Chapter 3 Wave-Functions and Valence-Bond
Structures for 1-Electron Bonds,
Electron-Pair Bonds, Pauling
“3-Electron Bonds” and “no Bonds”
For diatomic systems, an elementary survey will be presented here of types of
valence-bond structures and simple orbital wave-functions that may be used to
describe 1-electron bonds, electron-pair bonds, Pauling “3-electron bonds” and
“no-bonds”.
3-1 Diatomic Bonding and Antibonding Molecular Orbitals
If A and B are two atoms with overlapping atomic orbitals a and b, whose overlap
integral S ab  abdv is greater than zero, we may construct the bonding and antibonding molecular orbitals
ab
a b

     k and
ab
*
_
* a – b
    k
. The
parameters k and k* are constants (both greater than zero) that are related through
the requirement that the two molecular orbitals be orthogonal (i.e.
0
dv
ψ
ψ
*
ab
ab


. If k is chosen so that the energy of  ab is a minimum, then the
bonding molecular orbital has an energy which is lower than that of the orthogonal
antibonding molecular orbital. For 2
H
 , 2
H ,
2
He
 and
2
He , approximate contours
for these orbitals, which are constructed from overlapping 1s atomic orbitals, are
displayed in Figure 3-1.
Ó Springer International Publishing Switzerland 2016
R.D. Harcourt, Bonding in Electron-Rich Molecules,
Lecture Notes in Chemistry 90, DOI 10.1007/978-3-319-16676-6_3
35