18
Chapter 2 Pauling “3-Electron Bonds”, 4-Electron 3-Centre Bonding, and the Need …
2-3 Delocalized Molecular Orbital Theory for 4-Electron
3-Centre Bonding Units
In Section 2-2, we have indicated that the standard Lewis representation for a 4electron 3-centre bonding unit involves resonance between valence-bond structures of the general types (1) and (2), i.e.
(1)
(2)
Υ—A B
Υ A—B



A delocalized molecular orbital description of 4-electron 3-centre bonding is
also widely used
5,6 , and we shall describe three examples of the molecular orbital
theory here.
2-3(a) Symmetrical 4-electron 3-centre bonding:
-
3
H
The linear triatomic anion 3
H
 with four electrons and three overlapping 1s atomic
orbitals is the simplest electron-excess system that may be used to describe the
molecular orbital procedure. The atomic orbitals y, a and b are displayed in
Figure 2-8, and linear combinations of these orbitals may be constructed.
Figure 2-8: Atomic and molecular orbitals for 4-electron 3-centre bonding unit of 3
H
 .
Because y and b are symmetrically-equivalent atomic orbitals, the delocalized
molecular orbitals have the forms given by Eqn. (1),
1
1
y b
a
k
   
, 2 y b
   , 3
3
y b
a
k
   
(1)
for which 1
k and 3
k are constants, both greater than zero. (Orthogonality of ψ 1
and ψ 3 relates k 3 to k 1 .)