Free energy perturbation radicals

PMO Fo) stands for a paper-and-pencil procedure that allows one to differentiate between the energies of odd-alternate PAH radicals, anions, and cations (24, 38). The calculations are carried out within the free-electron perturbational MO framework. The effects of electronic charge are accounted for by a procedure that makes use of the formal principles of the HMOa) technique, a method used in HMO calculations by Wheland and Mann (39), and by Streitwieser (40). The HMOa) calculations require an iterative solution for HMO eigenvalues and eigenvectors, whereas the PMO.Fo) procedure requires only a single hand calculation (to be described later). 

The first indication of the existence of a captodative substituent effect by Dewar (1952) was based on 7t-molecular orbital theory. The combined action of the n-electrons of a donor and a captor substituent on the total Jt-electron energy of a free radical was derived by perturbation theory. Besides the formulation of this special stabilizing situation and the quotation of a literature example [5] (Goldschmidt, 1920, 1929) as experimental evidence, the elaboration of the phenomenon was not pursued further, neither theoretically nor experimentally. 

Spin-density distributions are inherent features of free radicals. Esr experiments take place when the radical is in its electronic ground state and the measurement of the spin distribution constitutes only a minute perturbation of the system. This feature and the fact that esr hyperfine splitting can be measured with high precision makes the esr method ideally suited for the study of substituent effects. Therefore, if spin delocalization is accepted as a measure of stabilization, the data in Table 6 provide quantitative information. However, these are percentage values and not energies of stabiliza-... 

Correlation of the effect of substituents on the rates of reactions with early transition states often is best accomplished in terms of perturbational molecular orbital theory, and polar effects can play a major role for such reactions [100, 101]. Essentially this theory states that energy differences between the highest occupied molecular orbital (HOMO) of one reactant and the lowest unoccupied molecular orbital (LUMO) of the other reactant are decisive in determining the reaction rate the smaller the difference in energy, the faster the predicted rate of reaction [102,103]. Since the HOMO of a free radical is the SOMO, the energy difference between the SOMO and the alkene HOMO and/or LUMO is of considerable importance in determining the rates of radical additions to alkenes [84],... 

In addition to the capability of detecting very low concentration of free radicals as transients in a chemical reaction, ESR spectroscopy provides experimentally the following very important sources of chemical information on their structure. (a) The resonant position referred to as the g value is directly determined by the separation of the energy levels of the radical under investigation. Variation of the g value is interpreted in terms of the perturbation by the spin-orbit interactions, and may be used as a probe to study substitution effects and changes in molecular structure (14,15). (b) The width... 

In real media, nitroxides change their orientations with respect to the external magnetic field due to the Brownian thermal rotational mobility usually characterized by the rotational correlation time, The anisotropic hyperfine interaction between the unpaired electron and nitrogen nucleus is modified by these changes with a frequency dependent on Xj. In this way, frequency-dependent perturbations are generated, which modify the energy levels and transition probabilities in the system. As a result, the line shape of ESR spectra of nitroxides (and of other free radicals in which anisotropic magnetic interactions occur) depends on the correlation time x. ... 

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