Ehrhart Series and Lattice Triangulations

We express the generating function for lattice points in a rational polyhedral cone with a simplicial subdivision in terms of multivariate analogues of the h-polynomials of the subdivision and “local contributions” of the links of its nonunimodular faces. We also compute new examples of nonunimodal h ^*-vectors of reflexive polytopes. Supported by the Clay Mathematics Institute.     

Condensation of free volume in structures of nematic and hexatic liquid crystals

Eight novel liquid crystalline materials were prepared containing highly branched terminal chains, either 2,4,4-trimethylpentyl or 3,5,5-trimethylhexyl. All materials exhibit nematic mesophases, with additional smectic (Sm) C, hexatic B and SmI phases for certain homologues. Analysis by small- and wide-angle X-ray scattering reveals continual build-up of the correlation length within the nematic phases, where we also observe splitting of the small angle peak into four lobes, indicating pretransitional Sm fluctuations. Connoscopy confirms the nematic phase to be uniaxial and optically positive. We observe that in the solid state, the molecules exist as staggered antiparallel pairs as a consequence of the sterically demanding bulky terminal group, and this would also appear to manifest in the hexatic B phase, where the layer spacing was found to be greater than the molecular length. If true, this is an example of pair formation driven by sterics rather than dipole–dipole interactions and suggests that reentrant systems driven purely by steric frustration may be found.     

Propene activation by the oxo-iron active species of taurine/alpha-ketoglutarate dioxygenase (TauD) enzyme. How does the catalysis compare to heme-enzymes?

Density functional calculations on the oxygenation reaction of propene by a model for taurine/alpha-ketoglutarate dioxygenase (TauD) enzyme are presented. The oxo-iron active species of TauD is shown to be a powerful and aggressive oxidant, which is able to hydroxylate C-H bonds and epoxidize C=C bonds with low barriers. In the case of propene oxygenation, the hydroxylation and epoxidation mechanisms are competitive on a dominant quintet spin state surface. We have compared the mechanism and thermodynamics of TauD with oxo-iron heme catalysts, such as the cytochromes P450, and found some critical differences. The TauD model is found to be much more reactive toward oxygenation of substrates than oxo-iron complexes in a heme environment with much lower reaction barriers. We have analyzed this and assigned this to the strength of the O-H bond formed after hydrogen abstraction from a substrate, which is at least 10 kcal mol(-)(1) stronger in five-coordinated oxo-iron nonheme complexes than in six-coordinated oxo-iron heme complexes. Since, the metal in TauD enzymes is five-coordinated, whereas in heme-enzymes it is six-coordinated there are some critical differences in the valence molecular orbitals. Thus, in oxo-iron heme catalysts one of the antibonding pi orbitals is replaced by a low-lying nonbonding delta orbital resulting in a lower overall spin state. Moreover, heme-enzymes have an extra oxidation equivalent located on the heme, which is missing in non-heme oxo-iron catalysts. As a result, the oxo-iron species of TauD reacts via single-state reactivity on a dominant quintet spin state surface, whereas oxo-iron heme catalysts react via two-state reactivity on competing doublet and quartet spin states.     

What external perturbations influence the electronic properties of catalase compound I?

We have performed density functional theory calculations on an active-site model of catalase compound I and studied the responses of the catalytic center to external perturbations. Thus, in the gas phase, compound I has close-lying doublet and quartet spin states with three unpaired electrons: two residing in pi(FeO) orbitals and the third on the heme. The addition of a dielectric constant to the model changes the doublet-quartet energy ordering but keeps the same electronic configuration. By contrast, the addition of an external electric field along one of the principal axes of the system can change the doublet-quartet energy splitting by as much as 6 kcal mol(-1) in favor of either the quartet or the doublet spin state. This sensitivity is much stronger than the effect obtained for iron heme models with thiolate or imidazole axial ligands. Moreover, an external electric field is able to change the electronic system from a heme-based radical [Fe=O(Por*+)OTyr-] to a tyrosinate radical [Fe=O(Por)OTyr*]. This again shows that oxo-iron heme systems are chameleonic species that are influenced by external perturbations and change their character and catalytic properties depending on the local environment.     

Vibrational dynamics of N-H, C-D, and C=O modes in formamide

By means of heterodyned two-dimensional IR photon echo experiments on liquid formamide and isotopomers the vibrational frequency dynamics of the N-H stretch mode, the C-D mode, and the C=O mode were obtained. In each case the vibrational frequency correlation function is fitted to three exponentials representing ultrafast (few femtoseconds), intermediate (hundreds of femtoseconds), and slow (many picoseconds) correlation times. In the case of N-H there is a significant underdamped contribution to the correlation decay that was not seen in previous experiments and is attributed to hydrogen-bond librational modes. This underdamped motion is not seen in the C-D or C=O correlation functions. The motions probed by the C-D bond are generally faster than those seen by N-H and C=O, indicating that the environment of C-D interchanges more rapidly, consistent with a weaker C-D...O=C bond. The correlation decays of N-H and C=O are similar, consistent with both being involved in strong H bonding.     

The effects of ionization potential depression on the spectra emitted by hot dense aluminium plasmas

Recent experiments at the Linac Coherent Light Source (LCLS) X-ray Free-Electron-Laser (FEL) have demonstrated that the standard model used for simulating ionization potential depression (IPD) in a plasma (the Stewart–Pyatt (SP) model, J.C. Stewart and K.D. Pyatt Jr., Astrophysical Journal 144 (1966) 1203) considerably underestimates the degree of IPD in a solid density aluminium plasma at temperatures up to 200 eV. In contrast, good agreement with the experimental data was found by use of a modified Ecker–Kröll (mEK) model (G. Ecker and W. Kröll, Physics of Fluids 6 (1963) 62–69). We present here detailed simulations, using the FLYCHK code, of the predicted spectra from hot dense, hydrogenic and helium-like aluminium plasmas ranging in densities from 0.1 to 4 times solid density, and at temperatures up to 1000 eV. Importantly, we find that the greater IPDs predicted by the mEK model result in the loss of the n = 3 states for the hydrogenic ions for all densities above ≈0.8 times solid density, and for the helium-like ions above ≈0.65 solid density. Therefore, we posit that if the mEK model holds at these higher temperatures, the temperature of solid density highly-charged aluminium plasmas cannot be determined by using spectral features associated with the n = 3 principal quantum number, and propose a re-evaluation of previous experimental data where high densities have been inferred from the spectra, and the SP model has been used.     

Combination of cationic surfactant-assisted solid-phase extraction with field-amplified sample stacking for highly sensitive analysis of chlorinated acid herbicides by capillary zone electrophoresis

This report describes a novel online field-amplified sample stacking (FASS) procedure to analyze 16 chlorinated acid herbicides. By using a poly(vinyl alcohol) (PVA)-coated capillary to reduce electroosmotic flow and introducing a methanol-water plug before sample loading, the sample injection time could be very long without loss of sample and separation efficiency. Under the optimized condition, the FASS procedure could provide great sensitivity enhancement (5000-10 000-fold) and satisfactory reproducibility (relative standard deviations of migration times less than 2.4%, relative standard deviations of peak areas less than 8.0%). Combined with cationic surfactant-assisted solid-phase extraction (CSA-SPE), the limit of detection of the herbicides ranged from 0.269 to 20.3 ppt, which are two orders lower than those of the US Environmental Protection Agency standard method 515.1. The CSA-SPE-FASS-CE method was successfully applied to the analysis of local pond water.     

Qmd-plot: a graphical utility for rapid preliminary analysis of time series of fluctuating data, developed in the context of molecular dynamics simulations

Qmd-plot is a utility to obtain rapid information about past or on-going simulations, or real-time data collections, in the form of graphs of recorded variables (x, y, ...), as x-y plots or as a function of simulated or real time. Time series records in the data file must be named. Variable names and their locations in the data file are initially unknown to the program, but are identified in a first scan, in which header records are located on the basis of a predefined key (that can be changed interactively). The names of the time series are then presented in an interactive menu, from which the user can repeatedly specify a graph to be viewed. Qmd-plot has been developed in the context of molecular dynamics simulations. We give examples of time series and x-y plots made from output of the sigma program. Qmd-plot code is a Java application; source and class files can be obtained free from the authors.     

A new acylated triterpene from the roots of Chaenomeles japonica

A new acylated triterpene together with prunasin, (-)-epicatechin, daucosterol, and three triterpenes, ursolic, oleanolic, and pomolic acids was isolated from the root of Chaenomeles japonica (THUNB.) LINDL. (Rosaceae) and determined to be 3-O-(E)-3, 5-dihydroxycinnamoylursolic acid on the basis of NMR and FAB-MS experiments.