1
5.61 Physical Chemistry
Lecture #31±
HÜCKEL
MOLECULAR
ORBITAL
THEORY
In
general,
the
vast
majority
polyatomic
molecules
can
be
thought
of
as
consisting
of
a
collection
of
twoelectron
bonds
between
pairs
of
atoms.
So
the
qualitative
picture
of
σ
and
π
bonding
and
antibonding
orbitals
that
we
developed
for
a
diatomic
like
CO
can
be
carried
over
give
a
qualitative
starting
point
for
describing
the
C=O
bond
in
acetone,
for
example.
One
place
where
this
qualitative
picture
is
extremely
useful
is
in
dealing
with
conjugated
systems
–
that
is,
molecules
that
contain
a
series
of
alternating
double/single
bonds
in
their
Lewis
structure
like
1,3,5hexatriene:
Now,
you may
have
been
taught
in
previous
courses
that
because
there
are
other
resonance
structures
you
can
draw
for
this
molecule,
such
as:
that
it
is
better
to
think
of
the
molecule
as
having
a
series
of
bonds
of
order
1
½
rather
than
2/1/2/1/…
MO
theory
actually
predicts
this
behavior,
and
this
prediction
is
one
of
the
great
successes
of
MO
theory
as
a
descriptor
of
chemistry
.
In
this
lecture,
we
show
how
even
a
very
simple
MO
approximation
describes
conjugated
systems.
Conjugated
molecules
of
tend
to
be
planar,
so
that
we
can
place
all
the
atoms
in
the
xy
plane.
Thus,
the
molecule
will
have
reflection
symmetry
about
the
zaxis:
z
Now,
for
diatomics,
we
had
reflection
symmetry
about
x
and
y
and
this
gave
rise
to
π
x
and
π
y
orbitals
that
were
odd
with
respect
to
reflection
and
σ
orbitals
that
were
even.
In
the
same
way,
for
planar
conjugated
systems
the
orbitals
will
separate
into
σ
orbitals
that
are
even
with
respect
to
reflection
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2
5.61 Physical Chemistry
Lecture #31±
and
π
z
orbitals
that
are
odd
with
respect
to
reflection
about
z.
These
π
z
orbitals
will
be
linear
combinations
of
the
p
z
orbitals
on
each
carbon
atom:
z
In
trying
to
understand
the
chemistry
of
these
compounds,
it
makes
sense
to
focus
our
attention
on
these
π
z
orbitals
and
ignore
the
σ
orbitals.
The
π
z
orbitals
turn
out
to
be
the
highest
occupied
orbitals,
with
the
σ
orbitals
being
more
strongly
bound.
Thus,
the
forming
and
breaking
of
bonds
–
as
implied
by
our
resonance
structures
–
will
be
easier
if
we
talk
about
making
and
breaking
π
bonds
rather
than
σ
.
Thus,
at
a
basic
level,
we
can
ignore
the
existence
of
the
σ
orbitals
and
deal
only
with
the
π
orbitals
in
a
qualitative
MO
theory
of
conjugated
systems.
This
is
the
basic
approximation
of
Hückel
theory,
which
can
be
outlined
in
the
standard
5
steps
of
MO
theory:
1)
Define
a
basis
of
atomic
orbitals.
Here,
since
we
are
only
interested
in
the
π
z
orbitals,
we
will
be
able
to
write
out
MOs
as
linear
combinations
of
the
p
z
orbitals.
If
we
assume
there
are
N
carbon
atoms,
each
contributes
a
p
z
orbital
and
we
can
write
the
µ
th
MOs
as:
N
π
µ
=
∑
c
i
µ
p
z
i
i
=
1
2)
Compute
the
relevant
matrix
representations.
Hückel
makes
some
radical
approximations
at
this
step
that
make
the
algebra
much
simpler
without
changing
the
qualitative
answer.
We
have
to
compute
two
matrices,
H
and
S
which
will
involve
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 Spring '08
 greenwood
 Calculus, Physical chemistry, Chemical bond, Huckel, pz orbitals

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