𝟐 ′′
Vibronic Analysis of the 𝑨 𝑬 State
of NO3
Terrance J. Codd*, John Stanton†,
and Terry A. Miller*
* The Laser Spectroscopy Facility, Department of Chemistry and Biochemistry
The Ohio State University, Columbus, Ohio
† Department of Chemistry, The University of Texas at Austin, Austin, Texas
Previous Work A E NO3
2
 Hirota and colleagues reported observation of the 401 and 201 bands of the
electronically forbidden A 2 E   X 2 A2 transitiona
 First broad range spectrum was taken by Deev et al. in an ambient CRDS
experimentb
 Several bands were assigned in this work and evidence of strong JT coupling was
reported
2
2
 Jacox and Thompson recorded FTIR spectra of the A E   X A2 transition in a
Ne matrix experimentc
 It significantly extended the spectral range and made several more assignments
 They reported evidence of weak JT coupling in 4
 Most recently, Takematsu et al. have reported the observation of the vibronically
forbidden origin of the A 2 E   X 2 A2 transition and observed several hot bandsd
 They refined the position of the origin band to 7062.25 cm-1 and reported a
second peak roughly 8 cm-1 to the blue
a. K. Kawaguchi, T. Ishiwata, E. Hirota, I. Tanaka. Chem. Phys. 231, 193 (1998).
E. Hirota, T. Ishiwata, K. Kawaguchi, M. Fujitake, N. Ohashi, I. Tanaka. J. Chem. Phys. 107, 2829 (1997)
b. A. Deev, J. Sommar, M. Okumura. J. Chem. Phys, 122, 224305 (2005).
c. M. E. Jacox, W. E. Thompson. J. Phys. Chem. A, 114, 4712-4718 (2010).
d. K. Takematsu, N. C. Eddingsaas, D. J. Robichaud, M. Okumura, Chem. Phys. Lett., 555, 57-63 (2013)
The “important” electronic states of NO3
THE A-X ELECTRONIC SPECTRUM OF NO3: SOME THEORETICAL RESULTS AND IDEAS
John F. Stanton and Christopher S. Simmons
66th OSU International Symposium on Molecular Spectroscopy, TJ03, June 20-24 ,2011
X̃2A2′
 4e 1e 1a2 
2
2
1
X̃2A2′
0 cm1
 4e 1e 1a2 
2
1
2
7064 cm1
Ã2Eb′′
 4e 1e 1a2 
1
Ã2Ea′′
2
15105 cm1
B̃2Ea′
2
B̃2Eb′
Ã2Ea′′
Ã2Eb′′
B̃2Ea′
B̃2Eb′
The “important” electronic states of NO3
THE A-X ELECTRONIC SPECTRUM OF NO3: SOME THEORETICAL RESULTS AND IDEAS
John F. Stanton and Christopher S. Simmons
66th OSU International Symposium on Molecular Spectroscopy, TJ03, June 20-24 ,2011
X̃2A2′
 4e 1e 1a2 
2
2
1
Ã2Ea′′
Ã2Eb′′
B̃2Ea′
3 ,4
X̃2A2′
B̃2Eb′
3 ,4
0 cm1
 4e 1e 1a2 
2
1
2
7064 cm1
Ã2Eb′′
 4e 1e 1a2 
1
2
15105 cm1
2
JT
Ã2Ea′′
JT
2
JT
B̃2Ea′
2
B̃2Eb′
JT
A true multistate, multimode system with rich spectra and plenty of unsolved problems!
NO3 Vibronic Structure and Transitions
Vibronically allowed transitions:
 e"   v " 

  v        e   v   A1
e
(ground state)
 e"   v "    e 
or
Symmetry of electric dipole:
or
𝑒′′
𝑎2′′
𝑎1′′
1
Mode
1
2
3
4
Symmetric
stretch
Umbrella oop
bend
Antisymmetric
stretch
Antisymmetric
ip bend
3
Symmetry
D3h
a1 '
42
a2 "
11
e'
𝑒′′
21
e'
41
~
0
A 2 E" 0
~
X 2A2'
≈≈
≈
≈
𝜇𝑒(∥)
𝜇𝑒(⊥)
𝜇𝑒(∥)
MR-JC-CRDS Experimental Setup
SRS (1 m, 18 atm H2)
20 Hz, 8ns, 500 mJ
Nd:YAG pulse laser
20 Hz, 8ns, 100 mJ
Filters
Sirah Dye Laser
Raman Cell
1st or 2nd Stokes
2-10 mJ,Δν~3 GHz
Ring-down cavity with slit-jet
(absorption length ℓ = 5 cm)
L = 67 cm
PD
InGaAs
Detector
20 m
Fiber Optic
ℓ
R ~ 99.995 – 99.999%
@ 1.3 m
Vacuum Pump
Collimator
Room Temperature vs Jet-Cooled Spectra
Room Temperature
Jet Cooled
7700
7500
7500
7800
7600
7600
7900
7700
7700
Room temperature data from:
A. Deev, J. Sommar, M. Okumura. J. Chem. Phys, 122, 224305 (2005).
8000
7800
7800
8100
7900
8100
8200
8000
8200
wavenumber
wavenumber
wavenumber
8300
8100
8300
840
820
8400
a.u.
Jet-Cooled CRDS Data
7600
7800
8000
8200
8400
8600
a.u.
wavenumber (cm-1)
8800
9000
9200
wavenumber
(cm-1)
9400
9600
Vibronic Hamiltonian, H ev , for Nuclear Motion on the
Electronic Potential Energy Surface, V
H ev  TˆN  V
3D Plot of V showing Jahn-Teller Distortion
Quadratic Vibronic Hamiltonian
H ev 
TˆN 
p

3 N 62 p
p
1
1
2
i | Qi |    i | Qi ,r |2
2
i 1 r  ,  2

i 1
 kQ
i 1 r  , 
i
i ,r
Harmonic Oscillator
Linear Jahn-Teller
p
1
gii (Qi ,r ) 2

i 1 r  ,  2

p p , j i

i 1
s

j 1
1
cij (Qi ,r Q j ,r )

2
r  , 
p
1
bij Qi ,r Q j

2
i 1 r  , 
 
j 1
T. A. Barckholtz, T. A. Miller, Int Rev in Phys. Chem.17, 435-524 (1998)
Quadratic Jahn-Teller
Cross-Quadratic Jahn-Teller
Bi-linear Coupling
Vibronic Parameters
Hamiltonian Parameters
  2V 
i   

 Q Q 
 i , i , 0
 V
bij   
 Q Q
 i , j
2
 V
ki   
 Q
 i ,

 
0

 
0
  2V
gii   
 Q Q
 i , j ,

 
0
  2V
cij   
 Q Q
 i , j ,

 
0
Experimental Parameters
ki2  M i 
Di 


2  i3 
Ki 
gii
i
2 ′′
𝐴 𝐸 State Vibronic Interactions
| 0,1,0,0 
| 0,0,1,1 
K3,K4
b1,3
| 1,0,0,1 
b1,4
K3,K4
b1,4
| 1,0,1,0 
c3,4
D3
D4
c3,4
K3
D3
K4
b1,3
| 0,0,1,0 
c3,4
| 0,0,0,1 
K3,K4
D4
| 0,0,0,0 
|  |  1 , 2 , 3 , l3 , 4 , l4 
Vibronic Assignments
4 02
a.u.
4
210
1
0
210 410
110 210
310 110 410
7600
7800
8000
8200
8400
8600
wavenumber (cm-1)
210 430
1
0
a.u.
24
4
3
0
310 410
8800
2 30
2
0 1 2
0 0
14
210310 410
2 02 410
210310
102 410
310 402
1 2
2
0 30
wavenumber
(cm-1)
9000
9200
9400
4 50
2 30 410
9600
Complementary of Parallel and
Perpendicular Bands
 This means that we can use
(41 vibronic levels x a2)
a1
the observed perpendicular
combination bands to find
the position of the 𝑒′′
components of the
degenerate modes.
e
2 4
1
1
a2
= 21 vibrational
frequency
(vibrational symmetry a2)
e
21
a1
e
1
4
~
A 2 E"
a2
 e  
e 
 e  

≈
≈
~2 '
X A2
≈
Comparison of Observed and Simulated Line positions
4 02
210
210 410
a.u.
4
1
0
110 210
310 110 410
7600
7800
8000
8200
wavenumber
8400
8600
Comparison of Observed and Simulated Line positions
210 430
1
0
a.u.
24
4
8600
3
0
2
0 1 2
0 0
14
210310
2 02 410
310 410
8800
2 30
210310 410
1 2
0 0
23
4 50
2 30 410
310 402
102 410
9000
9200
wavenumber
9400
9600
Comparison of Observed and Calculated (John Stanton)
Line Positions (Parallel Bands Only)
Further work clearly needed
Conclusions
• Over 20 Vibronic Bands in the A 2 E   X 2 A2 Electronic
Transition have been Observed and Assigned
• The Structure of the A 2 E  State has been Well Stimulated
Including Linear and Quadratic Vibronic Interaction Terms
• Harmonic Frequencies for All 4 Vibrational Modes and JahnTeller Parameters for the e' Modes have been Obtained
• More Detailed Comparison to Calculations Forthcoming Imminently