T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
M OLECULAR ORBITAL THEORY
I
Total number of MO = number of AO
I
Bonding lower than AO / Anti-bonding higher than AO
I
Filling the orbitals: Pauli and Hund’s rule (max Spin)
I
I
>
⇡
>
BO = 1/2(nBe
nAB
e )
42 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
T HE OVERLAP
S=
RULES: If overlap along the bond:
Z
3
i jd r
, if perpendicular: ⇡, if orbitals orthogonal: S = 0 (+sign of S)
43 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
T HE OVERLAP
S=
RULES: If overlap along the bond:
Z
3
i jd r
, if perpendicular: ⇡, if orbitals orthogonal: S = 0 (+sign of S)
44 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
M OLECULAR ORBITAL THEORY
I
Total number of MO = number of AO
I
Bonding lower than AO / Anti-bonding higher than AO
I
Filling the orbitals: Pauli and Hund’s rule (max Spin)
I
Splitting:
I
BO = 1/2(nBe
>
⇡ >
nAB
e )
45 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
H2
Bond order: BO = 1/2(nBe
nAB
e ) = 1 ) H2 exists
46 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
H E2
Bond order: BO = 1/2(nBe
nAB
e ) = 0 ) He2 not stable
47 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
L I2
Bond order:
48 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
B E2
Bond order:
49 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
B2
s-p Interaction?
50 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
B2
Hund’s rule: S max
B2 paramagnetic!
51 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
C2
C2 : double ⇡ bond
52 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
N2
N2 : triple bond (2 ⇥ ⇡ + 1 ⇥ )!
53 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
O2
O2 : double bond & paramagnetic!
54 / 77
T HE HYDROGEN ATOM
S IMPLE MOLECULES
T HE H ARTREE -F OCK METHOD
M OLECULAR ORBITAL THEORY
I
Total number of MO = number of AO
I
Bonding lower than AO / Anti-bonding higher than AO
I
Filling the orbitals: Pauli and Hund’s rule (max Spin)
I
>
⇡
>
+ s-p interaction!
I
BO = 1/2(nBe
nAB
e )
I
MO theory semi-quantitative for homonulear molecule
I
Also useful for inorganic complexes (ligand field theory)
55 / 77