Transition states symbol

Ib, and Ic (see Chapter 13) are those of the transition state (the symbol is, by convention, used to label the transition state) ... 

Hughes and Ingold interpreted second order kinetic behavior to mean that the rate determining step is bimolecular that is that both hydroxide ion and methyl bromide are involved at the transition state The symbol given to the detailed description of the mech anism that they developed is 8 2 standing for substitution nucleophilic bimolecular... 

This description provides information, via conventional structures, about the constitution of reactants, products, and the intermediate. Transition state structures are more provisional and may attempt to show the electronic distribution and flow in this region of the reaction path. The curved arrow symbolism is often used, as shown in structure 1 for the first elementary reaction. 

In this reaction I" is the nucleophile, and Br" is called the leaving group (or nucleofuge). Beyond this, the classification symbolism may include a designation of the molecularity of the reaction. Molecularity is the number of reactant molecules included in the transition state. The above reaction is an 8 2 reaction, because both reactants are present in the transition state. On the other hand, this substitution... 

Here Z represents the reaction products. M is the transition state the double dagger symbol will always signify a quantity or structure relating to the transition state. Scheme I incorporates the equilibrium assumption by writing the conversion of the initial state into the transition state as an equilibrium. This assumption then allows us to apply statistical mechanics to the rate problem making use of Eq. (5-32), we have... 

The hypothesis that electron-pair donation from the a atom will stabilize this transition state leads to the difficulty that the attacking atom must carry more bonds than conventional valence bond symbolism admits. Despite this problem, the general idea is expressed by 7 and its relationship to 6 by resonance. It is possible that transition state stabilization can be obtained in this way by rehybridization of the entire molecule. Klopman et al. suggest that the a effect arises from... 

Figure 9. A schematic of a tunneling center is shown. is its typical size, is a typical displacement on the order of the Lindemann distance. The doubled circles symbolize the atomic positions corresponding to the alternative internal states. The internal contour, encompassing N beads, illustrates a transition state size, to be explained later in the text.

Figure 12. Two-dimensional cut through the potential surface for fragmentation of the transition state [OH - -CH3 F] complex as a function of the C—F bond length and the FCO angle. All other coordinates are optimized at each point of this PES. Pathway 1 is the direct dissociation, while pathway 2 leads to the hydrogen-bonded [CH3OH F ] structure. The letter symbols correspond to conhgurations shown in Fig. 11. Reprinted from [63] with permission from the American Association for the Advancement of Science. (See color insert.)...

The symbol will often be applied to a structure to indicate that it is intended as an attempted representation of a transition state (T.S.). 

The symbols ji, o and (0 are given respectively to the n systems, o bonds and lone p orbitals which participate in the transition state and the symbols (s) and (a) are indicated for their suprafacial and antarafacial use. The notation is completed by the number of electrons supplied by each component. Thus n2s denotes a two electron n system used in a suprafacial way. woa indicates a vacant p orbital used in an antarafacial way and so on. 

Application of the Kurz approach to CD-mediated reactions, whether they be accelerated or retarded, is straightforward (Tee, 1989), provided appropriate kinetic data are available. From the rate constants A u for the normal, uncatalysed reaction (2) and for the mediated ( catalysed ) reaction (k2 = kJKs) as in (3), application of simple transition state theory, in the manner shown above, leads to (9), where now Krs is the apparent dissociation constant of the transition state of the CD-mediated reaction (symbolized here as TS CD) into the transition state of the normal reaction (TS) and the CD. This constant and its logarithm, which is proportional to a free energy difference, is a valuable probe of the kinetic effects of CDs on reactions. 

Capon (1964 Capon and McManus, 1976) introduced a simple classification for reactions involving neighbouring group participation, in which G-n indicates participation by a nucleophilic group G in an n-membered cyclic transition state. For present purposes an extension of this symbolism is necessary in order that the abbreviations indicate the electrophilic centre also. 

To begin we are reminded that the basic theory of kinetic isotope effects (see Chapter 4) is based on the transition state model of reaction kinetics developed in the 1930s by Polanyi, Eyring and others. In spite of its many successes, however, modern theoretical approaches have shown that simple TST is inadequate for the proper description of reaction kinetics and KIE s. In this chapter we describe a more sophisticated approach known as variational transition state theory (VTST). Before continuing it should be pointed out that it is customary in publications in this area to use an assortment of alphabetical symbols (e.g. TST and VTST) as a short hand tool of notation for various theoretical methodologies. 

Of course, one is not really interested in classical mechanical calculations. Thus in normal practice the partition functions used in TST, as discussed in Chapter 4, are evaluated using quantum partition functions for harmonic frequencies (extension to anharmonicity is straightforward). On the other hand rotations and translations are handled classically both in TST and in VTST, which is a standard approximation except at very low temperatures. Later, by introducing canonical partition functions one can direct the discussion towards canonical variational transition state theory (CVTST) where the statistical mechanics involves ensembles defined in terms of temperature and volume. There is also a form of variational transition state theory based on microcanonical ensembles referred to by the symbol p,. Discussion of VTST based on microcanonical ensembles pVTST is beyond the scope of the discussion here. It is only mentioned that in pVTST the dividing surface is... 

From a mechanistic point of view [4], there are two extremes conceivable if the interaction between X and Y is weak, [XY] symbolizes a transition state and the reaction (la,a ) is a case of outer-sphere electron transfer. If, however, the interaction is strong enough that it leads to, e.g., covalent-bond formation between X and Y (Eq. 1 b), the product of that interaction is an intermediate ( adduct ) and the overall electron exchange between X and Y (via Eq. lb, b ) is then an example of inner-sphere electron transfer. 

The thermodynamic formulation of the transition state theory (TST), as applied to a unimolecular reaction described symbolically by... 

Any energy change (from the ground state to the transition state in a chemical reaction) that accounts (a) for the presence of a reaction barrier and (b) for the temperature dependence of a rate constant. This quantity is symbolized by and may also be referred to as the Arrhenius energy of activation and activation energy. 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

Chemical reactions with one or more intermediates separated by transition states (usually indicated by the superscript symbol t) ... 

A ratio in transition state theory (symbolized by k) that represents the probabihty that the activated complex will go on to form product(s) rather than return to reactants. In most cases, this value is approximately one however, if reactants do not obey the Boltzmann law or if the temperature is very high, then the coefficient can be less than one. See Transition-State Theory... 

More specifically, the geometry of the molecule at the transition state is used to compute a rotational partition function Q rot in which the principal moments of inertia Ia, lb, and Ic (see Chapter 13) are those of the transition state (the symbol is, by convention, used to label the transition state) ... 

Transition state theory treats a reacting system thermodynamically. Let us again take a bimolecular reaction between A and B. Transition state theory assumes that as A and B collide and start to react, they form a species called the activated complex, which corresponds to the A-B adduct at the peak of the energy hill lying between reactants and products. This activated complex is thus in a transition state and can either fall back to reactants or go on to form products. The activated complex is normally indicated with a double dagger symbol, AB. The reaction can thus be given as... 

FIGURE 8.4 Predicted energetics for various mechanisms for the S0j-H20 reaction transition states are marked with a i symbol (adapted from Morokuma and Muguruma, 1994). 

Often instead of using state designations molecular orbital terminology is used to describe a transition (vide infra). To be consistent with the accepted convention for state symbols the higher MO should be written first (15). Thus the absorption of molecular hydrogen at 1100 A., -... 

Transitions, particularly in simple molecules, are also expressed in terms of all the molecular orbitals involved and the state symbols are also included. For example the 1100 A., V—N transition in the hydrogen molecule may be written (15)... 

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