Transition-state theory basic assumptions

Transition State Theory [1,4] is the most frequently used theory to calculate rate constants for reactions in the gas phase. The two most basic assumptions of this theory are the separation of the electronic and nuclear motions (stemming from the Bom-Oppenheimer approximation [5]), and that the reactant internal states are in thermal equilibrium with each other (that is, the reactant molecules are distributed among their states in accordance with the Maxwell-Boltzmann distribution). In addition, the fundamental hypothesis [6] of the Transition State Theory is that the net rate of forward reaction at equilibrium is given by the flux of trajectories across a suitable phase space surface (rather a hypersurface) in the product direction. This surface divides reactants from products and it is called the dividing surface. Wigner [6] showed long time ago that for reactants in thermal equilibrium, the Transition State expression gives the exact... 

The rate constant predicted by conventional transition-state theory can turn out to be too small, compared to experimental data, when quantum tunneling plays a role. We would like to correct for this deviation, in a simple fashion. That is, to keep the basic theoretical framework of conventional transition-state theory, and only modify the assumption concerning the motion in the reaction coordinate. A key assumption in conventional transition-state theory is that motion in the reaction coordinate can be described by classical mechanics, and that a point of no return exists along the reaction path. 

The theory of multi-oscillator electron transitions developed in the works [1, 2, 5-7] is based on the Born-Oppenheimer s adiabatic approach where the electron and nuclear variables are divided. Therefore, the matrix element describing the transition is a product of the electron and oscillator matrix elements. The oscillator matrix element depends only on overlapping of the initial and final vibration wave functions and does not depend on the electron transition type. The basic assumptions of the adiabatic approach and the approximate oscillator terms of the nuclear subsystem are considered in the following section. Then, in the subsequent sections, it will be shown that many vibrations take part in the transition due to relative change of the vibration system in the initial and final states. This change is defined by the following factors the displacement of the equilibrium positions in the... 

Based on this assumption, most of the features of reaction dynamics become irrelevant and can be replaced by statistieal deseription, whieh enables us to focus our attention on local structures of phase spaee, that is, transition states. This assumption is the basic strategy of transition state theory. Thus in the traditional theory of chemical reactions, study of the transition states plays the key role. 

Three basic assumptions are involved in Eyring s transition state theory I. Statistical equilibrium between reactants and activated complexes. II. Classical motion along the reaction path. ... 

Figure 4.9. The basic assumptions of the transition-state theory.

This derivation has its roots in the transition-state theory and involves some assumptions about the dissociation mechanism. The effective temperature remains unknown unless a series of standards (molecules of known ZiMCA or AMCB) are measured under the same conditions. This means that the method necessitates a calibration using known affinities or basicities. It should be noted that the temperature of the resulting AMCA or AMCB is not Teff but corresponds instead to the temperature at which the standards were measured. As evidenced by the equality between the last two terms in Equation 6.7, entropy effects are neglected in this simplified treatment. This limitation has been addressed for systems where large variations in the degrees of freedom are associated with adduct formation, and a broadening of the scope of the kinetic method in the direction of entropy determinations (the so-called extended kinetic method ) has been proposed [121, 122]. 

One of the basic assumptions of this theory is that the polymerisation rate can be computed from the transition rate from an initial electronic state E to a final one Ef of the crystal at a given polymerisation state. The energies of these states depend on the nuclear configuration and their changes around the equilibrium positions for the initial and final electronic states can be expressed (43) in terms of vibrational oscillators which at a given temperature are either classical 1ui)c[Pg.181]

The QET is not the only theory in the field indeed, several apparently competitive statistical theories to describe the rate constant of a unimolecular reaction have been formulated. [10,14] Unfortunately, none of these theories has been able to quantitatively describe all reactions of a given ion. Nonetheless, QET is well established and even the simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Following this trail will lead us from the neutral molecule to ions, and over transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

It is well known from structural and kinetic studies that enzymes have well-defined binding sites for their substrates (3), sometimes form covalent intermediates, and generally involve acidic, basic and nucleophilic groups. Many of the concepts in catalysis are based on transition state (TS) theory. The first quantitative formulation of that theory was extensively used in the work of H. Eyring (4, 5 ). Noteworthy contributions to the basic theory were made by others (see (6) for review). As an elementary introduction, we will apply the fundamental assumptions of the TS theory in simple enzyme catalysis as follows. 

The rest of this paper will be devoted to the consideration of the second kind of reactions. I shall endeavour rather to emphasise the basic assumptions of the theory than to derive ready formulas. Especially on account of some discrepancies with experiment, I think that it may be useful to see that the transition state method is based, in addition to well-established principles of statistical mechanics, on only three assumptions, two of which arc generally accepted. 

Proton transfers in electronically excited states have not been amenable to any reasonable interpretation in terms of the theory of Marcus, in part due to the implicit assumption of the symmetry of the potential energy curves of reactant and product [24,38]. In contrast, ISM provides a simple interpretation of this kind of reactions [39]. The excited-state reactions appear to follow the same basic principles of their ground-state analogues the transition state bond order does not change appreciably from the ground to the excited state. However, the mixing entropy parameter X decreases an enhancement of the dipole moment upon eletronic excitation can increase the suddenness of the repulsive wall of the reaction and decreases X. 

It has often been naggingly remarked that the RRKM-QET theory can fit anything and predict nothing. To counter this criticism, many authors have multiplied skilful consistency checks (study of isotope effects, preparation of the ion via a bimo-lecular reaction or via charge reversal in addition to electron or photon impact, time-resolved studies all the way from the millisecond to the nanosecond timescales, etc.) and have removed arbitrariness via ab initio calculations of frequencies. However, it should be realized that ability to fit the experiments by no means implies that the theory is exact and that its basic assumptions (full energy randomization and existence of a good transition state) are fulfilled. It has been seen that Equation [1] cannot be grossly in error because of a mechanism of cancellation of errors. In contradistinction, KERDs (for which the cancellation of errors does not work because they basically depend on the numerator only) provide a much better way to test the validity of the... 

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