摘要
本文采用基于第一性原理的密度泛函理论，系统研究了以C_(60)为代表的富勒烯衍生物的几何构型及电荷性质。通过计算富勒烯内包化合物的势能面，研究了内包H、Li、Na、K、Be、Mg、Ca、N、P和As原子与碳笼的相互作用及内包原子在富勒烯笼里的运动情况；通过计算原子穿越碳笼的势能曲线，探讨了内包化合物M＠C_(60)(M=H，H_2，Li，Be，N)不同的形成机理，以及原子在笼内外之间运动的穿越机理或渗透机理；同时得到在N＠C_(60)中，氮原子和富勒烯笼的相互作用为范德瓦尔类型，氮原子稳定地存在于碳笼中心。从能量角度看，N原于是沿着弯曲的能量隧道逃逸富勒烯碳笼的，N原子穿越富勒烯笼的机理是插入机理；P原子与C_(60)的相互作用，类似于N原子与C_(60)的作用机理。
计算表明，M＠C_(60)(M=Li，Na，K，Be，Mg，Ca，N，P，As)的势能面，总体上呈现10个相对小的波谷和10个波峰，这是由富勒烯笼的几何结构所决定的。势能面上最高点位于碳原子上，较高点位于C-C键中心，波谷分别属于六元环和五元环中心。从能量的观点看，受原子半径大小的影响，Li，Na在富勒烯笼中可以在较小范围游荡，而K，Be，Mg，Ca则相对稳定在富勒烯笼中心附近。Li＠C_(60)和Be＠C_(60)中，原子在碳笼内和碳笼外都形成Li-C和Be-C键。发现氢分子穿越富勒烯C_(60)，C_(59)和C_(58)，氮和氢原子穿越C_(60)和C_(58)及Li原子穿越C_(58)_4-4-8(5)环中心的过程为插入机理；N、Be、H原子穿越C_(59)为混合机理，而Li和Be原子穿越C_(60)和C_(58)环中心为渗透机理。
通过对硼氮富勒烯内包第一周期到第四周期原子的结合能的研究，发现O和F可以和(BN)_n(n=12，16，20，24，28)形成稳定的内包化合物。对于较小的硼氮笼，如B_(12)N_(12)和B_(16)N_(16)，第一、二和三周期元素形成M＠B_(12)N_(12)和M＠B_(16)N_(16)包合物的结合能由小到大依次增加。第四周期元素则先由K降低到Ni，然后升高到Kr：从主族和惰性元素看，则是按周期递增的。总的来讲，M＠B_(12)N_(12)结合能较M＠B_(16)N_(16)是增加的。所有这些规律，大致是同原子半径的变化相一致(O，F除外)。这是由于B_(12)N_(12)和B_(16)N_(16)富勒烯笼的半径较小，分别是4.081A和5.156A，形成包合物时内包原子与外笼间的距离过小，相互排斥作用和内包原子的半径关系密切所致；同时B_(16)N_(16)笼半径较B_(12)N_(12)笼的半径已有明显增大，所以整体上结合能变小，相对热力学上较有利。M＠B_(20)N_(20)对于第一周期元素形成M＠B_(20)N_(20)包合物的结合能由H的-1.8030 eV降低到He的-1.2933eV：从主族和惰性元素看，则是按周期递增的；M＠B_(20)N_(20)包合物的规律不明显，可能是由于B_(20)N_(20)富勒烯笼的半径为6.271A，在形成包合物时，内包原子与笼间的距离大致在键长范围，影响结合能的各个因素如电荷间相互作用、范德瓦尔相互作用及成键因素等共同作用的结果。B_(24)N_(24)不同异构体的富勒烯在形成包合物时，稳定性顺序发生变化，稳定性最差O对称性的B_(24)N_(24)的包合物稳定性增加，S_8对称性的B_(24)N_(24)形成的多数元素包合物稳定性的次之，原先的最优构型S_4对称性的B_(24)N_(24)包合物稳定性变差。这和O对称性的B_(24)N_(24)球形构型笼内空间较大有关。对于M＠B_(28)N_(28)：大体上，包合物的稳定性按周期降低，在各周期，对于主族按序数增加，到惰性元素降低。副族元素的Mn、Fe、Co和Cu较其它元素的包合物稳定性明显增加。O、F和Fe由于电负性较大，在BnNn(n=12，16，20，24，28)中都能形成稳定的包合物。B和N的硼氮富勒烯内包物，硼氮富勒烯笼带正电荷，内包原子带负电荷。如果内包原子带负电荷，硼氮富勒烯笼带正电荷的包合物相对稳定；相反，内包原子带正电荷，硼氮富勒烯笼带负电荷的包合物相对不稳定。
First-principles density functional theory calculations were performed to investigate thegeometry structures and electronic properties of the classical and nonclassical fullerenes C_x(x=58, 59, 60, 62) with seven-, eight-, and nine-membered rings. Representative patch methodwas employed to generate the potential energy surface (PES). At the same time, theinteraction and the motion of an endohedral atom (such as H, Li, Na, K, Be, Mg, Ca,N, P and As) with the fullerene cage were discussed,. Different mechanisms of atomendohedral fullerenes complex M@C_(60) (M=H, H_2, Li, Be, N) are summarized, includingpenetration mechanisms and ring direct insertion mechanisms. In fullerene complex N@C_(60),the nitrogen-fullerene interaction belongs to the van der Waals type and nitrogen atom staysin the center of fullerene cage. Nitrogen atom escapes from the cage along a curving energytunnel. The mechanism of inserting a nitrogen atom inside fullerene cage to form anendohedral fullerene complex is ring penetration. The interaction mechanisms between aphosphorus atom and a fullerene cage resemble the case of nitrogen atom.
PES of M@C_(60)(M=Li, Na, K, Be, Mg, Ca, N, P, As) is characterized by a relatively flatcentral basin near the center of cage, as well as ten energy curves and ten energy peaks nearthe shell of fullerene cage. The PES is decided by the geometry structure of fullerene cage.The highest points of potential energy locate on the carbon atom of cage, the higher points onthe center of C-C bonds, the lower points in the center of six-ring or five-ring. According toenergy, Li, Na, C atoms can move around the center of fullerene cage, while K, Be, Mg atomsstay in the center of fullerene cage. In the endeohedral fullerene complex of Li@C_(60) andBe@C_(60), the Li-C or Be-C bond can be formed in a cage and out of a cage. The mechanismfor inserting a Li or Be atom into a fullerene cage to form endohedral fullerene is ringpenetration. According to the potential energy curves of H_2, H_2@C_(59), H_2@C_(58) and, N@C_(60),N@C_(58), H@C_(60), H@C_(58), the mechanism of inserting a H_2 or N or H into the fullerene cageto form an endohedral fullerene complex is direct insertion. Because of one peak and a curveout of cage in the potential energy curves for the penetration of nitrogen atom into fullereneC_(59), the mechanism for inserting N atom into fullerene cage C_(59) to form endohedral fullerenecomplex is ring penetration. Because of one peak and a curve out of cage, a curve in cage inthe potential energy curves of Li into fullerene C_(60), C_(59) and C_(58), Be into fullerene C_(60) and C_(58), the mechanism for inserting Li and Be atoms into those fullerene cages to form endohedralfullerene complexes is ring penetration.
Density functional theory calculations were also performed to investigate the bindingenergy of all elements from the first period to the fourth period doping into the boron-nitrogenfullerene cages forming ecndohedral fullerene complexes. The O and F can form stabilizationendohedral fullerene complexes with (BN)n (n=12, 16, 20, 24, 28). The binding energy of allelements from the first period to the third period formed endohedral fullerene complexes with(BN)_(16) increases. The binding energy of all elements of the fourth period formed endohedralfullerene complexes with (BN)_(20) reduces from K to Ni, and increases from Ni to Kr. Thebinding energy of some elements of the main group increases along the period and thebinding energy of M@B_(12)N_(12) is higher than that of M@B_(16)N_(16). These rules are accordantwith the bulk of atoms except O and F. The diameter of B_(12)N_(12) fullerene cage is 4.081(?)smaller than 5.156(?) of B_(16)N_(16). The distance of endohedral atom to shell of cage is small. Theinteraction between endohedral atom and fullerene cage is in close correlation with the radiusof atom. According to the radius of B_(16)N_(16) is bigger than of (BN)_(12), the binding energy ofM@(BN)n (n=12, 16) become smaller, and those is favorable on thermodynamics. Thebinding energy of the first period elements going into the B_(20)N_(20) fullerene cages formingM@B_(20)N_(20) reduces from -1.8030 eV of H to -1.2933eV of He. The binding energy of someelements of the main group formed M@B_(20)N_(20) increases along the period. Those rules areaffected by the radius of B_(20)N_(20) fullerene cage, interaction of electric charge and van derWaals type, forming bond factor. The stabilization of different isomers of B_(24)N_(24), such as O,S_4 and S_8, can change while an atom was put into the BN-fullerenes and endohedralcomplexes were made. M@B_(28)N_(28) has samiler rules with (BN)n (n=12, 16, 20). O, F and Fecan form stabilization endohedral fullerene complexes with (BN)n (n=12, 16, 20, 24, 28)correlating with activation of them. For endohedral B and N atoms of BN-fullerenes, there aresome positive charges on BN-fullerene cages and some negative electric charge B or N atom.
引文
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