Application of MO :
Stable Geometry
Molecular Orbital
§ Contain all information we need to know about a
molecule
§ All electrons are under the influence of all nuclei
§ MOs are obtained from linear combination of AOs
§ Symmetry adapted linear combination
§ Arrange MOs according to energy
§ AO energy, distance, overlap
§ Fill in electrons
§ Aufbau + Hund’s rule
100
HOMO & LUMO
§ Highest Occupied Molecular Orbital (HOMO)
§ Electron with the highest energy
à The most nucleophilic orbital
à Easily oxidized (reductant)
à Lewis basic site
§ Lowest Unoccupied Molecular Orbital (LUMO)
§ Empty orbital with the lowest energy
à The most electrophilic orbital
à Easily reduced (oxidant)
à Lewis acidic site 101
Molecular Orbital
LUMO
HOMO 102
How did we predict the geometry
§ For p-block element
§ The geometry of a molecule is predicted with VSEPR
103
How did we predict the geometry
§ For d-block element
§ The geometry can be predicted with Kepert model
§ modified from VSEPR, but ignores the repulsion from
non-bonding electrons
§ geometry is determined by the number of ligands
Coordination # Geometry Factors that lead to the breakdown of
(ligand) the Kepert model:
2 linear § Electronic effect
3 Trigonal planar § For d8 metals, square planar is
more common than
4 Tetrahedral
tetrahedral
5 Trigonal bipyramidal
Square pyramidal
§ Constraint ligands
6 octahedral § Ex. Porphyrin, tripodal ligands
104
Geometry of AH2 (A = 2nd row element)
§ Assuming two extreme geometries: linear & 90o bent
§ MO of linear AH2 (D∞h)
§ Atomic orbital of A:
s: A1g px,py:E1u pz:Au
§ Group orbital of 2H:
Ag Au 105
Geometry of AH2 (A = 2nd row element)
§ Assuming two extreme geometries: linear & 90o bent
§ MO of linear AH2 (D∞h)
Antibonding orbital
Nonbonding orbital
Bonding orbital
106
Geometry of AH2 (A = 2nd row element)
§ Assuming two extreme geometries: linear & 90o bent
§ MO of angular AH2 (C2v molecule on yz plane)
§ Atomic orbital of A:
s, pz: A1 px:B1 py:B2
§ Group orbital of 2H:
A1 B2 107
Geometry of AH2 (A = 2nd row element)
§ Assuming two extreme geometries: linear & 90o bent
§ MO of angular AH2 (C2v)
A
108
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953)
§ Angular coordinate
diagram
§ Correlation diagram
§ Describes how the
energy of each MO
changes as the
molecular geometry
is modified.
109
Geometry of AH2 (A = 2nd row element)
Set the H-A-H bond as z-axis --> the C2 axis of angular AH2 is x-axis
4a1 3sg
2su
2b2
1b1 1pu
3a1
x
1b2
1su
z
2sg
2a1
110
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953)
§ Obtained from theoretical calculation
111
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953)
§ Obtained from
theoretical calculation
§ The energy of the
molecule is mainly
determined by HOMO
§ If HOMO does not
change, then HOMO-1
112
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953) 3sg
4a1
§ From linear to bent 2su
§ degenerated pu splits into 2b2
nonbonding b1 and 1b1 1pu
bonding a1
3a1
§ The sigma-interaction in 1b2
1su
su is weakened in b2 2sg
2a1
§ The sigma-interaction in
sg is strengthened in a1
113
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953) 3sg
4a1
§ 1 or 2 electrons: 2su
§ Ex: H3+ (60o), LiH2+ (21o) 2b2
§ 3 or 4 electrons: 1b1 1pu
§ Ex: BeH2+ (20 or 73o), 3a1
BeH2 (180o), BH2+ (180o)
1b2
§ 5 or 6 electrons: 1su
2sg
§ Ex: BH2 (131o), CH2 (102o) 2a1
§ 7 or 8 electrons:
§ Ex: NH2 (103o), OH2 (104o)
114
Geometry of AH2 (A = 2nd row element)
§ Walsh diagram (1953)
115
Geometry of AH3 (A = 2nd row element)
Planar (D3h)
vs.
Pyramidal (C3v)
§ BH3
§ 6 e, planar
§ NH3
§ 8 e, pyramidal
116
Kepert Model
§ Modified from VSEPR, BUT ignores the repulsion from non-
bonding electrons.
§ Geometry is controlled by the number of ligand, and is
independent of the electronic configuration of the central metal.
Coordination Geometry Factors that lead to the
# breakdown of the Kepert model:
(ligand) § Electronic effect ??
2 linear § For d8 metals, square
?
3 Trigonal planar planar is more common
4 Tetrahedral than tetrahedral
5 Trigonal
bipyramidal § Constraint ligands
Square pyramidal § Ex. Porphyrin, tripodal
6 octahedral ligands 117
Distortion of ML6
§ Tetragonal elongation for octahedral ML6 complex
§ Only focused on the d-orbitals (FMOs of metal complexes)
D4h
Oh
b1g
a1g
b2g
eg 118
Distortion of ML6
§ ML6 complex with trigonal prism geometry
§ rigid bi-dentate ligands
§ d0 and d1 metals with small s-
ligand (H-, CH3-)
§ [TaMe6]-, [ZrMe6]2-, [WMe6]
§ stability can be explained
with MO theory
Ligand-based sigma-bonding MO 119
Distortion of ML5
§ Pure electrostatic repulsion predicts
the TBP to be more stable
§ main group, d0 and d10 metals
are expected to favor TBP
§ From MO, the stability
§ d1 ~ d4: TBP ≥ SP
§ d6 : TBP < SP
§ d8 ~ d10 : TBP > SP
120
Application of MO :
Reactivity
Molecular Orbital
Frontier Molecular Orbitals 122
MO of complicate molecules
§ Symmetry Adapted Linear Combination (SALC)
123
Frontier Molecular Orbital Theory
§ Frontier MOs are most likely to be involved in chemical
reaction (Kenichi Fukui, 1950’s)
§ Chemical reaction deals with redistribution of electrons
(bond breaking & forming )
§ Frontier MO:
§ Highest Occupied Molecular Orbital (HOMO)
§ Lowest Unoccupied Molecular Orbital (LUMO)
§ Reaction generally occurs between HOMO & LUMO
§ Symmetry is important. 124
Frontier Molecular Orbitals
§ Highest Occupied Molecular Orbital (HOMO)
§ Electron with the highest energy
à The most nucleophilic orbital
à Easily oxidized (reductant)
à Lewis basic site
§ Lowest Unoccupied Molecular Orbital (LUMO)
§ Empty orbital with the lowest energy
à The most electrophilic orbital
à Easily reduced (oxidant)
à Lewis acidic site 125
MO of complicate molecules
§ Ex: NH3
126
Properties of Amine
§ NR3
§ Basic, nucleophilic, reducing
§ H+ acceptor: NR3 + H+ à R3NH+
§ Electron pair donor: NR3 + Cr3+ à [Cr(NH3)6]3+
§ Nucleophile: NR3 + R’Br à R3NR’+ + Br−
§ Reductant: NR3 + NO+ à R3N•+ + NO
127
MO of complicate molecules
§ Ex: BH3
128
Properties of Borane
§ BR3: Lewis acidic, electrophilic, good electron acceptor
129
Nitration of naphthalene
§ Nitration of benzene (electrophilic substitution)
§ How about naphthalene?
8 9 1
7 2
6 3
5 10 4 130
Nitration of naphthalene
§ FMO of naphthalene
131
Frontier Molecular Orbital Theory
§ Reaction generally occurs between HOMO & LUMO
§ Symmetry is important.
§ Ex: Diels-Alder reaction
§ Thermally-allowed [4+2] cycloaddition reaction
132
Frontier Molecular Orbital Theory
§ Diels-Alder reaction
§ MO of diene & dienophile
133
Frontier Molecular Orbital Theory
§ Diels-Alder reaction
§ MO of diene & dienophile
134
Frontier Molecular Orbital Theory
§ How about [2+2]?
§ MO of alkene & alkene
135
Frontier Molecular Orbital Theory
§ How about alkene + vinyl cation?
§ MO of alkene & vinyl cation
E3 = − 1.41 β
E2 = α = 0
E1 = 1.41 β
↑↓
136
Frontier Molecular Orbital Theory
§ How about alkene + vinyl anion?
§ MO of alkene & vinyl anion
E3 = − 1.41 β
E2 = α = 0
↑↓
E1 = 1.41 β
↑↓
137
Can you answer these
questions?
Goal of General Chemistry II
C10H8
vs.
[MX4]n- vs.
Goal of General Chemistry II
Goal of General Chemistry II
C10H8
§ FMO of naphthalene
Goal of General Chemistry II
vs.
Goal of General Chemistry II
[MX4]n- vs.
Goal of General Chemistry II
§ Tetrahedral
§ Point Group Td
§ Si atomic orbitals
§ All AOs of Si are involved in Si-N sigma-bonds
Goal of General Chemistry II
§ Planar D4h
§ Si atomic orbitals (A1g, A2u, Eu)
§ Si-N sigma bond:
Γσ 4 0 0 2 0 0 0 4 2 0
è Gσ: A1g, B1g, Eu è s, --, (px, py) pz of Si is not involved
Goal of General Chemistry II
LUMO is LUMO is
s*-type orbital Non-bonding orbital
high in energy low in energy
Stable Reactive
HOMO is
s-type orbital HOMO is ligand-based orbital
low in energy Electrophilic site
Goal of General Chemistry II
Planarized silane
is much more
Lewis acidic
