Determination of the largest lyapunov index for short chaotic time sequences in self-oscillating chemical reactions

A method was developed for the determination of largest Lyapunov index for short chaotic time sequences with allowance for the presence of noise in the response of the system. For this purpose a simple unidimensional representation modelling the dynamics of irregular self-oscillations was investigated. Conditions were found for adequate determination of the largest Lyapunov index from the noise-distorted signals. The results were used to obtain the largest Lyapunov index for the Belousov—Zhabotinskii reaction taking place in an ideal-mixing closed reactor and in a constant-mixing flow-type reactor. Institute of Organic Chemistry, National Academy of Sciences of Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 3, pp. 136–142, May–June, 1997.     

Structural information content and Lyapunov exponent calculation in protein unfolding

A lattice model with Monte Carlo dynamics is used to carry out computer simulations of protein dynamics on a four α-helix bundle. The interaction energies in the model can be set so that either the helix bundle structure remains relatively stable or changed so that it unfolds. The computer model produces output that simulates experimental measurements relating to the structure. We show how this output can be used with analytical techniques of nonlinear dynamics to obtain important information about the complex underlying protein dynamics. Time-delay reconstruction plots of structural parameters of unfolding bundles resemble strange attractors in a space of dimension 3–4. We calculate Lyapunov exponents for these unfolding runs and find positive Lyapunov exponents implying chaotic dynamics. For stable runs the Lyapunov exponents are close to zero. We use these Lyapunov exponents to calculate the rate of loss of structural information during the unfolding process and show how the approach may be useful for investigating the folding dynamics of proteins. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2761–2769, 1998     

Thermodynamic criteria for estimating the kinetic parameters of catalytic reactions

Kinetic parameters are estimated using two criteria in addition to the traditional criterion that considers the consistency between experimental and modeled conversion data: thermodynamic consistency and the consistency with entropy production (i.e., the absolute rate of the change in entropy due to exchange with the environment is consistent with the rate of entropy production in the steady state). A special procedure is developed and executed on a computer to achieve the thermodynamic consistency of a set of kinetic parameters with respect to both the standard entropy of a reaction and the standard enthalpy of a reaction. A problem of multi-criterion optimization, reduced to a single-criterion problem by summing weighted values of the three criteria listed above, is solved. Using the reaction of NO reduction with CO on a platinum catalyst as an example, it is shown that the set of parameters proposed by D.B. Mantri and P. Aghalayam gives much worse agreement with experimental values than the set obtained on the basis of three criteria: the sum of the squares of deviations for conversion, the thermodynamic consistency, and the consistency with entropy production.     

实验控制Belousov-Zhabotinsky-CSTR化学混沌反应

用两种方法来控制在连续流动釜式反应器(CSTR)中的Belousov-Zhabotinsky(BZ)化学混沌反应:(1)自适应延迟时间反馈控制方案;(2)线性自相互作用控制方案。第一种控制方案是一种微扰控制,并能将BZ-CSTR化学混沌稳定控制到其内嵌的不稳定周期轨道(UPO)上去。这种方法的优越之外可以由系统延迟时间的自适应调节得以显示。第二种控制方案可以驱动BZ-CSTR混沌动力学到达一系列规则的动力学状态,这些动力学状态可能并不是混沌轨道中内嵌的本征轨道。在控制BZ-CSTR化学混沌反应的实验中,这两种方案显示出了很大的灵活性和有效性。     

Mew method for estimating polarity of chemical bonds

For alkali-metal and halogen atoms, a relationship has been established between their electronegativity (EN) and the charge on the atoms. Bond polarities have been determined in molecules and crystals of alkali-metal halides by the method of equalization of ENs of the bond partners. The reasons for differing dimensional behavior of metal and nonmetal atoms upon change in coordination are discussed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2701–2704, December, 1989.     

Temperature dependence of quantitative characteristics of chaotic regime in Belousov-Zhabotinskii reaction

In a Ferroin-catalyzed oscillatory Belousov-Zhabotinskii reaction, the temperature dependences of the largest Lyapunov exponent (LLE) and the induction period for a chaotic regime to appear are linear in the 285–308 interval when plotted on Arrhenius coordinates. For the LLE, the activation energies calculated for different concentrations of the catalyst are in the 82–126 kJ/mole interval, and for the induction period in the 61–95 kJ/mole interval. On the basis of the experimental data, it has been concluded that this autooscillatory chemical system, within a narrow range of catalyst concentrations, is relatively insensitive to random, small, external perturbations.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 29, No. 2, pp. 186–190, March–April, 1993.The authors wish to thank K. B. Yatsimirskii, Academician of the Academy of Sciences of Ukraine, for discussing the data obtain in this work.     

Kinetics of reactions in solution: Method for the treatment of data from non-isothermal chemical kinetic experiments

A new method is proposed for the treatment of kinetic data derived from non-isothermal kinetic experiments for the determination of the parameters of the Arrhenius equation. The results obtained from its application show the excellent precision of this method.

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Reaction calorimetry for the development of chemical reactions

A new reaction calorimeter is described that has been developed to study chemical reaction processes on a laboratory scale. It provides precise measurements of kinetic and thermal data, of heat transfer data, as well as of the physical properties of the reaction product. The reaction calorimeter is applied successfully in the development of chemical processes, in the evaluation of hazards and risks of chemical synthesis.Working principles and evaluation are described using the example of the nitration of benzaldehyde.     

On the distorted wave approximation for chemical reactions

Various procedures for constructing transition amplitudes for chemical reactions in the distorted wave approximation are demonstrated. Calculations are performed for the collinear reaction H+H₂(ν = 0) → H₂(ν = 0) + H at low energies. Comparison is made with exact results after unitarization is invoked through (1) exponential unitarization and (2) the Condon approximation. In the threshold region the Condon approximation gives quite reasonable agreement with exact results.     

On the simple Michaelis-Menten mechanism for chemical reactions

Several mathematical properties associated with the simple Michaelis-Menten mechanism for enzymatic reactions are proven. In particular it is shown that the usual interpretation of the slope of the experimental Michaelis-Menten rate law in terms of the reaction constants of the mechanism can be obtained, in the approximation in which the total concentration of the enzyme is small compared with the Michaelis-Menten constant, independently of the ratio between the total initial concentrations of the enzyme and substrate. Furthermore, the ratio of the total concentration of the enzyme to the Michaelis-Menten constant allows for the elimination of a fast variable in a singular perturbation method, yielding the Michaelis-Menten rate law as a first order approximation.     

Thermodynamic functions for state-selected chemical reactions

Thermodynamic functions for chemical reactions of state-selected reactants to state resolved products are introduced and discussed. The equilibrium constant, change in free energy and other thermodynamic functions can all be computed using standard thermochemical tables without any kinetic input. It is also shown that the usual type of thermodynamic cycles can be employed for reactions even when the reactants and/or products are state-selected.     

Modeling chemical reactions for drug design

Chemical reactions are involved at many stages of the drug design process. This starts with the analysis of biochemical pathways that are controlled by enzymes that might be downregulated in certain diseases. In the lead discovery and lead optimization process compounds have to be synthesized in order to test them for their biological activity. And finally, the metabolism of a drug has to be established. A better understanding of chemical reactions could strongly help in making the drug design process more efficient. We have developed methods for quantifying the concepts an organic chemist is using in rationalizing reaction mechanisms. These methods allow a comprehensive modeling of chemical reactivity and thus are applicable to a wide variety of chemical reactions, from gas phase reactions to biochemical pathways. They are empirical in nature and therefore allow the rapid processing of large sets of structures and reactions. We will show here how methods have been developed for the prediction of acidity values and of the regioselectivity in organic reactions, for designing the synthesis of organic molecules and of combinatorial libraries, and for furthering our understanding of enzyme-catalyzed reactions and of the metabolism of drugs.     

R-matrix theory for collinear chemical reactions

We apply R-matrix theory to the collinear II + II₂ exchange reaction. Within a natural collision coordinate frame we generalize the standard R-matrix formulae to apply to reactive systems which have two asymptotic matching surfaces. After writing the hamiltonian as H = H⁰ + V where H⁰ is a soluble reactive scaltering hamiltonian, we derive the Buttle correction which accounts for H⁰ exactly. The Buttle correction is necessary to speed convergence of the numerical results. Using a rather crude set of basis functions which are an orthonormal set of solutions of H⁰ we find that 150 even and odd type functions are necessary to achieve adequate agreement of transmission probabilities with close coupled results. Fewer functions are needed to account for the threshold behavior but the full number are needed to portray the resonance at 22.2 kcal/mole. Finally we generalize our formulae to apply to asymmetric exchange reactions.     

Symmetry rules for predicting the course of chemical reactions

Rules are given for a reaction of any molecularity which show whether it is allowed or forbidden by orbital symmetry properties. The rules are based on a rigorous treatment, but correspond to simple concepts in practice. A rough MO sequence for the reactants is all that is needed.

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Zusammenfassung Für Reaktionen beliebiger Molekularität werden Regeln dafür angegeben, ob die Reaktion aus Symmetriegründen erlaubt oder verboten ist. Diese Regeln werden streng hergeleitet, sind jedoch in der Praxis einfach anwendbar. Benötigt wird lediglich die Reihenfolge der MO der Reaktionen.

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Résumé On donne des règles de sélection pour une réaction de molécularité arbitraire selon les propriétés de symétrie orbitale. Les règles sont basées sur un traitement rigoureux mais correspondent en practique à des concepts simples. On a seulement besoin de connaître l'ordre des orbitales moléculaires des réactants.

     

Complexity index for the linear mechanisms of chemical reactions

A complexity measure is proposed for the kinetic models of chemical reactions with linear mechanisms. The index is related to the structure of fractional-rational kinetic laws for chemical reactions, as well as to the structure of cyclic graphs used to describe them. The complexity index is shown to be closely related to the detailed hierarchical classification and to the code of linear reaction mechanisms, recently introduced. A number of index properties are proved for two- and three-reaction routes. They reflect the influence of the various classification criteria, such as the number of reaction routes and intermediates, the type, class and subclasses of the mechanism, and the number of intermediates in each reaction route. Hierarchical levels of mechanisms with the same complexity (isocomplex mechanisms) are specified. Standard tables are presented with complexity indices for all topologically distinct linear reaction mechanisms having one to three reaction routes, two to six intermediates, and reversible elementary steps.[/p]     

Valency changes in chemical reactions

An analysis of valence changes in selected organic gas phase reactions, calculated on SINDO1 potential surfaces, is performed. It is shown that transition states and intermediates have diradical character if singlet and triplets states are nearly degenerate. As a consequence, normal valencies are expected in Woodward-Hoffman allowed reactions and reduced valencies in forbidden reactions. The formalism is also applied to cationic reactions, but the effects of valency changes are less pronounced.