Curved pi-conjugation, aromaticity, and the related chemistry of small fullerenes (< C60) and single-walled carbon nanotubes.

Theoretical investigation of C60 fullerene functionalization with tetrazine

To reveal new structure-property relationships in the nonlinear optical (NLO) properties of fullerenes that are associated with their open-shell character, we investigated the interplay between the diradical character (y(i)) and second hyperpolarizability (longitudinal component, γ(zzzz)) in several fullerenes, including C(20), C(26), C(30), C(36), C(40), C(42), C(48), C(60), and C(70), by using the broken-symmetry density functional theory (DFT; LC-UBLYP (μ=0.33)/6-31G*//UB3LYP/6-31G*). We found that the large differences between the geometry and topology of fullerenes have a significant effect on the diradical character of each fullerene. On the basis of their different diradical character, these fullerenes were categorized into three groups, that is, closed-shell (y(i)=0), intermediate open-shell (0<y(i)<1), and almost pure open-shell compounds (y(i)=/~1), which originated from their diverse topological features, as explained by odd-electron-density and spin-density diagrams. For example, we found that closed-shell fullerenes include C(20), C(60), and C(70), whereas fullerenes C(26) and C(36) and C(30), C(40), C(42), and C(48) are pure and intermediate open-shell compounds, respectively. Interestingly, the γ(zzzz) enhancement ratios between C(30)/C(36) and C(40)/C(60) are 4.42 and 11.75, respectively, regardless of the smaller π-conjugation size in C(30) and C(40) than in C(36) and C(60). Larger γ(zzzz) values were obtained for other fullerenes that had intermediate diradical character, in accordance with our previous valence configuration interaction (VCI) results for the two-site diradical model. The γ(zzzz) density analysis shows that the large positive contributions originate from the large γ(zzzz) density distributions on the right- and left-extended edges of the fullerenes, between which significant spin polarizations (related to their intermediate diradical character) appear within the spin-unrestricted DFT level of theory.

Interplay between the diradical character and third-order nonlinear optical properties in fullerene systems.

Based on the D3 C32 fullerene, the equilibrium geometries, electronic structures, and binding energies of the endohedral fullerenes X0/n+@C32 (X = H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P, n = 1–3) have been calculated using the DFT/B3LYP/6-31G(d) method. The results show that the C32 cages are slightly enlarged due to encapsulation, and the sizes of non-neutral molecules are smaller than the corresponding neutral ones. Cages containing Li, Na, and Ca and most of the cations, except Na+ and K+, are energetically favorable. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Theoretical studies of structures and stabilities of endohedral fullerenes X0/n+ @C32 (X = H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P, n = 1–3)

The self-consistent-charge density-functional tight-binding (SCC-DFTB) method is employed for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all pentagon/hexagon-bearing isomers of C38, C40, and C42 as the second part of a larger effort to catalogue the CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C20C180 [analogous data for C20C36 were published previously in Malolepsza et al., J Phys Chem A, 2007, 111, 6649]. Common features among the fullerenes are identified and properties characteristic for each specific fullerene cage size are discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Comparison of geometric, electronic, and vibrational properties for all pentagon/hexagon-bearing isomers of fullerenes C38, C40, and C42

14 systems of metal atoms, embedded inside the C 32 cage, have been calculated and analyzed using the ab initio quantum chemistry Gamess program. We study their electronic structure, compare their stability. The metal atom with even electrons interjected inside the C 32 cage is more stable than the metal atom with odd electrons. Ti@C 32 system is the most stable in the 14 metallofullerenes.

Theoretical study of metallofullerenes M@C32

In this paper, the three possible fullerene isomers of C40 and their derivatives are investigated employing ab initio methods with using 3 Gauss type orbitals instead of one Slater type orbital (STO-3G). Of the three structures, two have D5d symmetry [D5d(I) and D5d(II)], the other has Td symmetry. Through the full optimized calculation, the predicted order of stability for isomers is found to be D5d(I) > Td > D5d(II). Energies and properties of the negative ion and positive ions of different kinds of C40 are calculated. Generally, the stability of negative ions is better than positive ions. The hydrogenated C40 has also been studied. It can be concluded that the most active center for adding hydrogen is the vertex of three adjacent pentagons.

The structures of fullerene C40 and its derivatives

A formula is derived that allows one to determine the matrix elements of an arbitrary integral reciprocal power of the dimensionless displacement coordinate q of the harmonic oscillator from those ofq −1 in an exact manner. This relation is obtained from the use of the chain rule and irreducible tensors expressed in terms of the creation and annihilation operators of the harmonic oscillator.

A general expression for matrix elements of reciprocal powers of the displacement coordinateq in the harmonic oscillator basis

Chemical Geminal Charge Transfer, Vibronic Degeneracy Effects, and Doping Excitons in Superconductivity

Two-electron-bonding geminals ΨΛ(x1,x2), in cupric of superconductivity as well as in carbons of fullerenes out of four electrons ΨΛ(x1,x2,x3,x4), have been explained. In superconductivity cases, La8Sr8Cu8O28 and La12Sr4Cu8O30 with free 4 Cu in D4h have been considered. Fullerenes C40 (Td) and C48 (Oh) with free π radicals of 4 carbons in D4h have also been considered. Singlet and triplet geminals, 1,3 Ψ Λ (x 1 ,x 2 ), are in terms of 1,3 φ n,n+1 (x 1 ,x 2 )= 1 2 [φ n (x 1 )φ n+1 (x 2 )±φ n (x 2 )φ n+1 (x 1 )], in 4 Cu and 4 carbons of a2μ, egxz, egyz and b1μ or b2μ.

Manzheng Fu

Papers

Theoretical study of metallofullerenes M@C32

The structures of fullerene C40 and its derivatives

A general expression for matrix elements of reciprocal powers of the displacement coordinateq in the harmonic oscillator basis

Chemical Geminal Charge Transfer, Vibronic Degeneracy Effects, and Doping Excitons in Superconductivity

Special singlet and triplet geminal correlations for modeling fullerenes and superconductive cuprates