Week 4 M -...

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Unformatted text preview: Reflec%on
through
a
plane
of
symmetry
 (mirror
plane)
 •  Plane
of
symmetry.
Denoted
by
σ.
 •  If
the
plane
is
perpendicular
to
the
main
axis
of
 rota%on
Cn
then
it
is
labeled
σh.
(h
for
horizontal)
 •  If
the
plane
contains
the
principal
axis
of
rota%on
 then
it
is
labeled
σv.
(v
for
ver%cal)


 •  Dis%nguish
between
σv
using
prime
marks
(σv’).
 •  σv’
label
refers
to
the
plane
in
which
the
molecules
 lies.

 •  Special
type
of
σ
plane,
σd
contains
the
principal
 rota%on
axis
but
bisects
the
angle
between
two
 adjacent
C2
axes.
(d
for
dihedral).
 H2O
 XeF4
square
planar
 Use
of
the
prime
mark
for
the
Cn
 •  Principal
axis
:

 –  Axis
of
highest
molecular
 symmetry
(highest
value
of
n)
 •  Single
prime
(Cn’)
indicates
 that
the
axis
passes
through
 several
atoms
of
the
 molecule.
 •  Double
prime
(Cn”)
indicates
 that
it
passes
between
the
 outer
atoms.
 Use
of
the
prime
mark
for
the
σ
 •  σv
label
refers
to
the
plane
in
 which
the
molecules
lies.
 •  σd
contains
the
principal
rota%on
 axis
but
bisects
the
angle
 between
two
adjacent
C2
axes
 Reflec%on
through
a
centre
of
symmetry
 (inversion
centre).
 •  If
reflec%on
of
all
parts
of
a
molecule
through
 the
centre
of
the
molecule
produces
an
 indis%nguishable
configura%on.
(denoted
i).

 n‐fold
improper
rota%on
axis

 •  Rota%on
about
an
axis,
followed
by
reflec%on
 through
a
plane
perpendicular
to
this
axis.
 Denoted
Sn.
 •  Example
CH4.
 Iden%ty
operator.
 •  Simplest
operator.
Denoted
E.
leaves
the
 molecule
unchanged.
 Successive
opera%ons
 •  C33
=
E.
 •  C32
clockwise
same
as
C3
counterclockwise
 •  Improper
rota%on
axis:
S3
=
C3
x
σh.
 Example
BCl3
vs
PCl3.
 •  What
symmetry
elements
do
BCl3
and
PCl3
(a)
have
 in
common
and
(b)
not
have
in
common.
 •  (a)
BCl3
and
PCl3
have
in
common
E,
C3
and
3σv.
 •  (b)
BCl3
has
σh,
3C2
and
S3.
 Point
Groups
 •  Describing
molecules
in
terms
of
their
respec%ve
 point
groups
provides
informa%on
about
all
the
 symmetries
elements.
 •  Number
and
nature
of
the
symmetry
elements
of
 a
given
molecule
are
denoted
by
its
point
group.
 •  Either
C,
D
groups
or
special
groups:
tetrahedral,
 octahedral
and
icosahedral.
 Characteris%c
symmetry
elements
of
some
important
classes

 Point
 Characteris1c
symmetry
elements
 Group
 Comments
 C1
 E,
C1
 Cs
 E,
one
σ
plane
 Ci 
 E,
inversion
centre
 Cn
 E,
one
principal
n‐fold
axis
 S n
 Only
Sn
(n
even,
n≠2)
 Cnv
 E,
one
principal
n‐fold
axis,
n
σv
planes
 Cnh
 E,
one
principal
n‐fold
axis,
one
σh
plane
 The
Sn
axis
necessarily
follows
from
the
Cn
 and
one
Sn‐fold
axis,
coincident
with
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 axis.
 also
a
centre
of
inversion
 Dnh
 E,
one
principal
n‐fold
axis,
n
C2
axes,
one
 σh
plane,
n
σv
planes

and
one
Sn‐fold
axis.
 The
Sn
axis
necessarily
follows
from
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 also
a
centre
of
inversion
 Dnd
 E,
one
principal
n‐fold
axis,
n
C2
axes,
n
σv
 planes
and
one
S2n‐fold
axis.
 For
n=3
or
5
there
is
also
a
centre
of
 inversion
 Td
 tetrahedral
 Oh
 octahedral
 Ih
 Icosahedral
 C1
,
Cs,
Ci
point
group
 •  Molecules
that
appears
to
have
NO
symmetry.
 •  Only
symmetry
element
C1
and
E.
 •  Cs,
one
σ
plane
CHFCl2

 Characteris%c
symmetry
elements
of
some
important
classes

 Point
 Characteris1c
symmetry
elements
 Group
 Comments
 C1
 E,
C1
 Cs
 E,
one
σ
plane
 Ci 
 E,
inversion
centre
 Cn
 E,
one
principal
n‐fold
axis
 S n
 Only
Sn
(n
even,
n≠2)
 Cnv
 E,
one
principal
n‐fold
axis,
n
σv
planes
 Cnh
 E,
one
principal
n‐fold
axis,
one
σh
plane
 The
Sn
axis
necessarily
follows
from
the
Cn
 and
one
Sn‐fold
axis,
coincident
with
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 axis.
 also
a
centre
of
inversion
 Dnh
 E,
one
principal
n‐fold
axis,
n
C2
axes,
one
 σh
plane,
n
σv
planes

and
one
Sn‐fold
axis.
 The
Sn
axis
necessarily
follows
from
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 also
a
centre
of
inversion
 Dnd
 E,
one
principal
n‐fold
axis,
n
C2
axes,
n
σv
 planes

and
one
S2n‐fold
axis.
 For
n=3
or
5
there
is
also
a
centre
of
 inversion
 Td
 tetrahedral
 Oh
 octahedral
 Ih
 Icosahedral
 The
Cn
point
groups:
 •  The
Cn
point
groups
all
have
only
a
single
rota%onal
axis
(C5
in
the
 complex
[IF6O]‐
below).

 •  They
are
further
divided
into
Cn,
Cnv,
and
Cnh
point
groups.

 •  The
Cn
point
groups
have
no
other
symmetry
elements.
 •  The
Cnv
point
groups
have
also
n
mirror
planes
containing
the
Cn
 rota%onal
axis.

 •  The
Cnh
point
groups
also
have
a
σh
mirror
plane
at
right
angles
to
 the
principal
rota%onal
axis.
 O
 C5 iodine F
 [IF6O]‐
 F
 The
Cn
point
groups:
 •  
 Cn
axis
as
their
only
symmetry
element.

 •  They
generally
resemble
propellers
which
have
the
front
and
back
different.

 C3 triphenyl phosphine viewed down C3 axis C3 C3 triphenyl phosphine viewed from the side C3 C3 Cobalt(III) tris-glycinate viewed down C3 axis C3 Cobalt(III) tris-glycinate viewed from the side Characteris%c
symmetry
elements
of
some
important
classes

 Point
 Characteris1c
symmetry
elements
 Group
 Comments
 C1
 E,
C1
 Cs
 E,
one
σ
plane
 Ci 
 E,
inversion
centre
 Cn
 E,
one
principal
n‐fold
axis
 S n
 Only
Sn
(n
even,
n≠2)
 Cnv
 E,
one
principal
n‐fold
axis,
n
σv
planes
 Cnh
 E,
one
principal
n‐fold
axis,
one
σh
plane
 The
Sn
axis
necessarily
follows
from
the
Cn
 and
one
Sn‐fold
axis,
coincident
with
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 axis.
 also
a
centre
of
inversion
 Dnh
 E,
one
principal
n‐fold
axis,
n
C2
axes,
one
 σh
plane,
n
σv
planes

and
one
Sn‐fold
axis.
 The
Sn
axis
necessarily
follows
from
the
Cn
 axis
and
σh
plane.
For
n=2,
4
or
6
there
is
 also
a
centre
of
inversion
 Dnd
 E,
one
principal
n‐fold
axis,
n
C2
axes,
n
σv
 planes

and
one
S2n‐fold
axis.
 For
n=3
or
5
there
is
also
a
centre
of
 inversion
 Td
 tetrahedral
 Oh
 octahedral
 Ih
 Icosahedral
 Some
C2v
molecules:
 C2 σv P C2 S
 σv Phosphorus iodotetrafluoride (PF4I) σv C
 σv sulfur tetrafluoride (SF4) C2 σv σv carbonyl chloride (COCl2) ...
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This note was uploaded on 10/03/2011 for the course CHEM 113A taught by Professor Professornotknown during the Spring '09 term at San Jose State University .

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