Free radicals, electron spin density

Any molecular entity possessing an unpaired electron. The modifier unpaired is preferred over free in this context. The term free radical is to be restricted to those radicals which do not form parts of radical pairs. Further distinctions are often made, either by the nature of the central atom having the unpaired electron (or atom of highest electron spin density) such as a carbon radical (e.g., -CHs) or whether the unpaired electron is in an orbital having more s character (thus, radical molecular entity in a manuscript, the structure should always be written with a superscript dot or, preferably, a center-spaced bullet (e.g., -OH, -CHs, CF). 

In the case of organic free radicals, McConnell has shown that a simple empirical proportionality can be used to relate the observed hyperfme structure constant % and the unpaired electron spin density on the nearest carbon atom ... 

From the point of view of the solvent influenee, there are three features of an electron spin resonance (ESR) speetrum of interest for an organic radical measured in solution the gf-factor of the radical, the isotropie hyperfine splitting (HFS) constant a of any nucleus with nonzero spin in the moleeule, and the widths of the various lines in the spectrum [2, 183-186, 390]. The g -faetor determines the magnetic field at which the unpaired electron of the free radieal will resonate at the fixed frequency of the ESR spectrometer (usually 9.5 GHz). The isotropie HFS constants are related to the distribution of the Ti-electron spin density (also ealled spin population) of r-radicals. Line-width effects are correlated with temperature-dependent dynamic processes such as internal rotations and electron-transfer reaetions. Some reviews on organic radicals in solution are given in reference [390]. 

Preliminary studies have also been carried out on solutions of thallium compounds (see Table XIII). In every case studied, the enhancement was positive for both thallus and thallic compounds. However it was found that for thallus compounds the presence of free radical greatly broadened the n.m.r. signal, and that the observed enhancements were much larger than for thallic compounds. A similar explanation to that suggested for phosphorus has been used to explain this behaviour. In the thallus compounds the electron spin density from the free radical can be transmitted to the nucleus via the lone pair of electrons in the 65 orbital. In thallic compounds this lone pair is no longer available, and the unpaired electron density is then assumed to be transmitted via an indirect mechanism. 

Ayy is the principal value for the C—proton in a Jt-electron radical with spin density p = 1, and vo is the free proton frequency. When the external field is applied parallel fo the stretching direction (y) the maximum ENDOR frequency v+ is estimated to be c.a. 21 MHz at which point the signal changes its slope. By substituting the experimental values of Ayy and (v -vo) in Eq. (7.33), p(0) is evaluated. Due to the uncertainty of the exact value for Ayy the value of p(0) ranges between 0.11 and... 

The process of establishing a geometry for and assigning a ground-state electronic symmetry toa free radical is one of comparison of the measured hyperfine interactions with those (a) predicted theoretically, and (b) determined experimentally for iso-electronic species. Great reliance is placed on the isoelectronic principle free radicals having the same numbers of electrons and nuclei will have similar structures and unpaired electron spin density distributions. In cases where the isoelectronic principle cannot be invoked for lack of examples one must resort to the theoretical estimation of hyperfine interactions inorder to ascertain that a proposed electronic structure is consistent with the experimental parameters. 

The hyperfine structure of the spectrum gives most valuable information on the structure of individual radical ions — both on the presence of specific atoms in the free radical and on the electron-spin density distribution in the radical. The possibility of obtaining this information theoretically has been considered by a number of investigators [91-93]. In particular, McConnell has shown the existence of direct proportionality between the hyperfine coupling constant Aj, due to i protons in the C — H bonds of various aromatic systems, and the density of the unpaired TT-electron at the carbon atom ... 

Irradiation of the molecular radical anion of DESO, which has a yellow color, with light of X = 350-400 nm partially restores the red color and the ESR spectrum of the radical-anion pair. Similarly to the case of DMSO-d6 a comparison of the energetics of the photodissociation of the radical anion and dissociative capture of an electron by a DESO molecule permits an estimation of the energy of the hot electrons which form the radical-anion pair of DESO. This energy is equal to 2eV, similarly to DMSO-d6. The spin density on the ethyl radical in the radical-anion pair of DESO can be estimated from the decrease in hfs in comparison with the free radical to be 0.81, smaller than DMSO-d6. 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

Spin densities determine many properties of radical species, and have an important effect on the chemical reactivity within the family of the most reactive substances containing free radicals. Momentum densities represent an alternative description of a microscopic many-particle system with emphasis placed on aspects different from those in the more conventional position space particle density model. In particular, momentum densities provide a description of molecules that, in some sense, turns the usual position space electron density model inside out , by reversing the relative emphasis of the peripheral and core regions of atomic neighborhoods. 

Perhaps the most fruitful of these studies was the radiolysis of HCo(C0)4 in a Kr matrix (61,62). Free radicals detected in the irradiated material corresponded to processes of H-Co fission, electron capture, H-atom additions and clustering. Initial examination at 77 K or lower temperatures revealed the presence of two radicals, Co(C0)4 and HCo(C0)4 , having similar geometries (IV and V) and electronic structures. Both have practically all of the unpaired spin-density confined to nuclei located on the three-fold axis, in Co 3dz2, C 2s or H Is orbitals. Under certain conditions, a radical product of hydrogen-atom addition, H2Co(C0)3, was observed this species is believed to have a distorted trigonal bipyramidal structure in which the H-atoms occupy apical positions. 

Chain processes, free radical, in aliphatic systems involving an electron transfer reaction, 23,271 Charge density-NMR chemical shift correlation in organic ions, 11,125 Chemically induced dynamic nuclear spin polarization and its applications, 10, 53 Chemiluminescence of organic compounds, 18,187... 

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-... 

However, electron transfer-induced photoreactions in the presence of nucleophiles have attracted by far the greatest attention a rich variety of cyclopropane systems have been subjected to these reaction conditions. We will consider several factors that may affect the structure of the radical cations as well as the stereo- and regiochemistry of their nucleophilic capture. Factors to be considCTcd include (1) the spin and charge density distribution in the cyclopropane radical cation (the educt) (2) the spin density distribution in the free-radical product (3) the extent of... 

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