【作者】 唐春梅；

【导师】 邓开明；

【作者基本信息】 南京理工大学 ， 材料科学与工程， 2008， 博士

【摘要】 近年来由于相关理论和数值算法的飞速发展,使得密度泛函理论（densityfunctional theory,DFT）成为凝聚态物理、量子化学和材料科学的重要研究方法。本论文主要对经典富勒烯C₆₀、“遗失的富勒烯”C₇₂和C₇₄以及非典型富勒烯C₆₄的掺杂衍生物的几何结构、电子性质和光学性质等进行密度泛函研究。此外,本论文还对Si（100）-（2×1）表面吸附硫醇分子的相关性质等进行密度泛函研究。第一章简要介绍了富勒烯领域和表面科学的发展现状和发展前景。第二章简要介绍了密度泛函理论的基本框架和近年来的发展。密度泛函理论的发展以寻找适当的交换和关联能量泛函为主线。从最初的局域密度近似（local densityapproximation,LDA）、广义梯度近似（generally gradient approximation,GGA）到现在的非局域泛函、自相互作用修正和多种泛函形式的相继出现使得密度泛函理论可以提供越来越精确的计算结果。在发展方法和编制程序的同时,人们也常常使用一些已有的软件包进行材料物性研究。在本章的最后简单介绍了一些常用的密度泛函模拟计算软件包。第三章和第四章研究的是经典富勒烯C₆₀替代掺杂衍生物C₅₈Fe₂和内掺掺杂衍生物Fe@C₆₀的几何结构和电子性质。几何结构研究表明C₅₈Fe₂中的两个Fe原子替代C₆₀笼子中的一个[6,6]键时形成最稳定的结构,而Fe@C₆₀中的Fe原子在笼子内部稳定于靠近C₆₀的六边形中心处形成的结构最稳定。电子性质分析发现,C₅₉Fe分子和其中Fe原子的磁性完全淬灭,与C₅₉Fe截然不同的是,C₅₈Fe₂和Fe@C₆₀分子和其中的Fe原子都具有一定的磁性。第五章到第八章关注“遗失的富勒烯”C₇₂和C₇₄。本部分对实验上已经成功合成和分离的衍生物La₂@C₇₂、Si@C₇₄、Ba@C₇₄和La@C₇₄（C₆H₃Cl₂）进行密度泛函研究。对于几何结构而言,发现:在三种La₂@C₇₂同分异构体中,有着两对两两相邻五边形的La₂@C₇₂（#10611）结构最为稳定;半导体Si在C₇₄内部稳定于σ_h平面上靠近五边形中心处;而金属原子Ba和La在C₇₄内部稳定于σ_h平面上的C₂对称轴上靠近[6,6]双键处。对于电子性质而言,Si@C₇₄中的Si-C键既具有离子性又具有共价性。Ba@C₇₄和La@C₇₄的静态线性极化率分量α_xx和α_yy都是零。La@C₇₄笼子带有1μ_B的磁矩,而La@C₇₄（C₆H₃Cl₂）却有着闭壳层的电子结构。第九章和第十章研究非典型富勒烯C₆₄的外掺掺杂衍生物C₆₄X（X=Si和Ge）和C₆₄X₄（X=H、F、Cl、Br和I）的几何结构和电子性质。C₆₄的最低未占据轨道的波函数占据在三个直接相邻五边形上,因此该位置是化学反应中活性最强的区域,有利于外来原子在该位置的吸附,三个直接相邻五边形的公共顶点被确定为X原子在笼子外部最稳定的吸附位置。最稳定C₆₄Si和C₆₄Ge结构的反应热分别是1.82和0.49eV,表明从能量的角度来看该结构的合成反应可以进行。前线轨道理论（frontier orbitaltheory,FOT）能够很好地从理论上分析合成C₆₄Si和C₆₄Ge的可能性。随着原子序数的增加,C₆₄X₄（X=F、Cl、Br和I）的结构稳定性呈现一个逐渐降低的趋势,因为稳定性比C₆₄H₄差的C₆₄Cl₄已经在实验上成功合成,所以,C₆₄F₄将来一定可以在实验上被成功合成。C₆₄X₄（X=F、Cl、Br和I）的电负性也随着X的增加而逐渐降低,C-X基团的电负性因为加成位置的不同而不同。最后一章分析0.5ML覆盖度下Ally Mercaptan（ALM）/Si（100）-（2×1）表面的几何结构和电子性质。计算得到0.5ML覆盖度的ALM分子吸附到Si（100）-（2×1）表面上的吸附能是3.36eV,表明吸附从能量的角度来看可以进行。Si（100）-（2×1）、ALM/Si（100）-（2×1）和H/Si（100）-（2×1）的导带底和价带顶对应着不同K点,同时,费米面没有能级穿过,所以,三个表面都体现间接带隙半导体特性。当ALM分子吸附到满H原子吸附的Si（100）-（2×1）表面上时,能够降低体系的带隙。Si原子和C原子之间的电子转移和它们原子轨道之间的杂化说明ALM分子应该化学吸附在H/Si（100）-（2×1）上。更多还原

【Abstract】 With the progress in density functional theory（DFT）and its numerical methods,DFT has become a routine method for condensed matter theory,quantum chemistry and material science.In this dissertation,we study a variety of fullerene members and their derivatives,including classical fullerene C₆₀,"missing fullerene"C₇₂and C₇₄,and the unconventional fullerene C₆₄.The concerned properties include the geometric structure, electronic and optical properties.In addition,we also pay attention to the geometric, electronic properties of the Ally Mercaptan（ALM）molecule adsorbed on Si（100）-（2×1） surface.In the first chapter,we introduce the developments of the fullerene as well as the Si surface science.In chapter 2,we introduce the basic concept of DFT and review its recent progress. Finding a good exchange-correlation functional is one of the main targets in DFT.With the development of the modem functionals,from the local density approximation（LDA）and the generalized gradient approximation（GGA）to the more complicated functionals,DFT can obtain more and more accurate results.In addition,along with the development of methods,more and more new program packages have been used to study the properties of materials,thus,we introduce some program packages used usually in the dissertation in detail.In chapter 3 and chapter 4,we focus on the geometric and electronic properties of the Fe substitutional fullerene C₅₈Fe₂ and the Fe endohedral fullerene Fe@C₆₀.The geometric structure research indicates that two Fe prefer to substitute the two carbon atoms of the[6,6] double bond in the most stable C₅₈Fe₂ isomer,while the most favorable endohedral site of Fe is under the center of a hexagon ring in Fe@C₆₀.The electronic property analysis imply that the magnetic moments of Fe and the molecules in both Fe@C₆₀and C₅₈Fe₂ are preserved to some extent though there is hybridization between the Fe and C,in contrast to the completely quenched magnetic moment of the Fe and the molecule in C₅₉Fe.From chapter 5 to chapter 8,we pay our attention to the properties of the "missing fullerene" C₇₂and C₇₄derivatives,i.e,La₂@C₇₂,Si@C₇₄,Ba@C₇₄,and La@C₇₄（C₆H₃Cl₂）. In the respect of geometric structure,the La₂@C₇₂（#10611）isomer with the two-fused pentagons is found the most stable,while the most favorable endohedral site of the semiconductor Si is under the center of a pentagon ring on theσ_h plane,while the most favorable endohedral site for both Ba and La in the cage is off-center under the[6,6] double bond along the C₂ axis on theσ_h plane in C₇₄.Concerned to the electronic structure,the Si-C bond in Si@C₇₄contains both covalent and ionic characters.The calculated polarizability componentsα_xx和α_yyof Ba@C₇₄and La@C₇₄are zero.All the La@C₇₄isomers have 1μ_B magnetic moment,while the electronic structure of La@C₇₄ （C₆H₃Cl₂）is closed-shell.In chapter 9 and chapter 10,the structural and electronic properties of the exohedral unconventional fullerene derivatives C₆₄X（X=Si and Ge）and C₆₄X₄（X=H,F,Cl,Br,and I）are tudied.The wave functions of the lowest unoccupied molecular orbital of C₆₄are localized mainly around the triplet-pentagon-fusion,indicated as active sites in chemical reactions,facilitating atom to attach exohedrally.The vertex of the three fused pentagons in the C₆₄cage is confirmed as the most stable position to locate the X atom when four stable isomers of C₆₄X are calculated.The calculated reaction heats of the most stable C₆₄Si and C₆₄Ge isomers are 1.89 and 0.49eV,inferring the reactions to synthesize them are favorable.The frontier orbital theory（FOT）is used to study the possibility for synthesizing C₆₄X.On the other hand,it is discovered from the reactive heats,energy gaps and the largest vibrational frequencies that C₆₄F₄ should be the most stable of five C₆₄X₄ （X=H,F,Cl,Br,and I）molecules,since the less stable C₆₄Cl₄ has been successfully synthesized and isolated,therefore,C₆₄F₄ could be synthesized and isolated experimentally in future.The electronegativity of the fragment C-X of C₆₄X₄（X= F,Cl,Br,and I）is decreased along with the increase of the atom number of X.However,the electronegativity of the fragment C-X in the molecules is affected by the location site.In the last chapter,we focus on the structural and electronic properties of the 0.5ML-terminated ALM/Si（100）-（2×1）surface.The calculated absorption energy of the ALM molecule on the full-terminated H/Si（100）-（2×1）surface is 3.36eV,indicating that the adsorption is favorable in the view of energy.The bottom of the valence band and the top of the conduction band of Si（100）-（2x1）,ALM/Si（100）-（2×1）and H/Si（100）-（2×1） are at the different K point,in addition,there is no energy level through the fermi level, therefore,all three surfaces show the indirect semiconductor character.When the ALM molecules are adsorbed on the full-terminated H/Si（100）-（2×1）surface,the band gap is decreased to some degree.Known from both the electron transference and atom orbital hybridizations between the silicon and carbon of the Si-C bond,we come to the conclusion that the ALM molecule should be chemical adsorbed on the H/Si（100）-（2×1）surface更多还原