1. Analysis of bands of the 405 nm electronic transition of C3Ar
Yen-Chu Hsu, Yi-Jen Wang
Institute of Atomic and Molecular Sciences,
Academia Sinica, Taipei, Taiwan
Anthony Merer
Department of Chemistry, University of
British Columbia, Vancouver, Canada

2. C3 Important in astrophysics:- “Comet bands” at 405 nm (A1Pu – X1S+g).~
Important in astrophysics:-
“Comet bands” at 405 nm (A1Pu – X1S+g).
Interstellar medium
The A1Pu state has an exceptionally large splitting
between its Born-Oppenheimer components. ~
C3 can be made in the lab by 193 nm photolysis
of allene or propargyl bromide. Under very cold
conditions, with excess of Ar, C3Ar is formed.

3. Laser-induced fluorescence spectra of C3Ar, near the
100
Laser-induced fluorescence
spectra of C3Ar, near the
bands of the A1Pu – X1S+g
transition of C3 ~
04-0
Four bands have been
analyzed rotationally
02+0
C3 band
02-0
000
Upper state vibrational
quantum numbers of
the “parent” band of C3
DE / cm-1

4. A type
C type
(1A1 – 1A1)
(1B1 – 1A1)

5. Simulation of the 04-0 C type band of C3Ar Calculated spectrum:
FWHM = cm-1
T=1.7 K
Observed spectrum
K=1-0
K=3-2
K=1-2

6. Structure of the 04-0 C type band of C3Ar Calculated spectrum:
FWHM = cm-1
T=1.7 K
rQ0
Observed spectrum
K=1-0
* = impurity line
rP0
rR0 *
K=3-2
K=1-2 *
pP2
pQ2
rQ2
rR2 * * *

7. Nuclear spin statistics
Rotational analysis shows that only even-K levels
are present in the lower state. C
This means that the molecule
contains two equivalent atoms
with zero nuclear spin
(i.e. carbon atoms).
We deduce that the
molecule is T-shaped,
or nearly so. Ar

8. Simulation of the 04-0 A type band of C3Ar Observed spectrum
Calculated spectrum:
FWHM = cm-1
T=1.7 K

9. Structure of the 04-0 A type band of C3Ar Observed spectrum
qQ2
Observed spectrum
Calculated spectrum:
FWHM = cm-1
T=1.7 K
qR0 + qR2
qP0 + qP2
pert
pert

10. The anomalous upper state constants show that the
two upper levels are somehow perturbing each other.
It turns out that this is an angular momentum effect.
The degeneracy of the 04-0, P vibronic level of C3
is lifted in the lower symmetry of the C3Ar complex.
There are two consequences:-
The P level splits into A1 and B1 vibronic levels.
The angular momentum of the P level does not
go away in the lower symmetry, but reappears as
A- and B-axis Coriolis coupling between the A1
and B1 vibronic levels.

11. Energy level calculation
Following Howard et al and Hougen et al, the
angular momentum of the C3, P state is projected
onto the principal axis system (a,b,c) of the complex. z q a b x Pz v Ar C
Pa = -Px cos q + Pz sin q
Pb = Px sin q + Pz cos q
(Only Pz is non-zero)
Substitute Pa and Pb into the rotational Hamiltonian,
H = A(Ja-Pa)2 + B(Jb-Pb)2 + C(Jc-Pc)2

12. Some details The relevant parts of the rotational Hamiltonian are
H = AJa2 + BJb2 + CJc AJaPz sin q -2BJbPz cos q
rigid rotator
Coriolis terms
A “quenching” operator is needed, to split the P state:
< ±P; JK | H | ∓P; JK> = ½e
For maximum factorization the basis set is
|P±; JK±> = 2-½[|P> ± |-P>]  2-½[|J K> ± |J -K>]
Not surprisingly, the levels transform correctly under
C2v if sin q = 0 (i.e. an exactly T-shaped complex).
In practice the sin q term must be retained to allow for
averaging over the large amplitude bending motions.

13. Ground state tilt angle
The A rotational constant of C3Ar should be the same
as the B rotational constant of free C3, assuming the Ar
atom does not affect the bonding in the C3 part.
A(C3Ar) is larger than B(C3)
cm-1
cm-1 C
12.3o C
Therefore the top of the
T appears to be tilted. C
With these values of A and B,
the tilt angle is found to be 12.3o Ar

14. Structure of C3Ar
Since C3 itself is very floppy (n2 = 63 cm-1), another
possibility is that the C3 part of the complex is bent,
as suggested by ab initio calculations.
If so, is the complex planar? The inertial defect,
D″ = Ic-Ib-Ia, is not well determined
because no K″=1 levels exist.
However D″ ≈ 0.12 amu Å2
suggests that C3Ar is planar.
1.277 Å C C C
77o
3.813 Å
A structure that fits the
observed constants is Ar

15. Comparison with other molecules
Microwave and IR spectra have given data for
various similar molecules.
van der Waals
bond length
Tilt angle
Ar C3
3.81 Å
12.3o
Ar CO2
3.49
8.1
Ar N2O
3.46
7.1
7.5
Ar OCS
3.54
Ar C2H2 30
4.03

16. Intramolecular vibrational redistribution (IVR)
For the lowest excited states, excitation of every C3Ar
band near a given C3 band results in emission at the
same wavenumbers.
D0′
D0″
C3 band X ~ A
IVR
It appears that IVR
occurs to the lowest
level of the local
potential well.
The difference in the
well depths (D0′ - D0″)
can be determined.
It depends on v ′(C3)