brooks,Phys.Rev.B 65,195102(2002);S.Kern,R.A.Robinson,H.Nakotte,G.H.Lander,B.Cort,P.Watson,and F.A.Vigil,ibid.59,104(1999);G.Raphael and R.Lallement,Solid State Commun.6,383(1968).
[293]戴道生,钱昆明.铁磁学(上册),164页.中国北京:科学出版社,1996.
[294]R.G.Haire,J.M.Haschke,MRSBull.689(September 2001).
[295]F.D.Murnaghan,Proc.Natl.Acad.Sci.U.S.A.30,244(1944).
[296]M.Idiri,T.LeBihan,S.Heathman,and J.Rebizant,Phys.Rev.B 70,014113(2004).
[297]K.N.Kudin,G.E.Scuseria,and R.L.Martin,Phys.Rev.Lett.89,266402(2002).
[298]B.McCart,G.H.Lander,and A.T.Aldred,J.Chem.Phys.74,5263(1981).
[299]M.Wulff and G.H.Lander,J.Chem.Phys.89,3295(1988).
[300]F.H.Ellinger,The Metal Plutonium(The University of Chicago Press,Chicago,IL,1961).
[301]J.C.Martz,J.M.Haschke,and J.L.Stakebahe,J.Nuclear Materials 210,130(1904).