Geometry of the canonical Van Vleck transformation

Bloch's transformation from the zeroth‐order space for a perturbation problem to the corresponding space of exact eigenvectors, was found as a geometrically defined alternative to the algebraically constructed Van Vleck transformation. Klein's theorem of uniqueness transferred some of this geometrical interpretation to its canonical form . Quite recently Kvaal has taken a large step further by writing as a product of commuting planar rotations, obtained by describing and in terms of certain principal vectors and canonical angles. Kvaal's approach is now developed further, using a new commutation relation which simplifies algebraic manipulations substantially. It allows for a simple definition of an operator for the angle between and which has Kvaal's vectors and angles as eigenvectors and eigenvalues. Klein's theorem is refined in various ways. The impact of the approach on a number of previous results is considered. © 2015 Wiley Periodicals, Inc.     

Use of Raman spectroscopy to determine the kinetics of chemical transformation in yogurt production

The kinetics of chemical transformation during the yogurt production was obtained using micro-Raman spectroscopy: Raman spectra were obtained as a function of the incubation time in the fermentation process from milk to yogurt. The milk fermentation by the lactic acid bacteria produces morphological, chemical and textural changes. The chemical transformations were followed using micro-Raman spectroscopy, while the aggregation process and some textural properties through the use of dynamic light scattering, viscosity and pH. Samples with three different starter culture concentrations and different incubation temperatures were prepared. The results indicate the presence of two regimes: the first one (primary metabolism) is characterized by an increment in the initial number of bacteria to reach a high concentration according to the conditions of food, temperature and space, together with some initial chemical transformations. The second regime corresponds properly to the fermentation process accelerated by the continuous reduction in pH due to the lactic acid production; this is accompanied by physical and chemical changes where new structures are created. Knowledge of the kinetics of chemical and physical transformations allows having a better control of the final product with an increase in the quality and shelf life of the final product; problems like phase separation, homogeneity, particle size, acidity, etc., can be controlled.     

Stoichiometry and chemical metrology: Karl Fischer reaction

 Stoichiometry of analytical reactions is discussed as an important element of many primary methods (gravimetry, volumetry, spectrophotometry, etc.) and therefore, of chemical metrology as a whole. Variations in stoichiometry caused by non-equilibrium conditions, by changes in the reaction medium or by other factors can be a source of the dominant uncertainty component in the analytical measurement. Such a situation is illustrated with the Karl Fischer (KF) reaction which is widely used in aquametry. Two kinds of solvents used as a part of the reaction medium – alcohols and amides – are compared. The influence of the media on the stoichiometry of the reaction and, correspondingly, on the titre of the KF reagent is evaluated. Received: 4 November 1998 · Accepted: 22 December 1998     

Integral invariants in chemical kinetics

Integral invariants of classical mechanical systems are used for the mathematical treatment of equilibrium systems of chemical reaction kinetics. Some conserved quantities and Hamilton equations in chemistry are shown.

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Mean-field cooperativity in chemical kinetics

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, a cooperative behavior naturally emerges from the model; in particular, by means of various cooperative measures previously introduced, we highlight how the degree of cooperativity depends on the interaction strength among components. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of “susceptibility.” We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model p-body interactions, whose non-trivial cooperative capability is investigated too.     

Size-dependent phase transformation kinetics in nanocrystalline ZnS

Nanocrystalline ZnS was coarsened under hydrothermal conditions to investigate the effect of particle size on phase transformation kinetics. Although bulk wurtzite is metastable relative to sphalerite below 1020 degrees C at low pressure, sphalerite transforms to wurtzite at 225 degrees C in the hydrothermal experiments. This indicates that nanocrystalline wurtzite is stable at low temperature. High-resolution transmission electron microscope data indicate there are no pure wurtzite particles in the coarsened samples and that wurtzite only grows on the surface of coarsened sphalerite particles. Crystal growth of wurtzite stops when the diameter of the sphalerite-wurtzite interface reaches approximately 22 nm. We infer that crystal growth of wurtzite is kinetically controlled by the radius of the sphalerite-wurtzite interface. A new phase transformation kinetic model based on collective movement of atoms across the interface is developed to explain the experimental results.     

Tracking chemical kinetics in high-throughput systems

Combinatorial chemistry and high‐throughput experimentation (HTE) have revolutionized the pharmaceutical industry—but can chemists truly repeat this success in the fields of catalysis and materials science? We propose to bridge the traditional “discovery” and “optimization” stages in HTE by enabling parallel kinetic analysis of an array of chemical reactions. We present here the theoretical basis to extract concentration profiles from reaction arrays and derive the optimal criteria to follow (pseudo)first‐order reactions in time in parallel systems. We use the information vector f and introduce in this context the information gain ratio, χ_r, to quantify the amount of useful information that can be obtained by measuring the extent of a specified reaction r in the array at any given time. Our method is general and independent of the analysis technique, but it is more effective if the analysis is performed on‐line. The feasibility of this new approach is demonstrated in the fast kinetic analysis of the carbon–sulfur coupling between 3‐chlorophenylhydrazonopropane dinitrile and β‐mercaptoethanol. The theory agrees well with the results obtained from 31 repeated C? S coupling experiments.     

Effect of brownian diffusion on chemical kinetics

A new method of theoretical prediction of the kinetic rate constants of fast chemical reactions in solutions is presented. It takes into account the effect of finite diffusive displacements of the reacting molecules. The approach is based on the solution of the steady-state Fokker–Planck equation by the moments method of Grad developed in the theory of coagulation of aerosol particles. A comparison of the predicted rate constants with the experimental data provided by Schuh and Fischer for the self-reaction of tert-butyl radicals in n-alkanes shows a good correspondence.     

Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition

The canonical transformation (CT) theory has been developed as a multireference electronic structure method to compute high-level dynamic correlation on top of a large active space reference treated with the ab initio density matrix renormalization group method. This article describes a parallelized algorithm and implementation of the CT theory to handle large computational demands of the CT calculation, which has the same scaling as the coupled cluster singles and doubles theory. To stabilize the iterative solution of the CT method, a modification to the CT amplitude equation is introduced with the inclusion of a level shift parameter. The level-shifted condition has been found to effectively remove a type of intruder state that arises in the linear equations of CT and to address the discontinuity problems in the potential energy curves observed in the previous CT studies.     

Adjacency matrices and chemical transformation graphs

The vast numbers of molecular objects and chemical transformations of a substrate cannot be evaluated even intuitively, which necessitates the development of simple reaction monitoring methods. Here this problem is formulated for the first time, and possible solutions are substantiated.     

Understanding the kinetics of spin-forbidden chemical reactions

Many chemical reactions involve a change in spin-state and are formally forbidden. This article summarises a number of previously published applications showing that a form of Transition State Theory (TST) can account for the kinetics of these reactions. New calculations for the emblematic spin-forbidden reaction HC + N(2) are also reported. The observed reactivity is determined by two factors. The first is the critical energy required for reaction to occur, which in spin-forbidden reactions is often defined by the relative energy of the Minimum Energy Crossing Point (MECP) between potential energy surfaces corresponding to the different spin states. The second factor is the probability of hopping from one surface to the other in the vicinity of the crossing region, which is largely defined by the spin-orbit coupling matrix element between the two electronic wavefunctions. The spin-forbidden transition state theory takes both factors into account and gives good results. The shortcomings of the theory, which are largely analogous to those of standard TST, are discussed. Finally, it is shown that in cases where the surface-hopping probability is low, the kinetics of spin-forbidden reactions will be characterised by unusually unfavourable entropies of activation. As a consequence, reactions involving a spin-state change can be expected to compete poorly with spin-allowed reactions at high temperatures (or energies).     

Consequences of resonance tunnelling in chemical kinetics

The kinetic consequences of resonance tunnelling processes that may occur in chemical reactions are investigated in terms of a multi-centered unsymmetrical Eckart potential barrier. This potential function does not only simulate the possible existence of intermediate wells in the effective potential energy cut along the reaction path, but also is amenable to analytic solutions. The reaction rate as well as its dependence on temperature, reduced mass,Q-value, activation energy and barrier diffuseness are evaluated for successively increasing the number of barrier stages. Comparisons between results due to single and multi-humped potential energy barriers are made and discussed.     

Comments on current aspects of chemical kinetics

An aged kineticist was awakened in 1989 from a 50-year slumber. After arduous study he sized-up the present situation, with occasional reflections on the state of knowledge in 1939.     

Recent advances in studying energy transfer kinetics by using TBP as a chemical probe

The characteristic properties of TBP and the advantage of using TBP as an energy donor or an acceptor have been described. TBP can be used as a probe for detecting the excited states of alkanes, more reliable G values of alkanes have been obtained. The rate constants of the energy transfer for TBP-alkanes binary systems have been determined. The energy transfer process is controlled by diffusive motion of the reactive species. TBP also can be used as a probe for detecting the geminate ion pairs of alkanes.     

Dosimetric studies and chemical kinetics of Resazurin dye and its possible use as radiation dosimeter

Journal of Radioanalytical and Nuclear Chemistry - The structural and optical properties of the neutron irradiated PMMA doped by 5 wt% RhB have been investigated. Fourier transform infrared...     

Stoichiometry of uranyl hydrolysis reaction in acidic aqueous solutions from the evidence of oxygen exchange kinetics

The kinetics of uranyl oxygen exchange with water molecules in aqueous solutions was studied in the pH range 1–4 and uranium concentration range 10^–4–0.1 M. It was confirmed that the exchange is stimulated by hydrolyzed uranyl species. From the evidence of data on the kinetics of uranyl oxygen exchange the reaction stoichiometry of uranyl hydrolysis was determined. The scheme of uranyl hydrolysis involving formation of (UO₂)₂(OH)₂²⁺, (UO₂)₂(OH)₃⁺, and other hydrolyzed species was proposed. To cite this article: L.G. Mashirov et al., C. R. Chimie 336 (2004).

Résumé

Étude de l'hydrolyse de l'uranium hexavalent en milieu acide par échange isotopique de l'oxygène. L'échange isotopique de l'oxygène de l'ion uranyle avec les molécules d'eau a été étudié dans le domaine de pH de 1 à 4 et de concentration en uranium de 10^–4 à 0,1 M. Cet échange a lieu par l'intermédiaire d'espèces hydrolysées de U(VI). La stoechiométrie des formes hydrolysées de U(VI) est déduite des vitesses d'échange isotopique. En particulier, les espèces (UO₂)₂(OH)₂²⁺ et (UO₂)₂(OH)₃⁺ ont été clairement identifiées. Un schéma d'hydrolyse est proposé. Pour citer cet article : L.G. Mashirov et al., C. R. Chimie 336 (2004).     

Reparametrization of models of non-stationary chemical kinetics as a method of investigation of the inverse problem

A new approach to solve the inverse problem of the non-stationary chemical kinetics by a reparametrization of the initial model is suggested. This approach permits to obtain all solutions of IP in the case of a finite number or some parametric functions in the case of the infinite number of solutions.     

Grand canonical ensemble approach to electrochemical thermodynamics,kinetics, and model Hamiltonians

The unique feature of electrochemistry is the ability to control reaction thermodynamics and kinetics by the application of electrode potential. Recently, theoretical methods and computational approaches within the grand canonical ensemble (GCE) have enabled to explicitly include and control the electrode potential in first principles calculations. In this review, recent advances and future promises of GCE density functional theory and rate theory are discussed. Particular focus is devoted to considering how the GCE methods either by themselves or combined with model Hamiltonians can be used to address intricate phenomena such as solvent/electrolyte effects and nuclear quantum effects to provide a detailed understanding of electrochemical reactions and interfaces.