Theory of Reaction Rates as Based on the Stoichiometric Number Concept

Horiuti, Jurô

doi:10.1111/j.1749-6632.1973.tb51052.x

Cited by 88 publications

(38 citation statements)

References 36 publications

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“…He was trying to figure out the number of independent pathways in heterogeneous systems [31]. The Horiuti criteria are also based on topological arguments, and therefore, the conclusions obtained can be taken with a great deal of confidence.…”

Section: Enumeration Of Synthetic Pathways: the Horiuti Criteriamentioning

confidence: 99%

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The Catalytic Binuclear Elimination Reaction: Importance of Non-linear Kinetic Effects and Increased Synthetic Efficiency

Garland

2015

Topics in Organometallic Chemistry

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In the context of metal-mediated organic synthesis, cooperativity and synergism are rather broad terms which are often used to denote systems where unusual rate or selectivity effects are observed. These effects can be exhibited by monometallic, heterobimetallic and even multimetallic systems. The present contribution looks exclusively at one of the simplest cases, namely, systems possessing simultaneously both mononuclear and dinuclear complexes (hence both monometallic and heterobimetallic are included, but multimetallic systems are excluded). In Sect. 1, a brief introduction to the general area and a working definition for catalytic binuclear elimination reaction (CBER) is provided. In Sect. 2, we step back and classify the broad range of systems under consideration in order to enumerate the host of reaction networks considered, the potential for non-linear kinetic effects and how this relates to concepts of synthetic efficiency. In Sect. 3, we return to specific examples of CBER, how they fit into the overall context of the systems classification and how they can be identified in an unambiguous manner using in situ spectroscopic techniques. Indeed, tests can be constructed which permit the experimentalist to check crucial features and characteristics consistent with CBER. The present contribution focuses on the subarea in which CBER systems exist and hence CBER's scope for organic syntheses.

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Section: Enumeration Of Synthetic Pathways: the Horiuti Criteriamentioning

confidence: 99%

“…No intrinsic rate non-linearities exist in spite of the network complexity. The systematic evaluation of the number of independent synthetic routes in an arbitrary network was clearly developed in a mathematical framework by Horiuti [31].…”

Section: King and Altmanmentioning

confidence: 99%

The Catalytic Binuclear Elimination Reaction: Importance of Non-linear Kinetic Effects and Increased Synthetic Efficiency

Garland

2015

Topics in Organometallic Chemistry

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“…The calculation results X(1) for such an example together with the singular values a are presented in Table 5.1 (the number of points is 50, the number of points in the multiple steady-state region is 36). The estimates X (1) correspond to the choice of the bound of the minimal singular value which exceeds a12. As follows from Estimates obtained by using the SVD method may be improved with the aid of ridge regression [36].…”

Section: Applicationsmentioning

confidence: 99%

Kinetic Polynomial: A New Concept of Chemical Kinetics

Lazman

Yablonskii

1991

Patterns and Dynamics in Reactive Media

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Abstract. A system of quasi-steady-state equations for a single pathway mechanism of a catalytic reaction can always be reduced to a polynomial in terms of the steady state reaction rate, a kinetic polynomial. The coefficients of this polynomial are polynomials in the parameters of the elementary reaction rates. The form of the lowest coefficient of the polynomial ensures the thermodynamic validity of this form of representation of quasi-steady-state equations. The properties of the kinetic polynomial are discussed in connection with such concepts of chemical kinetics as "molecularity", "stoichiometric number" .Possible applications of this form are: asymptotic analysis of steady-state kinetic models as well as analysis of steady-state multiplicity; description of the steady-state dependences of the reaction rate, determining relations between kinetic constants when solving the inverse problem.On the basis of kinetic polynomial explicit equations for the steady-state rate in case when one of the steps is rate-limiting, and in the neighbourhood of equilibrium have been derived.Algorithm of computation of the kinetic polynomial and its realisation on the basis of computer algebra are described.

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“…Within its framework, the number of overall stoichiometric equations corresponding to the linearly dependent re action routes may not be linearly independent (only physically independent) [ 1 ] - [4]. The problem of deter mining the number Q of linearly independent overall reactions was dealt with by Horiuti [3] and by Temkin [2], [4].…”

mentioning

confidence: 99%