First-Principles Study Of Interaction Between An Endohedral Atom And A Fullerene Cage

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@C₆₀ (M=H, H₂, Li, Be, N) are summarized, includingpenetration mechanisms and ring direct insertion mechanisms. In fullerene complex N@C₆₀,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@C₆₀(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@C₆₀ andBe@C₆₀, 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 H₂, H₂@C₅₉, H₂@C₅₈ and, N@C₆₀,N@C₅₈, H@C₆₀, H@C₅₈, the mechanism of inserting a H₂ 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 fullereneC₅₉, the mechanism for inserting N atom into fullerene cage C₅₉ 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 C₆₀, C₅₉ and C₅₈, Be into fullerene C₆₀ and C₅₈, 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@B₁₂N₁₂ is higher than that of M@B₁₆N₁₆. These rules are accordantwith the bulk of atoms except O and F. The diameter of B₁₂N₁₂ fullerene cage is 4.081(?)smaller than 5.156(?) of B₁₆N₁₆. 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 B₁₆N₁₆ 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 B₂₀N₂₀ fullerene cages formingM@B₂₀N₂₀ reduces from -1.8030 eV of H to -1.2933eV of He. The binding energy of someelements of the main group formed M@B₂₀N₂₀ increases along the period. Those rules areaffected by the radius of B₂₀N₂₀ fullerene cage, interaction of electric charge and van derWaals type, forming bond factor. The stabilization of different isomers of B₂₄N₂₄, such as O,S₄ and S₈, can change while an atom was put into the BN-fullerenes and endohedralcomplexes were made. M@B₂₈N₂₈ 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.