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5.80 SmallMolecule Spectroscopy and Dynamics
Fall 2008
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View Full Document 5.80 Lecture #3
2
Fall, 2008
Page 1 of 9 pages
Lecture #3
2
: The H
2
CO A
~
1
A
2
←
X
~
1
A
1
Transition
H
2
CO was 1st (asymmetric top) polyatomic electronic transition to be rotationally analyzed.
G. H. Dieke and G. B. Kistiakowsky
Phys. Rev.
45
, 4 (1934).
It is more complicated than linear HCCH because many values of the K
a
rotational quantum number can
have significant thermal population in the
V
′′
= 0 level. For a linear molecule in a
∑
state, K
a
= 0, and
= 0 in
V
=0.
The S
1
←
S
0
transition in H
2
CO
* is electronically forbidden in C
2v
(a)
[(x, y, z) = (c, b a)]
* the excited state is expected and appears to be non planar  hence C
2v
may not be relevant.
* “quasiplanar” molecule – inversion barrier is low resulting in
staggering
of bending levels
* 3 distinct transition mechanisms, each with its own selection rules, contribute to A
~
—X
~
system.
Outline:
i. classification of orbitals and normal modes
ii. what do we expect (geometry and vibrational structure of S
1
)
iii. “vibronically” rather than electronically allowed system – false origin, promoter mod
iv. surprise in hot band spectrum – peculiar spacings in upper state outofplane bend
v. low barrier to inversion through planarity
Next time:
Vibronic Coupling (beyond FranckCondon)
Body fixed axis system:
y
* *
0
b
a
z
x
(c, b, a) = (x, y, z) specific
correspondence
inertial
point group
axes
axis labels
Molecular orbitals from atomic orbitals:
IP
CO
14.014eV
IP
H
13.595
∴
H atom 1s orbitals lie above CO HOMO
IP
C
11.264
IP
O
13.614
∴σ
2s,
π
2p are polarized toward O
5.80 Lecture #3
2
C
2v
E
C
2
(z)
σ
v
(xz)
σ
v
(yz)
A
1
1
1
1
1
A
2
1
1
–1
–1
B
1
1
–1
1
–1
B
2
1
–1
–1
1
Fall, 2008
Page 2 of 9 pages
*** see p. 2002 ***
T
z
= a
“Report on Notation”
R
z
z is axis of symmetry
T
x
= c, R
y
T
y
= b, R
x
x
⊥
to plane
Figure 1: Correlation of the orbitals of planar H
2
XY to those of the united molecule Y
2
and to those of 2H + XY.
The
variable along the abscissa is the XH distance. Note that at the left, since Y
2
is homonuclear, the orbitals are
σ
g
,
u
,
π
g
,
π
u
while at the right, since XY is heteronuclear, the
g
,
u
characteristic does not strictly apply. However, just as at the left, the
orbitals
2s
are mixtures (but not 50:50 mixtures) of the 2
s
orbitals of X and Y and similarly for the other XY orbitals. The
order of
π
(u)
2
p
and
σ
(g)
2
p
is reversed at the right compared to the left in accordance with the situation in CO as compared to
O
2
(see Herzberg, Vol. I, p. 346). At the left, the splitting of
π
u
and
π
g
into b
2
(
π
inplane) and b
1
(
π
⊥
plane) corresponds to
breaking the cylindrical symmetry of the C + H + H = O united atom.
σ
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.
 Spring '04
 RobertField
 Mole

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