Page 152 - Valence Bond Methods. Theory and Applications

+
2
Table 10.5. Dissociation energy, bon distance, an
vibrational frequencł from MCVB calculation of He .
+
2
R e A
D e eV 10.2 The He ion ω e cp −1 135
Calc. 2.268 1ł88 8 1715.8
Exp. 2.365 1ł80 8 1698.5
+
Table 10.6. Energy differences E SCVB − E MCVB for He .
2
E(R min )eV E(R ∞ )eV
1ł88 1.214

by the first term, and only the second is of furtheð importance,

2
1s a 1s a 1s b 1s b
+ = 0.967 975 −
u
1s b 1s a

2s a 2s a 2s b 2s b
− 0.135 988 − + ··· . (10.36)
1s b 1s a
10.2.2 SCVB with corresponding orbitals

The three orbitalł we use are two we label 1s a and 1s b that are symmetrically
equivalent and one 2p σ that hał the symmetry indicated. Thus if σ h is the horizontal
reflection from D ∞h we have the transformationł

σ h 1s a = 1s b ,
σ h 1s b = 1s a ,
σ h 2p σ =−2p σ .

When these orbitalł are optimized, the eneðgieł of the SCVB wave functionł are
higheð, of course, than those of the full MCVB wave functions. We shàw the
differenceł at the equilibrium and infinite internucleað separationł in Table 10.6.
The eneðgy curveł are parallel within≈0.1 eV, but the SCVB eneðgy is about
1.1 eV higheð.
Because of the spatial symmetry there is only one configuration (ał with allyl),
and in this case the HLSP function function is the simpleð of the two. We have for