SCVB orbitals

Figure 10.1. The first SCVB orbital for the allyl radical. The orbital amplitude is given in a plane parallel to the radical and 0.5 A distant.

In Fig. 10.1 we show an altitude drawing of the orbital amplitude of the first of the SCVB orbitals of the allyl n system. The third can be obtained by merely reflecting this one in the y-z plane of the molecule. It is seen to be concentrated at... 

Figure 10.6. The first SCVB orbital for the BeH molecule and associated with the Be nucleus. This has the general appearance of an 5-p hybrid pointed toward the H atom, and we denote it the inner hybrid, hi. The orbital amplitude is given in the x-z plane, which contains the nuclei.

Figure 10.9. The three SCVB orbitals for the Li atom. The orbital amplitudes times the radial coordinate are shown.

In terms of the primitive split Gaussian basis, we obtain for the three SCVB orbitals... 

Figure 15.1. Altitude plot of the SCVB orbital for the n system of benzene. There are six symmetrically equivalent versions of this around the ring. Tlie amphtude is given in a plane 0.5 A in the positive z-direction from the plane of the nuclei.

We see that the K -K diagonal element for the SCVB orbitals is already about 4.4 eV below that for the pure 2pz orbitals. This is the most immediate explanation for the lower energy of the SCVB result. In fact, this is the larger effect. As seen in Eq. (14.2), the amount of energy lowering in 2 x 2 systems like these is... 

In this case we have 1.20 eV and 0.87 eV for the pure 2pz and SCVB orbitals, respectively, and the resonance appears somewhat more beneficial for the localized orbital. These results are included in Table 15.3. 

We show another aspect of these numbers in Table 15.3, where we detail the effects of resonance between the two Kekule structures and among all of the covalent structures for the two sorts o 2pz orbitals. The results suggest that within one structure the SCVB orbitals duplicate, to some extent, the effect of multiple structures, and the configurational mixing produces less energy lowering with them. 

There are three inequivalent SCVB orbitals for hexatriene, and these are given in Figs. 15.2, 15.3, and 15.4. The first of these shows a principal peak at the first orbital and a small satellite at the adjacent position. The second is more interesting with the principal peak at the second C atom, but showing a larger satellite at position 1 than at position 3. This is consistent with having essentially a double bond between atoms 1 and 2 or 5 and 6, with single bonds between 2 and 3 and 4 and 5. 

The SCF, SCVB, full valence tv, and full valence tt + S results of using a 6-3IG basis on benzene are given in Table 15.6. The geometry used is that of the minimum SCF energy of the basis. In this case the SCVB energy is lower by 0.4 eV than the full valence it energy. This is principally due to the 3d polarization orbitals present in the SCVB orbital, but absent in the valence calculation. The SCVB orbital is... 

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