Unpaired electron spin density

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. 

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... 

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-... 

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. 

An alternate model has been proposed (296-298) that attempts to interpret the data in terms of a single mixed state. For this model S is no longer a good quantum number. The unpaired electron spin density at the metal and the wave function that represents the single state are functions of temperature and pressure. This latter model was considered as a possibility by Leipoldt and Coppens. In their structure of the Fe(Et2Dtc)3 complex at 297 and 79°K they attempted an analysis of the temperature parameters at 297°K. The analysis could not distinguish between a mixed-spin state and a mixture of two different spin states (403). 

In hemes and hemoproteins contact shifts arise if finite amounts of unpaired electron spin density are delocalized from the iron orbitals into the jr-orbital systems of the porphyrin and the axial ligands, as indicated by the arrows in Fig. 25. Electron density is then further transferred from the aromatic ring carbon atoms to the protons (Fig. 2), thus giving rise to contact interactions. The measured isotropic contact coupling constants for the protons, A in Eq. (4), can be related to the integrated spin density on the neighboring ring carbon atom by (McConnell (73)] Bersohn (5) Weissman (107). 

The notation Q y means the McConnell constant for a nucleus Y attached to an atom X in sp2 configuration and bearing unpaired electron spin density on its pz orbital. The notation Q y means the McConnell constant for the nucleus of atom X in the same moiety. 

Although many naturally occurring and designed materials are magnetic due to incorporation of paramagnetic ions or metal atoms, organic-based magnets are composed of molecules or (in the case of polymers) monomeric repeat units. Each molecule must have net unpaired electron spin density. Several example radical spin units are shown in Scheme 1. The unpaired spin may be... 

The low-atomic-character state (85MA) can be interpreted (19) in terms of the loose ion-pair picture (Fig. 6), or alternatively, as a large-radius monomeric state [af, estimated (17) to be in the region 10-15 A], Experimental magnetic parameters and unpaired electron spin densities at the metal nucleus for the MA species are shown in Table II. 

Observed line widths are metal dependent. However, values of j.U5i, the unpaired electron (spin) density at the metal nucleus, are approximately independent of the metal atom for potassium, rubidium, and cesium species. As such, the states a Ma(A = 39, 85, 133) are best described as true hydrogenic states in this disordered medium. 

Notice too that in the present argument the (unpaired-electron) spin density should appear primarily on the sites with an excess free-valence sum, especially for those such sites more well separated from opposite-type sites with non-zero free valence. Yet further too if distant sites need to be spin-paired, then there should be a low-lying higher-spin excited state where the spin-pairing is violated. For finite conjugated molecules this further leads to agreement with the spin result of Eq. 

Trivalent gadolinium with f7 configuration has isotropic distribution of electrons and hence cannot produce pseudo contact shift. However, when the Lewis acid-base interaction is partly covalent, the unpaired electron spin density influences the molecular framework of the base and causes an LIS known as contact shift. Gd(III) is used to ascertain the contributions of contact shift to the measured LIS. 

Polymerization of thiophenes by oxidative coupling has been discussed earlier <1996CHEC-II(2)491>. The generally accepted mechanism for the electropolymerization of thiophene may also be valid in the case of chemical oxidative polymerization. The steps involved are formation of a radical cation, spin-pairing of two such radical cations to form a dihydrodimer dication, loss of protons with concomitant rearomatization, and repetition of this cycle with the dimer. Couplings take place at the position of highest unpaired-electron spin density. 

CIDEP. Following the treatment discussed above, the unpaired electron spin density in radical 1 in a radical pair is given by the expression... 

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 ... 

The Fermi contact shift describes the influence of the unpaired electron spin on nnclear chemical shifts as a resnlt of throngh-bond hyperfine conpling. The contact shift is caused by the presence of unpaired electron spin density at the observed nnclens. Thns, spin density must be transferred to an s orbital of the nnclens of interest, which is typically achieved through spin polarization. In the case of a single, isolated spin state for a molecule in solution, contact shift can be described by... 

Contact shifts are determined by unpaired electron spin density at the nucleus being observed (equation 13) and... 

The large isotropic component is due to the unpaired electron spin density in the carbon 2s orbital, and this value (544MHz) can be used to derive an estimate of the carbon 2 s orbital contribution to the molecular orbital. Since the theoretical isotropic coupling constant for is 3777MHz, then C2s = 544/3777 = 0.144. The anisotropic dipolar part of the hyperfine arises from unpaired spin density in the 2p orbital. However because the dipolar contribution in Equation 1.52 cannot be reduced to zero, this implies that a fraction of the spin density is allocated to the 2p orbital perpendicular to the molecular plane. Therefore, the dipolar component of Equation 1.52 must be further decomposed into two symmetrical tensors oriented along the z and x axes ... 

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