Week 6 M - Character
table
for
C2v
 • 

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Unformatted text preview: Character
table
for
C2v
 •  How
to
read
and
use
character
tables.
 Point
group
 Symmetry
elements
 Mulliken
symbols
 A,
B
indicate
non‐degenerate
 E
refers
to
doubly
generate
 T
means
triply
degenerate
 Linear,
RotaGon
 z
transforms
as
A1
 z
forms
a
basis
for
A1
 quadraGc
 z
axis
coincides
with
principal
axis
of
rotaGon
 Labels
used
with
character
tables
 Label
for
the
irreducible
representaGons
 •  symmetric
means
a
character
of
1
and
anGsymmetric
means
a
 character
of
‐1.
 •  LeLers
are
assigned
according
to
the
dimension
of
the
 irreducible
representaGon.
 •  Subscript
1
designates
a
representaGon
symmetric
to
a
C2
 rotaGon
perpendicular
to
the
principal
axis
and
subscript
2
for
 anGsymmetric.
If
there
are
no
perpendicular
C2,
then
it
is
 according
to
verGcal
plane.
 •  Subscript
g
(gerade)
designates
representaGon
symmetric
to
 inversion
and
u
(ungerade)
for
anGsymmetric
to
inversion.
 •  Single
primes
are
symmetric
to
σh
and
double
primes
are
 anGsymmetric
to
σh.

 Character
table
for
C3v
 C3v
 C3v
character
table
 •  Example
NH3
 Character
table
for
D4h
 •  #
of
symmetry
elements
:
2
x
4
x
2
=
16.
 PtCl42‐
 ProperGes
of
characters
of
Irreducible
 RepresentaGons
in
Point
groups
 ProperGes
of
characters
of
Irreducible
 RepresentaGons
in
Point
groups
 #
of
symmetry
elements
in
point
group
 •  To
idenGfy
all
the
operaGons
in
a
point
group,
the
 following
check
can
be
carried
out:
 –  Assign
1
for
C
or
S,
2
for
D,
12
for
T,
24
for
O
or
60
for
I.
 –  MulGply
by
n
for
a
numerical
subscript.
 –  MulGply
by
2
for
a
leLer
subscript
(s,
v,
d,
h,
i).
 •  Example:
 –  C3v
:
1
x
3
x
2
=
6
operaGons
(E,
2C3,
3σv).
 –  D2d
:
2
x
2
x
2
=
8
operaGons
(E,
2S4,
C2,
2C2’,
2σd).
 RepresentaGon
flow
chart
for
C2v
 Character
table
for
C3v
 •  Example
:
NH3
 •  #
of
symmetry
elements
1
x
3
x
2
=
6.
 C3v
 ProperGes
of
the
Character
for
C3v
 AddiGonal
features
of
character
tables
 •  In
character
table
2C3
indicates
2
C3
axis
in
the
same
class
leading
to
the
same
 results
(rotaGon
in
clockwise
and
counterclockwise
direcGons).
 •  In
D
group,
C2
axis
perpendicular
to
the
principal
axis
are
designated
with
 primes:
a
single
prime
if
axis
passes
through
several
atoms
and
a
double
prime
if
 axis
passes
in
between
atoms.
 •  When
mirror
plane
is
perpendicular
to
principal
axis
(i.e.
horizontal),
the
 reflecGon
is
called
σh.
Other
planes
are
labeled
σv
and
σd.
 •  
The
expression
to
the
right
of
the
character
table
indicate
the
symmetry
of
 mathemaGcal
funcGons
of
the
coordinates
x,
y
and
z
and
rotaGon
about
the
axes
 (Rx,
Ry,
Rz).
 •  Matching
the
symmetry
operaGons
with
the
top
row
of
the
character
table
will
 confirm
any
point
group
assignment.

 •  These
can
be
used
to
find
the
orbitals
that
match
the
representaGon
(i.e.
x
for
px
 and
xy
for
dxy).
 Chiral
molecules
 •  A
molecule
is
CHIRAL
if
it
is
non‐superimposable
on
 its
mirror
image.
 •  Two
mirror
images
are
known
as
opGcal
isomers
or
 enanGomers.
 •  Chiral
moleculescan
rotate
the
plane
of
plane‐ polarized
light.
OPTICAL
ACTIVITY.
 Chiral
molecules
 •  A
molecule
is
said
to
be
chiral
if
it
has
no
symmetry
 operaGon
(other
than
E),
or
if
it
has
ONLY
PROPER
 ROTATION
AXIS

 EnanGomers
 •  EnanGomers
are
 disGnguished
by
 using
Δ
and
Λ
 Only
cis‐isomer
is
chiral
 DefiniGon
and
notaGon
for
chiral
complexes
 right‐handedness
 led‐handedness
 VibraGonal
spectroscopy
 Molecular
electron
excitaGon
 ElectromagneGc
spectrum
 excitaGon
of
 molecular
valence
 electrons
 energeGc
ejecGon
 excitaGon
and
 of
core
electrons
 ejecGon
of
core
 electrons
 Molecular
vibraGon
 Molecular
rotaGon
 VibraGonal
Spectroscopy
 •  VibraGonal
spectroscopy
is
concerned
with
the
 observaGon
of
the
degrees
of
vibraGonal
 freedom.
 •  A
molecule
with
n
atoms
have
3n
degrees
of
 freedom
describing
the
translaGonal
(3),
 vibraGonal
and
rotaGonal
(3)
moGons
of
the
 molecule.
 •  How
many
vibraGonal
modes
are
there
for
a
 given
molecular
species?
 Two
classes
of
molecular
vibraGons
 •  Two distinct classes of molecular vibrations, stretching and bending. •  Stretching vibrations change the bond length while bending vibrations change the bond angle. •  These two classes may be subdivided into different types depending on how the atoms move relative to each other. –  stretching (symmetric and asymmetric) –  bending (scissoring, rocking, wagging and twisting)
 Stretching
 symmetric
stretch
 asymmetric
stretch
 Bending
 scissoring
 rocking
 wagging
 twisGng
 A
normal
mode
of
an
oscillaGng
system
is
a
paLern
of
moGon
in
which
all
parts
of
the
system
 move
sinusoidally
with
the
same
frequency.
The
modes
are
normal
in
the
sense
that
they
can
 move
independently,
that
is
to
say
that
an
excitaGon
of
one
mode
will
never
cause
moGon
of
a
 different
mode.

 Use
of
character
tables
to
idenGfy
all
the
 moGons
of
a
molecule
 Example
SiH2Cl2

 z
 y
 Character
table
 Si
 Cl1
 Cl2
 x
 
C 2 
σv(xz) 
σv(yz) 


h
=
4
 A1 
+1 
+1 
+1 
+1 


z 



x2,
y2,
z2
 
+1 
+1 
‐1 
‐1 


Rz 




xy
 B1 H2
 
E A2 H1
 C2v 
+1 
‐1 
+1 
‐1 


x,
Ry 



xz
 B2 
+1 
‐1 
‐1 
+1 


y,
Rx 



yz
 Draw
x,
y
and
z
vectors
on
all
atoms
 How
the
vectors
are
affected
by
symmetry?
 ...
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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.

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