Probing the dependence of long-range, four-atom interactions on intermolecular orientation: 3. Hydrogen and iodine

Two-laser, action spectroscopy experiments have been performed in the I(2)B-X, υ'-0 spectral region on H(2)···I(2) and D(2)···I(2) complexes to investigate the dependence of the H(2)/D(2) + I(2) intermolecular interactions on orientation. The spectra contain features associated with at least two different conformers of the ground-state H(2)/D(2)···I(2)(X,υ' = 0) complexes; one conformer has a preferred T-shaped geometry with the H(2)/D(2) moiety localized in a potential minimum that is orthogonal to the I-I bond axis, and the second conformer has a linear geometry with the H(2)/D(2) moiety positioned in minima at either end of the I(2) molecule, along the bond axis. Those features associated with complexes containing para-H(2)(j = 0), ortho-H(2)(j = 1), ortho-D(2)(j = 0), and para-D(2)(j = 1) are also assigned. The linear conformers are found to be more strongly bound than the T-shaped conformers with binding energies of 118.9(1.9) cm(-1) versus 91.3-93.3 cm(-1) for the ortho-H(2)···I(2) complexes and 144.2(2.1) cm(-1) versus 107.9 cm(-1) for the para-D(2)···I(2) complexes, respectively. Electronic structure calculations of the complexes containing ICl and I(2) with H(2), He, Ne, and Ar were performed to reveal the nature of the interactions and to shed insight into the origins of the different binding energies. The most stable minima in the H(2)/D(2) + I(2)(B,υ') excited-state potentials have T-shaped geometries. Calculated energies and probability amplitudes of the excited-state levels provide insight into the different excited-state intermolecular vibrational levels accessed by transitions of the two ground-state conformers.     

Willmore energy for joining of carbon nanostructures

Numerous types of carbon nanostructure have been found experimentally, including nanotubes, fullerenes and nanocones. These structures have applications in various nanoscale devices and the joining of these structures may lead to further new configurations with more remarkable properties and applications. The join profile between different carbon nanostructures in a symmetric configuration may be modelled using the calculus of variations. In previous studies, carbon nanostructures were assumed to deform according to perfect elasticity, thus the elastic energy, depending only on the axial curvature, was used to determine the join profile consisting of a finite number of discrete bonds. However, one could argue that the relevant energy should also involve the rotational curvature, especially when its size is comparable to the axial curvature. In this paper, we use the Willmore energy, a natural generalisation of the elastic energy that depends on both the axial and rotational curvatures. Catenoids are absolute minimisers of this energy and pieces of these may be used to join various nanostructures. We focus on the cases of joining a fullerene to a nanotube and joining two fullerenes along a common axis. By comparing our results with the earlier work, we find that both energies give similar joining profiles. Further work on other configurations may reveal which energy provides a better model.     

The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Polynomial identities,indices, and duality for theN=1 superconformal modelSM(2, 4v)

We prove polynomial identities for theN=1 superconformal modelSM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses theq-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq-series on the fermionic side. We use these polynomials to demonstrate a dual relation underqq ^–1 betweenSM(2, 4v) andM(2v–1, 4v). We also introduce a genralization of the Witten index which is expressible in terms of the Rogers false theta functions.Dedicated to the memory of Claude Itzykson.     

Kinetics of nonisothermal polymer crystallization

We adopt a cluster size distribution model to investigate the kinetics of nonisothermal polymer crystallization. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different cooling rates. The incubation period is also investigated at different cooling rates and initial temperatures. The relationship between cooling rates and incubation time is presented graphically and compared with experimental measurements. The initial temperature (relative to melting point) has a significant effect on nonisothermal crystallization. A comparison of moment and numerical solutions of the population balance equations shows the influence of Ostwald ripening. Agreement between modeling results and experimental measurements at different cooling rates supports the application of the distribution kinetics model for nonisothermal crystallization.     

Spatial localization of ligand binding sites from electron current density surfaces calculated from NMR chemical shift perturbations

Rapid, accurate structure determination of protein-ligand complexes is an essential component in structure-based drug design. We have developed a method that uses NMR protein chemical shift perturbations to spatially localize a ligand when it is complexed with a protein. Chemical shift perturbations on the protein arise primarily from the close proximity of electron current density from the ligand. In our approach the location of the center of the electron current density for a ligand aromatic ring was approximated by a point-dipole, and dot densities were used to represent ligand positions that are allowed by the experimental data. The dot density is increased in the region of space that is consistent for the most data. A surface can be formed in regions of the highest dot density that correlates to the center of the ligand aromatic ring. These surfaces allow for the rapid evaluation of ligand binding, which is demonstrated on a model system and on real data from HCV NS3 protease and HCV NS3 helicase, where the location of ligand binding can be compared to that obtained from difference electron density from X-ray crystallography.     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

The vibrational predissociation spectra of the H5O2 +RGn(RG = Ar,Ne) clusters: correlation of the solvent perturbations in the free OH and shared proton transitions of the Zundel ion

Predissociation spectra of the H(5)O(2) (+)RG(n)(RG = Ar,Ne) cluster ions are reported in energy regions corresponding to both the OH stretching (3350-3850 cm(-1)) and shared proton (850-1950 cm(-1)) vibrations. The two free OH stretching bands displayed by the Ne complex are quite close to the band origins identified earlier in bare H(5)O(2) (+) [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)], indicating that the symmetrical H(5)O(2) (+) "Zundel" ion remains largely intact in H(5)O(2) (+)Ne. The low-energy spectrum of the Ne complex is simpler than that observed previously for H(5)O(2) (+)Ar, and is dominated by two sharp transitions at 928 and 1047 cm(-1), with a weaker feature at 1763 cm(-1). The H(5)O(2) (+)Ar(n),n = 1-5 spectra generally exhibit complex band structures reflecting solvent-induced symmetry breaking of the Zundel core ion. The extent of solvent perturbation is evaluated with electronic structure calculations, which predict that the rare gas atoms should attach to the spectator OH groups of H(5)O(2) (+) rather than to the shared proton. In the asymmetric complexes, the shared proton resides closer to the more heavily solvated water molecule, leading to redshifts in the rare gas atom-solvated OH stretches and to blueshifts in the shared proton vibrations. The experimental spectra are compared with recent full-dimensional vibrational calculations (diffusion Monte Carlo and multimode/vibrational configuration interaction) on H(5)O(2) (+). These results are consistent with assignment of the strong low-energy bands in the H(5)O(2) (+)Ne spectrum to the vibration of the shared proton mostly along the O-O axis, with the 1763 cm(-1) band traced primarily to the out-of-phase, intramolecular bending vibrations of the two water molecules.