Electron density radii

What does this equation tell us For this wavefunction, the angular wavefunction Y is a constant, 1/2tti/2 , independent of the angles, which means that the wavefunction is the same in all directions. The radial wavefunction R(r) decays exponentially toward zero as r increases, which means that the electron density is highest close to the nucleus (e° =1). The Bohr radius tells us how sharply the wavefunction falls away with distance when r = a ), t i has fallen to 1/e (37%) of its value at the nucleus. 

The quantity p2 as a function of the coordinates is interpreted as the probability of the corresponding microscopic state of the system in this case the probability that the electron occupies a certain position relative to the nucleus. It is seen from equation 6 that in the normal state the hydrogen atom is spherically symmetrical, for p1M is a function of r alone. The atom is furthermore not bounded, but extends to infinity the major portion is, however, within a radius of about 2a0 or lA. In figure 3 are represented the eigenfunction pm, the average electron density p = p]m and the radial electron distribution D = 4ir r p for the normal state of the hydrogen atom. 

Of particular interest is the result that for a radius of around 0-55 A the electron density in the chloride ion falls nearly to zero for this conclusion has... 

The relative change of the mean-square nuclear radius in going from the excited to the ground state, A r )/ r ), is positive for u. An increase in observed isomer shifts S therefore reflects an increase of the s-electron density at the Ru nucleus caused by either an increase in the number of s-valence electrons or a decrease in the number of shielding electrons, preferentially of d-character. 

Fig. 3 Due to the anisotropic distribution of the electron density, halogen atoms show a negative electrostatic potential and a larger radius (rmax) in the equatorial region and a positive electrostatic potential and a smaller radius (rmjn) in the polar region. As a consequence of this, halogens behave as nucleophiles at the equator and as electrophiles at the pole...

Figure 2.2 A contour plot of the electron density in a plane through the sodium chloride crystal. The contours are in units of 10 6 e pm-3. Pauling shows the radius of the Na+ ion from Table 2.3. Shannon shows the radius of the Na+ ion from Table 2.5. The radius of the Na+ ion given by the position of minimum density is 117 pm. The internuclear distance is 281 pm. (Modified with permission from G. Schoknecht, Z Naiurforsch 12A, 983, 1957 and J. E. Huheey, E. A. Keiter, and R. L. Keiter, Inorganic Chemistry, 4th ed., 1993, HarperCollins, New York.)...

The definition of the radius of an ion in a crystal as the distance along the bond to the point of minimum electron density is identical with the definition of the radius of an atom in a crystal or molecule that we discuss in the analysis of electron density distributions in Chapter 6. The radius defined in this way does not depend on any assumption about whether the bond is ionic or covalent and is therefore applicable to any atom in a molecule or crystal independently of the covalent or ionic nature of the bond, but it is not constant from one molecule or crystal to another. The almost perfectly circular form of the contours in Figure... 

Figure 5.2 (a) Electron density contour map of the CI2 molecule (see Chapter 6) showing that the chlorine atoms in a CI2 molecule are not portions of spheres rather, the atoms are slightly flattened at the ends of the molecule. So the molecule has two van der Waals radii a smaller van der Waals radius, r2 = 190 pm, in the direction of the bond axis and a larger radius, r =215 pm, in the perpendicular direction, (b) Portion of the crystal structure of solid chlorine showing the packing of CI2 molecules in the (100) plane. In the solid the two contact distances ry + ry and ry + r2 have the values 342 pm and 328 pm, so the two radii are r 1 = 171 pm and r2 = 157, pm which are appreciably smaller than the radii for the free CI2 molecule showing that the molecule is compressed by the intermolecular forces in the solid state. 

Here we see clearly the large concentration of density around the oxygen nucleus, and the very small concentration around each hydrogen nucleus. The outer contour is an arbitrary choice because the density of a hypothetical isolated molecule extends to infinity. However, it has been found that the O.OOlau contour corresponds rather well to the size of the molecule in the gas phase, as measured by its van der Waal s radius, and the corresponding isodensity surface in three dimensions usually encloses more than 98% of the total electron population of the molecule (Bader, 1990). Thus this outer contour shows the shape of the molecule in the chosen plane. In a condensed phase the effective size of a molecule is a little smaller. Contour maps of some period 2 and 3 chlorides are shown in Figure 8. We see that the electron densities of the atoms in the LiCl molecule are only very little distorted from the spherical shape of free ions consistent with the large ionic character of this molecule. In... 

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