A “Hybrid Plane” with spin-orbit interaction

In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin ½ and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind.     

A simple model of thin-film point contact in two and three dimensions

We treat a free spinless quantum particle moving on a configuration manifold which consists of two identical parts connected in one point. Most attention is paid to the three-dimensional case when these parts are halfspaces with Neumann condition on the boundary; we also discuss briefly a more general boundary conditions. The class of admissible Hamiltonians is constructed by means of the theory of self-adjoint extensions. Among them, particularly important is a two-parameter family whose elements are invariant with respect to exchange of the halfspaces; we compute the transmission coefficient for each of these extensions. We discuss also the motion on two planes considered in our recent paper, obtaining another characterization of the admissible Hamiltonians. In conclusion, the two situations are compared as models for point-contact spectroscopical experiments in thin metal films.On leave of absence fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.On leave of absence fromNuclear Centre, Charles University, V Holeovikách 2, 180 00 Prague 8, Czechoslovakia.     

Electrostatic calculation of the substituent effect: an efficient test on isolated molecules

The energy of a disubstituted molecule has often been approximated by simple electrostatic formulas that represent the substituents as poles or dipoles. Herein, we test this approach on a new model system that is more direct and more efficient than testing on acid-base properties. The energies of 27 1,4-derivatives of bicyclo[2.2.2]octane were calculated within the framework of the density functional theory at the B3LYP/6-311+G(d,p) level; interaction of the two substituents was evaluated in terms of isodesmic homodesmotic reactions. This interaction energy, checked previously on some experimental gas-phase acidities, was considered to be accurate and served as reference to test the electrostatic approximation. This approximation works well in the qualitative sense as far as the sign and the order of magnitude are concerned: beginning with the strongest interaction between two poles, a weaker interaction between pole and dipole, and the weakest between two dipoles. However, all the electrostatic calculations yield energies that are too small, particularly for weak interaction, and this fundamental defect is not remedied by some possible improvements. In particular, variation of the effective permittivity would require a physically impossible value less than unity. The explanation must lie in a more complex distribution of electron density than anticipated in the electrostatic model. It also follows that possible conclusions about the transmission of substituent effects "through space" have little validity.     

Open quantum systems and Feynman integrals: Some problems

A few open problems of mathematical physics are presented. They concern open quantum systems and Feynman path integrals; some of them are technical, while others are of conceptual importance.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

Enthalpies of formation of methoxybenzoic acids and their dependence on structure

The energy of combustion of 2,5-dimethoxybenzoic acid has been determined using a static bomb calorimeter. The vapor pressures of the compound have been measured over a 18 K temperature interval by the Knudsen effusion technique. Heat capacity measurements betweenT=270 K andT=338 K were carried out by DSC. From these experimental results the standard molar enthalpies of combustion, sublimation, and formation in the crystalline and gaseous state at the temperature 298.15 K have been derived. With this compound, the series of mono- and dimethoxy-benzoic acids have been completed. Their_f H _m ^o values were expressed by an additive relationship, taking into account the number of methoxy groups and the number of all 1,2 interactions: an accuracy of 3.3 kJ·mol^–1 was achieved. In an alternative approach the substituent effect of the methoxy groups was evaluated within the framework of isodesmic reactions. The effect of disubstitution was referred to mono derivatives and the excess energy—the so-called buttressing effect—was evaluated (2–24 kJ· mol^–1 for individual bis derivatives). These values were explained in terms of the conformation of the methoxy group around the C_ar-O bond.     

Electron distribution on an intramolecular hydrogen bond: A semiempirical AM1 study

Dipole moments of seven molecules were studied by AM1, each containing an intramolecular hydrogen bond between a hydroxyl group and a carbonyl or nitro group as hydrogen acceptors. The hydrogen bond causes two electron shifts: from H to O within the hydroxyl group and from C to O within the carbonyl group. The latter is accompanied by withdrawal of electrons from even more distant atoms. If the total electron density change is expressed as a vector, its direction is close to the direction of the O-H bond. This electron redistribution is in agreement with the previous, somewhat, puzzling experimental results. However, it differs from the commonly accepted picture according to which electron density changes on the hydrogen acceptor moiety are less important than those on the O-H bond.Dedicated to Professor Viktor Gutmann on the occasion of his 70th birthday.     

Effects of ion-pairing reagents on the electrospray signal suppression of sulphonated dyes and intermediates

High-performance liquid chromatography/mass spectrometry (HPLC/MS) analysis of anionic species such as sulphonic acid dyes and intermediates requires volatile ion-pairing mobile phase additives. Six di- and trialkylammonium acetates were compared with tetraalkylammonium salts and ammonium acetate in the concentration range 0-20 mmol l(-1) as mobile phase additives for HPLC/MS of polysulphonated compounds. The effects of the structure and concentration of the ion-pairing reagents on the electrospray response of mono-, di- and tetrasulphonic aromatic acids and acid dyes were studied in detail. Further, five different mass analysers and instrument geometries were compared. A higher signal decrease is observed with linear geometry instruments in comparison to orthogonal or even Z-spray geometry mass spectrometers. The concentration of mobile phase additives has a significant influence on the abundance ratios of multiply charged ions in the mass spectra of polysulphonated compounds. The competing ions of sulphonic acids may also cause significant signal suppression.