中文摘要：

采用密度泛函理论中的广义梯度近似,对X@C20F20（X=He,Ne,Ar,Kr）几何结构和电子结构进行了计算研究.几何结构优化发现：惰性气体原子X内掺到X@C20F20笼后,均稳定于碳笼中心,随着内掺X原子序数的增大,X原子对C20F20笼的影响越来越大.能隙、内掺能和振动频率计算表明：内掺X原子使得X@C20F20的稳定性得到了显著提升,X@C20F20（X=He,Ne,Ar,Kr）都具有良好的稳定性,并且随着X原子序数的增大,其稳定性也基本呈现逐渐增强的趋势.电子结构研究发现：X原子对X@C20F20费米能级附近的占据轨道基本没有贡献,而对其未占据轨道贡献较大.计算还发现：在X@C20F20中,He和Kr分别从X@C20F20的C笼上获得了0.126和0.271个电子,而Ne和Ar却分别向C笼转移了0.060和0.012个电子.由此可见：X原子与C原子之间都发生了电荷转移,C笼上的C原子与惰性气体原子X间形成了一定的离子键.

英文摘要：

Several years ago, scientists could already introduced noble gas atoms（He, Ne, Ar, Kr, and Xe） into C_（60） and higher fullerenes. For the specific cases of He and Ne, the calculations suggested that both atoms are slightly bound inside C_（60） through simultaneous van der Waals interactions with all 60 carbons. The cavity in dodecahedrane is much smaller than that in C_（60）, but the experimental study found that by bombarding dodecahedrane with fast, neutral helium atoms, He@C20F20 is formed. The structures of C20F20 and C20F20 are similar. Are noble gas atoms also stable in the C20F20？ and, are there charges transferring between noble gas atoms and the carbon cage？ In this paper, the generalized gradient approximation based on density functional theory is used to analyze the geometric and electronic structures of the endohedral fullerene X@C20F20（X = He, Ne, Ar, Kr）. The geometric optimization shows that the noble gas atoms X are all stable in the center of C20F20 cage. The C—C bond lengths of the X@C20F20 increase with the atomic number X increasing, while the C—F bond length is hardly changed. The inclusion energies of the X@C20F20（X = He, Ne, Ar, Kr） are 1.359, 3.853, 11.276 and 15.783 eV respectively. These are all positive, which shows that the X@C20F20 have good thermodynamic stabilities, and the thermodynamic stabilities of the X@C20F20 are enhanced with the increase of X atomic number. The energy gaps of the X@C20F20（X = He, Ne, Ar, Kr） are 5.179, 4.882, 5.874 and 6.205 eV respectively, which are greater than that of C20F20. It indicates that the X@C20F20 have better dynamic stabilities than C20F20. In addition, the vibration frequencies of the X@C20F20（X = He, Ne, Ar, Kr） are all positive.These indicate that the stability of C20F20 is significantly improved when the X atom is introduced into the cage, and is gradually increasing with the increase of X atomic number. The electronic structures demonstrate that the X atom has no contribution to the occupied molecular