Transcript NH3Columbus2013.pptx

Modeling the Spectrum of the 2n2 and
n4 States of Ammonia to Experimental
Accuracy
John C. Pearson & Shanshan Yu
Jet Propulsion Laboratory, California Institute of Technology,
Pasadena CA 91109
Molecular Spectroscopy Symposium 2013
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Motivation
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In 2010 we asked if the spectrum of 2n2/n4 could be modeled to experimental
accuracy
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The answer is NO with the previous formulation of the Hamiltonian
The same applies to all other ammonia bands lying above n2
The perils of ammonia have lead to widespread belief that we cannot fit the
LAM-inversion and small amplitude vibration
A huge effort has gone into spectroscopic potential to explain ammonia
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It is important in hot exoplanets
While this has extended assignments, assignments are still quite limited in J
There is lot of high quality data for example:
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Sasada et al., 1992, JMS 151, 33
Cottaz et al., 2000, JMS 203, 285
NH3 inversion-normal vibration quantum mechanics worked out in detail
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Full contact transformations performed
Simpler than 3-fold internal rotation
See Urban, 1988, JMS 131, 133-153 and references therein
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History
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Hamiltonian formulation fits the ground state and n2 to experimental accuracy
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Yu et al., 2010, JCP 133, 174317
Extrapolation and physical meaning of constants are known challenges, but it
does model all experimental line positions correctly
Predicted intensities of DK=3 transitions do not agree with experimental data
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Up to a factor of 100 differences!
2n2/n4 Hamiltonian accounts of l-doubling and Coriolis but otherwise it is exactly
the same formulation used in the ground state
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This applies to higher lying states as well.
Two possibilities
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Something is fundamentally wrong with our understanding of NH3
Something is wrong with the Hamiltonian as applied or as formulated
Given the amount of theory the second possibility was the starting point
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Quantum Mechanics 1/3
A relatively simple to read review of NH3 quantum mechanics was presented by
Sarka & Schrötter, JMS 179, 195-204 (1996)
H  H diag  H nondiag
Here Hdiag is diagonal in the basis of symmetric (s) and antisymmetric (a)
wavefunctions and is the standard symmetric top Hamiltonian modified with an
energy for the origin of (s) and (a) and an on-diagonal DK=6 term
H nondiag  H 3  H 4 nd  H 5  H 6 nd  ...
Here the subscript number is the power of the operators
H 3  i J 3  J 3 


 i J J  J   i J , J  J 
  J J  J , J    J  J , J 
H 4 nd   J 3  J 3 , J z
H5
H 6 nd
2
3

J
2
J
3

3


K
3

z 
2
z
3

K
3
 
3

3

3
z 
Where [A,B]+ denotes the usual anticommutator AB+BA
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Quantum Mechanics 2/3
Parameters with , j, k are represented by nondiagonal symmetric matrices
Parameters with , j, k are represented by nondiagonal antisymmetric
matrices
Ground state and n2 Hamiltonians have only  parameters i.e. only symmetric
operators
The n4 state is l-doubled (K-l is the good quantum number) resulting in 4 states
l=1,-1 (a) and l=1, -1 (s)
Sasada et al. 1992 and Cottaz et al. 2000 Hamiltonian:
– Diagonal part of Hamiltonian (DK=6 term) results in “K-type interactions” in n4
– Coriolis interactions between 2n2 and n4 DK=Dl=+/-1
– “l-type” interaction D(K-l)=0 between l=1 and l=-1 in n4
– And D(K-l)=3 interactions i.e. <a|Hnondiag|b> where <a| and <b| have different
overall a/s symmetry
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Quantum Mechanics 3/3
The <a|Hnondiag|b> part of the Hamiltonian:
i, v4l , v20 , J , K H nondiag i, v4l , v20 , J , K 
 a  1 0
s
 ,1 ,0 , J , K  1 H nondiag  ,11 ,00 , J , K 
s
a
a 0 0
a
a
a
 ,0 ,2 , J , K  2 H nondiag  ,11 ,00 , J , K   ,11 ,00 , J , K  2 H nondiag  ,00 ,20 , J , K 
s
s
s
s
 a  1 0
s
s
a
 ,1 ,0 , J , K  3 H nondiag  ,11 ,00 , J , K   ,11 ,00 , J , K  3 H nondiag  ,11 ,00 , J , K 
s
a
a
s
 a  1 0
a
a
a
 ,1 ,0 , J , K  4 H nondiag  ,00 ,20 , J , K   ,00 ,20 , J , K  4 H nondiag  ,11 ,00 , J , K 
s
s
s
s
a 0 0
s
 ,0 ,2 , J , K  3 H nondiag  ,00 ,20 , J , K
s
a
All matrix elements previously used are symmetric i.e.  terms
– Same as ground state and n2
– Should we expect this to work for 2n2 and n4?
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2n2 and n4
cm
-1
2000
a
n2
s
1500
1000
n2
DE = 284.70
5
9
8
7
6
4
l=-1
l=1
l=-1
l=1
>
>
DE = 1.10
an
s 4
a DE = 35.69 3
s
2
500
0
1
DE = 0.79
gs a
s
0
l=0
l = -1 or 1
The splitting in 2n2 is much larger than in n4 in addition the primary interaction
Involves the 2n2 (s) and the n4 l=1 (a) other interactions are more isolated.
Numbers correspond to SPFIT V labels
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Do we need antisymmetric  terms?
Only one known attempt to include  terms (Belov et al. JMS, 84, 288-304 (1988))
– Uncertainty was twice value (n2 state)
Validity of contact transformations was the subject of Sarka & Schötter JMS
179, 195-204 (1996) Paper.
– Contact transformation to remove  and  possible in very large inversion
splitting i.e. isolated state limit
– Intermediate inversion splitting contact transformation can remove  (i.e. ground
state and n2)
– Small inversion splitting contact transformation can remove 
– Contact transformations such as these must be applied to the dipole
 Not in the intensity calculations for ground state and n2
Contact transformations generally require an isolated state
– The n4 & 2n2 states are degenerate and have two orders of magnitude difference
in inversion splitting.
– Unreasonable that a single transformation would work for both states
– Perturbations can also amplify small effects
The  terms should not be ignored in n4 & 2n2
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Additional D(K-l)=3 Terms 1/2
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Between (a) and (s) in 2n2
Between (a) and (s) in n4 l=1 and l=-1
Between (a) and (s) in n4 l=1/-1 and l=1/-1
Between (s/a) and (s/a) 2n2 and n4 Dl=1 DK=4
Between (s/a) and (s/a) 2n2 and n4 Dl=-1 DK=2
The n4 mode is antisymmetric so interactions with 2n2 are s-s and a-a
Within the 2n2 or n4 the symmetric terms

H 4 nd   J 3  J 3 , J z


Results in a 23JKVV (#1 & 3) for the same l and 21JKVV (#2) for Dl=2 in SPFIT
With in 2n2 or n4 the antisymmetric terms

H 3  i J 3  J 3

Results in a 22JKVV (#1 & 3) for the same l and 20JKVV (#2) for Dl=2 in SPFIT
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Additional D(K-l)=3 Terms 2/2
The symmetric term between 2n2 and n4 Dl=1 DK=4

H 4 nd   J 3  J 3 , J z


Results in a 64JKVV term (#4)
The antisymmetric term between 2n2 and n4 Dl=1 DK=4

H 3  i J 3  J 3

Result is a 63JKVV term (#4)
The symmetric term between 2n2 and n4 Dl=-1 DK=2

H 4 nd   J 3  J 3 , J z


Results in a 62JKVV term (#5)
The antisymmetric term between 2n2 and n4 Dl=-1 DK=2

H 3  i J 3  J 3

Results in a 61JKVV term (#5)
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Previous Data Sets
Historical 2n2 and n4 band data
– Cottaz et al., 2000, JMS 203, 285
– Sasada et al., 1992, JMS 151, 33 (inc microwave lines)
– Lellouch et al., 1987, JMS 124, 333 (inc new assignments)
– Papoušek et al., 1986, J. Mol. Struct. 141, 361
– Urban et al., 1984, Can. J. Phys 62, 1775
– Weber et al., 1984, JMS 107, 405
Historical Hot band 2n2-n2 data
– D’Cunha, 1987, JMS 122, 130
– Hermanussen, Bizzarri & Baldacchini, 1986, JMS 119, 291 (inc new assignments)
– Sasada et al., 1986, JMS 117, 317
Historical laser measurements
– Chu, Li, & Cheo, 1994, JSQRT 51, 591
– Hillman, Jennings, & Faris, 1979, Appl. Opt. 18, 1808
– Kostiuk et al., 1977, IR Phys. 17, 431
– Sattler et al., 1981, JMS 88, 347 & JMS 90, 297
– Nereson, 1978, JMS 69, 489
– Bischel, Kelly, & Rhodes, 1976, Phys. Rev. A 13, 1829
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New Data
AC Discharge Emission Spectrum 20-650cm-1
– Pirali & Vervloet, 2006, Chem. Phys. Lett. 423, 376
Long path low pressure Synchrotron absorption Spectrum 20-650cm-1
~2000 new lines assigned
– Rotation-Inversion 2n2-2n2, n4-2n2, n4-n4
– Hot bands n4-n2 & 2n2-n2
A few hundred additional submillimeter frequency measurements
127-117 n2 S-A
108-99 2n2 S-n4 S l=1
105-104 n4 S l=1-2n2 S
107-98 2n2 S-n4 S l=1
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117-106 2n2 S-n4 S l=1
116-105 n4 S l=1-2n2 S
101-91 n4 A-S l=-1
106-107 2n2 S- n4 S l=1
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Fitting results
Fits all but a few microwave transitions to <<1 MHz
– A few of the outliers have been confirmed to be bad
Fits the high J forbidden D(K-l)=3 band data
– Urban et al., 1984, Can. J. Phys 62, 1775
– Only a few lines are problematic
Allowed numerous additional assignment in
– Hermanussen, Bizzarri & Baldacchini, 1986, JMS 119, 291
– Lellouch et al., 1987, JMS 124, 333
High J lines from discharge and Hot spectrum are being added
– Does require more constants but looks like it will fit all
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Preliminary Fitting Results
Interaction
n4 (a) to (s) with l =1 to l =1 and l =-1 to l =-1
2n2 (a) to (s)
n4 (a) to (s) with l =1 to l =-1 and l =-1 to l =1
2n2 and n4 (s) to (s) and (a) to (a) Dl =+1 DK=4
2n2 and n4 (s) to (s) and (a) to (a) Dl =-1 DK=2
 (MHz)
-13.4893(34)
-24.9295(131)
-7467.594(125)
0.131851(190)
15.8611(247)
Note
 (MHz)
1.8059(32)
(a)
367.935(233)
-177.248(135) (b)
0.71083(154)
-1298.672(93) (b)
(a) Calculated values from ground state force field =2.93 MHz, =0.45
MHz
(b) Effectively a Coriolis interaction
Most important is all of previous data (a few bad lines excluded) fits to a
reduced RMS of 1.4 Including ~400 microwave transitions
Should fit all with a few more higher order constants.
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Conclusions
The antisymmetric DK=3 terms cannot be excluded in NH3 when there are
interacting states
– The interactions preclude the contact transformations required to re-formulate
the Hamiltonian in a way that eliminates  in both states.
The dipole moment in the ground and n2 states needs to account for the contact
transformation made to eliminate the  terms in the analysis.
– This probably accounts for the observed problem in the DK=3 transitions
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Acknowledgement
This work was performed at the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration
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