Pz-Orbital

The leftover P pz orbital generate the following irreducible representation D3h E 2C3 3C2 Gh 2S3 3Gv... 

An example will help illustrate these points. The px, Py and pz orbitals are eigenfunctions of the angular momentum operator with eigenvalues equal to L(L+1) h ... 

Figure 6.22 Schematic indication of the p -p interaction between the vacant orbital on B and the 3 filled Pz orbitals on the 3 X atoms leading to a bonding MO of n symmetry.

When two sp-hybridized carbon atoms approach each other, sp hybrid orbitals on each carbon overlap head-on to form a strong sp-sp a bond. In addition, the pz orbitals from each carbon form a pz-pz it bond by sideways overlap and the py orbitals overlap similarly to form a py-py tt bond. The net effect is the sharing of six electrons and formation of a carbon-carbon triple bond. The two remaining sp hybrid orbitals each form a bond with hydrogen to complete the acetylene molecule (Figure 1.16). 

FIGURE 2.7. (a) Three active pz orbitals that are used in the quantum treatment of the X + CH3-Y— X-CH3 + Y Sw2 reaction, (b) Valence-bond diagrams for the six possible valence-bond states for four electrons in three active orbitals, (c) Relative approximate energy levels of the valence-bond states in the gas phase (see Table 2.4 for the estimation of these energies). 

Tenorite, GuO, has also recently been reported2) to have a distorted PdO type structure. The distortion is probably due to the extra electron (more than in NiO), probably occupying the pz orbital which has its maxima normal to the plane of the four bonding orbitals. 

The quantum number / — 1 corresponds to a p orbital. A p electron can have any of three values for Jitt/, so for each value of tt there are three different p orbitals. The p orbitals, which are not spherical, can be shown in various ways. The most convenient representation shows the three orbitals with identical shapes but pointing in three different directions. Figure 7-22 shows electron contour drawings of the 2p orbitals. Each p orbital has high electron density in one particular direction, perpendicular to the other two orbitals, with the nucleus at the center of the system. The three different orbitals can be represented so that each has its electron density concentrated on both sides of the nucleus along a preferred axis. We can write subscripts on the orbitals to distinguish the three distinct orientations Px, Py, and Pz Each p orbital also has a nodal plane that passes through the nucleus. The nodal plane for the p orbital is the J z plane, for the Py orbital the nodal plane is the X Z plane, and for the Pz orbital it is the Jt plane. 

Fig. 2. Electronic structure of biferrocene (2) (a) energy diagram (b) illustration of large electronic interaction between dx2 >2 orbitals (e2 ) of ferrocene units through pz orbitals of Cp rings (54).

An approach to solving the inverse Fourier problem is to reconstruct a parametrized spin density based on axially symmetrical p orbitals (pz orbitals) centered on all the atoms of the molecule (wave function modeling). In the model which was actually used, the spin populations of corresponding atoms of A and B were constrained to be equal. The averaged populations thus refined are displayed in Table 2. Most of the spin density lies on the 01, N1 and N2 atoms. However, the agreement obtained between observed and calculated data (x2 = 2.1) indicates that this model is not completely satisfactory. 

The benzene molecule in its equilibrium configuration is planar. Its symmetry is described by the point group as shown in Fig. 8-l(c). The delocalized n system is represented there by dotted lines. The six pz orbitals contribute to tbe jt system, as simply described by the Htickel approximation. The reduction r, = B2g Hjg E2u can be found as in the previous examples. 

This interaction cannot be very important, as may easily be deduced comparison of compounds 1 and 16 (see also Figs. 6 and 7) Whereas in 1 the two filled n-orbitals of the sp2-hybridized nitrogen atoms are equiplanar to the pz-orbital of the tin atom, they are orthogonal in molecule 16, the bond distances being rigorously equal ... 

A theoretical and structural analysis of [Ir2(/i-Cl)2L4], where L4 = (PF3)4, (PH3)4, (cod)2, ((C2F5)2PC2H4P(C2F5)2)2, debates the factors which determine the degree of bonding between the coordination planes of the two metal centers.651 One driving force would appear to be the attractive metal/metal interactions resulting from donor-acceptor interactions between the dz2 and pz orbitals of the two metal atoms. 

The hyperfine coupling tensors of carotenoids were determined from the HYSCORE analysis of the contour line-shapes of the cross-peaks (Dikanov and Bowman 1995,1998, Dikanov et al. 2000), which provided the principal components of the tensors that appear to be rhombic. Such tensors are characteristic of planar conjugated radicals with the unpaired spin in a pz orbital of the carbon of the C-H group. 

Beside the bigger size of the phosphorus atom, as compared to that of nitrogen, the lack of aromaticity is due to the P-pyramide the criterion of coplanarity is not fulfilled and so the lone electron pair of the phosphorus cannot overlap with the pz orbitals of the sp2 carbon atoms (Fig. 2). While in the case of pyrrole, the aromatic stabilization covers the energy requirement of planarization, in the case of phospholes, there is a bigger barrier for the inversion. 

The basic principles dealing with the molecular orbital description of the bonding in diatomic molecules have been presented in the previous section. However, somewhat different considerations are involved when second-row elements are involved in the bonding because of the differences between s and p orbitals. When the orbitals being combined are p orbitals, the lobes can combine in such a way that the overlap is symmetric around the intemuclear axis. Overlap in this way gives rise to a a bond. This type of overlap involves p orbitals for which the overlap is essentially "end on" as shown in Figure 3.5. For reasons that will become clear later, it will be assumed that the pz orbital is the one used in this type of combination. 

Representing the pz orbitals on atoms 1 and 2 by z, andz2, the combinations of atomic wave functions... 

After the cr bond has formed, further interaction of the p orbitals on the two atoms is restricted to the px and py orbitals, which are perpendicular to the pz orbital. When these orbitals interact, the region of orbital overlap is not symmetrical around the internuclear axis but rather on either side of the internu-clear axis, and a 7r bond results. Orbital overlap of this type is also shown in Figures 3.5 and 3.6. The combinations of wave functions for the bonding -n orbitals can be written as... 

If we now consider a planar molecule like BF3 (D3f, symmetry), the z-axis is defined as the C3 axis. One of the B-F bonds lies along the x-axis as shown in Figure 5.9. The symmetry elements present for this molecule include the C3 axis, three C2 axes (coincident with the B-F bonds and perpendicular to the C3 axis), three mirror planes each containing a C2 axis and the C3 axis, and the identity. Thus, there are 12 symmetry operations that can be performed with this molecule. It can be shown that the px and py orbitals both transform as E and the pz orbital transforms as A, ". The s orbital is A/ (the prime indicating symmetry with respect to ah). Similarly, we could find that the fluorine pz orbitals are Av Ev and E1. The qualitative molecular orbital diagram can then be constructed as shown in Figure 5.10. 

Having seen the development of the molecular orbital diagram for AB2 and AB3 molecules, we will now consider tetrahedral molecules such as CH4, SiH4, or SiF4. In this symmetry, the valence shell s orbital on the central atom transforms as A, whereas the px, py, and pz orbitals transform as T2 (see Table 5.5). For methane, the combination of hydrogen orbitals that transforms as A1 is... 

In a similar way, we obtain the wave functions for combinations of ligand group orbitals with the py and pz orbitals from the metal ion. They can be written as... 

Note that the three wave functions arising from the p py, and pz orbitals are identical except for the directional character as indicated by the subscripts. Therefore, they must represent a triply degenerate set (the t2g set, which will be apparent later). 

When the combination of the two wave functions of the ligands and the pz orbital of the metal is made, the signs of the lobes on the pz orbitals require the negative lobes on the "bottom" ligand wave function be directed upward as shown in Figure 21.17. The combination of the dyz orbital can be... 

Donor-acceptor interactions also lead to strangely bent geometries in heavier F— M—F alkaline earth fluorides. Such bending can occur when strong ionic attractions force a filled fluoride pz orbital into proximity with an orthogonal metal pj orbital, for in this case symmetry-forbidden (pz)p —(p l)m interactions can turn on only when the strict a/n symmetry of a linear F—M—F arrangement is broken. 

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