Intersecting-state model

Density functional theory (DPT) offers the opportunity to calculate the energies of nuclear configurations of polyatomic systems with an increasing efficiency. Direct dynamics , where the energies of the nuclear configurations are calculated as they are reached by a trajectory, promise to bypass the need for a PES in rate calculations. However, chemists need more general and structure-motivated methods to interpret and predict reactivity. Semi-anpirical methods may play a significant role in this respect, because they offer a simple, accurate and structure-related approach to chemical reactivity. 

The distinctive features of semi-anpirical methods are the use of experimental information on reactants and products, and simplified potential models to calculate the transition-state structure and energy. A semi-anpirical model that provides useful transition-state data on bond-breaking-bond-forming reactions is the intersecting/interacting state model aSM) [16,17], 

ISM is a unidimensional reactivity model based on the diabatic method originally proposed by Evans and Polanyi [18] and on the conservation of the bond order along the reaction coordinate of the bond-energy-bond-order (BEBO) first proposed by Johnston and Parr [19]. Eor a reaction of the type 

The success of the method in calculating the horizontal separation d from the properties of the reactants and products ultimately determines its abiUty to provide reasonable estimates of the activation energy. According to the ISM, the separation d is the sum of the reactive bonds extensions from their equilibrium to their transition-state configurations. For a reaction such as that of mechanism (VIII), this is the sum of the extension of the BC bond with that of the AB bond 

the method requires a relation between the bond extensions and a parameter that can be calculated for any arbitrary bond-breaking-bond-forming reaction. A very interesting relationship involving bond lengths was found by Pauling [20], who showed that they can be related to the corresponding bond orders n, 

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The self-exchange electron-transfer (SEET) process, in which a radical is trapped by the parent molecule, has been studied using the intersecting-state model (ISM).91 Absolute rate constants of SEET for a number organic molecules from ISM show a significant improvement over classical Marcus theory92-94 in the ability to predict experimental SEET values. A combination of Marcus theory and the Rips and Jortner approach was applied to the estimation of the amount of charge transferred in the intramolecular ET reactions of isodisubstituted aromatic compounds.95... 

The 1977 review of Martynov et al. [12] discusses existing mechanisms of ESPT, excited-state intramolecular proton transfer (ESIPT) and excited-state double-proton transfer (ESDPT). Various models that have been proposed to account for the kinetics of proton-transfer reactions in general. They include that of association-proton-transfer-dissociation model of Eigen [13], Marcus adaptation of electron-transfer theory [14], and the intersecting state model by Varandas and Formosinho [15,16], Gutman and Nachliel s [17] review in 1990 offers a framework of general conclusions about the mechanism and dynamics of proton-transfer processes. 

The Intersecting State Model (ISM) [72,77] strengthened our understanding of TET. According to ISM, the RC used in TET is determined by the bond order at the transition state [78]. TET was then successfully applied to cycloadditions to olefins [79]. 

Modeling the Reaction Rate Intersecting-State Model. 157... 

We would like to observe here that all CT AIM contributions f (B) and k (A) are negative, e.g., when p > Pa then dNf < 0 and similarly, when Pb > Pk then dNj > 0. Thus, the A- and B-resolutions partition the overall CT stabilization into the stabilizing reactant-atom contributions, while the (A, B)-resolution views the CT process as the process of activating a basic reactant (removal of Nct electrons from B) followed by the charge stabilization in the acidic reactant (adding Nct electrons to A). A similar approach is adopted in the intersecting-state model (Fig. 7) which is the subject of the Sect. 3.2.3. 

In order to relate CS of reactants A and B to the CT reaction rate an intersecting-state model (ISM) has recently been proposed [36], with the relevant potential energy curves defined in the electron population space. We again consider the reactive system = A—B and the associated potential energy surface Ejj(Na, Nb), given by the second-order Taylor expansion in the reactant population displacements from the initial configuration, = (A (B ), before CT (see Figs. 6 and 7) ... 

UNDERSTANDING CHEMICAL REACTIVITY THROUGH THE INTERSECTING-STATE MODEL... 

Before pursuing the model further it is useful to compare the values of d estimated through the intersecting-state model (ISM) with the sum of bond extensions at the transition state, d, given by potential-energy surface calculations, for some elementary reactions. For the reaction H -t- H2 H2 + H (1hh=0-7416 A), d can be estimated through eq(29) with... 

Within the intersecting-state model, the reaction energy barrier is determined by the shape of the potential energy curves of AB and BC and the geometric criterion for the configuration of the transition state given by eqs(17) and (29). 

Pross and Shaik [23] have proposed a qualitative valence-bond (VB) configuration model to describe how reaction energy profiles can be built from VB configurations. Structures for the transition states such as the ones previously presented can be considered within that VB-model. Yates [24] has recently made a comparative study of several intersecting state models, with respect to the problem of photochemical proton transfers, and has concluded that ISM is one of the most general. 

To account for the disparity, Kreevoy and Lee consider -1< 6 1. Even within the limiting conditions of the theory of Marcus, the one-dimensional Intersecting-state Model can accommodate the disparity progress of the Kreevoy-Lee model negative values for the parameter 8 correspond to ni[Pg.176]

Methyl transfer reactions, X" + CH3Y XCH3 + Y" (X and Y are halogen atoms), which are an important class of Sn2 nucleophilic substitutions, have also been studied within the intersecting-state model fiamework [43]. As will be shown, the overall pattern is similar to that of proton transfers for reactions in solution, but is different for reactions in the vapour phase, because, owing to the masses involved, quantum mechanical tunnelling does not dominate thermal activation. 

ABSTRACT. A theoretical study of the electron self-exchange in porphyrins and in cytochrome c, and of the free-energy dependence of poq)hyrin-cytochrome c systems ows that these reactions are not easily amenable to an explanation in the framework of the theory of Marcus. On the other hand the intersecting-state model can be used to calculate the self-exchange rates and ] ovide an useful rationalization of the free-energy relationsh obs ed in these systems. 

The detailed structural information on the cytochrome c system, its biological relevance and the inability to offer an adequate explanation of its features with the current theories of electron transfer, prompted us to apply an alternative model to predict and rationalize the electron transfer rates observed. In the following, we present the intersecting-state model and apply it to the calculation of the self-exdiange rates of a synthetic analogue of a cytochrome and to cytochrome c itself. The model is then applied to rationalize the photochemical and thermal ET reactions between metallocytochrome c and metallouroporphyrins. Our calculations show that these systems are amenable to a quantitative explanation by the theoretical model we employ. 

Fonnosinho, S. J. in Understanding Chemical Reactivity Through the Intersecting-State Model, Fonnosinho, S. J. Csizmadia, I. G. Amaut, L. G. (Eds.) NATO ASI, Kluwer, Dordrecht, 1991 pp 159. 

Mechanism (I). In this chapter we merge the approaches of the Interacting/ Intersecting State Model (ISM) to atom and proton transfer reactions" with treatment of electron transfer reactions by this same model. Transition-state energies and effective reaction frequencies are calculated and used to obtain the rate constants of representative CPET. 

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