Polyatomic molecules - Cobalt

The set of linear equations reads
C ( α− E)
+ C β = 0
11
12
C β + C ( α− E)
+ C β =0
11 12
13
C
12
β
+C
12
( α− E)
= 0
We get
1 1 1
1 1
1 1 1
ψ = ϕ + ϕ + ϕ ; ψ = ϕ − ϕ ; ψ = ϕ − ϕ + ϕ
2 2 2
2 2 2 2 2
1 1 2 3 2 1 3 3 1 2 3
3. (a) In the ' free electron molecular orbital' (FEMO) theory, the electrons
in a conjugated molecule are treated as independent particles in a box
of length L . Sketch the form of the two occupied orbitals in butadiene, predicted
by this model and predict the minimum excitation energy of the molecule.
Comments on the relation to the π - orbitals obtained in Atkins. What are the
similarities and the differences. What are the differences between the spacing
of the orbitals in the two methods.
Answer
2 2
n h
2 n x
En = =
⎛ π
, n = 1,2,3....... and ψ sin
⎞
2
n
8mL
L ⎝ L ⎠
The Orbitals of the three first levels are given by :
FMO
Huckel
E 3 =
9h 2
8mL 2 ,
α−.62β
4 h 2
E 2 =
8mL 2 ,
α+.62β
E 1 =
h 2
8mL 2 ,
α+1.62β