Delocalized /Molecular Orbitals
Delocalized Orbitals;
Bonding and Antibonding MOs
●  This
is an alternative to the “localized
orbital” model.
●  Slightly
more complicated
– Better at explaining bonding in some
molecules, especially those where
antibonding orbitals are filled
➼  Very often, either model works; in such
cases the easiest is often preferable.
CHEM 107
T. Hughbanks
Why another model?
●  Localized
orbital picture is clumsy or
completely fails to explain some
observations, for example,
– Resonance structures are clumsy (a “fixup” for Lewis structures)
– Some magnetic properties
●  Also, localized picture is qualitative - can’t
predict bond strengths, etc. Molecular
orbital theory is the most common starting
point for quantitative treatments of bonding.
Diamagnetism of N2 vs.
Paramagnetism of O2
liquid O2
O2 — “Lewis diagram” failure
●  Lewis
structure is simple:
.. ..
O
..
O
..
●  No
unpaired electrons, no formal
charges; seems to be a “good” structure
●  Problem:
O2 is paramagnetic (has
unpaired electrons)
Paramagnetism
●  Magnetic
properties of electrons lead to
magnetic properties of molecules (just
like for atoms).
●  Paramagnetism implies the presence of
one or more unpaired electrons.
➽ Need a improved theory of the bonding
in O2 to explain its magnetism.
Molecular Orbitals
●  Basic
premise of this model is to merge
atomic orbitals to make completely new
orbitals which can not be assigned to a
particular atom.
●  Contrast with localized orbital picture,
in which an electron pair is either
localized in a bond or on one atom in a
lone-pair orbital.
Delocalized Orbitals: H2
●  Start
with simplest molecule
●  Combine 1s atomic orbitals from 2 H atoms
●  2 possible combinations:
Add orbitals (“in phase”).
Constructive interference
→ “bonding orbital”
Subtract orbitals (“out of phase ”).
Destructive interference
→ “antibonding orbital”
H2 : the simplest covalent bond
• Bonding and antibonding sigma MO’s are
formed from 1s orbitals on adjacent atoms.
antibonding
molecular
orbital
bonding
molecular
orbital
Nature of the H-H σ bond
Schematic diagram
Energy
antibonding orbital
bonding orbital
●  We
can fill orbitals and write electron
configurations just like for an atom.
Bond Order, H2
# of Bonding electrons - # antibonding electrons
2
Energy
BO =
If the elecrons are all paired,
BO = # of Bonding pairs - # antibonding pairs
• Electrons in bonding molecular orbitals add
stability.
• Electrons in antibonding molecular orbitals
reduce stability.
●  Bond
order =
1/2 (# bonding e-’s - # antibonding e-’s)
●  For H2: bond order = 1
Energy
He2?
What happens to a H2 molecule
if one of the electrons is excited
to the anti-bonding orbital?
Original BO =
↓
σ*1s
1s
●  For
He2: bond order = 0 — He2 is not stable
p orbitals → σ, π orbitals
●  Molecules
with valence electrons in p
orbitals are slightly more complicated.
– Need to form both σ and π orbitals
●  As in localized orbital picture,
– σ orbitals from “head-on” mixing
– π orbitals from “side-on” mixing
●  Form bonding and antibonding orbitals
↑
σ1s
excited state H2
σ*1s
1s
H-atom
2−0
=1
2
1s
New BO =
1− 1
=0
2
↑↓
σ1s
ground state H2
hν
1s
H-atom
Energy
2nd Row molecules like N2, O2, etc.
Sideways overlap of atomic 2p orbitals that lie in the same
direction in space give π-bonding and antibonding MOs.
2nd Row molecules like N2, O2, etc.
N2?
●  No
unpaired electrons
Energy
is
(1σ)2(1σ*)2(2σ)2 (π)4
●  Bond Order = 3
Energy
●  Configuration
●  diamagnetic
(nonmagnetic)
●  Lewis
O2?
Localized & Delocalized Orbitals
●  Configuration
●  Two
unpaired electrons
(recall Hund’s rule)
diagram:
●  Paramagnetic!
●  2
Energy
is
(1σ)2(1σ*)2(2σ)2 (π)4 (π*)2
●  Bond Order = 2
●  Lewis
diagram :N≡N:
Models, NOT 2 kinds of molecules
●  The
Lewis model is fairly simple and
explains some observed properties, but
is not complete enough to explain other
properties (like paramagnetism of O2).
Examples
●  What
are the bond orders and number
of unpaired electrons in
F2?
O2– ?
NO ?
Energy
2nd Row molecules like N2, O2, etc.
An Old Exam Question
●  The
ionization energy (IE) of O2 is smaller than
the ionization energy of atomic oxygen (1314
kJ/mol vs. 1503 kJ/mol). The IE for N2 is
larger than the ionization energy of atomic
nitrogen (1503 kJ/mol vs. 1402 kJ/mol).
●  Explain the difference between these two cases
using the electron configurations (and MO
diagrams) for the diatomic molecules.
●  Hint: Compare the nature of the electrons lost
for atoms vs molecules in both cases!