Regioselective Exohedral Functionalization of La@C82 and its 1,2,3,4,5‐Pentamethylcyclopentadiene and Adamantylidene Adducts

The first regioselective functionalization of La@C₈₂ by two different groups has been performed. Bis‐adducts of La@C₈₂ with Cp* and adamantylidene were synthesized by using two different routes and characterized. Spectroscopic analysis and theoretical calculations reveal that the addition position is controlled by the charge density and p‐orbital axis vector value of the fullerene cage.     

A localized electrons detector for atomic and molecular systems

The local value of the single-particle momentum provides a direct three-dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient, and therefore is an ideal localized electrons detector (LED). The results introduced here extend to molecular systems our study of the single-particle local momentum in atomic systems (Bohórquez and Boyd in J Chem Phys 129:024110, 2008; Chem Phys Lett 480:127, 2009). LED is able to clearly identify covalent and hydrogen bonding interactions by depicting distinctive regions around the bond critical points, emerging as a complementary tool in conventional atoms in molecules studies. The local variable we introduce here is an intuitively interpretable 3D electron-pairs locator in atoms and molecules that can be computed either from theoretical or experimentally derived electron densities.     

Novel Polymer Monolithic Column for Hydrophilic Compounds

A hydrophilic polymer-based monolithic column was prepared from water-soluble crosslinking agents for liquid chromatography. The column media were prepared with a diacrylate monomer, aqueous polyethylene glycol, methanol, and a water-soluble radical initiator. A fused silica capillary column, which was significantly modified by vinyl groups, was utilized as the outer column in order to control polymer shrinkage. We optimized the modification of the capillary column, composition of the monomer and porogen, and polymerization condition. The optimized column exhibited high hydrophilicity and achieved the baseline separation of nucleobases by using only a buffered solution as the mobile phase. Additionally, another column prepared from binary water-soluble crosslinking agents exhibited lower nonspecific adsorption of several proteins. Basically, we would show the possibility of a new type of polymer monolith prepared from water-soluble crosslinker and water-soluble porogenic solvent, and they can be used for chromatographic separation without non-specific hydrophobic interaction.     

Two Regioisomers of Endohedral Pyrrolidinodimetallofullerenes M2@Ih‐C80(CH2)2NTrt (M=La,Ce; Trt=trityl): Control of Metal Atom Positions by Addition Positions

The two regioisomers of endohedral pyrrolidinodimetallofullerenes M₂@I_h‐C₈₀(CH₂)₂NTrt (M=La, Ce; Trt=trityl) were synthesized, isolated, and characterized. X‐ray crystallographic analyses of [6,6]‐La₂@I_h‐C₈₀(CH₂)₂NTrt and [6,6]‐Ce₂@I_h‐C₈₀(CH₂)₂NTrt revealed that the encapsulated metal atoms are located at the slantwise positions on the mirror plane that parallels the pyrrolidine ring. Paramagnetic NMR analyses of [6,6]‐ and [5,6]‐Ce₂@I_h‐C₈₀(CH₂)₂NTrt were also carried out to clarify the metal positions. As for the [6,6]‐adduct, the metal positions obtained by paramagnetic NMR analysis agree well with the X‐ray structure. In contrast, paramagnetic NMR analysis of the [5,6]‐adduct showed that the two Ce atoms are collinear with the pyrrolidine ring. We also compared the observed paramagnetic effects of the pyrrolidinodimetallofullerenes with those of other cerium‐encapsulating fullerene derivatives such as bis‐silylated Ce₂@I_h‐C₈₀ and a carbene adduct of Ce₂@I_h‐C₈₀. We found that the metal positions can be explained by the electrostatic potential maps of the corresponding [6,6]‐ and [5,6]‐adducts of [I_h‐C₈₀(CH₂)₂NTrt]^6?. These findings clearly show that metal positions inside fullerene cages can be controlled by means of the addition positions of the addends. In addition, the radical anions of the pyrrolidinodimetallofullerenes were prepared by bulk controlled‐potential electrolysis and characterized by X‐band EPR spectral study.     

Room-temperature single photon sources with definite circular and linear polarizations

We report experimental results of two room-temperature single photon sources with definite polarization based on emitters embedded in either cholesteric or nematic liquid crystal hosts. In the first case, a cholesteric 1-D photonic bandgap microcavity provides circular polarization of definite handedness of single photons from single colloidal semiconductor quantum dots (nanocrystals). In these experiments, the spectral position of the quantum dot fluorescence maximum is at the bandedge of a photonic bandgap structure. The host does not destroy fluorescence antibunching of single emitters. In the second case, photons with definite linear polarization are obtained from single dye molecules doped in a planar-aligned nematic liquid crystal host. The combination of sources with definite linear and circular polarization states of single photons can be used in a practical implementation of the BB84 quantum key distribution protocol.     

Asymptotic coefficients for Gaussian radial basis function interpolants

Gaussian radial basis functions (RBFs) on an infinite interval with uniform grid pacing h are defined by ?(x;α,h)≡exp(-[α²/h²]x²). The only significant numerical parameter is α, the inverse width of the RBF functions relative to h. In the limit α→0, we demonstrate that the coefficients of the interpolant of a typical function f(x) grow proportionally to exp(π²/[4α²]). However, we also show that the approximation to the constant f(x)≡1 is a Jacobian theta function whose coefficients do not blow up as α→0. The subtle interplay between the complex-plane singularities of f(x) (the function being approximated) and the RBF inverse width parameter α are analyzed. For α≈1/2, the size of the RBF coefficients and the condition number of the interpolation matrix are both no larger than O(10⁴) and the error saturation is smaller than machine epsilon, so this α is the center of a “safe operating range” for Gaussian RBFs.     

Three ways to solve the Poisson equation on a sphere with Gaussian forcing

Motivated by the needs of vortex methods, we describe three different exact or approximate solutions to the Poisson equation on the surface of a sphere when the forcing is a Gaussian of the three-dimensional distance, ∇²ψ=exp(-2?²(1-cos(θ))-C^Gauss(?)${\nabla }^2\psi =\exp (-2{?}^2(1-\cos (\theta ))-C^{\mathit{Gauss}}(?)$. (More precisely, the forcing is a Gaussian minus the “Gauss constraint constant”, C^Gauss$C^{\mathit{Gauss}}$; this subtraction is necessary because ψ$\psi$ is bounded, for any type of forcing, only if the integral of the forcing over the sphere is zero [Y. Kimura, H. Okamoto, Vortex on a sphere, J. Phys. Soc. Jpn. 56 (1987) 4203–4206; D.G. Dritschel, Contour dynamics/surgery on the sphere, J. Comput. Phys. 79 (1988) 477–483]. The Legendre polynomial series is simple and yields the exact value of the Gauss constraint constant, but converges slowly for large ?$?$. The analytic solution involves nothing more exotic than the exponential integral, but all four terms are singular at one or the other pole, cancelling in pairs so that ψ$\psi$ is everywhere nice. The method of matched asymptotic expansions yields simpler, uniformly valid approximations as series of inverse even powers of ?$?$ that converge very rapidly for the large values of ?  (?>40)$(?>40)$ appropriate for geophysical vortex computations. The series converges to a nonzero O(exp(-4?²))$O(\exp (-4{?}^2))$ error everywhere except at the south pole where it diverges linearly with order instead of the usual factorial order.     

A hybrid particle approach for continuum and rarefied flow simulation

A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N₂ over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber.     

Cutting planes for semidefinite relaxations based on triangle-free subgraphs

We show how to separate a doubly nonnegative matrix, which is not completely positive and has a triangle-free graph, from the completely positive cone. This method can be used to compute cutting planes for semidefinite relaxations of combinatorial problems. We illustrate our approach by numerical tests on the stable set problem.     

Field measurement of wheel—rail impact force at insulated rail joint

Experimental Techniques - When wheels pass over insulated rail joints (IRJs) a vertical impact force is generated. The ability to measure the impact force is valuable as the force signature helps...