Generalized 1/Z expansion for heteronuclear molecules

We have first studied empirical regularities in various series of heteronuclear diatomic molecules between the energy E, the total number of electrons N, the equilibrium distance R_e and Z? = (Z₁Z₂)^1/2 where Z₁e and Z₂e are the nuclear charges in the diatom. In particular, for various alkali halide series, R_e²|E|/N^5/3 is shown to correlate rather simply with Z?R_e³. Some theoretical basis is afforded by generalizing the 1/Z expansion used early by the writers in work on homonuclear diatomics. Finally, when Z₂/Z₁ → ∞, a model is presented which predicts a finite asymptotic bond length and this prediction is confronted with available experimental data for both heteronuclear diatoms and for the polyatomic series CH₄ to SnH₄.     

Ernst Foradori

Ohne Zusammenfassung     

The limiting angle of certain riemannian brownian motions

Let M be a Cartan-Hadamard manifold of dimension d ≧ 3, let p ? M and x = exp {r(x)θ(x)} be geodesic polar coordinates with pole p and let X be the Brownian motion on M. Let Sect_M(x) denote the sectional curvature of any plane section in M_x. We prove that for each c > 2, there is a 0 < β < 1 such that if - L²r(x)^2β ≦ Sect_M(x) ≦ -cr(x)^?2 for all x in the complement of a compact set, then lim_{t → ∞} θ(X_t) exists a.s. and defines a nontrivial invariant random variable. The Dirichlet problem at infinity and a conjecture of Greene and Wu are also discussed.     

Mass spectrometric study of persistent acid metabolites of nonylphenol ethoxylate surfactants

A mass spectrometric study was carried out on two nonylphenoxycarboxylic acids, NP1EC and NP2EC (where 1 and 2 indicate the number of ethoxylate units attached to the nonylphenoxy moiety), that are persistent metabolites of widely used nonionic surfactant nonylphenol ethoxylates. In a gas chromatographic/mass spectrometric (GC/MS) study of the methyl esters of NP1EC and NP2EC, two series of fragment ions were observed in electron ionization (EI) mass spectra; m/z (179 + 14n, n = 0-7) and m/z (105 + 14n, n = 0-4) for NP1ECMe and m/z (223 + 14n, n = 0-7) and m/z (107 + 14n, n = 0-5) for NP2ECMe. Similarity indices were used to compare quantitatively the mass spectra of isomers. The mass spectra of two isomers were found to be similar whereas those of the remaining isomers were readily distinguishable from each other. The abundant fragment ions of the two NPECMes were investigated further by GC/MS/MS; product ions resulting from cleavage in the alkyl moiety, cleavage in the ECMe moiety and cleavage in both moieties were detected. Possible structures of the nonyl groups in the two esters were inferred. GC/chemical ionization (CI) mass spectra of the NPECMes with isobutane as reagent gas showed characteristic hydride ion-abstracted fragment ions shifted by 1 Da from those in the corresponding EI mass spectra. The sensitivity of a selected ion monitoring quantitation method for the NPECMes is enhanced under CI conditions compared with that under EI conditions. With electrospray ionization MS/MS, [M - H](-) ions of NP1EC (m/z 277) and NP2EC (m/z 321) were observed and, upon collision-induced dissociation of [M - H](-) of each of the two acids, fragment ions of m/z 219 corresponding to deprotonated nonylphenol, were observed in each case. Based on this observation, a rapid, simple and reliable selected product ion quantitation method is proposed for NP1EC and NP2EC.     

Study of the neurotransmitter dopamine and the neurotoxin 6-hydroxydopamine by electrospray ionization coupled with tandem mass spectrometry

Electrospray ionization combined with tandem mass spectrometry has been applied to a study of dopamine and 6-hydroxydopamine, an important neurotransmitter and a well-known neurotoxin, respectively. Both protonated and deprotonated molecules were observed for the two compounds. Upon collision-induced dissociation of protonated and deprotonated 6-hydroxydopamine molecules, the number of fragmentation pathways observed was greater than that observed with protonated and deprotonated dopamine molecules; the greater proclivity to fragment of the former is due to the 6-substituted hydroxyl group, which is para to the 3-OH group and ortho to the CH2CH2NH2 group. Furthermore, 6-hydroxydopamine showed a greater propensity to oxidize than did dopamine when sample solutions were kept uncovered in the air for 24 h prior to mass spectrometric examination. Radical structures of the four main oxidation products of 6-hydroxydopamine have been suggested on the basis of their product ion mass spectra; one or more of these oxidation products may be responsible for the cytotoxic property of 6-hydroxydopamine.     

Exactly Solvable Model Mimicking the H<Subscript>2</Subscript> Molecule in the Limit of Large Nuclear Masses

Avoiding the limitations of the Born–Oppenheimer approximation remains an issue of continuing importance in molecular physics. If we take the H₂ molecule as a prototype, then one uses, in some sense, the ratio of electron mass m to nuclear mass M as an expansion parameter, sometimes cited to be explicitly (m/M)^1/4. Here, we employ a model of such a two-electron diatomic molecule set up by Makarewicz [Am. J. Phys. 54 (1986) 178] to study the exact ground-state wave function obtained by treating electrons and nuclei on the same footing, Of course, to obtain such a wave function analytically means adopting model force laws, both for confinement and for the interelectronic interaction. From the exact wave function and ground-state energy, contact is finally established with the large nuclear mass limit.     

Pair density related to one‐electron information for the ground state of spin‐compensated two‐electron systems

The recent study by Joubert on effects of Coulomb repulsions in a many‐electron system has focused attention on an integral identity involving the pair density. This has motivated the derivation presented here of a vectorial differential form related to this integral result. Our differential identity is then illustrated explicitly by using (i) an exact ground‐state wave function for the so‐called Hookean atom having external potential energy (1/2)kr², with k = 1/4, and (ii) Moshinsky's model in which both the interparticle interaction and the external potential are of harmonic type. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The radial part of Brownian motion II. Its life and times on the cut locus

Summary This paper is a sequel to Kendall (1987), which explained how the Itô formula for the radial part of Brownian motionX on a Riemannian manifold can be extended to hold for all time including those times a whichX visits the cut locus. This extension consists of the subtraction of a correction term, a continuous predictable non-decreasing processL which changes only whenX visits the cut locus. In this paper we derive a representation onL in terms of measures of local time ofX on the cut locus. In analytic terms we compute an expression for the singular part of the Laplacian of the Riemannian distance function. The work uses a relationship of the Riemannian distance function to convexity, first described by Wu (1979) and applied to radial parts of -martingales in Kendall (1993).The first author's research was supported by a visiting fellowship awarded by the UK Science and Engineering Council, by travel funds provided by a European Community SCIENCE initiative, by the Max-Planck-Institute of Bonn, and by a grant from NSA     

Highly efficient, enantioselective synthesis of (+)-grandisol from a C2-symmetric bis(alpha,beta-butenolide)

[reaction: see text] A new, very efficient, enantioselective synthesis of the sexual attracting insect pheromone (+)-grandisol has been developed, in which the key step is the double [2 + 2] photocycloaddition of ethylene to a bis(alpha,beta-butenolide) readily available from D-mannitol. The C2 symmetry of the substrate and the appropriate protection of the central diol unit are the crucial features for the high diastereofacial discrimination during the cycloaddition process.     

Phenomenology and scaling of electron scattering cross sections from “almost spherical” molecules over a wide energy range

Total cross sections for electron scattering on “quasi spherical” (CH₄, SiH₄, GeH₄) molecules have been analyzed phenomenologically over a wide energy range. Regions, at low and high energies can be usefully represented by simple analytical formulae. Regularities associated with characteristic points such as the Ramsauer minima have been exposed. Comparison with other simple hydrides (NH₃, H₂O, H₂S) allows the demonstration of a possible correlation between the maximum value of the total cross section and the bond length. Some points of contact with first-principles theory are noted and in particular the energy at which the maximum cross section occurs, is related to the occurrence of a partial wave resonance. In the absence of complete data for GeH₄, prediction of characteristic points in the low energy cross section proves possible via the phenomenological analysis. Similarly, in the high energy regime, predictions of the cross section for SnH₄ is made from data on the lighter molecules of the series, using non-relativistic Thomas-Fermi self consistent field scaling.