Activated complex, “loose

At R > 400 pm the orientation of the reactants looses its importance and the energy level of the educts is calculated (ethene + nonclassical ethyl cation). For smaller values of R and a the potential energy increases rapidly. At R = 278 pm and a = 68° one finds a saddle point of the potential energy surface lying on the central barrier, which can be connected with the activated complex of the reaction (21). This connection can be derived from a vibration analysis which has already been discussed in part 2.3.3. With the assistance of the above, the movement of atoms during so-called imaginary vibrations can be calculated. It has been attempted in Fig. 14 to clarify the movement of the atoms during this vibration (the size of the components of the movement vector... 

In activated complex, one degree of vibration has been considered of a different character from the rest, since it corresponds to a very loose vibration... 

The transition state theory (also known as absolute reaction rate theory) was first given by Marcellin (1915) and then developed by Erying and Polanyi (1935). According to this theory, the reactant molecules are first transformed into intermediate transition state (also known as activated complex). The activated complex is formed by loose association or bonding of reactant... 

Figure 12. Comparison of simple RRKM rate-energy curves, using three different loose activated complexes giving the same rates at the energy corresponding to about 10 s" . Calculations are shown for Eq values of 1.86 and 3.10 eV. The three transition states are (a) uniform frequency multiplier of 0.9 (—) (b) four low-frequency vibrations (—) (c) low-frequency vibration to internal rotor ( -). The corresponding values are as follows 1.86 eV, (a) = 8.2 eu, (b) = 4.9 eu, (c) = 1.6 eu 3.10 eV (a) = 6.9 eu, (b) = 4.9 eu, (c) = 2.9 eu. Also shown is the semiclassical RRK functional form...

For the la mechanism, associative interchange, the interaction between M and L is more advanced in the transition state than in the case of the Id. The M-L bonding is important in defining the activated complex. Both of these interchange mechanisms are loosely connected to the Sn 2-type mechanism. 

Ligand Polarization. Polarization is the most important immediate consequence of ligand coordination. The fact that ligand polarization can assist some of the ligand reactions was first expounded in detail and used by Meerwein 14, 24), Meerwein also provided (but never published) the first interpretation of the way in which coordination may affect the path of the activated complex along the reaction coordinate. Fairly comprehensive reviews of this type of reaction are available 11, 18), However, the kinetic aspects have rarely been discussed in detail (except for biochemical cases 23, 8)), because comparative experimental data are meager. Therefore, the examples cited below fall into several loosely related groups. 

The mechanism of decarboxylation of /3-lactones has attracted much attention. The gas-phase decomposition of 2-oxetanone is a unimolecular first-order process. It has a considerably lower energy of activation than the pyrolysis of oxetane and a much higher entropy of activation, indicating a loose activated complex (69JA7743). The ease of the reaction is greatly affected by the electronic effect of substituents at position-4, but not at position-3. The Hammett treatment of a series of rrans-4-aryl-3-methyl-2-oxetanones gave a good correlation with [Pg.374]

Calculation of the partition functions for reactants is straightforward, but the partition function for the activated complex needs explanation. The activated complex has been shown to have the unique feature of a free translation along the reaction coordinate over the distance occupied by the activated complex. The statistical mechanical quantity for this free translation has already been factorized out from the total partition function for the activated complex in the derivation. This has been done simply because doing so allows cancellation of some awkward terms in the derivation of the rate constant equation. This is why the symbol has appeared along with the symbol f, this latter indicating that the process is one of forming the activated complex, often very loosely termed activation. Q/ is now a partition function per unit volume for the activated complex but with one crucial term missing from it, i.e. the term for the free translation. This is more fully explained in the section below. 

It should be noted that the result in Eq. (7.59) is strictly valid only in the classical high-temperature limit which, except for very high temperatures, is not well satisfied for typical vibrational frequencies. Qualitatively, a similar result will also be obtained when the exact vibrational partition functions are used in Eq. (7.58). Rotational contributions were also neglected, but the moments of inertia associated with the activated complex are often larger than the moments of inertia of the reactant. Thus, we have very often that > Q, and large pre-exponential factors may often arise due to a loose transition state as well as due to a substantial change in geometry between the reactant and the activated complex. 

Sunner et al. (1989) used a semiempirical treatment to theoretically evaluate the rate coefficients of hydride transfer reaction sec-C3H7 + iso-C4H10 — C3F18 + tert-C4Hg. Their kinetic scheme is based on a loose and excited chemically activated complex (C3H7 C4H10) formed at the Langevin rate. The complex can decompose back to reactants or form the products of the hydride transfer... 

Reaction Classes. These decomposition reactions fall into two classes (o) those for which a formal activation energy, ea (Fig. 10a), for the reverse association process exists (b) those for which the reverse process has little or no activation energy (Fig. 10b). These distinctions correspond roughly to the character of the activated complex—whether loose or not. Riceub has discussed the relation between the association activation energy and the zero-point energy requirements for formation of the complex. 

The activation energy for the various complexes is in the range of 32-237 kJ/mol. This low value probably indicates that the ligands are loosely bound to the metal ion. The negative values of A S indicate more ordered structure in the activated complex than the reactants. 

Fig. 5-4. Schematic one-dimensional enthalpy diagram for the exothermic bimolecular Finkelstein reaction Cl -I- CFI3—Br Cl—CH3 -I- Br in the gas phase and in aqueous solution [469, 474, 476]. Ordinate standard molar enthalpies oi (a) the reactants, (b, d) loose ion-molecule clusters held together by ion-dipole and ion-induced dipole forces, (c) the activated complex, and (e) the products. Abscissa not defined, expresses only the sequence of (a). ..(e) as they occur in the chemical reaction.

Organic reactions can be loosely grouped into three classes depending on the character of the activated complex through which these reactions can proceed dipolar, isopolar, and free-radical transition-state reactions [15, 468]. 

In other words, whether or not an Sn2 reaction has a tight or loose activated complex will not only depend upon the nature of the reactants Y and R-X, in solution it will also be affected by the nature of the solvent. Better solvation of the activated complex of a type II Sn2 reaction by solvents with improved EPD/EPA properties will lead to a loosening of the activated complex. Transferring this activated complex from solution to the gas phase, with subsequent loss of the charge-separation stabilizing solvation, will therefore increase its tightness cf. also [499]. 

There are two classes of reactions for which Eq. (10) is not suitable. Recombination reactions and low activation energy free-radical reactions in which the temperature dependence in the pre-exponential term assumes more importance. In this low-activation, free-radical case the approach known as absolute or transition state theory of reaction rates gives a more appropriate correlation of reaction rate data with temperature. In this theory the reactants are assumed to be in equilibrium with an activated complex. One of the vibrational modes in the complex is considered loose and permits the complex to dissociate to products. Figure 1 is again an appropriate representation, where the reactants are in equilibrium with an activated complex, which is shown by the curve peak along the extent of the reaction coordinate. When the equilibrium constant for this situation is written in terms of partition functions and if the frequency of the loose vibration is allowed to approach zero, a rate constant can be derived in the following fashion. 

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