A molecular theory of stress–strain relationship of spherulitic materials

A primitive molecular theory for stress–strain relationship of spherulitic polymers is presented based on a consideration of changes in conformational free energy in the tie chains and floating chains located between crystalline lamellae within an ideal spherulite which is assumed to undergo an affine deformation. Numerical stress–strain curves are calculated as a function of temperature, crystallinity, and tie chain fraction.     

Geometric theory of trigger waves — A dynamical system approach

We propose a geometric model for wave propagation in excitable media. Our model is based on the Fermat principle and it resembles that of Wiener and Rosenblueth. The model applies to the propagation of excitations, such as chemical and biological wave fronts, grass fire, etc. Starting from the Fermat principle, some consequences of the assumptions are derived analytically. It is proved that the model describes a dynamical system, and that the wave propagates along ignition lines (extremals). The theory is applied to the special cases of tube reactor and annular reactor. The asymptotic shape of the wave fronts is derived for these cases: they are straight lines perpendicular to the tube, and involutes of the central obstacle, respectively.     

Approximation of the electron–proton mass ratio as a series in powers of $$\uppi $$

Eddington in 1923, first identified four dimensionless numbers, derived from combinations of the basic physical constants, which are known as the “Eddington constants”. In formulating these dimensionless numbers, Eddington, a leading physicist of his time, claimed that they are characteristic of the structure and dynamics of the Universe at large, on the microscopical scale and at the macroscopical scale. Recently, there has been suggested a possible way of accounting for the magnitude of one of these four dimensionless constants, indicated as the “fine structure constant”, \(\upalpha \), that first emerged from studies of the atomic line spectrum of H. A simple power series in the product \(\hbox {e}\cdot \uppi \) has been proposed, that fits the measured value of the fine structure constant to better than 9999 parts in 10,000. Following along these lines, the authors here propose a simple power series expansion in \(\uppi \) that agrees with the currently accepted measurement of the value of the electron–proton mass ratio (m/M), or \(\upbeta \), to better than 999 parts in 1000.     

A theoretical study of CO adsorption on gold by Hückel theory and density functional theory calculations

It is crucial to understand the nature of CO adsorption on gold so as to elucidate the mechanism of low-temperature CO oxidation on nanogold catalysts. We performed theoretical analysis of CO adsorption on gold by using Hückel theory and density functional theory (DFT) calculations. Hückel theory indicates that CO adsorption on gold is dominated by the electron distribution at the Au atom, which is greatly affected by neighboring Au atoms, coadsorbed or doping species. The increase of σ-bonding electrons should weaken the CO adsorption, while the increase of π-electrons should strengthen the adsorption. DFT calculations proved this prediction quantitatively for various systems, including CO adsorption on a Au(100)-hex surface with locally varying subsurface configurations and CO coadsorption with acceptor or donor species.     

A density functional theory study of the ��mythic�� Lindlar hydrogenation catalyst

A Lindlar catalyst is a popular heterogeneous catalyst that consists of 5?wt.% palladium supported on porous calcium carbonate and treated with various forms of lead and quinoline. The additives strategically deactivate palladium sites. The catalyst is widely used for the partial hydrogenation of acetylenic compounds in organic syntheses. Alkyne reduction is stereoselective, occurring via syn addition to give the cis-alkene. Even if it has been employed for about 60?years, there is a lack of molecular level understanding of the Lindlar catalyst. We have applied density functional theory simulations to understand the structure and the nature of the interplay between the multiple chemical modifiers in the Lindlar catalyst. Indeed, the poisons influence different parameters controlling selectivity to the alkene: Pb modifies the thermodynamic factor and hinders the formation of hydrides, while quinoline isolates Pd sites thus minimizing oligomerization.     

On the extraction of spectra of components from spectra of mixtures. A development in factor theory—II

The theory of factor analysis developed in Part I [A. Muller and D. Steele, Spectrochim. Acta 46A, 817 (1990) [1] is extended to cases where m > 3, m being the number of factors. The effect of increasing the number of independent parameters by m(m-1) for T′ and the subsequent changes produced in the transformed eigenspectra, are investigated. Applications to actual spectra of mixtures of: (A) butan-2-one, ethyl ethanoate, cyclohexane and oct-1-ene (B) butan-2-one, ethyl ethanoate, cyclohexane and 2-methylpentane and (C) oct-1-ene, butan-2-one, ethyl ethanoate, cyclohexane and 2-methyl-pentane are presented. Using standard target techniques, an alternative approach is developed for the m> 3 case. This is based on transformation of the leading three eigenspectra, followed by identification and elimination of a component in a repetitive manner, until completion. The problems associated with the implementation of the Beer-Lambert Law are explored the need for accurate determination of a suitable wavenumber block to ensure the removal of the correct amount of each component, is examined. The ability to recognize at least one of the m component spectra per programme cycle is demonstrated.     

On the extraction of spectra of components from spectra of mixtures. A development in factor theory—I

The theory of factor analysis is extended to permit the computer based extraction of the spectra of pure components from spectra of mixtures. A simultaneous linear, non-orthogonal transformation of the eigenspectra and eigenvectors is used to generate all positive absorbances and concentrations within noise level. Applications to actual spectra of mixtures of: (A) ethyl ethanoate, butan-2-one and oct-1-ene; (B) ethyl ethanoate, butan-2-one and cyclohexane; and (C) butan-2-one, cyclohexane and 2-methylpentane are presented. The effects of changes in signs of the constrained diagonal elements of the transformation matrix is investigated. To explore the ability of the software to cope with component spectra in which there are no wavenumbers at which one component dominates an artificial set of mixtures is examined. Recognizable spectra are extracted. It appears that, even when there are no wavenumbers at which one component dominates, the condition of finding “the sum of squares of negative absorbances/concentrations” near zero is adequate to yield useful spectra for library searches.     

Current trends in the development of A. M. Butlerov’s theory of chemical structure

The chemical structure concept developed by A. M. Butlerov supplemented by the views on spatial (J. H. van’t-Hoff and J. A. Le Bel) and electronic (G. Lewis) configurations of molecules constitute the basis of the classical theory of chemical structure. The advent of quantum mechanics and development of the computer chemistry extended and enhanced the conceptual basis of theoretical chemistry, which nevertheless retains its independent value and cannot be reduced to direct physical definitions. The review deals with the evolution of the key concepts of the classical theory of chemical structure and introduction of new notions and approaches to analysis of the structure and reactivity problems, which is associated with the advent of the quantum mechanics and quantum chemistry views and methods.     

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.     

A new theory for symmetric orbital and tensor

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A density functional theory investigation of CrSin (n=1–6) clusters

Clusters of the form CrSi_n (n=1–6) were investigated computationally using a density functional approach. In particular, geometry optimizations were carried out under the constraint of well-defined point group symmetries at the B3LYP level employing a pseudopotential method in conjunction with double zeta basis sets. In this article, the resulting total energies, Mulliken atomic net populations, overlap populations, fragmentation energies and geometries of CrSi_n (n=1–6) are presented and discussed, together with natural populations and natural electron configurations. In addition, we comment on the charge transfer within the clusters. From this analysis, the 3d orbital of the Cr atom in CrSi_n (n=1–6) cluster absorbs electrons. From this tendency, conclusions are drawn with respect to the electronic populations and the chemical bond between Si and Cr as well as Si and Si.     

Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using M?ller-Plesset-type (MP) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, self-consistency can be neglected since the long-range correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, self-consistency effects are found to be much smaller than long-range correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the short-range energy functional term while freezing its functional derivative, namely, the short-range local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

A kinetic energy fitting metric for resolution of the identity second-order Møller-Plesset perturbation theory

A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order M?ller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation of the error in the correlation energy, compared to standard M?ller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order M?ller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.     

A generalized harmonic oscillator model of energy level particles and NNS distribution——A unified theory for NNS distribution of energy level fluctuation spectra

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Tungsten atomizer – theory of atomization mechanism of some volatile analytes

Several types of chemical reactions may participate in the evolution of free atoms in a tungsten furnace. Reactions may take place either in the homogeneous or heterogeneous phase. The assumed reactions may be classified into four types according to the phases in which they take place. Reactions occurring in the gaseous phase, i.e. in the inner volume of the furnace, are kinetically more significant. However, for atomization of easily volatile analytes heterogeneous reaction between gaseous compounds and between condensed salts of analytes and the solid surface of the furnace become significant. With regards to the reaction mechanisms during drying, pyrolysis and atomization of nitrates of volatile analytes, three basic types of chemical reactions may be assumed. Free atoms of analytes arise by evaporation of the elementary form of analytes at atomization temperature, where the particular analyte in its elementary form is produced by direct reduction of analyte nitrate by tungsten or by hydrogen at higher temperatures. Precursory reactions of atom formation are reduction reactions which occur between analyte nitrates and tungsten, between analyte nitrates and hydrogen, as well as reactions of thermal dissociation of relevant nitrates. The importance of particular types of precursory reactions for formation of metallic analytes or their oxides is documented by dependence of Gibbs energy values of particular reactions on the temperature.     

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.     

Equilibrium Chemistry in $${\text {BCl}}_3$$ BCl 3 – $${\text {H}}_2$$ H 2 –Ar Plasma

Plasma Chemistry and Plasma Processing - The approach, which was developed earlier for modeling chemical reactions in laser induced plasmas, is applied to radio-frequency discharge plasmas. The...