Sizing the BFGS and DFP updates: Numerical study

In this study, we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained optimization. Our numerical results imply that, for use with the DFP update, the Oren-Luenberger sizing factor is completely satisfactory and selective sizing is vastly superior to the alternatives of never sizing or first-iteration sizing and is slightly better than the alternative of always sizing. Numerical experimentation showed that the Oren-Luenberger sizing factor is not a satisfactory sizing factor for use with the BFGS update. Therefore, based on our newly acquired understanding of the situation, we propose a centered Oren-Luenberger sizing factor to be used with the BFGS update. Our numerical experimentation implies that selectively sizing the BFGS update with the centered Oren-Luenberger sizing factor is superior to the alternatives. These results contradict the folk axiom that sizing should be done only at the first iteration. They also show that, without sufficient sizing, DFP is vastly inferior to BFGS; however, when selectively sized, DFP is competitive with BFGS.This research was supported in part by NSF Cooperative Agreement No. CCR-88-09615, AFOSR Grant 89-0363, DOE Grant DEFG05-86-ER25017, and AR0 Grant 9DAAL03-90-G-0093. This paper was presented at the ICIAM 91 International Conference, Washington DC, July 1991.The authors thank all those individuals who took part in the lively discussions concerning this material following the ICIAM 91 presentation. These discussions influenced the current version of the paper. The first author also thanks Maria Cristina Maciel for assistance and support during the earlier stages of the research.This author is currently a Graduate Student in the Mathematics Department, University of California at Riverside, Riverside, California, and has participated in the Summer Student Visitor Program at the Center for Research in Parallel Computation of Rice University for the past two years.     

Transmission mechanisms of inter-proton long-range couplings in substituted anisoles

Inter-proton long-range and ring couplings were measured in o-anisaldehyde and in seven disubstituted anisoles. In order to investigate the transmission mechanisms of long-range couplings with the methoxy group, partially restricted molecular orbital (PRMO) calculations were carried out within the FPT-INDO method on o-anisaldehyde. σ- and π-electron, and through-space transmitted components were separated. For the energetically favoured trans-OMe conformation a through-space component was found for the couplings of the methyl protons with the ortho-proton, and it was found that its sign, as well as its magnitude, depends on their relative positions. If free rotation, however, is assumed for the methyl group, the averaged value for this coupling constant is negative.     

The use of partially restricted molecular orbitals to investigate transmission mechanisms of spin-spin coupling constants. I. Theσ andπ contributions within the FPT INDO method

Partially restricted INDO MO Calculations have been carried out to separate the -electron contributions to spin-spin coupling constants in ethylene, butadiene, benzene and toluene. Results reproduce very well known trends such as the pathway invariance, the alternation in sign and the methyl group replacement rule.Comisión de Investigaciones Científicas (CIC, Pcia.Bs.As.) fellow.     

Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 ¹J_CH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of ¹J_CH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Solid phase extraction of organophosphorus,triazine, and triazole-derived pesticides from water samples. A critical study

A critical study using C18 SPE columns for the determination of organophosphorus, triazine, and triazole-derived pesticides, nap-ropamide, and amitraz is presented. The type of sorbent, sorbent mass, flow rate in the extraction process, sample concentration of the different compounds, sample volume, pH, and ionic strength were evaluated. Special emphasis was placed on the evaporation step of eluates prior to GC determinations and on prefiltration of sample waters. Pesticide recovery is linear over a wide range of concentrations for most of compounds under study. Under general extraction conditions losses can be expected for amitraz, pro-metryn, prometon, dimethoate, penconazole, and propiconazole. At 100 ng L^?1, enhanced responses are produced for mevinphos, simazine, malathion, triadimefon, methidathion, and phosmet, which can be attributed to matrix effects. At basic pH, recovery of prometon, prometryn, and penconazole are improved. Low flow rates and high ionic strength enhance the recovery of prometon and prometryn. For phosmet, the influence of sample volume was established. Likewise, the influence of sorbent quantity was established for phosmet and dimethoate. Losses during the evaporation step were observed for mevinphos, dimethoate (> 50%), penconazole, propiconazole, and prometon (30%). Prefiltration of sample waters did not cause significant variations in the whole process of extraction. Impurities arising from the sorbent materials were not detected.     

Triiodolead(II) complexes. structure and Raman spectra

The crystals of tetramethylammonium triiodolead(II) are hexagonal with = 9.7823(11) A, c = 7.9167(8) A and γ = 120.0, Z = 2, space group P6₃/m. The structure was solved by direct methods and refined by least-squares techniques to a conventional R = 2.97% for the 312 independent reflections. The structure consists of chains of PbI₃ units running along the c axis. Each lead atom is octahedrally coordinated to six iodides with a Pb---I bond distance of 3.223 A. The tetramethylammonium cations sit in holes in the packing of the iodide ions. The cations are disordered.

The Raman spectra of salts of this species formed with several tetraalkylammonium cations are also reported and the bands tentatively assigned.     

Synthesis, Characterization And Biphasic Catalysiswith RuCl(η5-C5H5)(TPPMS)2

A synthetic route is reported for the water soluble complex RuCl(h⁵- C₅H₅)(TPPMS)₂(1), (TPPMS = (C₆H₅)₂P(C₆H₄-m-SO₃Na) and characterized by UV-Vis, FTIR, ¹H, ¹³C NMR and GC-MS. Complex 1 is a good catalytic precursor in biphasic media (toluene/ water) for 1-hexene hydrogenation under moderate reaction conditions (e.g. 500 psi H₂, 100°C) giving good yields of n-hexane, and smaller amounts of cis-2-hexene and trans-2-hexene. Other organic substrates (cinnamaldehyde, crotonaldehyde, cyclohexene, acetone and butylaldehyde) are hydrogenated.     

Preparation,X-ray crystal structure and 13C- and 1H-NMR study of 1-methyl-2-(N-methyl-N-phenylglycyl)-3-(N-methylanilino)indole

Reaction of N-methylaniline with 40% glyoxal yields 1-methyl-2-(N-methyl-N-phenylglycyl)-3-(N-methylanilino)indole ( 1a ) as the main product together with 1-methyl-3-(N-methylanilino)indole ( 1b ). The reaction appears to be general for aromatic secondary amines since N-ethylaniline and N-phenylbenzylamine yield the corresponding indoles. The structure of 1a has been verified by single crystal X-ray diffraction. Compound 1a (C₂₅H₂₅N₃O) crystallized in the triclinic space group Pl? with cell dimensions a = 10.085(3)Å, b = 10.371(3)Å, c = 11.908(5)Å, α = 74.2(3)°, β = 74.7(3)° and γ = 60.7(2)° with Z = 2. The complete ¹H and ¹³C nmr assignment of indoles 1a and 1b was achieved from two-dimensional HETCOR and COSY spectra with the aid of homonuclear and heteronuclear double resonance experiments.     

Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. III: INDO CHF calculations of orbital and dipolar contributions to spin–spin coupling constants involving protons

The self-consistent perturbation theory is used to calculate noncontract contributions to spin–spin coupling constants involving protons. Molecular wave functions were obtained with a modified version of the INDO method which includes hydrogen 2p orbitals in its basis set. It is found that in many cases the orbital and dipolar terms are by no means negligible, being particularly important in geminal H? H couplings. Results reported in this paper for this type of coupling, reproduce experimental trends in the series CH₄, NH₃, and OH₂. In general, noncontact terms are found to decrease as the number of bonds separating the interacting nuclei increases.