Application of cholesky-like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives

When viewed as a square two-indexed matrix, the array of atomic orbital-based, two-electron integrals (ij|kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where there exists significant basis near redundancy, the rank (r) of the (ij|kl) ≡ V_l,J matrix of integrals will be significantly smaller than the matrix dimension M. When this occurs, it proves computationally tractable to decompose the M-dimensional matrix V into components L ( V = LL ^T) which contain all of the information needed to form the full V matrix. The Cholesky algorithm allow such a decomposition to be carried out and forms the basis of the work described here. The method is found to be highly successful in reducing the number of integrals and integral derivatives that must actually be calculated. In particular, results on the C₂ molecule indicate that the algorithm can be superior to traditional methods of integral derivative generation if the orbital basis is large enough to contain appreciable near redundancy. In contrast, results on benzene with a more spatially delocalized basis show that conventional methods are preferred whenever substantial basis (near) redundancy is not present.     

Synchrotron X‐ray study of ortho­rhombic Rb3Ta5O14 with a modified pyrochlore structure

The structure of a new orthorhombic trirubidium pentatantalum oxide (Rb₃Ta₅O₁₄) phase with Pnma symmetry was identified from a half sphere of synchrotron X‐ray data measured at a wavelength of 0.85 Å. This notionally linked TaO₆ octahedral structure broadly consists of three different modifications of the pyrochlore ring motif with layer stacking normal to (205) planes. Successive pyrochlore layers do not simply stack normal to these planes but are offset along the [100] axis. An unusual aspect of this structure is the occurrence of TaO₅ trigonal bipyramids in structurally complex regions where the modified pyrochlore rings connect.     

TIME-RESOLVED FLUORESCENCE STUDIES OF SPINACH CHLOROPLASTS–EVIDENCE FOR THE HETEROGENEOUS BIPARTITE MODEL

Abstract— Fluorescence lifetimes of spinach chloroplasts were measured with a modelocked dye laser and time-correlated single photon counting. Information about energy transport and functional organization of the chloroplasts is revealed by such time-resolved fluorescence studies. Quenching experiments using treatment with UV light or the chemical agent dibromothymoquinone are consistent with the notion that there is heterogeneity associated with PS II units and that such heterogeneity is reflected over the entire time range of fluorescence decay, not just in a single component. Phosphorylation experiments were also carried out which permit us to relate these kinetic studies to previous steady state observations.     

Rapid,clean, and mild O-acetylation of alcohols and carbohydrates in an ionic liquid

Archetypal O-acetylation reactions of alcohols and carbohydrates proceed rapidly in high yield under mild conditions in a dicyanamide based ionic liquid, that is not only an effective solvent but also an active base catalyst.     

Exploring privileged structures: the combinatorial synthesis of cyclic peptides

Head-to-tail cyclic peptides have been reported to bind to multiple, unrelated classes of receptor with high affinity. They may therefore be considered to be privileged structures. This review outlines the strategies by which both macrocyclic cyclic peptides and cyclic dipeptides or diketopiperazines have been synthesised in combinatorial libraries. It also briefly outlines some of the biological applications of these molecules, thereby justifying their inclusion as privileged structures.     

Quantitative capillary gel electrophoresis assay of phosphorothioate oligonucleotides in pharmaceutical formulations

Quantitative capillary gel electrophoresis (QCGE) has been developed for the accurate quantitation of a 21-mer phosphorothioate oligonucleotide, ISIS 2922, and its degradation products in an intravitreal formulation. The electrokinetic mode of injection employed by CGE necessitates formulation of the external reference standard in a sample matrix similar to that of the drug product and the use of an internal standard for improved accuracy and precision. The analytical method detailed in this paper has demonstrated the necessary accuracy, precision, linearity, range, selectivity and ruggedness for use in routine drug product analysis and stability monitoring of phosphorothioate oligonucleotides.     

Critical reevaluation of proximity effects in the barton oxidation and related intramolecular reactions

The limiting factor to account for the increased rate of intramolecular reactions between functional groups as opposed to their intermolecular counterparts can and has been explained both by proximity effects and by activation energy. Neither explanation has emerged as the single most important reason in all or even the majority of cases studied. We have therefore reexamined the spatiotemporal hypothesis of Menger and the transition-state energy approach of Houk on a consistent set of compounds subjected to the Barton oxidation or related reactions in an effort to more clearly define the reasons for the proximity effect. For the 26 structures studied, neither hypothesis provides a consistent, quantitative explanation although the transitionstate energy hypothesis offered the most promise. © John Wiley & Sons, Inc.     

Phonatory Impairment in Parkinson''s Disease: Evidence from Nonlinear Dynamic Analysis and Perturbation Analysis

Many persons with Parkinson's disease (PD) will eventually experience vocal impairment as their condition advances. Using standard perturbation analyses (parameters like jitter and shimmer) to measure fluctuations in phonatory signal may inhibit researchers from recognizing severely disordered patterns that seem to be present in the voices of some PD patients. Nonlinear dynamic analysis can quantify these aperiodic patterns, which indicate severe pathology that is usually characterized perceptually by hoarseness. Here, sustained vowel phonations of a heterogeneous group of PD subjects (20 women and 21 men) were compared with those of a control group (22 women and 18 men) based on results of nonlinear dynamic analyses (D(2)) and perturbation analyses. Results showed PD subjects as a whole to have significantly higher D(2) values than control subjects (P = 0.016), which indicates increased signal complexity in PD vocal pathology. Differences in the comparison of these two groups were significant in jitter (P = 0.014) but nonsignificant in shimmer (P = 0.695). Furthermore, the performance on these three measures was affected by subject sex. Nonlinear dynamic analysis showed significantly higher D(2) in the female PD group than in the female control group (P = 0.001), but jitter and shimmer did not show such a difference. The male PD group had statistically higher jitter than the male control group (P = 0.036), but these groups did not differ in D(2) or shimmer. Overall, nonlinear dynamic analysis may be a valuable method for the diagnosis of Parkinsonian laryngeal pathology.