2pv orbital

It may be proper at this stage to lead the reader back to the stage where we constructed the localized orbitals of a CH2 group. At that time two valence orbitals were set aside—the 2pv orbital, and the outer (2s, 2pr) hybrid. Both of these orbitals lie in the. r, y plane. Now in our description of cyclopropane, we used bond orbitals to describe the CC bonding these bond orbitals are derived from in-plane (xy y) hybrids on each carbon. The two hybrids which are required on each carbon atom—in ordet to participate in two bond orbitals—are built precisely from the 2py orbital and the (2s, 2pj.) out combination on each CH2 group. 

In the interaction of the local 2pv orbitals, two more bonding molecular orbitals are formed against one less bonding. In all previous cases the opposite occurred. This is due to the negative overlap between adjacent 2py orbitals—whether, by convention, all positive lobes point in the clockwise direction, or whether all positive lobes point in the anticlockwise direction. The two bonding 2pv combinations in fact fall below the two antibonding (hybrid 2s, 2px) combinations. The former each have two electrons while the latter are empty. The six electrons of the three C—C bonds are nicely accounted for. The method creates simultaneously the acc and or c molecular orbitals of cyclopropane (note that the latter three lie relatively close in energy). 

Figure 3.13 shows approximate representations of the 2px and 2p orbitals. To construct the two bonding orbitals b] and b2 we place the H atoms along the directions of the 2p and 2pv orbitals of the O atom to give maximum overlap of a Is orbital of H with the 2p, and 2py 0 orbitals (Figure 3.13). This bonding model implies a bond angle of 90° for the water molecule, which is not in very good agreement with the observed angle of 104.5°.

Double and triple bonds, particularly those in carbon molecules, are often described in MO terms. Thus a double bond is described as consisting of a a bond formed by the overlap of an sp hybrid orbital on each carbon atom and a tt bond formed by the sideways overlap of either the 2p or 2p orbitals (Figure 3.18). A cr orbital has cylindrical symmetry like an atomic s orbital whereas a ir orbital, like an atomic p orbital, has a planar node passing through the nucleus of each of the bonded atoms. A triple bond is similarly described as consisting of a cr orbital and two ir orbitals formed from both the 2p and 2pv orbitals on... 

Ans. They are oriented differently in space. The 2px orbital lies along the jr axis the 2pv orbital lies along the y axis the 2p. orbital lies along the z axis. 

The character with respect to reflexion in one of the infinite number of vertical planes requires some explanation. It is best to choose a particular vertical plane such as that represented by the xz plane. Reflexion in any of the vertical planes has no effect upon the two 2p orbitals, which gives 2 as their character. Reflexion of the two 2pv orbitals in the xz plane does not change them in any way their character is 2. The reflexion of the two 2p orbitals in the xz plane causes their y values to change sign, and because they are otherwise unaffected, their character is -2. The resultant character of the six 2p orbitals, with respect to the operation, ov, is given by 2 + 2 - 2 = 2. 

The molecular orbitals are completed by the interaction of the two sets of 2px and 2pv orbitals to give doubly degenerate lrc (bonding) and 2n (anti-bonding) levels ... 

To illustrate this explicitly, let us consider the 2px and 2pv orbitals of the nitrogen atom in ammonia, which belongs to the group C3l>. These orbitals are represented or described by the following eigenfunctions ... 

Figure 3.13 The formation of two bonding orbitals bi and b2. (a) The overlap of the 2p and 2pv orbitals of an oxygen atom with the Is orbitals of two hydrogen atoms Hi and H2 leads (b) to the two bonding orbitals, b[ and b2-...

Boron has the structure ls22s22plx, and we know that it forms a covalent compound, boron trichloride experimental work shows that there are three equal strength B—Cl bonds in the molecule. A good explanation of this is that hybrid orbitals are formed from boron 2s, 2pv and 2pv orbitals. This is illustrated in Figure 15b. The hybrid orbitals lie in the same plane and are known as sn2 hybrids, since they are formed from one s and two p orbitals. Note that each of the hybrid orbitals will be only partly filled, since there are only three electrons of principal quantum number 2 to be allocated. The layout of the BC13 molecule is shown in Figure 15c. The calculated bond angle for sp2 hybrids is 120°, and this is confirmed experimentally. 

Now let s combine two 2pv orbitals. The lobes of these orbitals (like those of the 2p orbitals but unlike those of 2pz), are perpendicular to the molecular axis. Figure 4.19 shows the combination (2p>A + 2p)B). In this combination the amplitude of the wavefunction is increased between the nuclei but only above and below the molecular axis. 

Fig. 8.28. Tlie Slater-type oibitals shown as contours of the section at = 0. Hie background coirespraids to the zero value of the orbital, the darker regions to the negative, the brighter to the positive value of the oibital. (a) 2px and (b) 2py, and their linear combination (c) equal to cos + sin5 2/iy. which is alsoa 2p oibital, but rotated 1 5 with respect to the 2pv orbital In panels fd) and (el we show the normalized Zv and 2p orbitals, which will now be mixed in various pn xations (f) the 1 1 ratio. i.e., the sp l tridization, (g) the 1 t/2 ratio, i.e., the sp hybridizatiim, and (h) the 1 y/3 ratio, i.e., the sf hybridization.

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