Week 6 F - Vibra&onal
modes
of
SiH2Cl2
...

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Unformatted text preview: Vibra&onal
modes
of
SiH2Cl2
 We
now
have:‐
 
two
stretching
modes
of
the
SiCl2
group
with
symmetry
A1
and
B2
 
two
of
the
SiH2
group
with
symmetry
A1
and
B1
 Symmetry
species
of
vibra&ons
are:‐
 
4A1
+
A2
+
2B1
+
2B2
 The
remaining
five
modes
must
be
deforma&ons
(angle
bending
vibra&ons)
 As
with
stretches,
we
must
treat
symmetry‐related
atoms
together
 
E 
C2 
σxz 
σyz
 
+1 
+1 
+1 
 
+1 From
the
character
table,
this
 belongs
to
the
symmetry
 species
A1
 We
call
the
mode
of
vibra&on
 δsym
SiCl2
(or
SiCl2
scissors)

 z
 y
 x
 
E 
C2 
σxz 
σyz
 
+1 
+1 
+1 
 
+1 From
the
character
table,
this
 belongs
to
the
symmetry
 species
A1
 We
call
the
mode
of
vibra&on
 δsym
SiH2
(or
SiH2
scissors)
 z
 y
 x
 
E 
C2 
σxz 
σyz
 
+1 
‐1 
+1 
 
‐1 From
the
character
table,
this
 belongs
to
the
symmetry
 species
B1
 We
call
the
mode
of
vibra&on
 ω
SiH2
(or
SiH2
wag)
 z
 y
 x
 
E 
C2 
σxz 
σyz
 
+1 
‐1 
‐1 
 
+1 From
the
character
table,
this
 belongs
to
the
symmetry
 species
B2
 We
call
the
mode
of
vibra&on
 ρ
SiH2
(or
SiH2
rock)
 z
 y
 x
 
E 
C2 
σxz 
σyz
 
+1 
+1 
‐1 
 
‐1 From
the
character
table,
this
 belongs
to
the
symmetry
 species
A2
 We
call
the
mode
of
vibra&on
 τ
SiH2
(or
SiH2
twist)
 x
 y
 Vibra&onal
modes
of
SiH2Cl2
 Overall,
we
now
have:‐
 
two
stretching
modes
of
the
SiCl2
group 
 
 
 

 
A1
+
B2
 
two
of
the
SiH2
group 
A1
+
B1
 
 
 
 
 
 
 
 
five
deforma&on
modes 
 
 
 
 
 
 

 
2A1
+
A2
+
B1
+
B2
 Together,
these
account
for
all
the
modes
we
expect:
 
 

4A1
+
A2
+
2B1
+
2B2
 IR
and
Raman
spectroscopies
 When
monochroma&c
radia&on
is
incident
upon
a
sample
then
this
light
will
interact
with
the
 sample
in
some
fashion.
It
may
be
reflected,
absorbed
or
scaTered
in
some
manner.

 IR
Spectrography
‐
Absorp&on
 I0(ν)
 Laser
 I(ν)
 Sample
 detector
 Raman
Spectrography
‐
ScaTering
 Sample
 ν0
 Laser
 ν0 ‐
Rayleigh
 ν0 ± νΜ ‐
Raman
 detector
 Selec&on
rules
for
Infrared
(IR)
or
 Raman
ac&ve
mode
of
vibra&on
 •  For
a
mode
of
vibra&on
to
be
IR
ac&ve,
it
must
give
rise
 to
a
change
in
the
molecular
electric
dipole
moment.
 •  For
a
mode
of
vibra&on
to
be
Raman
ac&ve,
it
must
 give
rise
to
a
change
in
the
polarizability
of
the
 molecule.
 –  Polarizability
is
the
ease
with
which
the
electron
cloud
 associated
with
the
molecules
is
distorted.
 •  Rule
of
mutual
exclusion:
(ONLY
FOR
 CENTROSYMMETRIC
MOLECULES,
that
contains
a
 centre
of
symmetry)
 –  Vibra&ons
that
are
IR
ac&ve
are
Raman
inac&ve
and
vice
 versa.
 How
can
we
use
Character
table
to
determine
whether
a
 par&cular
mode
of
vibra&on
is
IR
or
Raman
ac&ve
 •  If
the
symmetry
label
(e.g.
A1,
B1,
E)
of
a
normal
 mode
of
vibra&on
is
associated
with
x,
y
or
z
in
the
 character
table,
then
the
mode
is
IR
ac&ve.
 •  If
the
symmetry
label
(e.g.
A1,
B1,
E)
of
a
normal
 mode
of
vibra&on
is
associated
with
a
product
term
 (e.g.
x2
or
xy)
in
the
character
table,
then
the
mode
 is
Raman
ac&ve.
 Vibra&onal
modes
of
SiH2Cl2
 Overall,
we
now
have:‐
 
two
stretching
modes
of
the
SiCl2
group 
 
 
 

 
A1
+
B2
 
two
of
the
SiH2
group 
A1
+
B1
 
 
 
 
 
 
 
 
five
deforma&on
modes 
 
 
 
 
 
 

 
2A1
+
A2
+
B1
+
B2
 Together,
these
account
for
all
the
modes
we
expect:
 
 

4A1
+
A2
+
2B1
+
2B2
 Both
IR
and
Raman
Ac&ve
 •  Use
IR
to
differen&ate
between
linear
and
bent
 molecules.
(different
#
of
observed
absorp&ons).
 SO2
 •  •  •  CO2
 Point
group:
C2v.
 •  Point
group:
D∞h.
 #
of
degrees
of
vibra&onal
freedom
=
 •  #
of
degrees
of
vibra&onal
freedom
=
 3n‐6
=
3.
 3n‐5
=
4.
 Three
fundamental
modes
of
vibra&on.
 •  Four
fundamental
modes
of
vibra&on.
 same
energy
therefore
 degenerate
 Using
Character
table
 •  For
the
symmetric
stretch
of
the
molecule,
 –  which
vectors
are
led
unchanged
by
the
symmetry
 elements
 E
 C2
 σv(xz)
 σv’(yz)
 1
 1
 1
 1
 match
the
row
for
the
symmetry
type
A1.
 Using
Character
table
 •  For
the
asymmetric
stretch
of
the
molecule,
 –  which
vectors
are
led
unchanged
by
the
symmetry
 elements
 E
 C2
 σv(xz)
 σv’(yz)
 1
 ‐1
 ‐1
 1
 match
the
row
for
the
symmetry
type
B2.
 SO2
has
3
(3n‐6)
degrees
of
vibra&onal
freedom
 •  a
bending
mode
(change
in
the
O‐S‐O
bond
 angle).
 •  Effect
of
each
symmetry
opera&on
of
C2v
on
 bond
angle.
 E
 C2
 σv(xz)
 σv’(yz)
 1
 1
 1
 1
 Scissoring
mode
has
A1
symmetry
 For
SO2
 •  SO2
has
A1
and
B2
normal
modes
of
vibra&on.
 •  A1
modes
are
both
IR
and
Raman
ac&ve.
 •  same
for
B2.
 A1
 B2
 A1
 C3v
vs.
D3h
molecules
 •  IR
able
to
differen&ate
XY3
molecules
with
C3v
 or
D3h
symmetry.
 •  IR
spectra
D3h
:
3
absorp&on
bands.
 •  IR
spectra
C3v
:
4
absorp&on
bands.
 •  Even
with
T
shaped
molecules
(ClF3)

 XY6
molecules
with
Oh
symmetry
 •  3x7
‐
6
=
15
degrees
of
vibra&onal
freedom.
 •  Only
1
IR
ac&ve
vibra&ons
(T1u)
 A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u 
E 
1 
1 
2 
3 
3 
1 
1 
2 
3 
3 
8C3 

1 
1 
‐1 
0 
0 
1 
1 
‐1 
0 
0 
6C2 

1 
‐1 
0 
‐1 
1 
1 
‐1 
0 
‐1 
1 
6C4 

1 
‐1 
0 
1 
‐1 
1 
‐1 
0 
1 
‐1 
3C2
=(C4)2
i 



1 
 
1 
1 
 
1 
2 
 
2 
‐1 
 
3 
‐1 
 
3 
1 
 
‐1 
1 
 
‐1 
2 
 
‐2 
‐1 
 
‐3 
‐1 
 
‐3 
6S4 
1 
‐1 
0 
1 
‐1 
‐1 
1 
0 
‐1 
1 
8S6 
1 
1 
‐1 
0 
0 
‐1 
‐1 
1 
0 
0 
3σh 
1 
1 
2 
‐1 
‐1 
‐1 
‐1 
‐2 
1 
1 
6σd 
1 
‐1 
0 
‐1 
1 
‐1 
1 
0 
1 
‐1 
linear,rota>ons 
 
 
 
 
 
 

 
 
 
 
 
(Rx,
Ry,
Rz) 
 
 
 
 
 
 
 

 
 
 

 
 
 

 
(x,
y,
z) 
 

 
 
 

 
quadra>c
 
x2+y2+z2 

 

 
(2z2‐x2‐y2,
x2‐y2)
 

 
(xz,
yz,
xy) 

 ...
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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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