On the number of conjugacy classes of a finite solvable group II

We prove that a finite solvable group G has at least (49p+1)/60 conjugacy classes whenever p is a prime such that p² divides the order of G. We also construct an infinite family of finite solvable groups, where this bound is attained.     

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.     

Electrospray ionization mass spectrometric study of encapsulation of amino acids by cyclodextrins

Electrospray ionization (ESI) mass spectrometry has been used to study inclusion (host-guest) complexes of cyclodextrins (CDs) with amino acids. Host-guest complexes formed in solution are stable for characterization by ESI mass spectrometry: The relative abundances and the stoichiometry of the complexes formed in solution can, thus, be determined in the gas phase. The studies verified that β- and γ-cyclodextrin better accommodate protonated amino acids than α-cyclodextrin, and that chemically modified cyclodextrins such as heptakis(2,6-di-O-methyl)-β-cyclodextrin (DM-β-CD) may show profound improvement in complexation. The preferential formation of DM-β-CD-aromatic amino acid over DM-β-CD-aliphatic amino acid complexes is confirmed by the experiments, and the relative gas-phase stabilities determined by repeller-collimator collision-induced dissociation show an identical trend to the complexation in solution. Although molecular mechanics studies also may predict the encapsulation preference of protonated amino acids by cyclodextrins, only small differences in the total complexation energies are obtained because of the inability of the calculations to consider hydrophobic interactions. An experimental approach based on ESI mass spectrometry is, therefore, more reliable in predicting host-guest interactions that involve cyclodextrins and amino acids than the theoretical calculations that employ molecular mechanics models.     

Sodium-23 Nuclear Magnetic Resonance Spectroscopy

With the availability of Fourier transform spectrometers, ²³Na-NMR spectroscopy has become an important tool. It affords direct insight into solvation and ion pairing phenomena, both in organic and in bio-inorganic systems. Monitoring the chemical shifts and linewidths of ²³Na signals gives access to binding constants, reorientational correlation times and the microdynamics of the sodium coordination shell. The binding of other cations can also be studied by ²³Na-NMR spectroscopy, in competition experiments.     

Enhancement of phosphoprotein analysis using a fluorescent affinity tag and mass spectrometry

A fluorescent affinity tag (FAT) was synthesized and was utilized to selectively modify phosphorylated serine and threonine residues via beta-elimination and Michael addition chemistries in a 'one-step' reaction. This labeling technique was used for covalent modification of both phosphoproteins and phosphopeptides, allowing identification of these molecular species by fluorescence imaging after solution- or gel-based separation methods. In addition to the strong fluorescence of the rhodamine tag, a commercially available antibody can be used to enrich low-abundance post-labeled phosphopeptides present in complex mixtures. Application of this methodology to phosphorylation-site mapping has been evaluated for a phosphoprotein standard, bovine beta-casein. Initial results demonstrated low femtomole detection limits after fluorescence image analysis of FAT-labeled proteins or peptides.     

Investigating bidentate and tridentate carbamoylmethylphosphine oxide ligand interactions with rare-Earth elements using electrospray ionization quadrupole ion trap mass spectrometry

Electrospray ionization (ESI) quadrupole ion trap mass spectrometry (QIT-MS) and collisionally activated dissociation (CAD) were used to evaluate the rare-earth binding properties of two hydrophobic carbamoylmethylphosphine oxide (CMPO) ligands, the normal bidentate variety, (t-BuC6H4)2P(O)CH2C(O)N(i-Bu)2 (A), a new potentially tridentate extractant, (t-BuC6H4)2P(O)CH[CH2C(O)N(i-Bu)2]C(O)N(i-Bu)2 (B), and tributyl phosphate. The mass spectral results obtained from analysis of 1% HNO3/methanol solution containing the ligands and dissolved lanthanide salts reveal that the favorable stoichiometries of the ligand/metal/nitrate complexes are 2:1:2 for the bidentate ligand A, 1:1:2 for the tridentate ligand B, and 3:1:2 for the monodentate tributyl phosphate. These observed stoichiometries correlate with the number of available binding sites on each ligand as well as with potential steric effects. Energy-variable collisionally activated dissociation experiments showed that for the 2:1:2 complexes involving ligand A or B, as the ionic radius of the bound metal decreased, the removal of nitric acid required less energy and resulted in less extensive spontaneous solvent coordination. This experimental trend suggests that, as the ionic radius of the lanthanide ion decreases, a pair of the carbamoylmethylphosphine ligands is able to more completely solvate the bound metal ion thereby weakening the nitrate-metal interaction.     

Direct Clay-Catalyzed Friedel-Crafts Arylation and Chlorination of the Hydrocarbon Adamantane

Multiple chlorinations and arylations at the tertiary positions of adamantane are promoted by FeCl₃-doped K10 montmorillonite in CCl₄ or in aromatic solvents. The process, remarkably easy to implement, can be tailored to selective formation of monosubstituted 1-adamantyl derivatives or 1,3-disubstituted adamantanes. The process achieves alkylation at the meta- and para-positions of toluene leading to a purely statistical distribution and displays no substrate specificity in competition experiments between toluene and benzene.     

Photoelectron spectra of cyclopolysilanes

Summary He (I) PE spectra of cyclopentasilane and cyclohexasilane show excellent agreement with STO-3 G + ab initio calculations. The HOMO in both compounds is of (SiSi) 3 p character. First IP's appear at 9.4 and 9.6 eV respectively.

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Photoelektronenspektren von Cyclopolysilanen (Kurze Mitt.)

Zusammenfassung Die He (I) PE-Spektren der Cyclosilane Si₅H₁₀ und Si₆H₁₂ zeigen ausgezeichnete Übereinstimmung mit STO-3 G + ab initio Rechnungen. Beide Ringe besitzen HOMO's mit (SiSi) 3 p Charakter. Die ersten Ionisierungspotentiale liegen bei 9.4 bzw. 9.6 eV.