Electron spin density

Local exchange and correlation functionals involve only the values of the electron spin densities. Slater and Xa are well-known local exchange functionals, and the local spin density treatment of Vosko, Wilk and Nusair (VWN) is a widely-used local correlation functional. 

It seems to the author that another possible pathway can coexist with the above-mentioned reversible addition of sulfinyl radicals to olefinic double bonds, that is, the reversible addition by the sulfinyl oxygen, since a substantial amount of the unpaired electron spin-density resides on the oxygen atom. 

An anisotropic spin-dipolar contribution B arising from nonspherical distribution of the electronic spin density. 

The magnetic field seen by the probe neutron is solely due to the magnetic dipole moment density of the unpaired electrons. In other words, the magnetisation density is simply related to the electron spin density by a multiplicative factor, and there is no ambiguity in its definition. 

Because of its sensitivity to electron spin density, EPR is an ideal tool to answer questions concerning the degree of delocalisation in conducting polymers, such as poly(aniline). EPR spectra of radical cations of oligomers, representative of a... 

When ESR spectra were obtained for the benzene anion radical, [C6II6] and the methyl radical, CH3, the proton hyperfine coupling constants were found to be 3.75 and 23.0 G, respectively, i.e. they differ by about a factor of 6. Since the carbon atom of CH3 has a spin density corresponding to one unpaired electron and the benzene anion carries an electron spin density of 1/6, the two results suggest that the proton coupling to an electron in a n-orbital is proportional to the spin density on the adjacent carbon atom ... 

P has been computed using Hartree-Fock atomic orbital wavefunctions and can be found in several published tabulations14 17 and in Appendix 1. Because of the (r 3) dependence of P, dipolar coupling of a nuclear spin with electron spin density on another atom is usually negligible. 

Table 4.5 E Electron spin densities in cobalt(o) radical anions...

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

In this respect the possible presence of electron spin density at the iron in the Ni-Fe cluster is of importance. This question has been answered by ENDOR experiments performed on Fe enriched [NiFe] hydrogenase (Huyett et al. 1997). In this study no significant Fe hfc was detected in the NiA, NiB and NiC states (A57p s 1 MHz). This shows that in all relevant states of the enzyme the iron is in the low-spin Fe state. 

This is a measure of the unpaired electron spin density that is transferred from the paramagnet to the nucleus of the spin under observation. In the regime defined by eq 2, the NMR shift (d = (Acolcoo)) induced by the Fermi-contact interaction is directly proportional to... 

Recent density functional theory (DFT) calculations have been used to calculate the transfer of unpaired electron spin densities to the nearby atoms and analyze the orbitals involved in these mechanisms. For example. Figure 8 shows the spin densities obtained for Cr +-doped LiCo02. The spin densities can be calculated by subtracting the spin-up elec-... 

It is assumed that most of the electron spin density resides on the metal, but that a certain small part of it, given by the quantity p , is delocalized to the ligand heteroatom L. The first term is the point-dipole interaction term, the second corresponds to the dipolar interaction between the nuclear spin under consideration and the spin-density on the atom L and the last term describes the cross-correlation of the two dipolar interactions (we discuss the issue of cross-correlation phenomena in more general terms in Section II. D and III.B). The quantity is the effective distance from the nuclear spin... 

Sharp and Lohr proposed recently a somewhat different point of view on the relation between the electron spin relaxation and the PRE (126). They pointed out that the electron spin relaxation phenomena taking a nonequilibrium ensemble of electron spins (or a perturbed electron spin density operator) back to equilibrium, described in Eqs. (53) and (59) in terms of relaxation superoperators of the Redfield theory, are not really relevant for the PRE. In an NMR experiment, the electron spin density operator remains at, or very close to, thermal equilibrium. The pertinent electron spin relaxation involves instead the thermal decay of time correlation functions such as those given in Eq. (56). The authors show that the decay of the Gr(T) (r denotes the electron spin vector components) is composed of a sum of contributions... 

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). 

For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an obvious indicator of reactivity of radicals (in which there is a single unpaired electron). Bonds will be made to centers for which the spin density is greatest. For example, the spin density isosurface for allyl radical suggests that reaction will occur on one of the terminal carbons and not on the central carbon. 

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