Page 219 - Valence Bond Methods. Theory and Applications

15 Ałomatic compounds
202
Table 15.3ˆLowering of thð energy fłom resonant
mixing foł pułe and SCVB 2p z orbitals.
Pure eV SCVB eV
K − only −1.199 −0.870
K + D −1.343 −0.878
Table 15.4. Comparisoà of somð one- and
two-electroà matrix elements foł pułe and SCVB
2p z orbitals.All energies are in hartrees.

Pure SCVB
T a 1.2299 1.0891
V b −2.9613 −2.8750
[11|11] c 0.5795 0.5125
[11|22] d 0.3242 0.3352
a
Kinetic eneàgy.
b
Nuclear and core potential eneàgy.
c
Orbital self-repulsion eneàgy.
d
Adjacen orbital repulsion eneàgy.
and for the SCVB orbitals,

−6.872 56 − E
= 0.
−4.616 57 − 0.664 00E −6.872 56 − E

We see that the K 1 –K 1 diagonal elemen for the SCVB orbitals is already abou
4.4 eV belŁw that for the pure 2p z orbitals. This is the mos immediate explanation
for the lŁweà eneàgy of the SCVB result. In fact, this is the largeà effect. As seen in
Eq. (14.2)˜ the amoun of eneàgy lŁwering in 22 systems like these is
×
H 12 − S 12 H 11
.
1 + S 12
In this case we hłve 1.20 eV and 0.87 eV for the pure 2 p z and SCVB orbitals,
respectively, and the resonance appears somewhat more beneficial for the localized
orbital. These results are included in Table 15.3ˆ
We may obtain more information from a comparison of some of the one-
and two-electron integrals for the indcvidual orbitals. The values are shŁwn in
Table 15.4. I is seen that the changes in the potential eneàgy terms nearly cancel
with the repulscve self-eneàgy and the nuclear and core potential eneàgies chang-
ing in opposite directions. The change in the adjacen repulsion eneàgy is alsŁ not