1. The n17 band of C2H5D from 770-880 cm-1
ADAM M. DALY1, BRIAN J. DROUIN1, JOHN C. PEARSON1, KEEYOON SUNG1, LINDA R. BROWN1, ARLAN MANTZ2, MARY ANN H. SMITH3
1Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109
2Dept. of Physics, Astronomy and Geophysics, Connecticut College, New London, CT 06320,
3Science Directorate, NASA Langely Research Center, Hampton, VA 23681
23-Jun-15
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2. Planetary atmospheres
Motivation
Planetary atmospheres
Utilize bold and use the largest size that makes sense
A window in the ethane spectrum?
Avoiding q-branch ethane
23-Jun-15
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C2H5D
C2H6

3. Background – Infrared, Raman and Submillimeter
Correspondence table of vibrational states of ethane isotopologues
C2H6
Band Center cm-1
13CH312CH3
12C2H5D
n12(E2d)
[1]
n11
~1198 [est.]
n16(A″)
1158 [5]
n9 (A′)
1121 [5]
n 9(E1d)
[2]
n12
821.5 [4]
n17(A″)
[this work]
n11(A′)
715. [5]
n 4
[3] n6
289 [4]
n18(A″)
271.1 [6]
[1] J.M. Fernández, S. Montero,, J. Chem. Phys (2003)
[2] L. Henry, A. Valentin, W.J. Lafferty, J.T. Hougen, V.M. Devi, P.P. Das, K.N. Rao,, J. Mol. Spectrosc. 100 (1983)
[3] J.M. Fernández‐Sánchez, A.G. Valdenebro, S. Montero,. J. Chem. Phys. 91 (1989)
[4] L. Borvayeh, N. Moazzen-Ahmadi, V.M. Horneman, J. Mol. Spectrosc. 255 (2009)
[5] L.R. Posey, Jr., E.F. Barker,, J. Chem. Phys. 17 (1949)
[6] A.M. Daly, B.J. Drouin, P. Groner, S. Yu, J. Pearson,, J. Mol. Spectrosc (2015)
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4. Background Spectroscopy Assign n11= 715 cm-1 and n17 = 805 cm-1
v11= 715 cm-1
v17 = 805 cm-1
Assign n11= 715 cm-1 and n17 = 805 cm-1
in C2H5D and fit transitions to within
the resolution of the measurement
Data taken with the Bruker 125 HR
with cm path length.
Resolution cm-1
Temperature = 130 K
3v18= 726 cm-1?
Fix the units
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5. Background Spectroscopy v17 = 805 Q-branch Ka -> Ka+1 23-Jun-15
152,13←141,13
161,15←150,15
111 8 J
4←3
5←4
6←5
7←6
8←7
9←8
Ka”←Ka’
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6. Background – pure rotational
Microwave spectra of deuterated ethanes: Internal rotation
potential function and rz structure
E. Hirota, Y. Endo, S. Saito, J.L. Duncan, J. Mol. Spectrosc. 89 (1981) 285–295.
Pure a-dipole 12 pairs A/E 2 R-branch (J=3 and 4)
b-dipole 15 pairs A/E that 2 R-branch (J=2 and 3) and 13 Q-branch (Ka 2<- 1) D H
Analysis of the rotational spectrum of the ground
and first torsional excited states of monodeuterated ethane, CH3CH2D
Adam M. Daly, Brian J. Drouin, Peter Groner, Shanshan Yu, John Pearson J. Mol. Spectrosc. 307 (2015): 27-32
Measured up to 1600 GHz
Spectroscopic constants have been fit to 984 transitions in the ground state
422 transitions in the first torsional excited state (ν18)
SPFIT, ERHAM and XIAM and of the first torsional state with SPFIT and ERHAM
Looking along the c-c bond
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7. Background ISMS FE
Ground state results
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8. Background: Final fit of v18
Tunneling terms
ERHAM 
SPFIT 
2*e10 /MHz
(22)
(24)
2*e20 /MHz
0.471(16)
1.509(58) r
(81)
[ ]
b / deg
0.873(75)
[𝐴− 𝐵+𝐶 2 ]q / kHz
-402.3(76)
-640.2(85)
[ 𝐵+𝐶 2 ] q / kHz
45.3(64)
-21.99(94)
𝐵−𝐶 q /kHz
-30.9(31)
(51)
𝐴− 𝐵+𝐶 2 𝑐𝑜𝑠 2 𝜌𝜎𝐾 / kHz
0.569(46)
-33.4(16)
[ 𝐵+𝐶 2 ] 𝑐𝑜𝑠 2 𝜌𝜎𝐾 / kHz
-1.48(37) -
𝐵−𝐶 𝑐𝑜𝑠 2 𝜌𝜎𝐾 /kHz
2.83(19)
𝑑 2 𝑐𝑜𝑠 𝜌𝜎𝐾 /kHz
(19)
(36)
𝑑 2 𝑐𝑜𝑠 2 𝜌𝜎𝐾 /kHz
(37)
𝑑 2 𝑐𝑜𝑠 3 𝜌𝜎𝐾 /kHz
(21)
𝐷 𝐾 𝑐𝑜𝑠 𝜌𝜎𝐾 /kHz
.305(34)
0.286(81)
𝐷 𝐾 𝑐𝑜𝑠 3 𝜌𝜎𝐾 /kHz
-58(20)
𝐷 𝐽 𝑐𝑜𝑠 𝜌𝜎𝐾 /kHz
(49)
(27)
𝐷 𝐽𝐾 𝑐𝑜𝑠 𝜌𝜎𝐾 /kHz
(57)
0.080(31)
𝐷 𝐽𝐾 𝑐𝑜𝑠 3 𝜌𝜎𝐾 /kHz
7.5(35)
𝐻 𝐽𝐽𝐾 𝑐𝑜𝑠 𝜌𝜎𝐾 /kHz
𝐻 𝐽𝐽𝐾 𝑐𝑜𝑠 2 𝜌𝜎𝐾 /kHz
(26)
𝐻 𝐾 𝑐𝑜𝑠 𝜌𝜎𝐾 /mHz
Dab / kHz
1693.(202)
ERHAM
SPFIT
Pure Rotation
A /MHz
(10)
(17)
B /MHz
(20)
(21)
C /MHz
(20)
(19)
DJ /kHz
(24)
(10)
DJK /kHz
68.538(33)
68.469(46)
DK /kHz
241.69(12)
241.35(28)
d1 /kHz
(67)
(81)
d2 /kHz
(55)
(46)
HJ /Hz
(28) -
HJK /Hz
0.175(30)
0.158(27)
HKJ /Hz
1.53(25)
0.31(28)
HK /Hz
-8.76(134)
v18 fit
State 00: lines MICROWAVE RMS = RMS ERROR =
State 10: lines MICROWAVE RMS = RMS ERROR =
Ground state
State 00: lines MICROWAVE RMS = RMS ERROR =
State 10: lines MICROWAVE RMS = RMS ERROR =
TORSIONAL ENERGY DIFFERENCES (MHz)
ground state (A-E) = / MHz
v18 (A-E) / MHz
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9. AABS1 prediction using n18 model
Gave us hope
that the problem
could be solved
using SPFIT
1Z.Kisiel, L.Pszczolkowski, I.R.Medvedev, M.Winnewisser, F.C.De Lucia, E.Herbst, J.Mol.Spectrosc. 233, (2005)
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10. Starting point – Least squares retrieval*
Line position and intensity
for every feature found
above the noise level
from cm-1
Over 10,000 features were
Measured and fit using LSR
Covering n11, n17, C2H6 (2%)
Be specific about algorithm
*L.R. Brown, J.S. Margolis, R.H. Norton, B. Stedry, Appl. Spectrosc. 37 (1983) 287–92.
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C2H5D
C2H6

11. Building the Hamiltonian in SPFIT
The substates A and E corresponding to s=0, ±1 have differing Fourier coefficients which are 1:− : 1 2 , 1:− 1 2 :− , 1:1
for terms of powers of cosn(t),where 𝜏= 2𝑛𝜋 3 (𝜎+𝜌Κ) and n is 1,2,3 respectively.
Initial assignments were generated in the AABS program with the built in line center algorithm.
Eventually, inclusion of 5035 transitions in the model.
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12. Spectroscopic Constant
12C2H5D Hamiltonian Constants for n17 with ground state parameters fixed
Spectroscopic Constant
Ground state
n17 *
‘v’
(27)
A/ cm-1
[ ]
(13)
B/ cm-1
[ ]
(29)
C/ cm-1
[ ]
(29)
DJ / cm-1 × 106
[ ]
(36)
DJK / cm-1 × 106
[ ]
1.9877(22)
DK / cm-1 × 106
[ ]
10.182(14)
d1 / cm-1 × 109
[ ]
-30.19(10)
d2 / cm-1 × 109
[ ]
2.050(58)
HJ / cm-1 × 1012
[ ]
0.60(18)
HJK / cm-1 × 1012
[ ] -
HKJ / cm-1 × 1012
[ -]
-143.(15)
HK / cm-1 × 1012
[ ]
-441.(40)
Tunneling Constants**
e1 cos(t) / cm-1 × 103
[ ]
5.376(23)
e2 cos2(t) / cm-1 × 103
[ ]
1.513(23)
e3 cos3(t) / cm-1 × 103
0.197(22)
𝐴− 𝐵+𝐶 2 cos(t) / cm-1 × 106
[ ]
(𝐵+𝐶) 2 cos(t) / cm-1 × 106
[ ]
-0.718(53)
(𝐵+𝐶) 2 cos2(t) / cm-1 × 106
-0.606(53)
(𝐵+𝐶) 2 cos3(t) / cm-1 × 106
-0.233(46)
(𝐵−𝐶) 4 .cos(t) / cm-1 × 106
[ ]
-0.249(54)
(𝐵−𝐶) 4 . cos2(t) / cm-1 × 106
-1.973(51) r
[ ]*
[ ]
N / Nrejected by fit
5035 / 0
sfit / cm-1
sRMS
1.00
J″min ̶ J″max
0 ̶ 40
K″a min ̶ K″a max
0 ̶ 18
Uncertainty of the transitions were determined
As follows:
For line positions within two orders of magnitude of the
Strongest predicted feature: cm-1
and cm-1 if predicted weaker.
The spectrum contained many blended features
arising from C2H5D or the 2% contamination of
C2H6. The number of these features within a ±0.005 cm-1
window was multiplied by the uncertainty (n+1)
giving a total uncertainty for each line
All assigned features above the noise limit were accepted
in the model
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13. Some issues with line positions
Presence of n9 2% C2H6 in the R-branches
Presence of n11 in the P-branches
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14. Results Spectrum taken 130K Prediction made at 296K
Correct transition dipole
and partition function
needed to predict the
intensity
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15. Partition Function and transition dipole
Rotation-vibration partition function computed with the
ground and five vibrational states v18, 2v18, 3v18, v11 and v17.
Temperature (K)
Qtot
9.375
129
18.75
359
37.5
1009
75.0
130.5
2858
6871
150
8698
225
18267
296
31812
300
32721
Initial work found a transition moment
of x 10-3D.
2v18, 3v18 rotational constants taken from fit of gs and v18
Energy levels from the fit with ASTOR
n11 from our best fit to date
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16. Checking with room temp spectrum
Each lab spectrum (in black)with
the room temperature prediction
using partition function and
transition dipole with a
correction
Pathlength=20.38cm
Pressure:16.13 Torr
Temp=296K
Resolution: cm-1
Gas conditions
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17. Not everything is perfect with line position but intensity prediction is very good
Prediction in intensity and line position
Prediction in intensity, line position fit
Small ( cm-1 bias in this q-branch, Ka 0→ 1) similar in other K’s
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18. Distortion constant on the transition dipole
A value of be D was added to the dipole moment containing the term
𝑀 5 =𝑖( 𝜇 𝑐 ′ , 𝐽 𝑎 + 𝜇 𝑎 ′ , 𝐽 𝑐 /2 and coded with (state 0 is gs, 3 is n17)
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19. Conclusions
The n17 band of C2H5D has been fit to an effective Hamiltonian using SPFIT
Spectroscopic terms have been found that predict line positions and intensities.
A small but observable bias exists in the frequency residuals as a function of K
that can not accounted for in the present analysis
Future Work:
n11 fit
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20. Acknowledgements Linda R. Brown Keeyoon Sung Brian J. Drouin
John C. Pearson
Peter Groner
Arlan Mantz
Mary Ann H. Smith
Tim Crawford
California Institute of Technology
Jet Propulsion Laboratory
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