Spin density difference maps

Figure 2. (A) Self-consistent spin-density map of Fe(lOO) obtained through a thirteen-layer calculation within GGA and DZSP basis, compared to (B) a seven-layer all electron FLAPW calculation Dashed contour lines correspond to negative spin density. Each contour line differs by a factor of 2 in both panels (A) and (B). The contours around the Fe sites in the upper panel (A) are an artifact of the pseudopotential. It is important to remark that due to the scaling little spin density differences between the two calculations can be magnified in the contour plot.

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. 

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 ... 

In those experiments, the solvent is distinguished from the host material by the huge difference in the transverse relaxation times. The technique to be described here monitors interdiffusion between two sample compartments initially filled with deuterated and undeuterated liquids (or gels) of the same chemical species. Bringing the compartments into contact initiates interdiffusion. Mapping of the proton spin density thus permits the evolution of the corresponding concentration profiles to be followed. 

We can find a V(N) lone-pair-like basin in the ELF space which, according to the 2.84 e population, involves the nitrogen lone pair and a large part of the unpaired electron. This latter agrees, by a difference of 0.17 e, with that of the integrated spin density however, all other valence basins contain a small amount of the radical population. The Laplacian map of the electron density shows that this monosynaptic valence basin is very compact. 

From a set of projections acquired under different angles (p in polar coordinates, a spin density map is reconstructed in back-projection imaging (cf. Section 6.1). For a 2D spin density Mq(jc, y) the projection onto an axis r which is at an angle (p with respect to the j -axis follows by integration over the space variable s orthogonal to r (Fig. 5.4.1),... 

Deoxvhemerythrin. Henrerythrin appears to retain its triply bridged crae structure in the deoxy form. A low (3.9 A) resoluticm difference electron density map of deoxyHr vs. metHr fi- n X-ray diffraction suggests that the iron atoms move slightly further apart in deoxyHr, but remain five and six coordinate, respectively (29). Confirmation of the iron coordination comes from near-IR absorption and circular dichroism spectra (40,46,47). Based on model high-spin ferrous complexes, the six coordinate iron is expected to give two of the three observed transitions near 10000 cm- while the five-coordinate iron accounts for the d-d transition at ca. 5000 cm-. ... 

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

The measured differential cross-sections depend on the rotationally and vibrationally averaged values of

. Allan et al. have discussed the interpretation of (e, 2e) experiments in terms of spin-coupled orbitals and have presented momentum-space electron density maps for individual orbitals for LiH, NH and the 7t electrons in CH2CHX(X = F,C1). The nonorthogonality of the spatial orbitals allows them to assume properties very different from those of MO theory this leads to striking differences in momentum space. 

---