Compactifications of Discrete Quantum Groups

Given a discrete quantum group we construct a Hopf -algebra which is a unital -subalgebra of the multiplier algebra of . The structure maps for are inherited from and thus the construction yields a compactification of which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra.Partially supported by Komitet Badań Naukowych grants 2P03A04022 & 2P03A01324, the Foundation for Polish Science and Deutsche Forschungsgemeinschaft.     

HS⇄LS transition in iron(II) two-dimensional coordination networks containing tris(tetrazol-1-ylmethyl)methane as triconnected building block

Novel tripodal ligand 1,1',1'-tris(tetrazol-1-ylmethyl)methane (111tz) and products of its reactions with perchlorate as well as with tetrafluoroborate salts of iron(II) are presented. The isostructural complexes, [Fe(111tz)?](ClO?)? and [Fe(111tz)?](BF?)?, were isolated as two-dimensional (2D) coordination networks revealing a honeycomb-like pattern with cages occupied by disordered anions. 111tz molecules act as a tridentate ligand bridging three adjacent Fe(II) ions, and the nitrogen N4 atom of six tetrazole rings (tz) is placed in octahedron vertices of FeN? chromophores. The complexes, crystallizing in the P3 space group, were characterized by variable-temperature single-crystal X-ray diffraction and variable-temperature magnetic susceptibility measurements. Variable-temperature magnetic susceptibility measurements show that both systems undergo abrupt and complete spin transition with T(1/2)(↑) = T(1/2)(↓) = 176 K for perchlorate and T(1/2)(↑) = 193.8 and T(1/2)(↓) = 192.8 K for the tetrafluoroborate analogue. Change of spin state in both complexes is accompanied by a thermochromic effect. The HS→LS transition in [Fe(111tz)?](ClO?)? involves shortening of the Fe-N4 bond lengths from 2.171(2) ? (293 K) to 2.002(1) ? (100 K). In [Fe(111tz)?](BF?)?, lowering of temperature from 293 to 100 K is accompanied by shortening of the Fe-N4 distances from 2.179(2) to 1.987(2) ?, respectively. Perchlorate in [Fe(111tz)?](ClO?)? or tetrafluoroborate anions in [Fe(111tz)?](BF?)? are engaged in the formation of intermolecular contacts within as well as with the neighboring 2D layer.     

Ultrasensitive laser spectroscopy for breath analysis

At present there are many reasons for seeking new methods and technologies that aim to develop new and more perfect sensors for different chemical compounds. However, the main reasons are safety ensuring and health care. In the paper, recent advances in the human breath analysis by the use of different techniques are presented. We have selected non-invasive ones ensuring detection of pathogenic changes at a molecular level. The presence of certain molecules in the human breath is used as an indicator of a specific disease. Thus, the analysis of the human breath is very useful for health monitoring. We have shown some examples of diseases’ biomarkers and various methods capable of detecting them. Described methods have been divided into non-optical and optical methods. The former ones are the following: gas chromatography, flame ionization detection, mass spectrometry, ion mobility spectrometry, proton transfer reaction mass spectrometry, selected ion flow tube mass spectrometry. In recent twenty years, the optical methods have become more popular, especially the laser techniques. They have a great potential for detection and monitoring of the components in the gas phase. These methods are characterized by high sensitivity and good selectivity. The spectroscopic sensors provide the opportunity to detect specific gases and to measure their concentration either in a sampling place or a remote one. Multipass spectroscopy, cavity ring-down spectroscopy, and photo-acoustic spectroscopy were characterised in the paper as well.     

Examples of non-compact quantum group actions

We present two examples of actions of non-regular locally compact quantum groups on their homogeneous spaces. The homogeneous spaces are defined in a way specific to these examples, but the definitions we use have the advantage of being expressed in purely C^∗-algebraic language. We also discuss continuity of the obtained actions. Finally we describe in detail a general construction of quantum homogeneous spaces obtained as quotients by compact quantum subgroups.     

Stereochemistry of organophosphorus cylic compounds—XV: Synthesis of tetramethylammonium salt of 2-oxo-2-thio-1,3,2,-oxazaphosphorinan and its crystal and molecular structures

2-Hydroxy-1,3,-2-oxazaphosphorinan-2-thione (5) was prepared by alkaline hydrolysis of 2-chloro-1,3,2-oxazaphosphorinan-2- thione (6). Treatment of the latter with sodium methoxide afforded the 2-methoxy-derivative 7 from which the tetramethylammonium salt of the thioacid 5 was obtained by the action of trimethylamine. The structure of this salt has been determined by the direct method and refined by least-squares to R = 0.0734, a = 12.303(4), b = 9.041(3), c = 10.419(2) Å, space group P2₁2₁2₁. The 2-oxo-2-thio-1,3,2-oxazaphosphorinanyl anion is in the chair form with the exocylic S and O atoms in an axial and equatorial position, respectively. An intermolecular H-bond between S and the endo-cyclic N atom is present in the solid-state structure.     

Dynamic correlation for MCSCF wave functions: An effective potential method

A method is suggested which allows the inclusion of dynamic correlation into CASSCF calculations. An effective Coulomb hole potential is added to the Hamiltonian. The potential has a simple form, which allows its implementation into existing LCAO programs using Gaussian integral packages. The parameters appearing in the potential are determined by fitting to empirical valence correlation energies for first row atoms. Calculations of ionization energies and electron affinities show considerable improvement compared to the MCSCF values. Test calculations on three molecules give the following results, H₂ r _e=0.745 (0.741) Å, D _e=4.62 (4.75) eV; N₂ r _e=1.099 (1.098) Å, D _e= 10.42 (9.91) eV; O₂ r _e=1.198 (1.207) Å, D _e=4.73 (5.21) eV. Experimental values within parenthesis. On leave from: Institute of Organic Chemistry, Polish Academy of Sciences, PL-01-224 Warszawa 42, ul. Kasprzaka 44, Poland.