Activation, relative free energies

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

Various statistical treatments of reaction kinetics provide a physical picture for the underlying molecular basis for Arrhenius temperature dependence. One of the most common approaches is Eyring transition state theory, which postulates a thermal equilibrium between reactants and the transition state. Applying statistical mechanical methods to this equilibrium and to the inherent rate of activated molecules transiting the barrier leads to the Eyring equation (Eq. 10.3), where k is the Boltzmann constant, h is the Planck s constant, and AG is the relative free energy of the transition state [note Eq. (10.3) ignores a transmission factor, which is normally 1, in the preexponential term]. 

Figure 14-4. Intrinsic reaction coordinate for the transesterification of the dinucleotide model with B3LYP and M06-2X functionals. Relative free energies of reaction and activation are provided in kcal/mol...

Figure 7.7 Free-energy diagrams for the formation of carbocations from protonated tertiary, secondary, and primary alcohols. The relative free energies of activation are tertiary < secondary primary.

Fig. 11 Unimolecular decomposition pathways of 2-oxepinoxy radical (1). The relative free energies (298 K, kcal/mol) at the B3LYP/ 6-311 + G(d,p)//B3LYP/6-31G(d) level are shown for each intemiediate relative to 1, and each free energy of activation is relative to the reactant for that specific step, [courtesy of Michael Fadden (J Phys Chem A 2000 104 8121-8130) Reprinted with permission of J Phys Chem A.]...

Relative Free Energies of Activation of Olefins in Type II Photosensitized Oxygenation Reactions... 

The most important factor in zeolite synthesis in the laboratory, or factory, is the rate of crystallization. Composition and concentration of the liquid solution acting on the solids is important to the process as is the absolute necessity of maximum disorder of the Si-O-Al bonds in the initial solids reacted (Zhdanov, 1970). It is thus evident that not only bulk chemical (equilibrium) factors are important in the initial crystallization of zeolites but also the. relative free energies of the reactants. It is apparent that zeolite equilibria are essentially aqueous i.e., that silicate equilibrium or approach to it is attained through reaction with solutions, and thus the solubilities of the solids present are of primary importance. If materials are slow to enter into solution they are essentially bypassed in the rapid crystallization sequence (Schwochow and Heinze, 1970 Aiello, et al , 1970). In most studies the zeolites precipitated from solution appear to respond to the laws concerning chemical activity of solutions (Zhdanov, 1970). 

Figure 13.1 Two-dimensional portrayal of relative free energies exhibited by the reactants, activated complex, and products of an SN2 reaction.

In a reaction under kinetic control, the product composition via transition states T.S.l and T.S.2 is determined by the relative rates of the alternative reactions, which are of course governed by the relative free energies of activation (AG ) of the rate determining step of each reaction (Fig. 1.1). Analysis of product composition over the whole time of the reaction will show a constant ratio. 

In the second approach the carbonyl function is incorporated in a chiral adjuvant (or auxiliary) which then stereoselectively directs a preferred attack of the organometallic reagent on the si- or re-faces of the carbonyl group, as determined by steric and electronic interactions. This results in two diastereoisomeric products in a ratio dependent on the relative free energies of activation. One such auxiliary is (12), derived from the readily available and optically pure ( + )-pulegone. 

Relative free energy, entropy, and enthalpy Relative solubility Transition temperature Critical water/solvent activity... 

Determination of Transition State Geometries and Relative Free Energies of Activation in Condensed Phase. ... 

Taft, R.W. (1953c). The Separation of Relative Free Energies of Activation to Three Basic Contributing Factors and the Relationship of These to Structure. J.Am.Chem.Soc., 75,4534-4537. 

Taft, R.W. (1953c) The separation of relative free energies of activation to three basic contributing factors and the relationship of these to structure. /. Am. Chem. Soc., 75, 4534—4537. 

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