Internuclear axes

Figure 4. Rehybridization as a function of pyramidalization angle. The rc-orbital axis vector (poavI approximation), is defined as that vector which makes equal angles to the three a-bonds at a conjugated carbon atom (Haddon 1988). The common angle to the three a-bonds (which are assumed to lie along the internuclear axes), is denoted 0OT. The average pyramidalization angle [(< — 90)°] shown for representative fullerenes (C ), was obtained from eqn (2) of Haddon et al. (19866) for n > 60.

In the case of righthanded circular polarized i -type excitation, when orientation of angular momenta takes place and the probability density of the angular momenta distribution is proportional to (1 — cos )2/2 (see (2.13)), only alignment of internuclear axes occurs, described by the probability density, which is proportional to (1/2)[1 + (sin20r)/2j. 

On the basis of their spatial symmetry, the molecular orbitals are denoted as a- and re-type orbitals, the main difference being that ff-type orbitals have cylindrical symmetry around the bond axes, while re-type orbitals have nodal planes (i.e., they vanish) at the internuclear axes. The er-type orbitals can be assumed to be localized, i.e., they define electronic density distributions only over specific regions of the molecule, while the re-type orbitals are delocalized, extending over the whole molecule. 

Recall (Chapter 5) that a ir bond has a nodal surface that includes the bond axis and that a tt bonding orbital will have lobes of opposite sign on each side of this nodal surface. From the standpoint of orbital symmetry, an octahedral complex could have up to twelve such bonds—two between the metal and each of the six ligands, although this number is never realized in an actual complex. Metal and ligand orbitals participating in IT bonds will lie perpendicular to the internuclear axes. Consider four potential metal-ligand tt interactions (1) (2) (3) and (4)... 

Fig. 6.6 Isodensity contour plots for planes containing the internuclear axes of H2 and L12 (reprinted with permission from ref. 67).

This would involve rotating Figures 9-2, 9-3, and 9-4 by 90° so that the internuclear axes are perpendicular to the plane of the pages. 

The utility of simple rotary resonance experiments for the determination of the magnitude and orientation of chemical shift tensors relative to one or more internuclear axes from MAS NMR experiments has been... 

There are two general conclusions of importance. First, the distance r(Z- X), where Z is the electron donor atom/centre in the complex B- XY, is smaller than the sum of the van der Waals radii ax and ax of these atoms. This result has been shown [179] to be consistent with the conclusion that the van der Waals radius of the atom X in the dihalogen molecule X is shorter along the XY internuclear axis than it is perpendicular to it, i.e. there is a polar flattening of the atom X in the molecule XY of the type suggested by Stone et al. [180]. This result has been shown to hold for the cases XY = CI2 [174], BrCl [175], C1F [176] and IC1 [178], but not for F2, in which the F atom in the molecule appears (admittedly on the basis of only a few examples) to be more nearly spherical [177]. 

Now we examine the bonding orbital antibonding orbital ax as well as their probability density functions schematic representation of cr is is shown in Fig. 3.1.5(a). In this combination of two Is orbitals, electron density accumulates in the internuclear region. Also, crls has cylindrical symmetry around the internuclear axis. 

The anisotropy of bond refractions, which can be determined by measuring the Kerr constant, is very useful for studying the nature of the chemical bond [194,195]. It shows that the valence electron cloud is ellipsoidal (with the longest axis in the internuclear direction) and its parameters depend on the polarity and the bond order. The experimental anisotropic bond refractions in molecules A2, AX, AXn, A2X , and M(CsH5)2 (Table SI 1.15) which conform to the formula ... 

Internuclear distances and bond angles are represented in units of A (1 A = 10" m) and degrees, respectively. The same but inequivalent atoms are discriminated by subscripts a, b, etc. In some molecules ax for rrxial and eq for equatorial are also used. 

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