The Caratheodory-Fejer extension theorem

A construction of Carathéodory and Fejér [1] produces a function which is bounded and analytic in the unit disk with specified initial coefficients. An operator generalization of the construction is now obtained for application to the invariant subspace problem. A formal proof [2] of the existence of invariant subspaces is given by the theory of square summable power series [3] in its vector formulation [4]. But the justification of the formal argument requires a determination of extreme points of a convex set [5]. A solution is now given to an extension problem for convex decompositions which arises in connection with the Carathéodory-Fejér theorem. A necessary condition for an extreme point is obtained as an application. The condition is conjectured to be sufficient.     

An inequality for the multivariate normal distribution

Herman Chernoff used Hermite polynomials to prove an inequality for the normal distribution. This inequality is useful in solving a variation of the classical isoperimetric problem which, in turn, is relevant to data compression in the theory of element identification. As the inequality is of interest in itself, we prove a multivariate generalization of it using a different argument.     

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short‐range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short‐range charge penetration correction modifying the charge‐charge, charge‐dipole and charge‐quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry‐Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono‐ and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER‐HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration‐corrected polarizable force fields highlighting the mandatory need of non‐spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short‐range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio‐ or bioinorganic systems in periodic boundary conditions. © 2016 Wiley Periodicals, Inc.     

Near-edge X-ray absorption fine structure spectroscopy of diamondoid thiol monolayers on gold

Diamondoids, hydrocarbon molecules with cubic-diamond-cage structures, have unique properties with potential value for nanotechnology. The availability and ability to selectively functionalize this special class of nanodiamond materials opens new possibilities for surface modification, for high-efficiency field emitters in molecular electronics, as seed crystals for diamond growth, or as robust mechanical coatings. The properties of self-assembled monolayers (SAMs) of diamondoids are thus of fundamental interest for a variety of emerging applications. This paper presents the effects of thiol substitution position and polymantane order on diamondoid SAMs on gold using near-edge X-ray absorption fine structure spectroscopy (NEXAFS) and X-ray photoelectron spectroscopy (XPS). A framework to determine both molecular tilt and twist through NEXAFS is presented and reveals highly ordered diamondoid SAMs, with the molecular orientation controlled by the thiol location. C 1s and S 2p binding energies are lower in adamantane thiol than alkane thiols on gold by 0.67 +/- 0.05 and 0.16 +/- 0.04 eV, respectively. These binding energies vary with diamondoid monolayer structure and thiol substitution position, consistent with different degrees of steric strain and electronic interaction with the substrate. This work demonstrates control over the assembly, in particular the orientational and electronic structure, providing a flexible design of surface properties with this exciting new class of diamond nanoparticles.     

Software for the calculation of isotope patterns in tandem mass spectrometry

Software, available at no cost on the Internet, is described which uses polynomial expansion algorithms to calculate the isotope patterns for precursor ion, neutral loss, and MSn product ion tandem mass spectra. Such information is useful for determining product ion and neutral loss composition, identification of analytes in complex samples, deconvolution of overlapping spectra, and correction of peak heights or areas in quantitative analysis. The effect of less than unit mass resolution on the isotope patterns is described and experimental examples of the use of the software are presented.     

Quantitative aspects of and ionization mechanisms in positive-ion atmospheric pressure chemical ionization mass spectrometry

The behavior in atmospheric pressure chemical ionization of selected model polycyclic aromatic compounds, pyrene, dibenzothiophene, carbazole, and fluorenone, was studied in the solvents acetonitrile, methanol, and toluene. Relative ionization efficiency and sensitivity were highest in toluene and lowest in methanol, a mixture of molecular ions and protonated molecules was observed in most instances, and interferences between analytes were detected at higher concentrations. Such interferences were assumed to be caused by a competition among analyte molecules for a limited number of reagent ions in the plasma. The presence of both molecular ions and protonated analyte molecules can be attributed to charge-transfer from solvent radical cations and proton transfer from protonated solvent molecules, respectively. The order of ionization efficiency could be explained by incorporating the effect of solvation in the ionization reactions. Thermodynamic data, both experimental and calculated theoretically, are presented to support the proposed ionization mechanisms. The analytical implications of the results are that using acetonitrile (compared with methanol) as solvent will provide better sensitivity with fewer interferences (at low concentrations), except for analytes having high gas-phase basicities.     

Synthesis of a stable radical anion via the one electron reduction of a 1,1-bis-phosphinosulfide alkene derivative

A new type of stable radical ligand featuring a 1,1-bis-phosphinosulfide alkene backbone has been prepared and characterized on the basis of X-ray diffraction, EPR and DFT studies.     

Bi5(dpd)6 within CH3CN](ClO4)3.3CH3CN: a supramolecular, tetrahedral pentabismuth cluster derived from a nonabismuth oxo/hydroxide

The novel tetrahedral [Bi(5)(dpd)(6) within CH(3)CN](ClO(4))(3).3CH(3)CN (dpd = di-2-pyridyl-gem-diolate) has been synthesized from [Bi(9)(mu(3)-O)(8)(mu(3)-OH)(6)](ClO(4))(5) and di-2-pyridyl ketone. The Bi(5) complex incorporates CH(3)CN via C-HO hydrogen bonding.