And electronic charge density

Here we introduced the operator of the total (nuclear and electronic) charge density of the L-th subsystem ... 

Surface electron charge density can be described in tenus of the work fiinction and the surface dipole moment can be calculated from it ( equatiou (Bl.26.30) and equation (B1.26.31)). Likewise, changes in the chemical or physical state of the surface, such as adsorption or geometric reconstruction, can be observed through a work-fimction modification. For studies related to cathodes, the work fiinction may be the most important surface parameter to be detenuined [52]. 

Nitrogen and sulfur are diagonally related in the periodic table and might therefore be expected to have similar electronic charge densities for... 

Xhe first of the two-electron integrals has a simple physical significance. The charge density of the electron labelled 1 is and the charge density... 

A Perturbation Theory is developed for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation. It is shown by this development that the first order correction for the energy and the charge density of the system is zero. The expression for the second order correction for the energy greatly simplifies because of the special property of the zero order solution. It is pointed out that the development of the higher order approximation involves only calculations based on a definite one-body problem. 

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.

Y is a strongly pi electron donor group. As previously noted in the results section, examples of Y from Table VI include centers of high pi electron charge density at carbon, sulfur, nitrogen, and oxygen. Also included in Table VI are examples of nucleophilic substitution transition states (cf. reactions 21 and 22) of the type... 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

Table 2.4 shows a comparison of the experimental and PPP-MO calculated electronic spectral data for azobenzene and the three isomeric monoamino derivatives. It is noteworthy that the ortho isomer is observed to be most bathochromic, while the para isomer is least bathoch-romic. From a consideration of the principles of the application of the valence-bond approach to colour described in the previous section, it might have been expected that the ortho and para isomers would be most bathochromic with the meta isomer least bathochromic. In contrast, the data contained in Table 2.4 demonstrate that the PPP-MO method is capable of correctly accounting for the relative bathochromicities of the amino isomers. It is clear, at least in this case, that the valence-bond method is inferior to the molecular orbital approach. An explanation for the failure of the valence-bond method to predict the order of bathochromicities of the o-, m- and p-aminoazobenzenes emerges from a consideration of the changes in 7r-electron charge densities on excitation calculated by the PPP-MO method, as illustrated in Figure 2.14. 

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

Destro R., Bianchi, R., Gatti, C. and Merati, F. (1991) Total electronic charge density of L-alanine from X-ray diffraction at 23 K, Chem. Phys. Lett., 186,47-52. 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Seminario, J. M., J. S. Murray, and P. Politzer. 1991. First-Principles Theoretical Methods for the Calculation of Electronic Charge Densities and Electrostatic Potentials. In The Application of Charge Density Research to Chemistry and Drug Design. Plenum Press, New York. 

If the average exchange potential is assumed to depend only on the local electronic charge density, its value at a point r is equal to the VEx(p) for a free-electron gas, and... 

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