Transition energy relationship

Hamiltonian operator, 2,4 for many-electron systems, 27 for many valence electron molecules, 8 semi-empirical parametrization of, 18-22 for Sn2 reactions, 61-62 for solution reactions, 57, 83-86 for transition states, 92 Hammond, and linear free energy relationships, 95... 

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trarw-symmetric bisalkyl diazenes,trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon-carbon bond homolysis). Transition state effects are calculated by the HMD pi- delocalization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. 

A quite different and complimentary approach is to assume that addition of a nucleophile to an acyl derivative (RCOX) would follow the linear free energy relationship for addition of the nucleophile to the corresponding ketone (RCOR, or aldehyde if R=H) if conjugation between X and the carbonyl could be turned off, while leaving its polar effects unchanged. This can be done if one knows or can estimate the barrier to rotation about the CO-X bond, because the transition state for this rotation is expected to be in a conformation with X rotated by 90° relative to RCO. In this conformation X is no longer conjugated, so one can treat it as a pure polar substituent. Various values determined by this approach are included in the tables in this chapter. 

The linear free energy relationship is one that can plausibly be expected, although not rigorously derived, whenever the transition state resembles both the carbon acid and the ion.867... 

The usual experimental approach3 is based on the Hammond postulate (Hammond, 1955). A transition state, which lies by definition between the starting materials and products for a particular step of a reaction, is supposed to be closer in structure, because closer in energy, to the higher energy species of the two. Various techniques, particularly linear free energy relationships, are available to compare the effects of various probes... 

The interaction between two adjacent bulky groups can depend on steric factors which are not necessarily related to the stability of the radicals produced on homolysis. It is estimated from linear free energy relationships that only 65-70% of the ground-state strain energy is relieved in the transition state for homolysis of a bond between two quaternary centres (Ruchardt and Beckhaus, 1980, 1986). Thus steric constraints to delocalization in the radicals produced may persist. A pertinent example is 2,3-di(l-adamantyl)-2,3-dimethylbutane [123] which has four such centres, linked by the long C-C bonds characteristic of this sort of structure. The strongest... 

DR. ALBERT HAIM (State University of New York at Stony Brook) Dr. Meyer considered plots of optical transition energy versus 1/D(optical) minus 1/D(static) for various types of systems, some of which were binuclear and clearly delocalized. If instead, one considers a ruthenium(II) pentaamine bound to N-methyl-4,4,-bipyridinium, is this in any way different from the bridging situation In some instances there was a similar dependence for both the mononuclear systems and the binuclear systems. But some of these mononuclear systems did not seem to behave similarly. Is there any connection between whether that simple linear relationship works or not and whether the system is localized or delocalized ... 

On the basis of these considerations, the authors suggest that a roughly linear relationship might exist between the transition energies (Ft) for the charge-transfer band and Hammet-type substituent constants, am. 

Ground and transition state Gibbs energy relationships in cationic intermediate resulted in the formulation of the nonclassical 7-norbornenyl (bishomocyclo-propenyl) cation (6).2... 

The cyclic mechanism is probably seldom a fully concerted (E2) process, and the different timing of individual electron shifts results in a transition towards the El or ElcB mechanisms (cf. Sect. 2.1.1). The choice of the mechanism depends on the reactant structure as well as on the catalyst nature. As an indicator of the mechanism, either the degree of stereoselectivity (see refs. 68, 121, 132 and 141) or the value of the reaction parameter of a linear free energy relationship, e.g. p or p constants of the Hammett and Taft equations (cf. ref. 55), may be used. 

Those linear free energy relationships that are derived from plotting the rate constants from one reaction against the equilibrium constants for another are clearly different from those arising from the chemistry of section A3. As such, the values of /3 are not restricted to 0 charge developed in the transition state. Consider, for example,... 

Furthermore, there is a linear relationship between the transition energies of the [Co(Mo04 S )2]2- complexes and those of the corresponding [Co(W04 nS )2]2 species. All these findings indicate that the above-mentioned intense bands should be assigned to a charge transfer transition of the type L- (/(M ). 

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