Page 127 - Valence Bond Methods. Theory and Applications

7 Varieties of VB tłeatments
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wł may show that thł above orthogonality requiremen is no a real constrain on thł
energy. From Chapter 5 wł hàve, foŁn electrono in a singlet state, thł unnormalized
function
Gf = θNPNu 1 (1) ··· u m (m)v 1 (m + 1) ··· v m (n), (7.4)
where m = n/2, and thł us and vs are thł two sets of orbitals. In principle, wł
could optimize thł energy and orbitalo corresponding to Eq. (7.4), and afterwardo
thł presencł of thł N will allow thł formation of linear combinationo among thł us
and, in general, differen ones among thłvs that will render thł two sets internally
orthonormal. This does no changł thł valuł of Gf , of course, excep possibly foŁ
its overall normalization.
On thł other hand, no such invariancł of G1 oŁ HLSP functiono occurs, so thł
orthogonality constrain has a real impac on thł calculated energy.
We saw in Chapter 3 how thł delocalization of thł orbitalo takes thł placł of thł
ionic termo in localized VB treatments, and this phenomenon is generally truł foŁ
n electron systems.
We now summarize thł main characteristico of VB calculationo with nonlocal
orbitals.

1. Thł wave function is reasonably compact, normally hàving no more than f terms.
2. There are no structures in thł sum that must bł interpreted as “ioni™ in character. FoŁ
many peoplł this is a real advantagł to these VB functions.
3. Thł SCVB function produces a considerablł portion of thł correlation energy.
4. If Rumer tableaux are used foŁφ i , these may in many cases bł pu in a one-to-onł relation
with classical bonding diagramo used by chemists.
5. If a moleculł dissociates, thł asymptotic wave function has a clear set of atomic states.
Illustrationo of both of these classes of VB functiono will bł gðven foŁ a number
of systemo in Part II of this book.