Electronic charge distributions

For a m (ticcnie with a coiitin iions electron charge distribution and n IIclear pmn i charges, the expression becomes ... 

Both attractive forces and repulsive forces are included in van der Waals interactions. The attractive forces are due primarily to instantaneous dipole-induced dipole interactions that arise because of fluctuations in the electron charge distributions of adjacent nonbonded atoms. Individual van der Waals interactions are weak ones (with stabilization energies of 4.0 to 1.2 kj/mol), but many such interactions occur in a typical protein, and, by sheer force of numbers, they can represent a significant contribution to the stability of a protein. Peter Privalov and George Makhatadze have shown that, for pancreatic ribonuclease A, hen egg white lysozyme, horse heart cytochrome c, and sperm whale myoglobin, van der Waals interactions between tightly packed groups in the interior of the protein are a major contribution to protein stability. 

The arrangement of electrons in an atom is described by means of four quantum numbers which determine the spatial distribution, energy, and other properties, see Appendix 1 (p. 1285). The principal quantum number n defines the general energy level or shell to which the electron belongs. Electrons with n = 1.2, 3, 4., are sometimes referred to as K, L, M, N,. .., electrons. The orbital quantum number / defines both the shape of the electron charge distribution and its orbital angular... 

The interaction of an electronic charge distribution p(r) with an electric potential /(r) gives an energy correction. 

No overlap of molecular electronic charge distributions (Pauli principle)... 

Fig. 9a,b. The molecular electronic charge distributions for a the nematogen 5CB b the ferroelectric DOBABMC, as constructed directly from the molecular electronic wavefunc-tions using n(f) = WMf -... 

I have reported this last example not for the sake of completeness in our discussion, but to underline a different point. Quantum chemistry, in the work of CTOup 1 and even more in the work of group II, put the emphasis on some properties which by tradition are not object of direct experimental determination. Electron charge distribution and MEP arejust two examples. The use of these quantities by theoreticians has spurred the elaboration of experimental methods able to measure them. This positive feedback between theory and experiment is an indication that quantum and experimental chemistry do not live in separate worlds. 

The trace vanishes because only p- and /-electrons contribute to the EFG, which have zero probability of presence at r = 0 (i.e. Laplace s equation applies as opposed to Poisson s equation, because the nucleus is external to the EFG-generating part of the electronic charge distribution). As the EFG tensor is symmetric, it can be diagonalized by rotation to a principal axes system (PAS) for which the off-diagonal elements vanish, = 0. By convention, the principal axes are chosen such that... 

The influence of a noncubic electronic charge distribution interacting with a Mossbauer nucleus may be exemplified by using point charges, for which the EFG is easy to calculate. A point charge <7 at a distance r = +y from a... 

Here, H0 is a Hartree local Hamiltonian that includes the Coulomb effects of both nuclei and average electronic charge distributions,... 

Fox, A.G., and Fisher, R.M. (1986) Accurate structure factor determination and electron charge distributions of binary cubic solid solutions, Phil. Mag. A, 53, 815-832. 

Figure 6.18 Contour maps of the ground state electronic charge distributions for the period 2 diatomic hydrides (including H2) showing the positions of the interatomic surfaces. The outer density contour in these plots is 0.001 au. (Reproduced with permission front Bader [1990].)...

In the 1920s it was found that electrons do not behave like macroscopic objects that are governed by Newton s laws of motion rather, they obey the laws of quantum mechanics. The application of these laws to atoms and molecules gave rise to orbital-based models of chemical bonding. In Chapter 3 we discuss some of the basic ideas of quantum mechanics, particularly the Pauli principle, the Heisenberg uncertainty principle, and the concept of electronic charge distribution, and we give a brief review of orbital-based models and modem ab initio calculations based on them. 

For gas-phase molecules the assumption of electronic adiabaticity leads to the usual Bom-Oppenheimer approximation, in which the electronic wave function is optimized for fixed nuclei. For solutes, the situation is more complicated because there are two types of heavy-body motion, the solute nuclear coordinates, which are treated mechanically, and the solvent, which is treated statistically. The SCRF procedures correspond to optimizing the electronic wave function in the presence of fixed solute nuclei and for a statistical distribution of solvent coordinates, which in turn are in equilibrium with the average electronic structure. The treatment of the solvent as a dielectric material by the laws of classical electrostatics and the treatment of the electronic charge distribution of the solute by the square of its wave function correctly embodies the result of... 

Figure 11.7 van der Waals bond caused by the creation of an instantaneous dipole. Momentary variations in the electron charge distribution of an atom causes a momentary dipole attraction between the asymmetric negative charge and the positive nuclear charge of another atom. 

In early work, Spiesecke and Schneider (59) pointed out that inductive effects alone cannot account for a- and -signal shifts. They held diamagnetic neighbor-anisotropy effects (63) arising from anisotropic electron-charge distributions responsible for the deviations in the electronegativity correlations. For bonds with conical symmetry they applied McConnell s magnetic point-dipole approximation (64) for the estimation of this contribution, Act ... 

Other atomic data needed, such as electronic charge distributions and screened potentials for partially stripped ions can presumably be based on available tabulations, although existing theoretical treatments have been based on simple and not necessarily accurate scaling relations. 

Many structures of zeolites can be described by certain structural units called building units, such as double 4 or 6 membered rings (D4R or D6R), structural sheets and rods. The main requirement for stmcture analysis of zeolites at present is not the refinement of electron charge distribution in the unit cell but the determination of the framework t5q)e stmctures, manner of arrangements of secondary building units or characterizing their lattice defects. 

Let us consider two neighboring atoms A and B (figure 1.5) and imagine that the electronic charge distribution is, for an infinitesimal period of time, asymmetrical. In this period of time, atom A becomes a dipole and induces a distortion in the electron cloud of atom B by attracting electrons from its positive edge atom B is then transformed, in turn, into a dipole. All the neighboring atoms... 

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