X-electron densities

Fig. 6-20. Charge distribution profile across an interface between metal and vacuum (MAO (a) ionic pseudo-potential in metal, (b) diffuse electron tailing away from the jellium metal edge, (c) excess charge profile. n(x) s electron density at distance x = electron density in metal x, = effective image plane On = differential excess charge On = 0 corresponds to the zero charge interface.

Fig. 1. Monosubstituted benzene electron densities (W = CH2 +, D = CHa - . Unparenthesized numbers are x-electron densities. Parenthesized numbers are forma] charges.

One way to achieve this would be by means of the acid promoted polarization of compound I. The proton-carbonyl oxygen association would reduce considerably the x-electron density of the already electron deficient 3 carbon of the enone group, probably to the extent of a carbenium ion (III) in sulfuric... 

In general, in allenes and butatrienes the charge redistributions of the ir and the a electronic systems follow a linear response system. For allenes the x electron density PccO. ) is inversely linearly related to the a electron density PccO- ) at that atom and directly proportional to the a electron density Pcd. ) at C3 (9). The a electron density Pcc(l ) at the substituted atom is related to the (group) electronegativity of the substituent. 

Figure 19. X—X electron densities for 1,2,3,4,5,6, hexa-hydrotricyclobuta[a,c,e]benzene. (Reprinted with permission from ref 183. Copyright 1994 Wiley-VCH Verlag GmbH.)...

Pyridine is a tertiary amine and a good base, as noted in Section 26.1.2. Because of this property, many of the electrophilic reagents used for aromatic substitution coordinate with the electron pair on nitrogen (an acid-base reaction). Specifically, the Lewis acids used in Chapter 21 for electrophilic aromatic substitution will coordinate with the electron pair on nitrogen, so they cannot be used. If electrophilic aromatic substitution does occur, the reaction is slow, and such reactions are difficult. Carbons 3 and 5, relative to nitrogen, have the greatest x-electron density (see IOC) and they are the major sites for reaction. The intermediates generated from pyridine in electrophilic... 

Substituent X Electron density in C 2p orbital Stabilization in kcal/moU... 

Above approximately 80 km, the prominent bulge in electron concentration is called the ionosphere. In this region ions are created from UV photoionization of the major constituents—O, NO, N2 and O2. The ionosphere has a profound effect on radio conmumications since electrons reflect radio waves with the same frequency as the plasma frequency, f = 8.98 x where 11 is the electron density in [147]. The... 

X-ray scattering arises from fluctuations in electron density. The general expression of the absolute scattered intensity (simplified as I(q) from now on) from the tliree-dimensional objects iimnersed in a different... 

Since the electron density p(x) oc /(v)p, where /(v) is die electron wavefiinction, this implies that the electron wavefiinction varies in a similarly step-wise fashion at the interface. This indicates that d i //dx, where s indicates that the derivative is evaluated at the surface, becomes infinite. Since the electron kinetic... 

This gives the total energy, which is also the kinetic energy in this case because the potential energy is zero within the box , m tenns of the electron density p x,y,z) = (NIL ). It therefore may be plausible to express kinetic energies in tenns of electron densities p(r), but it is by no means clear how to do so for real atoms and molecules with electron-nuclear and electron-electron interactions operative. 

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

For example, the Carbon-atom 3P(Ml=1, Ms=0) = [ p ppQ(x + p apoP ] and 3P(Ml=0, Ms=0) = 2-C2 [Ip Pp. aj + piap-iP ] states interact quite differently in a collision with a closed-shell Ne atom. The Ml = 1 state s two determinants both have an electron in an orbital directed toward the Ne atom (the 2po orbital) as well as an electron in an orbital directed perpendicular to the C-Ne intemuclear axis (the 2pi orbital) the Ml = 0 state s two determinants have both electrons in orbitals directed perpendicular to the C-Ne axis. Because Ne is a closed-shell species, any electron density directed toward it will produce a "repulsive" antibonding interaction. As a result, we expect the Ml = 1 state to undergo a more repulsive interaction with the Ne atom than the Ml = 0 state. 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

For XH bonds, where X is any heavy atom, the hydrogen electron density is not thought to be centered at the position of the hydrogen nucleus but displaced along the bond somewhat, towards X. The MMh- force field reduces the XH bond length by a factor of 0.915 strictly for the purposes of calculating van der Waals interactions with hydrogen atoms. 

The chemical shift is related to the part of the electron density contributed by the valence electrons, ft is a natural extension, therefore, to try to relate changes of chemical shift due to neighbouring atoms to the electronegativities of those atoms. A good illustration of this is provided by the X-ray photoelectron carbon Is spectmm of ethyltrifluoroacetate, CF3COOCH2CH3, in Figure 8.14, obtained with AlXa ionizing radiation which was narrowed with a monochromator. 

The ionosphere is subject to sudden changes resulting from solar activity, particularly from solar emptions or flares that are accompanied by intense x-ray emission. The absorption of the x-rays increases the electron density in the D and E layers, so that absorption of radio waves intended for E-layer reflection increases. In this manner, solar flares dismpt long-range, ionospheric bounce communications. 

In principle, it is possible to calculate the detailed three-dimensional electron density distribution in a unit cell from the three-dimensional x-ray diffraction pattern. 

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

---