Non-existence of a minimizer to the magnetic Hartree-Fock functional

In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization.      

Prescribing eigenvalues of the Dirac operator

In this note we show that every compact spin manifold of dimension ≥3 can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.     

Dynamics of spin-1/2 quantum plasmas

The fully nonlinear governing equations for spin-1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron-ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.     

Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

A widespread belief in the study of granular flow is the existence of “homogeneous cooling states”, i.e., self-similar solutions which would attract all solutions, faster than the equilibrium solution does. In most cases, the existence of these self-similar solutions is an open problem. Here we consider a one-dimensional model, which has been used for some years, and for which simple self-similar solutions do exist. However, we prove that the approximation is quite poor. Our proof makes use of the powerful and simple tools of mass transportation, and exploits the structure of the evolution equation, seen as a nonlinear transport equation.     

Systematic studies on the determination of Hg-labelled proteins using laser ablation-ICPMS and isotope dilution analysis

A method was developed for the precise and accurate determination of ovalbumin labelled with p-hydroxy-mercuribenzoic acid (pHMB) using polyacrylamide gel electrophoresis with ns-laser ablation–inductively coupled plasma mass spectrometry. Following systematic optimisation of the ablation process in terms of detection sensitivity, two different quantification strategies were applied: external calibration using standards of the derivatized protein after ¹³C⁺ normalization and, as a proof of concept, label-specific isotope dilution analysis (IDA) using pHMB enriched in the isotope ¹⁹⁹Hg. Due to the inhomogeneous distribution of the protein within the gel bands, it could be demonstrated that the IDA approach was superior in terms of precision and accuracy. Furthermore, it permits a reliable quantification, if more complex separation protocols are applied, as typically occurring analyte loss and degradation can be compensated for as soon as complete mixture of spike and sample is achieved. The estimated limit of detection was 160 fmol in the case of ovalbumin. In contrast to earlier studies using metals naturally present in proteins, no loss of mercury was observed during separation under denaturing conditions and other sample preparation steps. Using label-specific IDA, the measured isotope ratios in the gel corresponded to recoveries between 95% and 103%.     

Efficient organic monoliths prepared by γ-radiation induced polymerization in the evaluation of histone deacetylase inhibitors by capillary(nano)-high performance liquid chromatography and ion trap mass spectrometry

New monolithic HPLC columns were prepared by γ-radiation-triggered polymerization of hexyl methacrylate and ethylene glycol dimethacrylate monomers in the presence of porogenic solvents. Polymerization was carried out directly within capillary (250-200 μm I.D.) and nano (100-75 μm I.D.) fused-silica tubes yielding highly efficient columns for cap(nano)-LC applications. The columns were applied in the complete separation of core (H2A, H2B, H3, and H4) and linker (H1) histones under gradient elution with UV and/or electrospray ionization (ESI) ion trap mass spectrometry (MS) detections. Large selectivity towards H1, H2A-1, H2A-2, H2B, H3-1, H3-2 and H4 histones and complete separation were obtained within 8 min time windows, using fast gradients and very high linear flow velocities, up to 11 mm/s for high throughput applications. The method developed was the basis of a simple and efficient protocol for the evaluation of post-translational modifications (PTMs) of histones from NCI-H460 human non-small-cell lung cancer (NSCLC) and HCT-116 human colorectal carcinoma cells. The study was extended to monitoring the level of histone acetylation after inhibition of Histone DeACetylase (HDAC) enzymes with suberoylanilide hydroxamic acid (SAHA), the first HDAC inhibitor approved by the FDA for cancer therapy. Attractive features of our cap(nano)-LC/MS approach are the short analysis time, the minute amount of sample required to complete the whole procedure and the stability of the polymethacrylate-based columns. A lab-made software package ClustMass was ad hoc developed and used to elaborate deconvoluted mass spectral data (aligning, averaging, clustering) and calculate the potency of HDAC inhibitors, expressed through a Relative half maximal Inhibitory Concentration parameter, namely R_IC(50) and an averaged acetylation degree.     

Impact of concentration self-quenching on the charge generation yield of fullerene based donor-bridge-acceptor compounds in the solid state

A fullerene based Donor-Bridge-Acceptor (DBA) compound, incorporating a π-extended tetrathiafulvalene electron donor, is investigated with respect to its photophysics in solution versus solid state. Solid films of neat DBA are compared with blend films where the DBA compound is diluted in the inert, low dielectric, polymer poly(styrene). It is found that the moderate intermolecular electronic coupling and donor-acceptor separation (22 ?) in this case leads to the generation of more dissociated, intermolecular charges than a mixture of the donor and acceptor reference compounds. However, the increased intermolecular interactions in the solid state lead to the excited state of the fullerene suffering from concentration self-quenching. This is found to severely affect the charge generation yield in solid films. The impact of competing intra and intermolecular interactions in the solid state upon the film photophysics is analysed in terms of a kinetic model which includes both the effects of concentration self-quenching and the impact of film composition upon the dielectric stabilisation of charge separated states. We conclude that both concentration self-quenching and dielectric stabilisation are critical in determining the photophysics of the blend films, and discuss strategies based upon our observations to enhance the charge photogeneration properties of organic films and photovoltaic devices based upon DBA compounds.     

Chain folding in single crystals of tetrafluoroethylene copolymers

Molecular-mechanics calculations are performed on model folds proposed in the literature for single crystals of polytetrafluoroethylene crystallized in the phase stable below 19°C, in order to evaluate how they are modified when a fluorine atom is substituted by a bulky group, as occurs in fluorinated copolymers of tetrafluoroethylene. Only intramolecular effects are taken into account (isolated-chain model). An exhaustive analysis has been carried out of tetrafluoroethylene-hexafluoropropylene copolymer. Moreover, the lower energy folds found for such a copolymer have been examined for copolymers with chlorotrifluoroethylene and perfluoroalkylvinylethers, as comonomers. Our calculations show that all the considered comonomers can be arranged in the model folds proposed for the homopolymer, according to the imposed geometric constraints.