Spin-density map

Fig. 2.9.13 Qu asi two-dimensional random ofthe percolation model object, (bl) Simulated site percolation cluster with a nominal porosity map of the current density magnitude relative p = 0.65. The left-hand column refers to simu- to the maximum value, j/jmaK. (b2) Expedited data and the right-hand column shows mental current density map. (cl) Simulated NMR experiments in this sample-spanning map of the velocity magnitude relative to the cluster (6x6 cm2), (al) Computer model maximum value, v/vmax. (c2) Experimental (template) for the fabrication ofthe percolation velocity map. The potential and pressure object. (a2) Proton spin density map of an gradients are aligned along the y axis, electrolyte (water + salt) filling the pore space...

Papoular, R.J. and Gillon, B. (1990) Maximum entropy reconstruction of spin density maps in crystals from polarized neutron diffraction data, Europhys. Lett., 13(5), 429 134. 

Figure 1. Induced spin density map for MnCu(pba)(H20)j. 2H20 at 10K under 5 T in projection along the perpendicular to the basal plane. Solid and dashed lines are used respectively for negative and positive spin densities. Contour steps are 5 mpB/A2. The spin delocalisation is more pronounced toward the N atom than the O atoms.

Baron, V., Gillon, B., Plantevin, O. et al. (1996) Spin-density maps for an oxamido-bridged Mn(II)Cu(II) binuclear compound. Polarized neutron diffraction and theoretical studies, J. Am. Chem. Soc., 118, 11822-11830. 

Fig. 10 Bond lengths of a neutral and b radical cation, and c spin density mapping of AP-cyclopropy-N methylguanine radical cation optimized at the B3LYP/6-31G(d) level...

Second, the spin density maps must cover the atoms which are involved in the contacts. On the one hand, the localized d spins of the transition metal ions must paradoxically be sufficiently delocalized toward the ligand atoms. On the other hand, the n carriers of the donor set have to extend toward the peripheral atoms. In fact the electrons belonging to the two networks must meet at the intermolecular contact, otherwise the networks would ignore each other. 

As discussed earlier in this chapter, the spin density of a radical indicates where its unpaired electron resides. This in turn allows qualitative assessment of radical stability. A radical in which the unpaired electron is localized onto a single center is likely to be more labile than a radical in which the unpaired electron is delocalized over several centers. An even more useful indicator of radical stability and radical reactivity is provided by a so-called spin density map. Like the other property maps considered in this chapter, this measures the value of the property (in this case the spin density) on an electron density surface corresponding to overall molecular size. 

Property Map. A representation or map of a property on top of an Isosurface, typically an Isodensity Surface. Electrostatic Potential Maps, and HOMO and LUMO Maps and Spin Density Maps are useful property maps. 

Spin Density Map. A graph that shows the value of the Spin Density on an Isodensity Surface corresponding to a van der Waals Surface. 

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

Fig. 20. Spin density, and water diffusion images for a 2.2-inm-diameter, spherical silica catalyst support pellet. In-plane pixel resolution was 45 pm x 45 pm image slice thickness was 0.3 mm. (a) Spin-density map lighter shades indicate higher liquid content, (b) map (150 00 ms) lighter shades indicate longer values of Ti. (c) Diffusivity map ((0-1.5) x 10 m s ) lighter shades indicate higher values of water diffusivity within the pellet.

The structure-transport relationship characteristic of the catalyst pellet is shown by comparison of Figs 20a-c the spatial heterogeneity in the values of the molecular diffusion coefficient is much more consistent with the heterogeneity in the intensity shown in the Ti map than that of the spin-density map. Thus, we conclude that it is the spatial variation of local pore size that has the dominant influence on molecular transport within the pellet. 

Fig. 6 - Spin density maps for a paramagnetic F center at the surface (left) and in the bulk (right) of MgO. The lines are drawn in intervals of 0.001 e ohr Reproduced from ref. [55]. Copyright 1997 American Institute of Physics.

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),... 

Cu(II) region. Such a view is supported by the spin density map of Fig. 29, deduced from a polarized neutron diffraction investigation (58). 

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