SUPPLEMENTARY – 2
It is helpful to construct MO’s of a molecule from the linear combination of the
atomic orbitals, such that each linear combination does transform according to one of the
molecular symmetry species. Such linear combinations are called symmetry-adapted
wavefunctions.
iCii
Construction of MO’s of Homo- and Hetero- diatomic molecules: There are three general cases used for ordering MO’s due to the increasing ns - np gap
with atomic number from left to right in the periodic table, case1 for H2 to N2, case2 for
beyond O2 and case3 for hetero diatomic systems. These are shown below.
Case1
Case2
Case3
Molecular orbitals of H2
Molecular orbitals of H3 linear (Dh)
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
Molecular orbitals of H3 cyclic (D3h)
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
Correlation diagram of H3 linear (Dh) and H3 cyclic (D3h)
The correlation diagram clearly indicates that the molecular orbital energy levels changes
as the H3 changes from linear to cyclic (equilateral triangle) structure. In the case of
linear H3 the overlap between H1 and H3 is minimal, where as in the case of cyclic H3 the
overlap is substantial. This will bring the lowest MO (bonding) and the highest MO
(antibonding) down in energy. At the same time, the non-bonding MO (middle one) will
go up in energy, leading to a degenerate set of levels. Thus H3+ (two electrons) will be
triangular.
Construction of molecular orbitals based on the bond and group
orbitals: C-H bond orbitals
C
H
CH
C
H
C
H
CH
C-C bond orbitals
C
C
C
CC
CC
C
C
C
C
C
C
C
CC
C
CC
C
CH2 group orbitals
H
H
+
C
H
C
C
H
H
H
H
CH2
H
+
C
C
H
H
H
H
C
H
CH2
C
H
H
CH2
H
H
+
C
C
H
C
H
H
H
CH2
C
H
H
n
H
CH3 group orbitals
+
2S + 2Px ()
2Px
2S
CH3
+
2S + 2Px ()
1S + 1S + 1S
 CH3
CH3
 CH3
+
+
2Py
[ 1S - 1/2 (1S + 1S) ] 2Pz
1S - 1S
 CH3
 CH3
Construction of ethane (C2H6) molecular orbitals using C-C bond and
CH3 group orbitals: -
CH3
CH3
CH3
CH3
n
n
CH3
CH3
CH3
CH3
Construction of acetylene (C2H2) molecular orbitals using C-H bond
orbitals: -
H
H
C
C
H
CH
C
H
C
H
H
CH
Please refer to the Text Books listed for the course, especially 4 and 5