202
Chapter 14 Delocalization of a Lone-Pair Electron into a Vacant Antibonding Orbital
Addendum Chapter 14
1. Wiberg Valence for the A : B Electron-Pair Bond
The covalent-ionic resonance wavefunction for the A:B electron-pair bond can be
expressed according to Eqs. (27) and (28).
(A:B) = C 1 {A
.

.
B} + C 2 {A:
(-) B
(+) } + C 3 {A
(+) :B
(-) }
(27)
= C 1 {a(1)b(2) + b(1)a(2)} + C 2 {a(1)a(2)} + C 3 {b(1)b(2)}
(28)
For it, the Wiberg atomic valence (V ab = V ba = P aa .P bb )
13 for a diatomic electronpair bond can be expressed
14 according to Eqs. (29) and (30).
V ab = 2C 1
2 /D + 2C 1
2
C 2
2
/D
2 + 2C 1
2 C 3
2
/D
2 + 4C 2
2 C 3
2
/D
2
(29)
= V ab (covalent) 11 + V ab (covalent,ionic) 12 + V ab (covalent,ionic) 13
+ V ab (ionic,ionic) 2,3
(30)
in which D = 2C 1
2 + C 2
2 + C 3
2
.
The V ab of Eqn. (28) could be considered to be a valence analogue of the
covalent, covalent-ionic and ionic-ionic contributions to the charge-shift bonding
formulation
15,16 of the binding energy for the electron-pair bond.
2. Concerted 2-Electron Delocalizations
Some concerted, 2-electron delocalization of the Y electrons into the antibonding
molecular orbital φ ab * = k*a – b of A : B, (in which the two electrons occupy the
bonding molecular orbital φ ab = a + kb), is equivalent to the concerted
delocalization of these electrons into the Y-A bonding molecular orbital φ ya = y +
la, i.e. the identity of Eqn. (1)
|(y + φ ab *)
α
(y + λφ ab *)
β (φ ab )
α
(φ ab )
β
|  |(φ ya )
α
(φ ya )
β (φ ab )
α
(φ ab )
β
|
(1)
obtains
17a , with  = kl/(1 + kk*). The associated valence-bond structure for
|(φ ya )
α
(φ ya )
β (φ ab )
α
(φ ab )
β
| is Y A B, in which the φ ya and φ ab orbitals are not
orthogonal.
Similarly for a 3-electron 3-centre bonding unit with the wavefunction
|(y)
α
(φ ab )
α
(φ ab )
β
| for the valence-bond structure Y A B, the identity