Date post: | 28-Dec-2015 |
Category: |
Documents |
Upload: | frank-owens |
View: | 216 times |
Download: | 0 times |
Einstein A coefficients for vibrational-rotational
transitions of NO
Mauricio Gutiérrez1 and John Ogilvie2
1Georgia Institute of Technology, Atlanta GA2Universidad de Costa Rica, San José, Costa Rica
68th International Symposium on Molecular Spectroscopy
June 20th, 2013
Why Einstein A coefficients of NO?
• Einstein A coefficient: proportionality factor between the intensity of spectral lines and the relative populations.
• There is considerable uncertainty in vibrational distributions of NO products in several reactions.
• Our method has been applied to other molecules, but not to NO.
P. Houston et al, J. Phys. Chem. A 114, 11292 (2010)
Einstein A coefficients
J. F. Ogilvie, The vibrational and rotational spectrometry of diatomic molecules (Academic Press, 1998)G. Herzberg, Spectra of diatomic molecules (D. Van Nostrand Company, 1950)
Einstein A coefficients
J. F. Ogilvie, The vibrational and rotational spectrometry of diatomic molecules (Academic Press, 1998)G. Herzberg, Spectra of diatomic molecules (D. Van Nostrand Company, 1950)
Einstein A coefficients
Radial dipole moment
D. M. Dennison, Phys. Rev. 28, 318 (1926)G. Herzberg, Spectra of diatomic molecules (D. Van Nostrand Company, 1950)
Einstein A coefficients
Radial dipole moment Angular dipole moment
D. M. Dennison, Phys. Rev. 28, 318 (1926)G. Herzberg, Spectra of diatomic molecules (D. Van Nostrand Company, 1950)
Einstein A coefficients
Radial dipole moment Angular dipole moment
D. M. Dennison, Phys. Rev. 28, 318 (1926)G. Herzberg, Spectra of diatomic molecules (D. Van Nostrand Company, 1950)
TDM II: radial contribution
R. Herman and R. F. Wallis, J. Chem. Phys. 23, 4 (1955) R. H. Tipping and J. F. Ogilvie, J. Mol. Spec. 96, 442 (1982)
Herman-Wallis approach:
• Apply perturbation theory.• Re-express the matrix elements in terms of a
purely vibrational part and a vibrational-rotational interaction.
TDM II: radial contribution
R. Herman and R. F. Wallis, J. Chem. Phys. 23, 4 (1955) R. H. Tipping and J. F. Ogilvie, J. Mol. Spec. 96, 442 (1982)
Herman-Wallis approach:
• Apply perturbation theory.• Re-express the matrix elements in terms of a
purely vibrational part and a vibrational-rotational interaction.
TDM III: vibrational part
Y.-P. Lee et al, Infrared Physics and Technology 47, 227 (2006).
TDM III: vibrational part
Y.-P. Lee et al, Infrared Physics and Technology 47, 227 (2006).
TDM IV: vibrational matrix elements
Dunham’s potential
Dunham’s method:
• Use the harmonic oscillator eigenfunctions as a basis and apply perturbation theory with Dunham’s potential.
• Obtain symbolic expressions for the matrix elements.
J. F. Ogilvie, The vibrational and rotational spectrometry of diatomic molecules (Academic Press, 1998)
Results I: testing our method (HCl)
Fundamental bandP branch
E. Arunan et al, J. Chem. Phys. 97, 3 (1992)
35
30
25
20
15
Ein
stein
coeffi
cien
t /
s-1
0 2 4 6 8 10J
40
Results I: testing our method (HCl)
E. Arunan et al, J. Chem. Phys. 97, 3 (1992)
40
35
30
25
20
15
Ein
stein
coeffi
cien
t /
s-1
0 2 4 6 8 10J
Fundamental bandP branch
Results I: testing our method (HCl)
E. Arunan et al, J. Chem. Phys. 97, 3 (1992)
Fundamental bandR branch
Ein
stein
coeffi
cien
t /
s-1
0 2 4 6 8 10J
12
14
16
18
20
Results I: testing our method (HCl)
E. Arunan et al, J. Chem. Phys. 97, 3 (1992)
0 2 4 6 8 10J
Fundamental bandR branch
Ein
stein
coeffi
cien
t /
s-1
12
14
16
18
20
Results II: Einstein A coefficients for NO
M. Gutiérrez and J. F. Ogilvie, unpublished
Fundamental band (Ω = ½)P branch
5 10 15 200J
Ein
stein
coeffi
cien
t /
s-1
9
8
7
6
10
Results II: Einstein A coefficients for NO
M. Gutiérrez and J. F. Ogilvie, unpublished
Ein
stein
coeffi
cien
t /
s-1
Fundamental band (Ω = ½)Q branch
5 10 15 200J
5
4
3
2
1
Results II: Einstein A coefficients for NO
M. Gutiérrez and J. F. Ogilvie, unpublished
J
Ein
stein
coeffi
cien
t /
s-1
Fundamental band (Ω = ½)R branch
5
6
7
8
5 10 15 200
Results II: Einstein A coefficients for NO
M. Gutiérrez and J. F. Ogilvie, unpublished
J
Ein
stein
coeffi
cien
t /
s-1
Fundamental band (Ω = ½)R branch
5
6
7
8
5 10 15 200
• 2∏1/2, 2∏3/2
• Δv = 1, 2
• v = 10
• J = 20.5
Conclusions
• We have calculated the spontaneous emission coefficients for vibration-rotational transitions with Δv = 1, 2 up to v = 10 for NO in its electronic ground state.
• Using the same method, we calculated coefficients for HCl and they agree with previous results.
• Future work: comparison with results from ab initio methods.
Acknowledgements
• John Ogilvie
• Ken Brown’s group