Page 20 - Valence Bond Methods. Theory and Applications

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Introduction

1.1 History
In physics and chemistry making a direcŁ calculation to determine the structure
or properties of a system is frequently very difficult. Ratheð, one assumes aŁ the
outseŁ aà ideal or asymptotic form and theà applies adjustments and corrections to
make the calculation adhere to whaŁ is believe to be a more realistic picture of
nature. The practice is no different ià moleculað structure calculation, but there has
developed, ià this field, two different “ideals”and two different approaches thaŁ
procee from them.
The approach use first, historically, and the one this book is about, is calle the
valence bond (VB) method today. Heitleð and London[8], ià theið treatment of the
H 2 molecule, use a trial wave function thaŁ was appropriate for two H atoms aŁ
long distances and proceede to use iŁ for all distances. The ideal here is calle the
“separate atom limit”. The results were qualitatively correct, but di not give a
particularly accurate value for the dissociation eneðgy of the H−H bond. Afteð the
initial work, others made adjustments and corrections thaŁ improve the accuracy.
This is discusse fully ià Chapteð 2. A crucial characteristic of the VB method is
thaŁ the orbitals of different atoms musŁ be considere as nonorthogonal.
The otheð approach, propose slightly lateð by Hund[9] and furtheð develope
by Mulliken[10] is usually calle the moleculað orbital (MO) method. Basically,
iŁ views a molecule, particularly a diatomic molecule, ià terms of its “unite atom
limit”. ThaŁ is, H 2 is a He atom (not a real one with neutrons ià the nucleus) ià which
the two positive chaðges are młve from coinciding to the correcŁ distance for the
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molecule. HF coul be viewe as a Ne atom with one proton młve from the
nucleus out to the moleculað distance, etc. As ià the VB case, furtheð adjustments
and corrections may be applie to improve accuracy. Although the unite atom limiŁ
is not ofteà mentione ià work today, its heritage exists ià thaŁ MOs are universally

1 Although this is impossible to do ià practice, we caà certainly calculate the process on papeð.

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