Discrete mechanics and its application to the solution of the n-body problem

A theory of discrete mechanics is developed based on the results of D. Greenspan. Discrete dynamical equations in an inertial frame, in a coordinate system related to some material point, and in a rotating frame are given and the consistency, stability, and convergence of the methods are studied and some numerical examples presented.     

Complexing equilibria and redox potentials in the system Ag(II)/Ag(I)-1,10-phenanthroline in propylene carbonate

Predominance areas of various equilibria were identified and complex formation constants of Ag(I) with 1,10-phenanthroline were determined as well as the solubility product of the complex salt for Ag(phen)₂ClO₄ in propylene carbonate. The solubility product of AgNO₃ in propylene carbonate was estimated. The value of the formal potential of the system Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC was determined by chronovoltammetry. Differences in the stability of analogous complexes in water andPC are discussed.

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Die Gleichgewichtskonstante der Komplexierung und die Redoxpotentiale im System Ag(II)/Ag(I)-1,10-Phenantrolin in Propylencarbonat

Zusammenfassung Die Gebiete der Dominanz der einzelnen Gleichgewichte, die Bildungskonstanten ₁ und ₂ der Komplexe Ag(I) mit 1,10-Phenantrolin und der Wert des Löslichkeitsproduktes Ag(phen)₂ClO₄ in Propylencarbonat wurden bestimmt. Das Löslichkeitsprodukt von AgNO₃ in Propylencarbonat wurde abgeschätzt. Die Werte des formalen Potentials des Systems Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ inPC wurden mit Hilfe cyclischer Voltametrie ermittelt. Es wurden weiterhin die Unterschiede in der Stabilität analoger Komplexe in Wasser und in Propylencarbonat diskutiert.

     

Preparation and photocatalytic properties of silica-supported fine CdS powders

Summary Silica-supported cadmium sulfide, highly active in hydrogen photogeneration from water-methanol-KOH solution, was prepared by sulfidation of Cd²⁺-impregnated SiO₂. The samples consisted of colloidal-size hexagonal crystallites of CdS on amorphous SiO₂. A blue shift of a light absorption edge was observed for the samples with lower CdS content.

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Herstellung und photokatalytische Aktivität von feinen CdS-Pulvern auf SiO₂

Zusammenfassung Es wurde Cadmiumsulfid auf Kieselgel durch Sulfidierung von Cd²⁺-imprägniertem SiO₂ hergestellt, das eine außerordentliche Aktivität bei der Wasserstoff-Photogenerierung aus Wasser-Methanol-KOH-Lösungen zeigte. Der Katalysator bestand aus hexagonalen CdS-Kristalliten von kolloidalen Ausmaßen auf amorphem SiO₂. An Proben mit geringerem CdS-Gehalt wurde eine Blauverschiebung der Lichtabsorption an der Absorptionskante beobachtet.

     

Probability issues in molecular design: predictive and modeling ability in 3D-QSAR schemes

In the current work we investigated 3D-QSAR data by the use of the coupled leave-several-out (LSO) and leave-one-out (LOO) cross-validation (CV) procedures. We verified the above mentioned scheme using both simulated data and real 3D QSAR data describing a series of CoMFA steroids, heterocyclic azo dyes and styrylquinoline HIV integrase inhibitors. Unlike in standard analyses, this technique characterizes individual method not by a single performance metrics but screens a whole possible modeling space by sampling different molecules into the training and test sets, respectively. This allowed us for the discussion of the information included in the estimators validating cross-validation procedures, as well as the comparison of the efficiency of several 3D QSAR schemes, in particular, Comparative Molecular Field Analysis (CoMFA) and Comparative Molecular Surface Analysis (CoMSA). Moreover, it allows one to acquire some general knowledge about predictive and modeling ability in 3D QSAR method.     

Mutual Solubilities of Water and Alkanes

Summary.  The evaluation of mutual solubility data for systems water with n-alkanes, isoalkanes, and cycloalkanes along the three phase line is reported and a formula for the prediction of solubility of alkanes in water is developed. Then a cubic equation of state with an added term, which accounts for hydrogen bonding is used for correlation of liquid–liquid equilibrium data and for prediction of solubility of water in hydrocarbons using alkane in water solubility data. Comparison of the predicted and experimental solubilities is performed using all accessible experimental data. With this approach it is possible to predict the solubilities of water in alkanes with good accuracy over the temperature range up to about 20 K below critical temperature. Solubility of alkanes in water can also be calculated using experimental data for solubility of water in alkanes but results of these calculations are more sensitive to experimental errors of the data. Corresponding author: E-mail: macz@ichf.edu.pl Received August 5, 2002; accepted (revised) September 13, 2002 Published online March 13, 2003 RID="a" ID="a" Dedicated to Prof. Dr. H. Gamsj?ger on the occasion of his 70^th birthday anniversary     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

Attractive halogen–halogen interactions: F3CCl⋯FH and F3CCl⋯FCH3 dimers

The F₃CCl?FH and F₃CCl?FCH₃ dimers, which feature the halogen–halogen contacts, are investigated at MP2/6–311++G(d,p) and MP2/aug–cc–pVDZ levels of approximation. The binding energies of these complexes are found to be comparable to those of the weak hydrogen bonds. In both complexes the Cl?F are found to be significantly shorter than the sum of the corresponding van der Waals radii. The C–Cl?F contacts are also found to exhibit certain deviation from linearity. However, the energy differences between linear and bent structures are very small and primarily accounted for by electrostatic interactions between remote parts of the dimer. This indicates a high conformational flexibility of the halogen–halogen contacts and may help to explain the diversity of structural features in crystals formed by halogen-containing molecules. In both dimers the halogen–halogen interaction leads to certain shortening of the C–Cl electron accepting bond. This is accompanied by a small increase of the C–Cl stretching frequency. Hence, the two investigated dimers can possibly be classified as the blue-shifting halogen–halogen contacts.     

On the asymptotic behavior of dynamical maps for a finite quantum system

We give some remarks on the dynamical evolution (also nonlinear) of finite quantum system. We are interested int-asymptotic behavior of density matrices in the Liouville space formalism and we show that for nonlinear dynamical semigroups, as well as for the dynamical maps that do not form semigroups, the stationary time evolution may be attained for finite time in contrast to the motion generated by the linear dynamical semigroup. Recently the problem of constructing a nonlinear analog of quantum mechanics with nonlinear wave equation playing the role of the Schrödinger equation has been investigated by some authors; see for example Mielnik (1974), Bergmann (1968). Our work is related to this investigation and gives a characteristic feature of the nonlinear time evolution.