Charge density difference

Fig. 7. Maps of the electronic charge density in the (110) planes In the ordered twin with (111) APB type displacement. The hatched areas correspond to the charge density higher than 0.03 electrons per cubic Bohr. The charge density differences between two successive contours of the constant charge density are 0.005 electrons per cubic Bohr. Atoms in the two successive (1 10) planes are denoted as Til, All, and T12, A12, respectively, (a) Structure calculated using the Finnis-Sinclair type potential, (b) Structure calculated using the full-potential LMTO method.

Figure 1. The charge-density difference (bonding charge density) between NiaX and the superposition of neutral Ni and X atomic charge densities on the (001) planes for (a) X = A1 and (b) X = Si. The solid (dotted) contours denote contours of increased (decreased) density as atoms are brought together to form the NiaX (X = Al, Si) crystal. Contours start from 4.0 X 10 e/(a.u.) cind increase successively by a factor of root 2.

Some n-electron charge density differences between the ground and first excited states calculated by the PPP-MO method for 4-aminoazobenzene,... 

A very illustrative and useful way to study the rearrangements of electron distributions is represented by charge density difference diagrams. Fig. 11 shows the spatial details of Aq (Eq. 34) in the (zy) plane of the Li+-OH2 complex 208>. 

Fig. 22. Total charge distribution and charge density differences upon formation of a HOH-F complex in the plane of the water molecule (maps are taken from Ref. 208>)...

Fig. 23. Integrated charge density and integrated charge density differences in the system HOH-F- complex. (Nuclear geometry from Ref. 203))...

Figure 1.17. Electron charge density difference contour map for CO on Ni(100) and CO on Ni(100)/H in atop sites, derived from DFT calculations.

Figure 2.6. Molecule-atom charge density differences for H2 and H 2 molecules. From Ref. [29].

Figure 2.25. Charge density difference plot of N2 adsorbed on Ni(100). Regions of electron loss are indicated with dashed outer line and increase with full line. We have chosen a plane containing the interacting metal atom with one N2 molecule in the same plane. From Ref. [3].

Figure 2.29 shows charge density differences for CO adsorbed on Ni compared to CO in gas phase [3]. The results for the total density are rather similar to what has been observed elsewhere [58,66,67] and there interpreted in terms of the simple frontier orbital picture illustrated in the upper part of Figure 2.17. The left part of Figure 2.29 shows the total difference in the charge density and it is very similar to...

Figure 2.43. Charge density differences induced by adsorption of acetylene in the two different sites on Cu(110) showing (top) the HBE species and (bottom) the LBE species. The induced changes in the charge density are compared with those generated for the gas phase molecule by a singlet to triplet - it excitation. From Ref. [92].

Figure 2.44. Charge density difference plotted in a plane containing the metal atoms and the carbon skeleton of the ethylene molecule. The difference is taken between interacting and non-interacting molecules and metal cluster for the adsorbed cases. For the gas phase molecule (top), the difference between the singlet and triplet state is shown. From Ref. [85].

Figure 2.50. Charge density difference plotted along the —H plane (top) and the —H plane (bottom). From Ref. [95].

Figure 2.55. Charge density difference plots for Pt— (left) and Pt—HO (right) bonding species. From Ref. [106].

The development of electrophoretic techniques afforded possibilities for fractionations based on charge density differences. Duxbury (1989) has reviewed applications of different electrophoretic separation methods, including zone electrophoresis, moving boundary electrophoresis, isotachophoresis, and isoelectric focusing (IEF). Preparative column electrophoresis (Clapp, 1957) and continuous flow paper electrophoresis (Hayes, 1960 summarized by Hayes et al., 1985) methods have been used to separate components isolated from sapric histosol soils. These techniques allowed separation of polysaccharides from the colored components the electrophoretograms of the colored components were diffuse, showing a continuum of components of different charge densities. 

It would be pointless to draw up a classification system that takes account of several fractions based on charge density differences, or even differences in solubilities in organic solvent systems. Consideration might be given to the hymatomelanic acid, or the alcohol-soluble component described by Hoppe-Seyler (1889). It would be important to distinguish between the FA fraction (or the material that is soluble in acidic and basic media) and the FAs as defined by the IHSS (or the fractions recov-... 

This receptor shows a remarkable selectivity for Mg2+ over Ca2+ under physiological conditions and has found applications in 19F NMR probes and ratiometric fluorescent sensors based on wavelength shifts.[62] In high concentrations, however, both Ca2+ and Mg2+ can be bound. The similarity of fluorescence enhancements with both ions is the result of essentially identical conformational changes produced upon complexation. Each ion-bound state effectively decouples the amine substituent from the oxybenzene unit, so that PET is similarly suppressed. This means that the charge density difference between the two cations is of secondary importance in these conformationally switchable systems. 

The charge density difference maps from the Gunnarsson et al." calculations are compared with experiment107 and with Hartree-Fock results108 in Figure 12. There are differences between theory and experiment which are not presently resolved to the author s knowledge. 

Figure 12 Charge density difference maps 0/N2 from ref. 99, compared with HF results of ref. 108...

Bond distances and angles of both molecules reproduce well available experimental data. In both compounds, the charge density difference between the oxygen (d ) and the sulfur (d ) atom increases in the S,0-trans one because of the synergy between the Jt co tt, ng and through-space S —O CT iterations. 

Charge-density difference maps from the band calculation (crystal minus superimposed free atoms) clearly show charge transfer, but the limited basis set precludes detailed comparison with experiment. 

X (units of lattice constant) Figu re 8.20 Charge density difference [LSDA + U] - LSDA (U = S.leN) for bulk NiO taken through a (100) plane of the rock salt cubic unit cell, centered on a Ni ion. Taken from ref [113]. 

Fig. 16 (a) Calculated valence charge density for a Pd monolayer (top) and clean Ta(110). (b) Calculated valence charge density for the Pd/Ta(110) system, (c) Charge density difference obtained by subtracting the superposition of the charge densities of the Pd monolayer and Ta(l 10) from that of Pd/Ta(110). Dashed lines indicate a decrease in the electron density. Reprinted from ref [33]. 

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