Surface spin density

Besides molecular orbitals, other molecular properties, such as electrostatic potentials or spin density, can be represented by isovalue surfaces. Normally, these scalar properties are mapped onto different surfaces see above). This type of high-dimensional visualization permits fast and easy identification of the relevant molecular regions. 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

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 the job is completed, the UniChem GUI can be used to visualize results. It can be used to visualize common three-dimensional properties, such as electron density, orbital densities, electrostatic potentials, and spin density. It supports both the visualization of three-dimensional surfaces and colorized or contoured two-dimensional planes. There is a lot of control over colors, rendering quality, and the like. The final image can be printed or saved in several file formats. 

The unpaired electron in benzyl radical is shared by the benzylic carbon and by the nng carbons that are ortho and para to it as shown by the spin density surface in Figure 119 Delocalization of the unpaired electron from the benzylic carbon to the ortho and para positions can be explained on the basis of resonance contributions from the fol lowing structures... 

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. 

Electron densities, bond densities, and spin densities, as well as particular molecular orbitals may be displayed as graphical surfaces. In addition, the value of the electrostatic potential or the absolute value of a particular molecular orbital may be mapped onto an electron density surface. These maps provide information about the environment around the accessible surface of a molecule. Electrostatic potential maps show overall charge distribution, while orbital maps reveal likely sites for electrophilic and/or nucleophilic attack. Surface displays may be combined with any type of model display. 

Spin Density Surfaces. Electrons have a property called spin that allows them to exist in either of two spin states spin up or spin down . Almost all of the molecules that you will encounter will involve each spin-up electron paired to a spin down electron. Thus, the number of spin up and spin down electrons will be the same, and the electron clouds due to each spin will be identical. 

The spin density surface is a tool which helps us find the unpaired electrons in these unusual molecules. Spin density is defined as the difference between the spin up and spin down electron clouds, and a spin density surface is constructed by connecting together points in the electron cloud where the spin density has an arbitrarily chosen value. 

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. 

Radical stability can often be explained in the same way as ion stability molecules that delocalize unpaired electrons tend to be more stable. Display spin density surfaces for 1-propyl and 2-propyl radicals. In which is the unpaired electron more delocalized Is this also the lower-energy radical ... 

Spin density surface for 2-propyl radical shows location of unpaired electron. 

Examine the geometry of the most stable radical. Is the bonding in the aromatic ring fuUy delocalized (compare to model alpha-tocopherol), or is it localized Also, examine the spin density surface of the most stable radical. Is the unpaired electron localized on the carbon (oxygen) where bond cleavage occurred, or is it delocalized Draw all of the resonance contributors necessary for a full description of the radical s geometry and electronic structure. 

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. 

Examine the electrostatic potential map and spin density surface of Q radical anion (Q ). Draw all of the resonance contributors needed to account for these data. Examine the CO bond distances and spin density surface of QH radical (QH ). Draw all of the resonance contributors needed to account for these data. 

Display spin density surfaces for all radicals. For which radical is the unpaired electron least delocalized from the radical center For which is it the most delocalized Is there any relationship between degree of puckering of the radical center and extent of spin delocalization ... 

Spin density surface for benzyl radical shows location of the 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 ... 

Spin density surface for (henoxy radical shows location if the unpaired electron. 

The process is exothermic, suggesting that the phenoxy radical is particularly stable. Display the spin density surface for phenoxy radical. Is the unpaired electron localized or delocalized over several centers Is the unpaired electron in the a or 7t system Draw appropriate Lewis structures that account for your data. 

Examine the spin density surface for BHT radical. Is the unpaired electron localized or delocalized Examine BHT radical as a space-filling model. What effect do the bulky tert-butyl groups have on the chemistry of the species (Hint BHT radical does not readily add to alkenes or abstract hydrogens from other molecules.)... 

Compare the spin density surface for vitamin E radical to those of phenoxy and BHT radicals (see also Chapter 16, Problem 2). Are there significant differences among the three If so, elaborate. What is the function of the long alkyl chain in vitamin E Examine an electrostatic potential map for vitamin E radical. Do you expect it to be soluble in aqueous (polar) or non-aqueous (non-polar) environments, or both ... 

First, try to draw resonance contributors for both ground state and triplet anthrone. Then display a spin density surface for the triplet state of anthrone. (Note that the spin density surface shows the location of both unpaired electrons, one of which may be in a 7t orbital and one of which may be in a o orbital.) Where are the two unpaired electrons Are they localized or delocalized Given that spin delocalization generally leads to stabilization, would you expect the triplet state of anthrone to be stable ... 

Spin density surface for triplet anthrone locates the two unpaired electrons. 

Spin Density Surface. A surface of constant Spin Density. 

In molecular orbital terms, the stability of the allyl radical is due to the fact that the unpaired electron is delocalized, or spread out, over an extended 7T orbital network rather than localized at only one site, as shown by the computer-generated MO in Fig 10.3. This delocalization is particularly apparent in the so-called spin density surface in Figure 10.4, which shows the calculated location, of the unpaired electron. The two terminal carbons share the unpaired electron equally. 

Active Figure 10.4 The spin density surface of the allyl radical locates the position of the unpaired electron (blue) and shows that it is equally shared between the two terminal carbons. Sign in at www. thomsonedu.com to see a simulation based on this figure and to take a short quiz. 

Figure 16.20 A resonance-stabilized benzylic radical. The spin-density surface shows that the unpaired electron (blue) is shared by the ortho and para carbons of the ring.

Sjsj2 reaction and, 377-378 Benzylic radical, resonance in, 578 spin-density surface of, 578 Benzylpenicillin, discovery of, 824 structure of, 1 Benzyne, 575... 

Sphingomyelin, 1066-1067 Sphingosine, structure of, 1067 Spin density surface, allylic radical, 342... 

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