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

Dipolar truncation prevents accurate measurement of long-range internuclear distances between nuclei of the same spin species, eg, within (13)C-(13)C spin pairs in uniformly (13)C-isotope-labeled proteins, using magic-angle spinning solid-state NMR spectroscopy Accordingly, one of the richest sources of accurate structure information is at present not exploited fully, leaving the bulk part of the experimentally derived structural constraints to less accurate long-range (13)C-(13)C dipolar couplings estimated from methods based on spin diffusion through proton spins in the close environment In this paper, we extend our previous triple-oscillating field technique [N Khaneja and N C Nielsen, J Chem Phys 128, 015103 (2008)] for dipolar recoupling without dipolar truncation in homonuclear spin systems to a more advanced rf modulation with four independent oscillations and rotations involving nonorthogonal axes This provides important new degrees of freedom, which are used to improve the scaling factor of the recoupled dipole-dipole couplings by a factor of 25 relative to the triple-oscillating field approach This significant improvement, obtained by refocusing of otherwise defocused parts of the residual dipolar coupling Hamiltonian, may be exploited to measure much weaker (13)C-(13)C dipolar couplings (and thereby longer distances) with much higher accuracy We present a detailed theoretical description of multiple-field oscillating recoupling experiments, along with numerical simulations and experimental results on U-(13)C, (15)N-L-threonine and U-(13)C,(15)N-ubiquitin

Multiple-oscillating-field techniques for accurate distance measurements by solid-state NMR.

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.

The Wigner rotation is important in many branches of physics, chemistry, and engineering sciences. It is a group theoretical effect resulting from two Lorentz boosts. The net effect is one boost followed or preceded by a rotation. While the term "Wigner rotation" is derived from Wigner's little group whose transformations leave the four-momentum of a given particle invariant, it is shown that the Wigner rotation is different from the rotations in the little group. This difference is clearly spelled out, and it is shown to be possible to construct the corresponding Wigner rotation from the little-group rotation. It is shown also that the ABCD matrix for light beams in a laser cavity shares the same mathematics as the little-group rotation, from which the Wigner rotation can be constructed.

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Wigner rotations in laser cavities.

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

One-dimensional Schrödinger equation in the harmonic oscillator basis with various potentials☆

Two new methods to evaluate the sums over magnetic quantum numbers, together with Wigner rotation matrix elements, are formulated. The first is the coupling method which makes use of the coupling of Wigner rotation matrix elements. This method gives rise to a closed form for any kind of summation that involves a product of two Wigner rotation matrix elements. The second method is the equivalent operator method, for which a closed form is also obtained and easily implemented on the computer. A few examples are presented, and possible extensions are indicated. The formulae obtained are useful for the study of the angular distribution of the photofragments of diatomic and symmetric-top molecules caused by electric-dipole, electric-quadrupole and two-photon radiative transitions.

Shan-Tao Lai

Papers

Theoretical study of metallofullerenes M@C32

The structures of fullerene C40 and its derivatives

One-dimensional Schrödinger equation in the harmonic oscillator basis with various potentials☆

On the summations involving Wigner rotation matrix elements

Ab initio study on fullerene C44 and its hydrogenates