Electronic charge distribution for

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 -... 

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].)...

Fig. 6.3. Contour maps of the ground-state electronic charge distributions for the second- and thrid-row diatomic hydrides showing the positions of the interatomic surfaces. The first set of diagrams (a) also includes a plot for the ground state of the Hj molecule. The outer density contour in these plots is 0.001 au. The remaining contours increase in valne according to the scale given in the Appendix (Table A2). (a) The left-hand side 2, LiH 2, BeH 2, BH 2 right-hand side CH n, NH 2", OH n, HF 2+. (b)The left-hand side NaH 2-, MgH 2+, AIH 2+, SiH right-hand side PH 2-, SH "H. HCI 2. ...

The diamagnetic susceptibility anisotropies and molecular second moments of the electronic charge distributions for COCIF have been calculated by Maksic and Mikac [1303a], and these authors suggested that their calculated values showed that the experimentally derived second moments (calculated from the Zeeman effect in the Stark-modulated microwave... 

The H NMR spectrum of (1) has been described <84CHEC-I(5)847>. Several studies on C NMR investigation of (1) have appeared (Table 2) <80AJC499,80AJC1275,87JHC805). The comparison of the C NMR shifts and the calculated (INDO) electron charge distribution for (1) showed a satisfactory correlation <80JST(64)15>. 

It is interesting to correlate the electronic charge distribution for the two- and four-electron II3 systems with the treatment above. Using the wavefunctions shown in lugure 6.6 it is easy to generate the electron densities of6.10and 6.11. The details... 

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. 

By introducing reasonable values (about 2 for nitrogen, 4 for oxygen) for the electron affinity parameter relative to carbon, 8, and for the induced electron affinity for adjacent atoms (32/8i = Vio), we have shown that the calculated permanent charge distributions for pyridine, toluene, phenyltrimethylammonium ion, nitrobenzene, benzoic acid, benzaldehyde, acetophenone, benzo-nitrile, furan, thiophene, pyrrole, aniline, and phenol can be satisfactorily correlated qualitatively with the observed positions and rates of substitution. For naphthalene and the halogen benzenes this calculation does not lead to results... 

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... 

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... 

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 ... 

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