A trial phase function method for a class of λ-ω reaction-diffusion systems: Reduction to a Schrödinger type problem in an eigen sub-domain

The perturbed central force problem $\text{γ}{}_{\mathrm{xx}}\text{? ?}{}^2\text{γ}\text{a}\text{?}{}^2\text{+ γλ(γ) = 0, γ}\text{a}\text{?}{}_{\mathrm{x}}\text{+ 2}\text{a}\text{?}\text{γ}{}_{\mathrm{x}}\text{+ γ[}\text{}\text{?}\text{gw(γ}{}^1\text{) ?}\text{}\text{?}\text{gw(γ)] = 0}$ arising from the λ-ω system

$\text{α}\text{αt}\text{C}{}_1\text{C}{}_2\text{=}\text{λ}\text{?ω}\text{ω}\text{λ}\text{C}{}_1\text{C}{}_2\text{+}\text{α}\text{αt}\text{C}{}_1\text{C}{}_2$

where $\text{c}{}_1\text{=}\text{γ}\text{(x)cosθ(x,t), c}{}_2\text{=}\text{γ}\text{(x)sinθ(x,t), θ = σt ? ?∝}{}^{\mathrm{x}}\text{a}\text{?}\text{(x′)dx′}\text{and}\text{ω = ?}\text{}\text{?}\text{gw(}\text{γ}\text{)}$ is considered for the class $\text{λ}\text{=}\text{}\text{?}\text{gw}\text{= 1 ? g(}\text{γ}\text{)}$. The resulting linear equation in $\text{γ(x), γ}{}_{\mathrm{xx}}\text{+ 2}\text{a}\text{?}\text{γ}{}_{\mathrm{x}}\text{+}\text{γ[α}{}^2\text{+}\text{a}\text{?}{}_{\mathrm{x}}\text{?}\text{?}{}^2\text{a}\text{?}{}^2\text{] = 0}$ is solved with the aid of a class of trial phase functions $\text{a}\text{?}{}_{\mathrm{T}}\text{(x)}$ generated by the unperturbed central force problem for the case g(γ) = γ². An application of the Liouville-Green approximation procedure reduces the system to a Schrödinger type boundary value problem in an eigen sub-domain. The analytical estimates for α are in reasonable agreement with the results of numerical integration of the nonlinear system. The eigenfunctions γ(x) display expected oscillatory behaviour inside an eigen sub-domain. The higher modes and the span of the most extended centre structure are estimated and interpreted in the context of WKBJ connection formula.     

Studies in neutron depth profiling

This paper describes first the application of neutron depth profiling (NDP) for measuring the distribution of⁶Li in LiAlO₂ ceramics. Using a surface barrier detector for detecting³H produced in⁶Li(n, )³H,⁶Li was profiled to a depth of 14 m in the ceramics. Secondly, a new methodology is presented for NDP with enhanced capabilities based on measuring the energy of recoiling nuclei from (n, p) and (n, ) reactions by time-of-flight mass spectrometry. The scope of recoil nucleus time-of-flight mass spectrometry (RN-TOF-MS) includes profiling of¹⁰B,¹⁴N,¹⁷O,³³S,³⁵Cl,⁴⁰K. Probe depths may be of a few tens nanometers. RN-TOF-MS complements and refines NDP based on charged particle (p or ) spectrometry.     

Analytical implications of zeolites in overlayers at electrodes

A review is given of past and potential analytical and other applications of electrodes overlayered with zeolites.     

Rearrangements of some furan and banzofuran 1.5,-dienols

Isomers of 1-(2-furyl)-methyl-3-buten-ols and their benzofuran analogs were studied for their oxy-Cope and anionic oxy-Cope reactivity.     

The preparation of phenacylpyrazoles,acylpyrazoles, imidazolylisoxazoles and imidazolylpyrazoles from c(α)-dianions of oximes,phenylhydrazones and acylhydrazones

C(α),O-Dilithiooximes, C(α), N-dilithiophenylhydrazones, or C(α), N-dilithioacylhydrazones were prepared in an excess of lithium diisopropylamide (LDA) and condensed with a variety of esters followed by acid-cyclization to give substituted isoxazoles and pyrazoles.     

Discussion of the catalytic pathway of cysteine proteases based on AM1 calculations

The deacylation reaction of the cysteine protease papain was examined by AM1 reaction-coordinate calculations. The transition-state (TS) structure was extracted from the reaction pathway as corresponding to the maximum point along this minimum-energy pathway. Consistent with experimental kinetic data revealing that deacylation is about 60 times faster for thioester (---C(O)---S---) than dithioester (---C(S)---S---) intermediates, calculated E_a values are about 10 kcal mol⁻¹ lower for the former than the latter. The calculated partial atomic charges indicate that the C=O carbon in the thioester is a good site for nucleophilic attack whereas the corresponding C=S carbon in the dithioester is a poor site. The present calculations reveal that the enzyme's oxyanion hole contributes about 9 kcal mol⁻¹ toward reducing E_a for the anionic tetrahedral intermediate and TS structure. On the other hand, the presence of Asn in the putative Asn-His-Cys catalytic triad contributes only about l kcal mol⁻¹ toward reducing their E_a value. The presence of this Asn, however, did appear to stabilize His in its protonated form (ImH⁺) over its unprotonated form (Im). Two novel mechanisms are introduced to explain the unusual effect of a remote X substituent on the deacylation kinetics of the substrate family under consideration. The first mechanism invokes a “field effect” while the second mechanism embodies the concepts of induction and homoconjugation. The unique feature of these two mechanisms is that, unlike other proposed models, they circumvent the requirement for a close N…S interaction which has stimulated controversy.     

Molecular modeling studies of novel heteroarotinoids

The molecular structure and conformational properties of structurally related oxo and thio heteroarotinoids have been calculated by employing AM1 molecular orbital and both MM2P and Chem-X “optimize” molecular mechanics methods, and the results have been compared with crystal structure data. For the cis and trans oxo heteroarotinoids, MM2P gives values of the bridge torsion angles ?₁ and ?₂ in closest agreement with the crystal structure, and all three computational methods yield values of ?₁ and ?₂ within about 10° of that found in the crystal structures. All three computational methods locate a minimum-energy conformation for the trans isomer corresponding to the two bridged aryl rings being mutually perpendicular, in agreement with the crystal structure and similar to that found for the structurally analogous trans-stilbene. The calculated heteroring geometries also reproduce the twist-sofa conformation observed for the crystal structure. Calculated conformational energies versus ?₁ and ?₂ indicate broad energy wells about the minimum-energy conformation with barriers to rotation at the planar and perpendicular conformations, and with higher barriers found for the more sterically congested cis isomer. The corresponding cis and trans thio heteroarotinoids exhibit conformational properties similar to their oxo analogues. Both AM1 and MM2P fare poorly in reproducing the crystal structure values of the sulfur-containing bond lengths and bond angles. The C-S bonds found in these thio heteroarotinoids may possess more double-bond character than accounted for in the calculations. Also, the results suggest that the MM2P sulfur-related force-field parameters adopted for these calculations may require further refinement.     

Three-dimensional quantitative structure--property relationship (3D-QSPR) models for prediction of thermodynamic properties of polychlorinated biphenyls (PCBs): enthalpy of sublimation

Three-dimensional quantitative structure--property relationship (3D-QSPR) models have been constructed using comparative molecular field analysis (CoMFA) to correlate the sublimation enthalpies at 298.15 K of a series of polychlorinated biphenyls (PCBs) with their CoMFA-calculated physicochemical properties. Various alignment schemes, such as atom fit, as is, and inertial were employed in this study. Separate CoMFA models were developed using different partial charge formalisms, namely, electrostatic potential (ESP) and Gasteiger-Marsili (GM) charges. Among the four different CoMFA models constructed for sublimation enthalpy (Delta(sub)H(m)(298.15 K)), the model that combined atom fit alignment and ESP charges yielded the greatest self-consistency (r(2) = 0.976) and internal predictive ability (r(cv)(2) = 0.750). This CoMFA model was used to predict Delta(sub)H(m)(298.15 K) of PCBs for which the corresponding experimental values are unavailable in the literature.