Polyatomic molecules - Cobalt

2. (a) Consider the allyl molecule CH 2CHCH2.
Construct
the secular determinant and find the orbital energies for the
π - electron system. Find the molecular orbitals and scetch them.
You can make use of the results from the previous question on H3
(b) Do the same for cyclopropene
H
C
H 2 C
CH 2 HC
H
C
CH
Answer :
For (a) we get the secular determinant
α − E
β α−
E β
β α−
E
= 0
sin ce the two terminal hydrogens C 1 and C3
do not interact
α−
E β
β α−
E β
β α−
E
=
α−
E β
( α − E) ( ) − β β β
β ( α−
E) 0 ( α − E)
3 2 2
= ( α−E) −β ( α−E) −β ( α−E)
2 2
= ( α−E) α−E)
−2β
0
[ ] =
Thus
ε1 = α+ 2β;
ε2 = α;
ε3
= α−
2β