Theoretical Insight Into The Low-Dimensional Nano-Carbon Materials

This work was supported by the National Natural Science Foundation of China?NO.21171138,20673081?and the National Key Basic Research Program of China?No.2011CB209404,2012CB720904?.III F ullerene and carbon nanotube are two representative funcational nano-carbon materials.Fullerenes are spherical carbon cages that consist of exactly 12 pentagonal rings and a certain number of hexagonal rings.With encapsulating metal atoms or clusters,one kindof significant fullerene derivatives form,which are called as endohedral metallofullerenes?EMFs?.Carbon nanotubes?CNTs?are one-dimensional cylindrical nanostructures consisting of only hexagonal rings.Due to their novel physical and chemical properties,EMFs and CNTs have a great amount of promising applications in many fields such as electronics,material science,and biology.Through the quantum-chemical calculation,the geometry,electronic structure,chemical bond,chemical reactivity,and spectral properties of EMFs and CNTs have been systemically investigated.1.The Yb@C_2n?2n = 72,76,and 78?and M@C₇₆?M = Ca,Sr,and Ba?were explored firstly.On the one hand,C2v?11188?-C₇₂,C2?10612?-C₇₂ and C2v?19138?-C₇₆,C1?17459?-C₇₆ were determined to be the fullerene cages of Yb@C₇₂ and Yb@C₇₆,respectively,all of which violate the isolated pentagon rule?IPR?and have one pair of pentagon adjacencies.Interestingly,Yb@C₇₈ utilizes one IPR-satisfying cage,C2v?24107?-C₇₈.Because of the different fullerene cages,their electronic and spectral properties vary obviously.On the other hand,by studying the electronic and spectral properties of M@C₇₆?M = Ca,Sr,and Ba?,the encapsulated metal atoms with the same valence were found exhibit much smaller influence on the physical and chemical properties of mono-EMFs,compared with the cage structures.2.For Lu₂@C₇₆,the two atoms can form an unprecedented metal-metal bond inside the fullerene cage.Moreover,the Lu-Lu bond can hop rapidly between six equivalent configurations in the fullerene cage at room temperature.Dy₂@D5?285913?-C₁₀₀ was predicted to be the best candidate for Dy₂@C₁₀₀,not only because of its low potential energy but also thanks to the high thermodynamic stability.Interestingly,the cage structure of D5?285913?-C₁₀₀ is a very small capped single-walled carbon nanotubes?SWNTs?.3.Quantum-chemical calculations reveal that the Sc₂S@C₇₀ possesses an IPR-violating fullerene cage,C2?7892?-C₇₀,with two pairs of pentagon adjacencies,presenting as a new IPR-violating dimetallic sulfide endohedral fullerene.Furthermore,regarding the previous C₇₀-D5 h and C2v?7854?-C₇₀,our finding of C2?7892?-C₇₀ presents the third new fullerene cage structure of the famous C₇₀ species.The metallic carbide endohedral fullerene Y₂C₂@C₈₄ is determined to have a novel fullerene cage,C1?51383?-C₈₄,with one pair of pentagon adjacencies,since Y₂C₂@C1?51383?-C₈₄ shows the highest thermodynamic stability.Y₂C₂@C1?51383?-C₈₄ is the first example of metallic carbide endohedral fullerenes,which violates the isolated pentagon rule.The high-spin state of gadolinium nitride cluster fullerenes,Gd₃N@C2?22010?-C₇₈,was predicted to be slightly lower in energy than the low-spin state.A pronounced overlap between the cage orbitals and the metal atomic orbitals were exposed,which results in an important coupling between the Gd₃ N cluster and the carbon cage in the vibrational frequencies of Gd₃N@C₇₈.4.The Diels-Alder reactions of the free C₆₈ and endohedral Sc₃N@C₆₈ fullerene with 1,3-butadiene were explored theoretically.For the free fullerene,the product under thermodynamic control is obtained for the cycloaddition to the pentalentic [5,5] bond,whereas under kinetic control,it corresponds to the [5,6] bond around the pentagon adjacencies.The pentalentic [5,5] bond is found to be the most reactive site thermodynamically and kinetically.These results reveal that the C-C bonds around the pentagon adjacencies show the highest chemical reactivity,regardless of the free or endohedral fullerene.The encapsulation of the metallic cluster reduces the exohedral reactivity of fullerene remarkably due to the charge transfer from the cluster to the fullerene cage.The Diels-Alder cycloaddition of o-quinodimethane and Sc₃N@C₆₈ is assessed to have low energy barrier,presenting as the best candidates for experimentalists to purify and functionalize Sc₃N@C₆₈.5.When benzyne is cycloadded upon armchair single-walled CNTs?SWNTs?,the [2 + 2] cycloaddition reaction follows the diradical mechanism whereas the [4 + 2] cycloaddition reaction adopts the concerted mechanism.Even if the SWNT diameter increases,the [2 + 2] cycloadduct is always the most thermodynamically stable product.However,the SWNT diameter plays an important role in determining the kinetically favored cycloaddition type.6.For Stone-Wales defective armchair SWNTs,the [5,6] bond exhibits the highest chemical reactivity toward 1,3-dipoles,which is even higher than the perfect carbon bond.Besides azomethine ylide,nitrile ylide and nitrile imine are demonstrated to react facilely with defective SWNTs.The 1,3-dipolar cycloaddition reactivity of defective SWNTs is found to be moderately dependent on the diameters of SWNTs.The larger the diameter of the SWNT have,the lower the chemical reactivity the defective SWNT displays.