Examination of the statistical method in the conjugated circuit theory

Summary The recently proposed statistical method for the calculation of resonance energies in the conjugated circuit theory is tested on the example of polyacenes. It is found that for the estimation of the resonance energy with a 10% average error, the method requires a sample consisting of about 20 (randomly chosen) Kekulé structures. Further increase of the sample size gives no significant gain in the accuracy of the method.

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Überprüfung der statistischen Methode in der Konjugierten-Ring-Theorie

Zusammenfassung Die unlängst vorgeschlagene statistische Methode in der Konjugierten-Ring-Theorie (conjugated circuit theory) wird am Beispiel der Polyacene getestet. Es wurde festgestellt, daß für die Abschätzung der Resonanzenergien bei einem mittleren Fehler von 10% für diese Methode ungefähr 20 (willkürlich gewählte) Kekulé-Strukturen nötig sind. Weitere Erhöhung dieser Anzahl bringt keine signifikante Verbesserung der Genauigkeit der Methode.

     

On a resonance energy model based on expansion in terms of acyclic moments: Exact results

Summary The new concept of the resonance energy in conjugated hydrocarbons introduced by Jiang Y, Zhang H (1989) Theor Chim Acta 75:279 is further developed. This model is based on expansion of the -electron energy in terms of moments which are also equal to numbers of closed walks in a molecular graph. The reference system is established by counting only acyclic walks, i.e. those tracing only on acyclic subgraphs. Because acyclic walks could be counted only up to some finite length, the energy of the reference system has been evaluated by truncating higher terms in the expansion. In this paper a finite expression for the energy of the same reference system is derived, thus allowing its exact evaluation. The exact values differ significantly from the truncated ones. This difference, as well as the discrepancy between exact results and chemical experience, are discussed.     

A new theoretical approach to the empirical resonance energies of the aromatic hydrocarbons

In the framework of the Hückel MO approximation, the differences in total binding energy between a given molecule and the corresponding distorted Kekulé-type structure are calculated for a variety of benzenoid hydrocarbons. The total binding energy is assumed to be given by the sum of the -electron and -electron binding energies. It is shown that there is a good linear relationship between the calculated differences in total binding energy and the -electron delocalization energies (DE) as obtained by using the simple Hückel MO method. This provides a physical basis for the use of the -electron DE as a theoretical index to the empirical resonance energy (RE). Further, by examining the changes in -electron binding energy between a given molecule and the corresponding distorted Kekulé-type structure, it is concluded that in benzenoid hydrocarbons the main contributor to the RE is not the -electron DE but the compressional energy of bonds.     

A simple and sensitive assay of nucleic acids based on the enhanced resonance light scattering of zwitterionics

A new assay of nucleic acids at nanogram level was established based on the enhanced resonance light scattering (RLS) signals of two zwitterionics cocamidopropyl hydroxysultaine (HSB) and lauryl betaine (BS-12). Under optimum conditions, the weak RLS signal of HSB is enhanced by nucleic acids, and the enhanced RLS intensity is proportional to the concentration of nucleic acids in the range of 0.02–7.3 mg l⁻¹ for calf thymus DNA and 0.01–8.6 mg l⁻¹ for fish sperm DNA. The detection limits were 1.5 ng ml⁻¹ for calf thymus DNA and 1.9 ng ml⁻¹ for fish sperm DNA. Plasmid DNA extracted from K-12-HB101 colt was determined with satisfactory results.     

A rapid and sensitive method for the determination of trace proteins based on the interaction between proteins and Ponceau 4R

The interactions between proteins and Ponceau 4R (PR) in aqueous solution have been studied by the techniques of resonance light scattering (RLS) spectroscopy, the absorption spectroscopy, zeta potential assay and circular dichroism (CD) spectrum. The dry PR can assemble on the surface of protein via electrostatic and hydrophobic forces to produce an associated compound of protein-PR, this compound can enhance the RLS of protein. Based on this fact, a simple, rapid, and sensitive method has been developed for the determination of proteins at nanogram level by RLS technique with a common spectrofluorimeter. Under optimum conditions, the linear range is 0.10-39.2 μg mL⁻¹ for the determination of both bovine serum albumin (BSA) and human serum albumin (HSA). The detection limits (S/N = 3) are 6.96 ng mL⁻¹ for BSA and 5.71 ng mL⁻¹ for HSA, respectively. There is almost no interference from amino acids, most of the metal ions, and other coexistent substances. The method has been satisfactorily applied to the direct determination of the total protein in human serum.     

Crystalline orientation of the InN films prepared by atmospheric pressure halide chemical vapor deposition

The structural analysis of the hexagonal InN film prepared on a Si(100) substrate by the AP-HCVD technique using InCl₃ and NH₃ as starting materials were carried out by the X-ray pole figure analysis. The deposited films consist of the hexagonal InN pillar crystals. It was found that the pillar crystals, which have random rotation around the 100 axis, were grown at an angle of 70–90° to the substrate.     

Resonance Rayleigh scattering, frequency doubling scattering and second-order scattering spectra of the heparin-crystal violet system and their analytical application

In pH 6.0-11.2 Britton-Robinson buffer solution, binding of heparin with crystal violet (CV) can result in a significant enhancement of resonance Rayleigh scattering (RRS) and resonance non-linear scattering, such as frequency doubling scattering (FDS) and second-order scattering (SOS). Their maximum scattering wavelengths, λ_ex/λ_em, appear at 492 nm/492 nm for RRS, 984 nm/492 nm for FDS and 492 nm/984 nm for SOS, respectively. The optimum conditions of the reaction, the influencing factors and the relationship between the three scattering intensities and the concentration of heparin have been investigated. New methods for the determination of trace amounts of heparin based on the RRS, FDS and SOS methods have been developed. The methods exhibit high sensitivities, the detection limit for heparin is 2.9 ng ml⁻¹ for the RRS method, 3.5 ng ml⁻¹ for the FDS method and 3.3 ng ml⁻¹ for the SOS method. The methods have good selectivity and were applied to the determination of heparin in heparin sodium injection samples with satisfactory results.     

Isolation and Characterization of Badge Hydrolysis Products

Heating a suspension of Bisphenol A diglycidyl ether (BADGE) in 20 : 80 tetrahydrofuran/water at 70°C and subsequent passage of the resulting solution through C18 columns allowed isolation and purification to > 97% of each of the two hydrolysis products 2-[4-(2,3-dihydroxypropoxy) phenyl]-2-[4-(2,3-epoxypropoxy)phenyl]propane (1HP) and 2,2-bis[4-(2,3-dihydroxypropoxy)phenyl] propane (2HP), which were characterized by UV, IR, ₁H and _I3C NMR spectroscopy and mass spectrometry.     

Extraordinary acoustic transmission,symmetry, blaschke products and resonators

The phenomenon of extraordinary acoustic transmission ( eat) in a resonator, which has recently been investigated experimentally, is studied theoretically. It is shown that the combination of a single propagating mode and a symmetry orthogonal to the direction of propagation for a resonator leads to eat. This is accomplished by decomposing the problem using symmetry, the Blaschke product and the properties of functions of a single complex variable which have modulus one on the real axis. The conditions of a resonator requires that the solution has singularities in the analytic extension to complex frequencies (resonances) and it is precisely near these resonances that we observe eat. The condition of a Blaschke product requires that there is a zero at the complex conjugate of the singularity and eat occurs when the solution on the real axis passes between these complex conjugate pairs of poles and zeros. A detailed numerical study of the problem is conducted and we show that once the single mode of propagation or the symmetry is broken then eat (at least perfect transmission) no longer holds generally.