Electron density, spatial distribution

Figure Al.3.22. Spatial distributions or charge densities for carbon and silicon crystals in the diamond structure. The density is only for the valence electrons the core electrons are omitted. This charge density is from an ab initio pseudopotential calculation [27].

The most popular of the scanning probe tecimiques are STM and atomic force microscopy (AFM). STM and AFM provide images of the outemiost layer of a surface with atomic resolution. STM measures the spatial distribution of the surface electronic density by monitoring the tiumelling of electrons either from the sample to the tip or from the tip to the sample. This provides a map of the density of filled or empty electronic states, respectively. The variations in surface electron density are generally correlated with the atomic positions. 

One of the most important uses of models is to show how electrons are distributed inside molecules The laws of quantum mechanics state that an electron s spatial location can not be precisely specified but the likelihood of detecting an electron at a particular loca tion can be calculated (and measured) This likelihood is called the electron density (see Chapter 1) and SpartanView can display three dimensional graphs that show regions of high and low electron density inside a molecule... 

In the perfect lattice the dominant feature of the electron distribution is the formation of the covalent, directional bond between Ti atoms produced by the electrons associated with d-orbitals. The concentration of charge between adjacent A1 atoms corresponds to p and py electrons, but these electrons are spatially more dispersed than the d-electrons between titanium atoms. Significantly, there is no indication of a localized charge build-up between adjacent Ti and A1 atoms (Fu and Yoo 1990 Woodward, et al. 1991 Song, et al. 1994). The charge densities in (110) planes are shown in Fig. 7a and b for the structures relaxed using the Finnis-Sinclair type potentials and the full-potential LMTO method, respectively. 

Figure 2. I. Spatial distribution of the main orbitals of N2 involved in molecular chemisorption on iron promoted by potassium (K or K20). Arrows indicate the direction of transfer of electron density.5...

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

The most stable shape for any molecule maximizes electron-nuclear attractive interactions while minimizing nuclear-nuclear and electron-electron repulsions. The distribution of electron density in each chemical bond is the result of attractions between the electrons and the nuclei. The distribution of chemical bonds relative to one another, on the other hand, is dictated by electrical repulsion between electrons in different bonds. The spatial arrangement of bonds must minimize electron-electron repulsion. This is accomplished by keeping chemical bonds as far apart as possible. The principle of minimizing electron-electron repulsion is called valence shell electron pair repulsion, usually abbreviated VSEPR. 

If we multiply the probability density P(x, y, z) by the number of electrons N, then we obtain the electron density distribution or electron distribution, which is denoted by p(x, y, z), which is the probability of finding an electron in an element of volume dr. When integrated over all space, p(x, y, z) gives the total number of electrons in the system, as expected. The real importance of the concept of an electron density is clear when we consider that the wave function tp has no physical meaning and cannot be measured experimentally. This is particularly true for a system with /V electrons. The wave function of such a system is a function of 3N spatial coordinates. In other words, it is a multidimensional function and as such does not exist in real three-dimensional space. On the other hand, the electron density of any atom or molecule is a measurable function that has a clear interpretation and exists in real space. 

Laidig, K. E. 1994. Density Functional Methods and the Spatial Distribution of Electronic Charge. Chem. Phys. Lett. 225, 285. 

The non-spherical charge density around Cu can be interpreted as due the hybridization of d electrons with higher-energy unoccupied s and p states. Among these states, hybridization is only allowed for dz and 4s by symmetry, and when this happens part of the dz state becomes unoccupied ( d hole )- These states are responsible for the spatial distribution of the deficiency in the map shown in fig. 6. The complementary empty states are important for EELS, which probe empty states. 

Any effect which alters the density or spatial distribution of electrons around a nucleus will alter the degree of shielding and hence its chemical shift. H chemical shifts are sensitive to both the hybridisation of the atom to which the H nucleus is attached sp, sp etc.) and to electronic effects (the presence of neighbouring electronegative/electropositive groups). 

Electron distributions are ascertained by means of a Mulliken population analysis of the ir-electron atomic populations (in the case of complete n-delocalization, each atom in the 67r-electron five-membered ring would have 1.20 7r-electrons associated with it) by determining the spatial extent of the localized orbitals of both the out-of-plane lone pair of the heteroatom and the C=C double bonds as well as through comparing the total electron density plots in planes parallel to the molecular plane. 

Cathodic corrosion inhibitors reduce the corrosion rate indirectly by retarding the cathodic process which is related to anodic dissolution. In this process, access to the reducible species such as protons, to electroactive site on the steel, is restricted. Reaction products of cathodic inhibitors may not be bonded to the metal surface as strongly as those used as anodic inhibitors. The effectiveness of the cathodic inhibitor is related to its molecular structure. Increased overall electron density and spatial distribution of the branch groups determine the extent of chemisorption on the metal and hence its effectiveness. Commonly used cathodic inhibitor materials are bases, such as NaOH, Na2C03, or NH4OH, which increase the pH of the medium and thereby also decrease the... 

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