To electron density

The dy. p and dp yi orbitals each interact with four point charges in precisely the same way as does the dyi yi orbital. Again the repulsion relates to electron density, so the total interaction of the combination is (4/ /2) + (4/ /2) = 16 of our repulsion units. In other words, the d.2 and dp y2 orbitals are degenerate in octahedral symmetry. 

Gillespie, R. J. Popelier, P. L. A. Molecular Geometry and Chemical Bonding jrom Lewis to Electron Densities Oxford University Press New York, 2001. 

Chemical bonding and molecular geometry from Lewis to electron densities / R.J. Gillespie, P.L.A. Popelier. 

The reactivity of organic compounds toward eh varies systematically (Hart and Anbar, 1970), the variation often attributable to electron density of a specific functional group. Other generalizations are the following ... 

The absorption of high-energy radiation depends only on the electron density of the medium. Mass density is a reasonable first approximation to electron density. More accurately, and conveniently, the average value of the ration of Z/A for the atoms, where Z is the atomic number and A is the atomic mass, can be used to calculate relative dose. 

Table 6-3. The effective image plane position of a metal in vacuum estimated as a function of electron density in metal x, distance at the effective image plane fiom the jellium metal edge rws = Wigner-Seitz radius (a sphere containing one electron) which is related to electron density n, in metal (1 / n, = 4 n / 3 ) au = atomic unit (0.529 A). [From Schmickler, 1993.]...

Rupp, B., Segelke, B.W., Krupka, H.I., Lekin, T., Shafer, J., Zemla, A., Topani, D., SneU, G., and Earnest, G. (2002).The TB structural genomics consortium crystallization facility towards automation from protein to electron density. Acta Crystallogr. D 58, 1514-1518. 

Intuitively, the correct application of restraints and constraints to electron density should improve the phases. To quantify this notion, it is useful, though unconventional, to proceed as if we are solving a system of non-linear equations. A solution of such a system requires at least as many... 

This chapter will address software systems to interactively fit molecular models to electron density maps and to analyse the resulting models. This chapter is heavily biased toward proteins, but the programs can also build nucleic acid models. First a brief review of molecular modelling and graphics is presented. Next, the best current and freely available programs are discussed with respect to their performance on common tasks. Finally, some views on the future of such software are given. 

DENSITY FUNCTIONAL THEORY—FROM WAVE FUNCTIONS TO ELECTRON DENSITY... 

For a given ring system, the electron density on sulfur was found to correlate quite well with measured reactivities. Similar trends and sensitivities to electron densities were observed for all thiophene ring systems (38). This is illustrated in Fig. 29, where the rate constants are normalized to... 

Chemical shift variations among N-methyl cations have been related to electron densities and, in the case of fV-methylpyridinium ions, to Hammett substituent constants.126 Upfield shifts of H,126-128 13C,126 and 14N nuclei126 are observed when electron-donating groups increase the electron density at the quaternized site. In instances where shift differences are large, application of these correlations to molecules giving isomeric products will enable conclusive identification of product structures to be made. 

From the fact that the ABCD system of dibenzotetraazapentalene 255 did not become an AA BB system on heating, even at 225°C, it was concluded339 that the valence isomerization tetraazapentalene tetraazacyclooctatetraene (Scheme 14, Section IV,B,2) did not occur. Hall, Stephanie, and Nordstrom341 have effected an analysis of the ABCD system of 255 and revealed the presence of two superimposed ABCD systems that give the molecule an element of symmetry. Chemical shifts conformed to electron densities calculated by Chia and Simmons (Section V,B,3).388 The same authors also studied the ABCD-... 

Ultimate acids and bases." Familiarity with the idea that acidity and basicity are related to electron density at reacting sites and charge-to-size ratio... 

In the same way. the, 97Au MCssbuuer spectrum of CsAu is very similar to that of [CslC222) Au (Chapter 12). indicating that the Au anion is present in both (Fig. M-V).44 Since the MOssbauer effect is a nuclear one. it is very sensitive to electron density at the nucleus and therefore lo both atomic charge and character. ... 

Figure 11.7 Changes in chemical shift due to electron density around the proton.

The relevant question regarding secondary IEs on acidity is the extent to which IEs affect the electronic distribution. How can an inductive effect be reconciled with the Born-Oppenheimer approximation Although the potential-energy function and the electronic wave function are independent of nuclear mass, an anharmonic potential leads to different vibrational wave functions for different masses. Averaging over the ground-state wave function leads to different positions for the nuclei and thus averaged electron densities that vary with isotope. This certainly leads to NMR isotope shifts (IEs on chemical shifts), because nuclear shielding is sensitive to electron density.16... 

Chapter 5. From Diffraction Data to Electron Density... 

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