Transcript Columbus acetylene 2008.ppt

Anomalous structure in the higher bending
~1
vibrational levels of the A Au state of C2H2
Anthony J. Merer
Institute of Atomic and Molecular Sciences, Academia Sinica,
Taipei, Taiwan 10617
Adam H. Steeves
Robert W. Field
Department of Chemistry, Massachusetts Institute of Technology,
Cambridge, MA 02139
~1
The A Au state of C2H2
Nearly 70 vibrational levels have now been assigned,
including every possible level up to 3600 cm-1. Two
interesting features have emerged recently:
1. Occurrence of angular momentum-like
structure in the overtones of the bending
vibrations, n4 and n6.
2. Extra vibrational levels which cannot be
accommodated in the vibrational structure
~1
of the S1-trans (A Au) state.
~1
The ungerade bending vibrations of C2H2, A Au:
n4 (torsion) and n6 (in-plane cis-bend)
H+
H
-C
C
n4 (au)
torsion
764.9 cm-1
-
C
+
H
C
H
n6 (bu)
in-plane cis bend
768.3 cm-1
IR-UV double resonance experiments by Utz et al. (1993)
showed that the two bending fundamentals are nearly degenerate
and extremely strongly Coriolis-coupled (za = 0.707). They
correlate with the n5 (cis-bend, pu) vibration of the ground state.
Vibrational structures of the pure bending polyads

J=K=0 levels
DE /
cm-1
5



4
Obs
(Observed and
calculated
energy levels,
less 765.0 vB)

3

Calc
2
1
3
0
vB = v4 + v6
-
2
1
-
0
a symmetry
b symmetry
1
-
1
2
3
4
vB
5
The patterns look as though an angular momentum, , is present,
giving an energy correction DE = l2.
Expansion of the rotational Hamiltonian
Hrot = A(Ja-Ga)2 + B(Jb-Gb)2 + C(Jc-Gc)2
Rigid rotator
First order Coriolis coupling
Vibrational angular momentum
(Usually ignored, but not so here!)
~
Matrix elements of the terms in the third line, for C2H2, A, n4 and n6:
= AJa2 + BJb2 + CJc2
- 2AJaGa - 2JbGb - 2JcGc
+ AGa2 + BGb2 + CGc2
<v4 v6 | H | v4 v6> = l (v4 + v6 +2v4v6)
<v4+2 v6-2 | H | v4 v6> = - l √(v4+1)(v4+2)v6(v6-1)
where l = A(za46)2 + B(zb46)2.
(zc46 = 0)
The vibrational angular momentum results in corrections to w4 and w6,
x46 and the Darling-Dennison resonance parameter k4466:
Dw = ½ Dx46 = - ¼ Dk4466 = l = 7.06 cm-1
Note: Dk4466 = -2Dx46
Pseudo-angular momentum structure
Assume there are two harmonic vibrations with the same frequency,
coupled through the term H = AGa2 + BGb2.
For v4+v6 = 4 and 5, the matrices of H are
v4+v6 = 5
v4+v6 = 4
|40> |22> |04>
4 -√24
0
ag l -√24 12 -√24
0 -√24
4
|31> |13>
10 -6
bg
l
-6 10
Eigenvalues:
0, 4l (twice), 16l (twice)
au
and
bu
|50> |32> |14>
5 -√40
0
l -√40 17 -√72
0 -√72 13
where l = ½ x46 = - ¼ k4466
= A(za46)2 + B(zb46)2
l (twice), 9l (twice), 25l (twice)
i.e. E = w(v4+v6) + l 2
Bending overtones and local mode behaviour
The parameters k4466 and x46 are both sums of anharmonicity and
angular momentum terms. The closer the ratio k4466/x46 is to -2, the
more exactly the energy level pattern follows the pseudo-angular
momentum formula E = l 2.
Similar pseudo-angular momentum structure is also found in the
stretching overtones of H2O, etc., when the anharmonicity leads to a
suitable k1133/x13 ratio. It indicates the onset of local mode behaviour.
~
In the bending overtones of C2H2, A, the parameters k4466 and x46
arise mostly from the Ga2 terms. As a result l ≈ -¼ k4466 ≈ ½ x46 is
positive, being roughly equal to A(za46)2 + B(zb46)2. For stretching
overtones the coupling arises principally from anharmonicity and is
necessarily negative.
The patterns of pseudo-angular momentum structure are therefore
inverted in bending overtones compared to stretching overtones.
Pseudo-angular momentum structure in H2O and C2H2
~
~
C2H2, A, v4+v6=4
H2O, X, v1+v3=4
14600
14537.5
=0
E / cm-1
45400
22
14400
14318.8
14221.2
2
14200
13-
13+
E / cm-1
45363.2
45350
45361.6
14000
45239.8
45206.9
2
45171.8
0
45200
13800
13828.3
4
0404+
k1133 = -155.0, x13 = -165.8 cm-1
(Mills and Robiette, 1985)
ag
bg
45300
45250
13830.9
=4
ag
bg
ag
45150
k4466 = -51.68, x46 = 11.39 cm-1
Cis-trans isomerization
Stanton et al. (1994) calculate that cis-trans isomerization of
~
C2H2, A occurs via a half-linear transition state near 4700 cm-1.
H
178o
C
6000
C
H
E / cm-1
4700 cm-1
4000
3200 cm-1
2000
1A
2
~
(1A2 – X1S+g is forbidden)
1A
u
0
Cis
Trans
Extra bands: do they represent cis-well levels
tunnelling through the isomerization barrier?
cis
trans
They are not triplets
(no Zeeman effect)
Ab initio calculations
predict no other singlet
electronic states in this
energy region
1A
2
They have very long
lifetimes
S1
1A
u
Possible cis-well K=0 and 2 sub-bands
IR-UV double resonance via n3+n4 Q branch
46227.1 cm-1
46175.4 cm-1
P6
5
4
3
2
K=0
1 2 3 45
3 P 6 5 4 32 Q 1 2 3 4 5
5
R
P
R
5 4Q
K=2, B
5
6
46160
5
4
46180
3
2P
5
P
Q
1
K=4
7 6 5 43
1 2 3 4 5
46200
Q
R
5
4
3 7 6 54 3 2
Q
1 2 3 4 56 7
K=2
3 45 R
2 3 4 5678
R
R K=3, 3151
K=0 au & bu, B5
46220
-1
E / cm
46240
Possible cis-well K=0 and 2 sub-bands
IR-UV double resonance via n3+n4 Q branch
46175.4 cm
P6
5
4
3
2
46227.1 cm-1
-1
K=0
1 2 3 45
R
P
5
4
3 7 6 54 3 2
Q
1 2 3 4 56 7
R
K=2
If these sub-bands belong to the cis-well, the rotational
structure of the K=0 sub-band shows that they are vibrationally B2
46160
46180
46200
46220
-1
E / cm
46240
Selection rules for the S1-cis
(1A2)
~
– X bands
~
Their intensity comes from the S1-trans (1Au) – X transition,
mapped onto the S1-cis state.
Levels with
Vibrational
symmetry
A1, B1
A2, B2
K′
will be seen as
″
0, 2
1
One-photon hot bands from n4″, Pg
1
IR-UV double resonance via n3, S+u
0
0, 2
IR-UV double resonance via n3+n4, Pu
1
1
One-photon cold bands from v=0, S+g
0
Even and odd K′ levels cannot appear in the same spectrum.
A and B species can be distinguished from the rotational branch structure.
Observed possible cis-well levels, and their vibrational symmetries
A1
A2
B2
45600
46000
A1
or A1
B1
B2
46400
E / cm-1
Ab initio calculated vibrational structure of the S1 cis-well
[Stanton et al. (1994) and Ventura et al. (2003); frequencies averaged]
1
0
A1
0
6
B2
500
1
1
2
4 3
A2 A1
6
A1
1000
1 1
1 1
46 36
B1 B2
-1
E / cm
3141 32
2
1
3
4
2
6
A1 A2 A1 A1 B2
1500
Observed possible cis-well levels, and their vibrational symmetries
A1
A2
B2
45600
46000
A1
or A1
B1
B2
46400
E / cm-1
Ab initio calculated vibrational structure of the S1 cis-well
[Stanton et al. (1994) and Ventura et al. (2003); frequencies averaged]
1
0
A1
0
6
B2
500
1
1
2
4 3
A2 A1
6
A1
1000
1 1
1 1
46 36
B1 B2
-1
E / cm
3141 32
2
1
3
4
2
6
A1 A2 A1 A1 B2
1500
Observed possible cis-well levels, and their vibrational symmetries
A1
A2
45600
B2
46000
B2
E / cm-1
A1
or A1
B1
46400
Tentative assignment of the cis-well vibrational levels
x33 = -9 cm-1
T00 (cis) – T00 (trans) = 2646 cm-1; the ab initio values are 3000 – 3400 cm-1
61
B2
0
A1
31 62 41
A1 A1 A2
3161 63 4161
B2 B2 B1
21 32
A1 A1
44844 cm-1
45000
45500
46000
E / cm-1
46500
Comparison of S1 cis-well vibrational frequencies
Experimental
Tentative
optical
n2 (C-C stretch)
Ab initio
Stanton et al.
(1994)
Lischka et al.
(2003)
1514
1659
1577 cm-1
n3 (cis-bend)
781
816
812 cm-1
n4 (torsion)
892
704
860 cm-1
n6 (asym. bend)
444
441
677 cm-1
J.F. Stanton, C. Huang and P.G. Szalay, JCP, 101, 1 (1994)
E. Ventura, M. Dallos and H. Lischka, JCP, 118, 1702 (2003)
Conclusions
The contributions to x46 and k4466 arising from the Ga2 terms
in the rotational Hamiltonian outweigh the contributions from
the anharmonic force field.
Since the ratio k4466 / x46 is not far from -2, the overtones of the
bending vibrations, n4 (torsion) and n6 (in-plane bend), display
pseudo-angular momentum structure, where the levels group into
pairs roughly following the energy expression E = l 2.
A number of vibrational levels which cannot be accommodated
~
in the vibrational structure of the S1-trans (A1Au) state possibly
~1
belong to the S1-cis (A A2) state. They have long lifetimes and
no Zeeman effect.
Some possible cis-well levels have been tentatively assigned,
suggesting that the cis-well lies ~ 2650 cm-1 above the trans-well.
Potential energy curves for cis and trans-bent acetylene
Cis-bent
10
Energy
(e.V.)
8
1A
2
3A
2
1A
1D
u
1 -
3B
2
Su
3 Su
1B
6
electron
configuration
pu3 pg1
2 1A
2
3 S+
2
3B
2
3A
u
u
1B
u
3B
u
1A
3D
u
3A
4
Trans-bent
3A
u
~
A (S1)
u
u
3B
u
/ HCC
60o
40o
20o
0o
20o 40o 60o
/ HCC
MR-CISD level calculations by E. Ventura, M. Dallos and H. Lischka, JCP 118, 1702 (2003)
P.E. surface for the S1 state of acetylene
-60o
saddle
cis
trans
q′
0
saddle
saddle
linear
Q3
+60o
q
H
H
saddle
Q6
q′
Q3 (trans bend)
trans
cis
-60o
The isomerization
coordinate combines
Q3 and Q6
H
ag
C
C
0
q
+60o
after Ventura
et al. (2003)
C
Q6 (in-plane
cis bend)
bu
C
H
~ ~
Selection rule for A – X bands: K′ – ″ = ±1
One photon excitation
Gerade
vibrational
level
K′
2
1
~
A
0
IR-UV double resonance
Ungerade
vibrational
level
K′
2
1
~
A
0
UV
″
UV
″
~
X, n4 (pg)
~
X, v=0
1
0
~
X, n3+n4 (pu)
1
~
X, n3 (su+)
0
IR
~
X, v=0
0
~
C2H2, A1Au
IR-UV double resonance, via n3, J=0
33B1
2133B1
33B3
(Ungerade vibrational levels)
B = bending
1
[3 B1 = 3141 plus 3161]
31B1
1
2
3 B 2131B1
1
2B
2132B1 2 1 1
23B
32B3
1
1
3
3B
21B3
B3
51
44000
2131B3
31 51
32 51
46000
45000
47000
33
One photon excitation
34
21 32
(Gerade vibrational levels)
35B1
2232B1
2132B3
etc.
34B1
-1
E / cm
48000
21 33
11 31
32
3
43000
1
22 31
21 31
31B2 21B2
21 B2
44000
45000
4
B
35
32 B2 2131B2
33 42
46000
E / cm-1
47000
~
Ungerade K-structure of the A state of C2H2 near 46000 cm-1
bu
au
3
3 B
Calculated
au bu
1
1 B
1
bu
1
1
1
3 5
au bu
aubu
21 B 3
bu
au
bu au
bu au
B
bu
Observed
bu
aubu
K=0
K=1
K=2
au
45900
?
?
bu au
au
aubu
45800
cis-well
46000
bu
46100
bu bu au
-1
E / cm
46200
5