Spin density plots

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. 

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. 

Fig.12. Qualitative MO scheme for complex 1 (St = 0, BS(1,1)) (top) and spin density plot with Mulliken spin populations (bottom).

Figu re 1.20 Spin density plot for (a) (H )(e ) centers located at a cationic reverse corner and (b) the complex formed by interaction with N2 or O2 molecules. On the left hand side the schematic potential energy curves for the interaction of O2 (solid curve) and N2 (dotted curve) molecules is shown. Negative values indicate bound states. Reproduced from reference [22]. 

In Figure 12.15 the planar local minimum form of G(—) is shown with a three-dimensional spin density plot. The spin density is localized on the hydrogen bonding sites and is similar to a dipole bound anion. Figure 12.16 presents a similar plot for the global minimum form of G(—). The NH2 group is twisted out of the plane,... 

FIGURE 45. Isocontour spin density plot in the molecular plane of phenoxyl radical. Contour levels are spaced by 0.0005 a.u. 

The EPR parameters calculated with DFT were in satisfactory agreement with the experimentally derived parameters. Experimental ENDOR measurements, as well as DFT spin density plots, reveal that the spin density is substantially delocalized over the Namine donor (15-18%) and the metal (73-78%) (183). Equally large spin densities have been observed for amines coordinated to [Rh (por)] species (134). Delocalization of the unpaired electron over the metal and the amine might contribute to the relative stability of these species. 

Figure 68. Spin density plots of [Ir (CH2=CH2)(Me3tpa)] + (above) and [ (—CH2—CH2 )(Me3tpa) (NCMe)] + (below).

Fig. 2.26 (a) Q-band FSE EPR (EIE) spectrum of peridinin triplet (A) absorption, (E ) emission (b) Davies ENDOR pulse sequence (c) Q-band H ENDOR spectra recorded at the three canonical orientations Xn, Yn, Zn, which are marked with arrows in the ESR spectrum of panel (a) using the conditions in panel (b). At the proton Larmor frequency vh a narrow and intense line is visible resulting from nuclear transitions in the mg = 0 manifold. The frequency axis gives the deviation from Vh in the respective spectra. The excitation wavelength was 630 nm. Left numbering and spin density plot of peridinin in its excited triplet state. The orientation of the ZFS tensor axes X, Y, and Z is also given. The figure is adapted from [51] with permission from the American Chemical Society... 

You can also plot ihe electrostatic polenlial. the total charge density. or the total spin density determined during a semi-enipincal or ah initio calculation. This information is useful in determining reactivity and correlating calculalional results with experimental data. Th ese examples illustrate uses of lb ese plots ... 

Many functions, such as electron density, spin density, or the electrostatic potential of a molecule, have three coordinate dimensions and one data dimension. These functions are often plotted as the surface associated with a particular data value, called an isosurface plot (Figure 13.5). This is the three-dimensional analog of a contour plot. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

Figure 4 Plot of spin density as a function of the number of classical structures.

For aromatic hydrocarbon radical anions, this approach works pretty well. Figure 2.7 shows a correlation plot of observed hyperfine splitting versus the spin density calculated from Hiickel MO theory. It also correctly predicts the negative sign of aH for protons attached to n systems. 

Figure 2.7 Correlation plot of observed coupling constant vs. computed spin density from Hilckel MO theory. See Table 2.1 for identification of points.

A) BLYP/DZVP optimized cluster model of the active centre of D. gigas [NiFe] hydrogenase and (B) contour plot at 0.005 e/a.u. of the unpaired spin density distribution in the active centre of D. gigas [NiFe] hydrogenase... 

This is plotted in the right-hand panel of Fig. 3.8 as a function of I/2 h. Remembering that h(R) - 0 as R - oo, we see that it shows the same square root distance-dependence as that displayed by the numerical self-consistent solution of the local spin density functional Schrddinger equation in Fig. 3.6. Thus, as the hydrogen molecule is pulled apart, it moves from the singlet state S = 0 at equilibrium to the isolated free atoms in doublet states with S = 2-... 

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