Decay behavior of least-squares coefficients in auxiliary basis expansions

Many quantum chemical methods, both wave function and density based, rely on an expansion of elements of the electron density in an auxiliary basis. However, little is known about the analytical behavior of the expansion coefficients and, in particular, about their rate of decay with distance. We discuss an exactly solvable model system and characterize the expansion coefficients for various fitting metrics and various dimensionalities of the auxiliary basis. In the case of Coulomb fitting, we find that the decay rate depends critically on the effective dimensionality D of the auxiliary basis, varying from O(r(-1)) to O(r(-3)) to O(e(-zetar)) for D = 1, 2, or 3.     

New pyridinium based ionic dyes for the hydrogen evolution reaction

The presented work comprised the synthesis and characterization of new ionic organic dyes as potential photosensitizer (PS) in the photocatalytic H₂ evolution reaction. The presented dyes are consisting of donor-π-acceptor (D-π-A) structures that are commonly used for organic dyes for organic solar cells. The acceptor is based on a cationic pyridinium moiety. Furthermore, a complex was synthesized, in which a D-π-A photosensitizer is linked as ligand to cobaloxime. The latter is a common proton reduction catalyst. The attached ligand enabled a fast intramolecular electron transfer to the cobalt center. The resulted complex showed high stability and potential in the homogeneous photocatalytic H₂ evolution reaction. Finally, one ionic dye showed a high activity when combined with TiO₂ and Pt in a heterogeneous hydrogen evolution reactions with a TOF of up to 407 h^?1.     

The Multiconfiguration Equations for Atoms and Molecules: Charge Quantization and Existence of Solutions

We prove the existence of ground-state solutions for the multiconfiguration self-consistent field equations for atoms and molecules whenever the total nuclear charge Z exceeds N–1, where N is the number of electrons. Moreover, we show that for arbitrary values of Z and N the scattering charge, i.e., the asymptotic amount of charge lost by an energy-minimizing sequence, is integer-quantized. Our analysis applies to the MC equations of arbitrary rank. As special cases we recover, in a new and unified way, the existence theorems of Zhislin [Zh60] for the N-body Schrödinger equation (infinite rank MC) and of Lieb & Simon [LS77] for the Hartree-Fock equations (rank-N MC). Our approach is a direct study of an invariant, orbital-free formulation in N-body space of the underlying variational principle. Proofs involve (i) the geometric N-body localization methods for the linear Schrödinger equation first introduced by Enss [En77] (and developed in [Sim77, Sig82]), which can be adapted to become powerful tools in nonlinear many-body theory as well, (ii) weak convergence methods from the theory of nonlinear partial differential equations, (iii) careful analysis of the structure of the one- and two-body density matrices of the bound and scattering fragments delivered by geometric localization, which allows us to overcome the fact that the rank of the fragments is not reduced by localization.     

A rapid and sensitive assay for determining human brain levels of farnesyl-(FPP) and geranylgeranylpyrophosphate (GGPP) and transferase activities using UHPLC–MS/MS

The isoprenoids farnesyl-(FPP) and geranylgeranylpyrophosphate (FPP and GGPP) are two major lipid intermediates in the mevalonate pathway. They participate in post-translational modification of members of the superfamily of small guanosine triphosphatases (GTPases; Ras, Rab, Rac, etc.) via prenylation reactions. Due to the important role of these proteins in a number of cell processes, in particular cell growth, division, and differentiation, investigation of the involvement of isoprenoids in these processes is of great interest. In a previously published report, we described a fully validated assay for the quantitation of the two isoprenoids using a high-performance liquid chromatography (HPLC)–fluorescence detection (FLD) method. The current work expands on the previous method and enhances it greatly by using a much faster state-of-the-art ultrahigh-performance liquid chromatography (UHPLC) technique coupled to tandem mass spectrometry (MS/MS). The method exhibited a linear concentration range of 5–250 ng/mL for FPP and GGPP in human brain tissue; it was shown to be unaffected by ion suppression and provided results almost six times faster than the HPLC–FLD assay. Comparison of UHPLC–MS/MS and HPLC–FLD yielded excellent comparability of the two assays for both isoprenoids. Based on the UHPLC–MS/MS assay, a novel in vitro test system was implemented to study enzyme specificity for distinct amino acid CAAX motifs, which is potentially useful for investigating target interactions of new therapeutics for diseases involving pathological regulation of isoprenoids and/or small GTPases.     

Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction

We demonstrate an extremely accurate method for measuring ultrabroadband, sub-10 fs pulses even if they exhibit a highly modulated spectrum, space-time coupling, or both. The method uses a spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction, which allows a zero additional phase measurement to be performed with a relatively low signal-to-noise ratio in real time and single shot.     

Synthèse d'analogues de dérivés dioxaprostanoïques à partir du d et du l-xylose

Epoxides 7, 8 and 9 have been prepared from d and l-xylose, and used for the synthesis of a precursor of ent-(11-oxa)PG 19 and of 9,13-and 7,11-dioxaprostanoïc acids 28 and 31. The site of the opening of the epoxidcs 7 and 9 with the carbanion derived from bis-(phenylth)romethane and with LiAlH₄ is shown by establishing structures of the products 11, 12, 20 et 21 by ¹³CNMR spectroscopy.