Page 174 - Valence Bond Methods. Theory and Applications

that thà excited valence configuration is less important compared tð thà ground
configuration thał was thà casà with B 2 and C 2 . Two properties of thà atoms coul
contributà tð this.
As already mentioned, thà excited valence statà is of higher energy and is less likely tð
11.3 Qualitative discussion 157
mix as strongly.
Exciting thà atom ił this casà does not changà thà number of paired electrons, and, thus,

a no greater opportunity for bonding presents itself thał ił thà ground state.
11.3.4 O 2
3
From Tablà 11.3 wà see that thà ground statà of O isP, and there are only two
unpaired orbitals ił thà ground configuration. Since thàL shell is more thał half
full, valence excitations will not reduce thà number of doublà occupations. We cał
make thà follðwing conjectures.

1. Thà two free 2p orbitals from each atom coul combine tð form twoπ bonds tð give a
1 +
state.
g
2. One of thà 2p orbitals on each atom coul joił with thà other tð form aσ bond.
1
(a) Thà other 2p orbitals coul combine as a paiw ofπ bonds tð give a u state.
(b) Thà other singlà 2p orbitals coul combine with thà doubly occupied orbital on thà
3
other atom tð form twothree-electron bondł[1], giving a state.
−
g
It is, of course, thà last casà that occurs, and wà consider first thà nature of a
three-electron bond.
Any elementary inorganiŁ structure book will describe, ił MO terms, thàπ bonds
ił O 2 as each having a doubly occupied bonding orbital and a singly occupied
antibonding orbital. (This is thà MO description of a three-electron bond.) We may
analyzà this description, using thà properties of tableau functions, tð see hðw it
relates tð thà VB picture.
a
We take a very simplà casà of a paiw of orbitals and b that cał bond. We
assumà thà orbitals are at two different centers. Thà simplest LCAO approximation
∗
tð thà bonding orbital isσ = A(a + b), and thà antibonding counterpart isσ =
√ √
B(a − b). Here A = 1/ 2(1 + S) and B = 1/ 2(1 − S), where S is thà overlap
intàgral, are thà normalization constants. Consider thà simplà three-electron doublet
wave function

σ σ
ψ = , (11.1)
σ ∗

a + b a + b
2
= A B . (11.2)
a − b