Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.     

Average peptide score: a useful parameter for identification of proteins derived from database searches of liquid chromatography/tandem mass spectrometry data

The quantity and variable quality of data that can be generated from liquid chromatography (LC)/mass spectrometry (MS)-based proteomics analyses creates many challenges in interpreting the spectra in terms of the actual proteins in a complex sample. In spite of improvements in algorithms that match putative peptide sequences to MS/MS spectra, the assembly of these lists of possible or probable peptides into a 'correct' set of proteins is still problematic. We have observed a trend in a simple relationship, derived from standard database search outputs, which can be useful in assessing the quality of a MS/MS-based protein identification. Specifically, the ratio of the protein score and number of non-redundant peptides, or average peptide score (APS), can facilitate initial filtering of database search results in addition to providing a useful measure of confidence for the proteins identified. This parameter has been applied to results from the analysis of multi-protein complexes derived from pull-down experiments analyzed using a two-dimensional LC/MS/MS workflow. In particular, the complex list of protein identifications derived from a drug affinity pull-down with immobilized ampicillin and an E. coli lysate was greatly simplified by applying the APS as a filter, allowing for facile identification of the penicillin-binding proteins known to interact with ampicillin. Furthermore, an APS threshold can be used for any data sets derived from electrospray ionization (ESI)- or matrix-assisted laser desorption/ionization (MALDI)-MS/MS experiments and is also not specific to any database search program.     

A variational proof of the Gauss-Bonnet formula

The classical Gauss-Bonnet formula has the form I(g_ij)=2, where I(g_ij) represents a sum of three terms each of which depends on the metric tensor g_ij. It is shown that the first variation I of I(g_ij) with respect to the metric g_ij vanishes and that for the Euclidean metric _ij we have I(_ij)=2. From this the formula I(g_ij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(g_ij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor g_ij and its derivatives up to the second order is obtained with the aid of results of Rund [1].     

Ternäre Halogenide der Seltenen Erden vom Typ A2MX5 (A = K,In, NH4, Rb,Cs; X = Cl,Br, I)

Ternary Rare-Earth Halides of the A₂MX₅ Type (A = K, In, NH₄, Rb, Cs; X = Cl, Br, I) Ternary rare-earth (=M) chlorides, bromides, and iodides In₂MCl₅, (NH₄)₂MCl₅, Rb₂MCl₅, Cs₂MCl₅, CsRbMCl₅, K₂MBr₅, Rb₂MBr₅, K₂MI₅, and Rb₂MI₅ have been synthesized. Single crystals of In₂PrCl₅, Rb₂PrCl₅, K₂PrBr₅, and K₂PrI₅ were grown and the structures refined. The other halides were characterized by x-ray powder patterns. They are isotypic either with K₂PrCl₅(orthorhombic, Pnma, Z = 4, hexagonal arrangement of chains of edge-connected polyhedra [PrX₇]) or with Cs₂DyCl₅ (orthorhombic, Pbnm, Z = 4, hexagonal arrangement of cis-corner-connected octahedra [DyCl₆]) which may be discriminated in structure field diagrams. The thermal expansion was investigated für Cs₂LuCl₅ and Rb₂PrX₅ (X = Cl, Br, I).     

Application of capillary reversed-phase high-performance liquid chromatography to high-sensitivity protein sequence analysis.

A continuous gradient elution method for capillary column (less than 0.32 mm I.D.) liquid chromatography was developed. Gradient eluent from a microbore liquid chromatograph was split ahead of the injector so that an accurate percentage (2-3%) of the mobile phase delivered by the pump flowed through the capillary column. The outlet of the column was connected to a length of 0.075 mm I.D. fused-silica capillary tubing which, in turn, was connected to a 6-mm optical path length longitudinal capillary flow cell. Fused-silica capillary columns of 0.32 mm I.D. were slurry-packed efficiently with 7-microns spherical, 300 A pore size, C8 bonded-phase particles, and evaluated in terms of their ability to resolve mixtures of proteins, peptides or phenylthiohydantoin (PTH)-amino acid derivatives. The gradient elution profiles agreed with those obtained using microbore (less than 2.1 mm I.D.) and larger bore columns. The minimum detectable amounts for proteins and PTH-amino acids on 0.32 mm I.D. capillary columns were 50 pg and 25 fmol, respectively. At a flow-rate of 3.6 microliters/min, proteins and peptides were recovered from the capillary columns in volumes of about 2-8 microliters. The use of a multiple-wavelength, forward-optics detector for identifying tryptophan- and tyrosine-containing peptides is discussed.