X@C20F20(X=He,Ne,Ar,Kr)几何结构和 电子结构的理论研究

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.

Theoretical studies of geometric and electronic structures of X@C20F20 (X=He,Ne, Ar,Kr)

Several years ago, scientists could already introduced noble gas atoms (He, Ne, Ar, Kr, and Xe) into C₆₀ and higher fullerenes. For the specific cases of He and Ne, the calculations suggested that both atoms are slightly bound inside C₆₀ through simultaneous van der Waals interactions with all 60 carbons. The cavity in dodecahedrane is much smaller than that in C₆₀, but the experimental study found that by bombarding dodecahedrane with fast, neutral helium atoms, He@C₂₀H₂₀ is formed. The structures of C₂₀F₂₀ and C₂₀H₂₀ 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 orbitals near the Fermi level of X@C₂₀F₂₀, and the contribution of the X atom to the unoccupied molecular orbitals is relatively large. The calculation also shows that the atoms of He and Kr obtain 0.126 and 0.271 electrons from the carbons of the C₂₀F₂₀ cage, while Ar and Ne transfer 0.060 and 0.012 electrons to the carbons of the cage repectively. Thus there are electrons transferring between the X atoms and the carbons of the cage, indicating that the formed C-X bonds of the X@C₂₀F₂₀ are ionic bonds.