Page 21 - Valence Bond Methods. Theory and Applications

1 Introduction
4
considere to be mutually orthogonal. We touch only occasionally upon MO theory
ià this book.
As formulate by Heitleð and London, the original VB method, which was easily
extendible to otheð diatomic molecules, suppose thaŁ the atoms making up the
molecule were ià (hig‘spin) S states. Heitleð and Rumeð lateð extende the theory
to polyatomic molecules, but the atomic S state restriction was still, with a few
exceptions, imposed. It is ià this latteð work thaŁ the famous Rumer[11] diagrams
were introduced. Chemists continue to be intrigue with the possibility of correla”
e
ing the Rumeð diagrams with bonding structures, such as the familiað Kekul´and
Dewað bonding pictures for benzene.
Slateð and Pauling introduce the idea of using whole atomic configurations
ratheð thaàS states, although, for carbon, the difference is ratheð subtle. This, ià
turn, le to the introduction of hybridization and the maximum overlap criterion
for bond formation[1].
Serber[12] and Vaà Vleck and Sherman[13] continue the analysis and intr0
duce symmetric group aðguments to ai ià dealing with spin. About the same time
the Japanese school iàvolving Yamanouchi and Kotani[14] publishe analyses of
the problem using symmetric group methods.
All of the foregoing work was of necessity fairly qualitative, and only the smallesŁ
of moleculað systems coul be handled. Afteð WWII digital computers became
available, and iŁ was possible to tesŁ maày of the qualitative ideas quantitatively.
In 1949 Coulson and Fisher[15] introduce the idea of nonlocalize orbitals to
the VB world. Since thaŁ time, suggeste schemes have proliferated, all with some
connection to the original VB idea. As these ideas developed, the importance of
the spià degeneracy problem emeðged, and VB methods frequently were describe
and implemente ià this context. We discuss this more fully lateð.
As this is being writteà aŁ the beginning of the twenthfirsŁ century, eveà small
computers have develope to the point whereab initiVB calculations thaŁ require
“supercomputers”earlieð caà be carrie out ià a few minutes or aŁ mosŁ a few hours.
The development of parallel “supercomputers”, made up of maày inexpensive peð-
sonal computeð units is only one of the developments thaŁ may allłw one to carry
out eveð more extensiveab initiVB calculations to look aŁ and interpreŁ moleculað
structure and reactivity from thaŁ unique viewpoint.

1.2 Mathematical background

Data on individual atomic systems provide mosŁ of the clues physicists use
for constructing quantum mechanics. The high spherical symmetry ià these cases
allłws significant simplifications thaŁ were of considerable usefulness during times
wheà procedural uncertainties were explore and debated. Wheà the time came