Toward the spectrum of free polyethylene: linear alkanes studied by carbon 1s photoelectron spectroscopy and theory

Trends in carbon 1s ionization energies for the linear alkanes have been investigated using third-generation synchrotron radiation. The study comprises CH(4), C(2)H(6), C(3)H(8), C(4)H(10), C(5)H(12), C(6)H(14), and C(8)H(18). Both inter- and intramolecular shifts in ionization energy have been determined from gas-phase spectra and ab initio calculations. The shifts are decomposed into initial-state and final-state contributions and are shown to relate to the fundamental chemical properties of group electronegativity and polarizability. By extrapolation, we predict C1s spectra of larger n-alkanes, converging toward isolated strands of polyethylene.     

Gas phase ESCA studies of trithiapentalene and its 2,5-dimethyl derivative

1,6,6a-trithiapentalene and its 2,5-dimethyl derivative have been studied in the gas phase by means of ESCA in order to elucidate the unusual type of S---S bonding in these molecules. The high resolution spectra show very wide S 2p lines from the terminal sulfur atoms due to vibrational broadening. The effect of core ionization on the S---S bond lengths in trithiapentalene has been estimated using the equivalent core approximation and the CNDO/2 method. Ground and final state potential curves have been calculated and explain qualitatively the differences in line widths for the terminal and central sulfur atoms. The observed chemical shifts agree with predictions from CNDO/2 and ab initio calculations.     

The electronic structure of free water clusters probed by Auger electron spectroscopy

(H2O)(N) clusters generated in a supersonic expansion source with N approximately 1000 were core ionized by synchrotron radiation, giving rise to core-level photoelectron and Auger electron spectra (AES), free from charging effects. The AES is interpreted as being intermediate between the molecular and solid water spectra showing broadened bands as well as a significant shoulder at high kinetic energy. Qualitative considerations as well as ab initio calculations explain this shoulder to be due to delocalized final states in which the two valence holes are mostly located at different water molecules. The ab initio calculations show that valence hole configurations with both valence holes at the core-ionized water molecule are admixed to these final states and give rise to their intensity in the AES. Density-functional investigations of model systems for the doubly ionized final states--the water dimer and a 20-molecule water cluster--were performed to analyze the localization of the two valence holes in the electronic ground states. Whereas these holes are preferentially located at the same water molecule in the dimer, they are delocalized in the cluster showing a preference of the holes for surface molecules. The calculated double-ionization potential of the cluster (22.1 eV) is in reasonable agreement with the low-energy limit of the delocalized hole shoulder in the AES.     

Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.     

Formation of monoaldehydes by cerium(IV) ammonium nitrate oxidation of unsymmetric dimethylnaphthalenes

When 1,2-, 1,3-and 1,6-dimethylnaphthalene are oxidized by Ce⁴⁺ in acetic acid the corresponding monoaldehydes are formed in better than 80% yield. In each case aldehyde formation takes place with a high degree of selectivity as the methyl-1- to methyl-2-naphthaldehyde ratio is better than 11:1. The selectivity may be explained from differences in reactivity as calculated within the frontier orbital method.     

Anomalous natural linewidth in the 2p photoelectron spectrum of SiF4

The silicon 2p photoelectron spectra for SiH4, SiF4, and SiCl4 have been analyzed to give the natural linewidths of the Si 2p hole states, which reflect the Auger decay rates of the states. For SiH4 the measured width of 38 meV is in approximate agreement with the prediction of the one-center model (32 meV), but that for SiF4 of 79 meV is more than 5 times the value of 14 meV predicted by this model. Approximate theoretical calculations indicate that valence electrons from the fluorine atoms of SiF4 play an important role in the Auger decay via interatomic processes.     

On some nonself mappings

Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ?K (?K the boundary of K) into K then T has a unique fixed point in K.     

Multicomponent structure in x-ray photoelectron spectroscopy of transition metal compounds

This paper is a summary of work in progress on a comprehensive study of the nature of satellite lines in x-ray photoelectron spectroscopy. The work can be broken down into three principal areas: (1) The satellite structure arising from photoionization in the K shell of transition metal compounds has been measured using CuKα x rays. From these data the relative importance of electron shake up and multiples splitting has been ascertained. (2) A systematic study of the satellite structure following photoionization in the 2p subshell of the metal ion for first row transition metal halides, hexacyano complexes, acetyl acetonates and other miscellaneous compounds. The data can be explained in terms of monopole excitation involving either charge exchange between ligand and metal orbitals or excitation of electrons in the 3d orbital. (3) A study of multiplet splitting in the 3s subshell of nickel for a series of NiFe_xCr _2-xO₄ alloys has been carried out and compared with measurements on the hyper field interactions from Mössbauer experiments.     

Size of neutral argon clusters from core-level photoelectron spectroscopy

Theoretical models of lineshapes in Ar2p photoionization spectra have been calculated for free, neutral argon clusters of different sizes. The lineshape models are fitted to experimental spectra and used to estimate the mean cluster size realized in the experiment. The results indicate that size estimators working from stagnation conditions [R. Karnbach, M. Joppien, J. Stapelfeldt, J. W?rmer and T.M?ller, Rev. Sci. Instrum., 1993, 64, 2838] may underestimate the mean cluster size.