Atomic spin densities

TABLE 13.1 Spin Densities (Atomic Units) of Carbon Atoms and Oxygen of the 2-naphthoxy Radical from MNDO-UHF Calculations and ESR Data... 

Spin den sitieshelp to predict the observed coupling con slants in electron spin rcsonan ce (HSR) spectroscopy. From spin density plots you can predict a direct relalitin sh ip between the spin density on a carbon atom an d th c couplin g con stan t assti-ciated with ati adjacent hydrogen. 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

Gunnarsson O and B I Lundqvist 1976. Exchange and Correlation in Atoms, Molecules, and Solids by the Spin-density-functional Formalism. Physical Review B13.-4274-4298. 

This simple model allows one to estimate spin densities at eaeh earbon eenter and provides insight into whieh eenters should be most amenable to eleetrophilie or nueleophilie attaek. For example, radieal attaek at the C5 earbon of the nine-atom system deseribed earlier would be more faeile for the ground state F than for either F or F. In the former, the unpaired spin density resides in /5, whieh has non-zero amplitude at the C5 site x=L/2 in F and F, the unpaired density is in /4 and /6, respeetively, both of whieh have zero density at C5. These densities refleet the values (2/L)F2 sin(n7ikRcc/L) of the amplitudes for this ease in whieh L = 8 x Rcc for n = 5, 4, and 6, respeetively. 

The CNDO and CNDO/S methods apply the ZDO approximation to all integrals, regardless of whether the orbitals are loeated on the same atom or not. In the INDO method, whieh was designed to improve the treatment of spin densities at nuelear eenters and to handle singlet-triplet energy differenees for open-shell speeies, exehange integrals... 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

In PMD radicals, the bond orders are the same as those in the polymethines with the closed electron shell, insofar as the single occupied MO with its modes near atoms does not contribute to the bond orders. Also, an unpaired electron leads the electron density distribution to equalize. PMD radicals are characterized by a considerable alternation of spin density, which is confirmed by epr spectroscopy data (3,19,20). 

The EPR spectra of semidione radical anions can provide information on the spin density at the individual atoms. "The semidione derived from butane-2,3-dione, for example, has a spin density of 0.22 at each oxygen and 0.23 at each carbonyl carbon. The small amount of remaining spin density is associated with the methyl groups. This extensive delocalization is consistent with the resonance picture of the semidione radical anion. 

Analyze the hyperfine coupling in the spectrum of the butadiene radical anion given in Fig. 12.PI I. What is the spin density at each carbon atom according to the McConnell equation ... 

Spin density (Section 10.3) A measure of the unpaired electron distribution at the various atoms in a molecule. 

All of the geometry optimizations for acetyl radical produce similar structures. Here are the predicted spin densities (labeled Total atomic spin densities in the Gaussian output) ... 

The table gives the computed spin densities for each atom (the value in parenthese following the substituent is its electronegativity). The illustrations are Lewis doi structures showing the primary resonance form for each structure and indicatinj unpaired electrons and lone pairs. 

In the aUyl radical, the spin density is divided between the two terminal carbon atoms In the four other compounds, the C2 carbon atom retains an unpaired electron. Foi the Mg and Be cases, both the C2 carbon atom and the substituent have an unpairec electron. In the Be compound, the spin density is localized mostly on the substitueni atoms, while for the Mg compound, a bit more of the density remains near the C carbon. 

Both the oxygen and sulfur atoms have two lone pairs while the C/ carbon has ar unpaired electron, and in both cases the double bond shifts from the two carbor atoms to the carbon and the substituent. In acetyl radical, the electron density i centered primarily on the C2 carbon, and the spin density is drawn toward the lattei more than toward the former. In contrast, the density is more balanced between thf two terminal heavy atoms with the sulfur substituent (similar to that in allyl radical with a slight bias toward the sulfur atom. These trends can be easily related to th< varying electronegativity of the heavy atom in the substituent. 

The first series of plots represent the limiting and perfectly balanced cases for the distribution of the electron density (positive values only are shown). These spin density plots show the excess density perfectly balanced between the two terminal heavy atoms for allyl radical, drawn toward the substituent for Be and pushed away from the substituent for acetyl radical. 

The second set of illustrations show the spin density plotted on the electron density isosurface the spin density provides the shading for the isodensity surface dark areas indicate positive (excess a) spin density and light areas indicate negative (excess P) spin density. For example, in the allyl radical, the spin density is concentrated around the two terminal carbons (and away from the central carbon). In the Be form, it is concentrated around the substituent, and in acetyl radical, it is centered around the C2 carbon atom. 

The usefulness of spin density surfaces can be seen in the following models of methyl radical, CH3, and allyl radical, CH2=CHCH2. In each case, the surface is shaped somewhat like a 2p atomic orbital on carbon. There are some interesting differences between the two radicals, however. While the unpaired electron is confined to the carbon atom in methyl radical, it is delocalized over the two terminal carbons in allyl radical. 

Spin density surface for the most stable radical formed by hydrogen atom abstraction from a model of a-tocopherol shows delocalization of the unpaired electron. 

Spin density surface for chlorine atom+methane transition state shows location of unpaired electron. 

Examine spin density surfaces for l-bromo-2-propyl radical and 2-bromo-l-propyl radical (resulting from bromine atom addition to propene). Eor which is the unpaired electron more delocalized Compare energies for the two radicals. Is the more delocalized radical also the lower-energy radical Could this result have been anticipated using resonance arguments ... 

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

The muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

Radicals with adjacent Jt-bonds [e.g. allyl radicals (7), cyclohexadienyl radicals (8), acyl radicals (9) and cyanoalkyl radicals (10)] have a delocalized structure. They may be depicted as a hybrid of several resonance forms. In a chemical reaction they may, in principle, react through any of the sites on which the spin can be located. The preferred site of reaction is dictated by spin density, steric, polar and perhaps other factors. Maximum orbital overlap requires that the atoms contained in the delocalized system are coplanar. 

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