Electronic structure of MgO-supported Au clusters: quantum dots probed by scanning tunneling microscopy

We investigate via density functional theory (DFT) the appearance of small MgO-supported gold clusters with 8 to 20 atoms in a scanning tunneling microscope (STM) experiment. Comparison of simulations of ultrathin films on a metal support with a bulk MgO leads to similar results for the cluster properties relevant for STM. Simulated STM pictures show the delocalized states of the cluster rather than the atomic structure. This finding is due to the presence of s- derived delocalized states of the cluster near the Fermi energy. The properties of theses states can be understood from a jellium model for monovalent gold.     

Speciation of halogenides and oxyhalogens by ion chromatography-inductively coupled plasma mass spectrometry

A speciation method utilizing ion chromatography coupled with inductively coupled plasma mass spectrometry is described for simultaneous analysis of eight halogenides and oxyhalogens: chloride, chlorite, chlorate, perchlorate, bromide, bromate, iodide and iodate. The method was applied for the analysis of drinking water samples collected from water treatment plants in areas in Finland, which are known to have high bromine concentrations in ground water. Water samples collected before and after disinfection were analyzed to get information about potential species conversion as a result of purification. Chloride and chlorate were the chlorine species found in these water samples, and iodine existed as both iodate and iodide. In the case of bromine, species conversion had taken place, since total bromine concentrations were increased during disinfection but bromide concentrations were decreased. No bromate was observed in the samples. The detection limits for all the chlorine species studied were 500 μg/l, for bromine species studied 10 μg/l, for iodide 0.1 μg/l and for iodate 0.2 μg/l.     

A comparative study on the behaviour of 1,3-diheterocyclopentanes (X = O,O; S,S; O,S) under electron impact. The formation of thioacetyl and thiiranyl cations

The electron-impact-induced mass spectra of 1,3-dioxolane (la), 1,3-dithiolane (2a) and 1,3-oxatbiolane (3a) and their 2-methyl (1b–3b) and 2,2-dimethyl [(CH₃)₂: 1c–3c or (CD₃)₂: 1d–3d] derivatives have been studied in detail to gain further insight into their ion structures and competing reaction pathways with low-resolution, high-resolution, metastable and collision-induced dissociation (CID) techniques. For compounds 1a–1d the most significant reaction is loss of H^˙ and CH₃^˙ by α-cleavage and a subsequent formation of CHO⁺ and C₂H₃O⁺ ions. The [M ? H]⁺ ions from 1a and 1b give a C₂H₃O⁺ ion which does not have the acyl cation structure as shown by their CID spectra. In compounds 3a–3d the sulphur-containing ions predominate, the C₂H₃O⁺ now having the acyl cation structure. 1,3-Dithiolanes (2a–2d) exhibit the most complicated fragmentation patterns. Furthermore the [M ? H]⁺ ion from 2a and [M ? CH₃]⁺ ion from 2b have different structures as well as the [M ? H]⁺ ion from 2b and [M ? CH₃]⁺ ion from 2c, as shown by their CID spectra. This can be utilized to explain why 3a–3c and 2a give principally a thiiranyl cation, whereas 2b gives a mixture of this and the thioacyl cation and 2c practically only the open-chain thioacetyl cation.     

Determination of the Dissociation Constants of Urocanic Acid Isomers in Aqueous Solutions

(E)- and (Z)-Urocanic acids are endogenous chemicals in the normal mammalian skin. The first and the second thermodynamic dissociation constants (pK _a1 and pK _a2) of urocanic acid isomers were determined using UV spectrophotometry in aqueous solutions. The values with standard deviation (pK _a1 = 3.43 ± 0.12 and pK _a2 = 5.80 ± 0.04) and (pK _a1 = 2.7 ± 0.3 and pK _a2 = 6.65 ± 0.04) were obtained to (E)- and (Z)-urocanic acids, respectively. The second dissociations were studied also by potentiometric titration in aqueous sodium chloride solutions up to the isotonic salt concentration (0.154 mol dm⁻³), and the second thermodynamic dissociation constants as well as activity parameters for both isomers were determined at temperature 25°C and for (E)-urocanic acid also at 37°C. The obtained pK _a2 values were close to those found by UV spectrophotometry. The equations for the calculation of the second stoichiometric dissociation constants of urocanic acid isomers on molality and molarity scale in aqueous sodium chloride solutions were derived. The obtained pK _a1 and pK _a2 values for (Z)-urocanic acid appear to be essentially lower than some previously reported values in literature.     

Arithmetical identities of the Brauer-Rademacher type

Summary LetA be a regular arithmetical convolution andk a positive integer. LetA _k (r) = {d: d ^k A(r ^k )}, and letf A _k g denote the convolution of arithmetical functionsf andg with respect toA _k . A pair (f, g) of arithmetical functions is calledadmissible if(f A _k g)(m) 0 for allm and if the functions satisfy an arithmetical functional equation which generalizes the Brauer—Rademacher identity. Necessary and sufficient conditions are found for a pair (f, g) of multiplicative functions to be admissible, and it follows that, if(f A _k g)(m) 0 f(m) for allm, then (f, g) is admissible if and only if itsdual pair (f A _k g, g ^–1 ) is admissible.Iff andg ^–1 areA _k -multiplicative (a condition stronger than being multiplicative), and(f A _k g)(m) 0 for allm, then (f, g) is admissible, calledCohen admissible. Its dual pair is calledSubbarao admissible. If (f A _k g) ^–1 (m) 0 itsinverse pair (g ^–1 , f ^–1 ) is also Cohen admissible.Ifg is a multiplicative function then there exists a multiplicative functionf such that the pair (f, g) is admissible if and only if for everyA _k -primitive prime powerp ⁱ either (i)g(p ⁱ ) 0 or (ii)g(p ) = 0 for allp havingA _k -type equal tot. There is a similar kind of characterization of the multiplicative functions which are first components of admissible pairs of multiplicative functions. IfA _k is not the unitary convolution, then there exist multiplicative functionsg which satisfy (i) and are such that neitherg norg ^–1 isA _k -multiplicative: hence there exist admissible pairs of multiplicative functions which are neither Cohen admissible nor Subbarao admissible.An arithmetical functionf is said to be anA _k -totient if there areA _k -multiplicative functionsf _T andf _V such thatf = f _T A _k f _V ^-1 Iff andg areA _k -totients with(f A _k g)(m) 0 for allm, and iff _V = g _T , then the pair (f, g) is admissible. The class of such admissible pairs includes many pairs which are neither Cohen admissible nor Subbarao admissible. If (f, g) is a pair in this class, and iff(m), (f A _k g) ^–1 (m), g ^–1 (m),f ^–1 (m) andg(m) are all nonzero for allm, then its dual, its inverse, the dual of its inverse, the inverse of its dual and the inverse of the dual of its inverse are also admissible, and in many cases these six pairs are distinct.A number of related results, and many examples, are given.     

Electron impact ionization mass spectrometry and intramolecular cyclization in 2-substituted pyrimidin-4(3H)-ones

Electron impact ionization mass spectrometry indicates that the behavior of W-unsubstituted pyrirnidin-4-ones with CH₂-R type substitution at C-2 differs from homologs that are N-substituted and/or 2-aryl- or 2-methyl-substituted. A dominant intramolecular cycliza-tion was found to occur between 3ZV (in agreement with the predominance of the 3NH tautomers) and the ortho positions of the aryl moiety in compounds with a CH₂-aryl substitution at C-2. Theoretical calculations with an AMI SCFR method on 2-, 6-, and 2, 6-disubstituted pyrimidin-4-ones support the mass spectrometric observations.     

Meet and join matrices in the poset of exponential divisors

It is well-known that (ℤ₊, |) = (ℤ₊, GCD, LCM) is a lattice, where | is the usual divisibility relation and GCD and LCM stand for the greatest common divisor and the least common multiple of positive integers. The number $ d = \prod\nolimits_{k = 1}^r {p_k^{d^{(k)} } } $ d = \prod\nolimits_{k = 1}^r {p_k^{d^{(k)} } } is said to be an exponential divisor or an e-divisor of $ n = \prod\nolimits_{k = 1}^r {p_k^{n^{(k)} } } $ n = \prod\nolimits_{k = 1}^r {p_k^{n^{(k)} } } (n > 1), written as d | _e n, if d ^(k) for all prime divisors p _k of n. It is easy to see that (ℤ₊\{1}, | _e is a poset under the exponential divisibility relation but not a lattice, since the greatest common exponential divisor (GCED) and the least common exponential multiple (LCEM) do not always exist.