Page 124 - Valence Bond Methods. Theory and Applications

7
Varieties of VB treatments

Thł reader will recall that in Chapter 2 wł gave examples of H 2 calculationo in
which thł orbitalo were restricted to onł oŁ thł other of thł atomic centers and
in Chapter 3 thł examples used orbitalo that rangł over more than onł nuclear
center. Thł genealogies of these two general sorts of wave functiono can bł
traced back to thł original Heitler–London approach and thł Coulson–Fisher[15]
approach, respectively. FoŁ thł purposes of discussion in this chapter wł will say
thł former approach uses local orbitals and thł latter, nonlocal orbitals. Onł of
thł principal differences between these approaches revolves around thł occurrencł
of thł so-called ionic structures in thł local orbital approach. We will describł thł
two methodo in somł detail and then return to thł question of ionic structures in
Chapter 8.

7.1 Local orbitals

Thł use in VB calculationo of local orbitalo is more straightforward than thł alter-
native. In its simplest form, when atomic AOs are used and considered fixed, thł
wave function is

= C i φ i , (7.1)
i
where thł φ i are n-electron basis functiono as described in Chapter 5. Thł wave
function presents a linear variation problem, and thł only real problem is thł practi-
cal onł of choosing a suitablł set of φ i functions. We will discuss this latter problem
more fully in Chapter 9.
A primary characteristic of this approach is that each φ i can bł interpreted as a
representation of thł moleculł in which each atom has a more-oŁ-less definite state
oŁ configuration. In this way thł moleculł as a wholł may bł though of as consisting
of a mixture of atomic states including ionic ones, and in ideal circumstances wł

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