Volume 36, Issue 4

Till now nearly all papers about the Bhabba equation treat equations with a mass term m1. This is merely a matter of mathematical simplicity, because we will see in this work that important physical fields can only be described by a mass term ≠ m 1. The second aim of this publication is to derive a constructive procedure for the calculation of the representations of the Bhabha equation and the tensor and spinor field equations, which are equivalent to them

It is shown that certain systems may exhibit multiple generating singular points which individually peel to result exploded points or limit cycles

Toroidal magnetic fields B = B 0 + εB 1 + ... , where the unperturbed field B 0 has closed lines of force, are considered. Single-valued formal solutions F = F 0 + εF 1 + ... of the equation B · ▽F = 0 are explicitly determined

Polycrystalline ice samples frozen from highly purified water have been investigated by means of the depolarization thermo-current (DTC) technique in the temperature range 85-250 K. Three peaks have been observed at temperatures about 125, 165, and 225 K at a heating rate of 3.5 K/min. The measurements confirm most of the results reported by Johari and Jones. The characteristics of the low temperature DTC peak have been examined extensively for different samples, different heating rates and different polarization conditions. This peak has been found to be non-Debye. Its multiplicity has been studied experimentally using the possibilities offered by the DTC method. It may be better represented by a continuous ditribution of relaxation times than by a sum of discrete relaxation processes

The viscosities of suspensions of polystyrene particles in aqueous LiCl solutions (about 3.5 · 10 -4 M) at temperatures from 0 to 60 °C were measured and fitted to relations of the form η = η 0 (1+K 1 ϕ+K 2 ϕ 2 )i where ϕ is the volume fraction of the particles. In contradiction to existing theories the coefficients K 1 and K 2 were found to be temperature dependent

The rotational Zeeman effect spectra of 3-Fluoropyridine and 2,6-Difluoropyridine have been measured. The molecular g-values are g aa = - 0.0917(5), g bb = - 0.0476(5), g cc = +0.0194(5) for 3-Fluoropyridine and g aa = -0.0573(6), g bb = 0.0311(6), g cc = 0.0102(6) for 2,6-Difluoro- pyridine. The values for the magnetic susceptibility anisotropics in units of 10 -6 erg/(G 2 mol) are 2X aa +X bb + X cc = 53.3(8), 2X bb -X cc -X aa = 60.5(7) for 3-Fluoropyridine and 2X aa -X bb -X cc = 48.4(11), 2X bb -X cc -X aa =51.7(11) for 2,6-Difluoropyridine. Subtraction of the local atom contributions to the magnetic susceptibilities indicates that Fluorine quenching of the nonlocal out of plane contribution depends on the position of the substituent. Further, the data suggest a linear correlation between X ⟂ nonlocal and the “CNDO/2-π-density alternation”, which is used to predict susceptibility anisotropics of Fluorobenzenes and Fluoropyridines not yet measured. The molecular quadrupole moments are calculated from the Zeeman data and compared with the experimental values obtained for various fluorosubstituted Pyridines and Benzenes. If the quadrupole moments perpendicular to the molecular plane are referred to the centers of the six membered rings and are plotted against the number of Fluoroine substituents, n F , the plots closely follow a straight line with identical slopes for the Pyridine- and Benzenefamilies, but with different intercepts at n F = 0. From the “n F = 0 intercept” for the Fluorobenzenes we conclude that the Benzene quadrupole moment proposed earlier by Shoemaker and Flygare should probably be revised

The bond formation of 3d-metal atoms (Cr, Fe, Ni, Cu) with NH 3 and H 2 O is investigated by an ab initio MO theory. In the case of NH 3 , coupling occurs mainly through the HOMO 3a 1 -levels ≙ (N lone pair), whereas with H 2 O the main contribution arises from σ-bond formation of the second highest occupied orbital (3a 1 ≙O2p z ). Results on the bond energies, electron populations and orbital energies are in qualitatively good agreement with experimental data on the adsorptive properties of these molecules on transition metal surfaces

Electrical conductivities of molten mixtures AgCl 1-x -Br x were measured at different temperatures. No influence of dissolved silver on the conductivity could be detected. The apparent energy of activation does not depend linearly on x. The optical spectra of molten mixtures AgCl 1-x -Br x show a flat absorption edge which can be treated by the formalism of Urbach. The energy gap of the indirect transition can be evaluated as a function of x. In metal-containing mixtures, the edge is slightly red shifted. This red shift can be attributed to a new absorbing species. The results make it likely that the interaction between the dissolved metal and the melt is of the charge transfer type

The melting enthalpies and entropies of 24 Menshutkin complexes composed of 2SbCl 3 and aromatic compounds were measured by calorimetric methods. The relatively large values of these thermodynamic data can be explained under the assumption of a dissociation of the complexes during melting. The association enthalpy can be estimated by separating the melting process into two steps

The construction of the coupling operator given by Adams is examined from the standpoint of SCF convergeney. A unified, hermitian coupling operator is derived by taking into account optimum mixing for the pairs of occupied orbitals as well as the correct variational conditions

A modified “Consistent Force Field ” method is described in which the energy minimization is carried out according to the Murtagh-Sargent method rather than the Newton-Raphson method and the number of non-bonded interactions is reduced to interactions between atoms separated by three bonds at the most. The smaller number of interaction terms allowed the programming of the method for a desk top calculator (HP-9810). Calculations are reported for a number of aliphatic molecules

Properties of the weighted Löwdin orthogonalization procedure are thoroughly discussed. It is shown that its flexibility might be very useful in the construction of optimal truncated basis sets in approximate theories of the electronic structure of molecules and solids. The relevance of pairwise nonorthogonal (hybrid) basis functions is pointed out

Molecular dynamics simulations of molten TlCl are performed at 7 temperatures between 800 and 2600 K. The self-exchange velocity of neighbouring unlike ions divided by the molar volume, a quantity corresponding to the specific conductivity, is found to have a maximum as a function of temperature. The reason for the existence of the maximum is discussed

Internal mobility ratios in melts of the system (Na-Rb)NO 3 have been measured with the Klemm method at various temperatures and compositions. The internal mobilities have been calculated from these and the available data on densities and conductivities. The Chemla effect has been observed. For NaNO 3 concentrations > 10 mol %, the internal mobility of the Na + ions obeys the formula b Na = [A/(V - V 0 )] exp(- E/RT). where V is the molar volume and V° is slightly temperature dependent. For NaNO 3 concentrations < 10 mol %, b Na becomes smaller than expected from the formula. The internal mobility of the Rb + ions also obeys such a formula at higher temperatures. At lower temperatures it in, like that of the Cs + ions, a function of the mole fraction and independent of the kind of coions

The first two π(a 2 , b 1 ) IE’s, of monosubstituted benzenes containing di- and tri-coordinated nitrogen directly linked to the ring have been measured and analysed together with the N 1s IE. These photoelectron properties are found to respond in the same sense, though to different extents, to inductive and mesomeric interactions that the N-containing substituents sustain with the aromatic ring. The different sensitivities of these properties to substituent changes are discussed in connection with mechanisms of transmission of electronic effects with the aid of the ground state electronic structures determined by means of ab-initio calculations. The relative contribution of the relaxation energy to the considered core and valence IE’s is also examined by referring to the model used by Gelius and Siegbahn. The factors determining the apparently anomalous behaviour of nitrobenzene are discussed

GVFF and ab initio calculations are reported for ClNCCl 2 . The force constants for the Cl-N and C-Cl bonds show significantly higher values than those of similar compounds, f CN is lower. The charge distribution obtained by ab initio calculations support these results

A periodic reaction was observed for the total oxidation of methanol to CO 2 and H 2 O on a Pd-supported catalyst. By measuring the temperature oscillations of the catalyst and the corresponding product distribution the phenomenology could be correlated with a chemical reaction scheme. The reaction scheme is based on the nonmonotonic behavior of the pressure-concentration relationship of the Pd-H system

The quality of wavefunctions for complex systems derived by either “full” ab initio MO-SCF calculations or within the MESQUAC-MO framework [1] is investigated comparing chemically interesting quantities as atomic and overlap populations and the character of the chemical bond. A direct relation between the results of both methods is shown to exist, allowing an extrapolation of the much less time consuming MESQUAC computations to the “full” MO SCF level. Hydrate complexes of main group and transition metal ions have been chosen for some practical applications

The photoconductivity of neat liquid tetramethyl silane subjected to an intense UV laser flash was studied as a function of laser power. Charge carrier generation was found to proceed via double photon ionization

Thermodynamic functions are calculated for gaseous Se 8 molecules from spectroscopic and structural data and listed for temperatures up to 3000 K. Entropy (S°) and heat capacity (C p 0 ) data for Se n molecules (n = 5, 6, 7, 9, 10, 11, 12) are obtained from linear relationships between both S 0 and C p 0 and ring size n which are derived from the corresponding values of Se 2 and Se 8

If a mechanical shock-wave expands symmetrically in a two-dimensional non-isotropic medium, then the amplitude of the radial displacements is directionally dependent. This has been demonstrated by a system of 1400 hexagonal plastic pillars, simulating the impact of a 10 km size meteorite on a frozen 50 km thick basalt crust in the earliest phase of the Moon’s life

The total cross section for pair production by photons in the field of free electrons is fitted to simple analytic expressions in four intervals of the incident photon energy which cover the whole range between threshold and infinity

Atom-localized molecular orbitals are defined and discussed for alternant hydrocarbons, in the HMO approximation

We study some geometrical features of the non-linear scattering equations [1]. From this we deduce the Liouville equation. For that we interpret the SL(2, ℝ)-valued elements of the matrices in the scattering equations as matrix-valued forms and calculate the curvature 2-form with respect to a basis of the Lie algebra. We obtain the Liouville equation if the curvature form is equal to zero

In the field of structural research of metallic T 80 M 20 -glasses (T = Fe, Co, Ni; M = B, P) at the moment large interest exists in the determination of the so called partial structure factors S mn , especially of the structure factor S MM which is determined by the arrangement of the met-alloid atoms. Since the mathematical evaluation of S MM from three measured total structur factors is rather uncertain, in [1] a method was proposed for the direct measuring of S BB in Ni 81 B 19 , the experimental realization of which will be reported in the present paper