1. ~ ~ DETERMINATION OF THE TRANSITION DIPOLE MOMENT OF THE A - X
ELECTRONIC TRANSITION OF THE C2H5O2
FROM THE PEAK ABSORPTION CROSS-SECTION.
DMITRY G. MELNIK AND TERRY A. MILLER
The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility,
120 W. 18th Avenue, Columbus, Ohio 43210
PHILLIP S. THOMAS
Faculty of Science, Leiden Institute of Chemistry, Netherlands

2. Research Motivation
Peroxy radicals (RO2) are important reactive intermediates in atmospheric
and combustion chemistry.
Intensity measurement of absorption of RO2 is species-selective
analytical tool to study atmospheric and combustion chemistry
Absorption cross-section : can be measured directly but has complex (T,P)-dependence
Transition dipole moment (TDM) :
a characteristic quantity which allows to obtain s at variety of
conditions, but hard to determine
characterizes radical potential energy surface
serves as a benchmark for quantum chemistry calculations

3. Experimental protocol
Production (R=C2H5):
Detection: (a)
Rotationally resolved HCl vibrational overtone
@ 1.8mm
Rotationally unresolved A-X RO2 1.3 mm ~ ~ hn
(a). D.G. Melnik, R. Chhantyal-Pun and T.A.Miller, J. Phys. Chem., 114, (2010)

4. Experimental spectra of C2H5O2
R band head,
origin,
G-conformer

5. Relationship between s(n) and me
Unresolved band
contour
Single resolved
rovibrational line
s(n)
s(n) n n

6. Partition function, Q(T), calculation
Assuming
we obtain the expression for Q(T):
Simple cases of partition functions:
Rigid rotor:
Ensemble of harmonic oscillators:
Rigid rotor approximation is accurate to ~ 1%
How do we treat vibrational anharmonic effects?

7. Weak anharmonicity approximation
Vibrational energy E(n) of a weakly anharmonic oscillator:
Corresponding partition function:
The last sum can be evaluated in the closed form, giving:
Expand in
power series and truncate
at term linear in
(n2+n)
Anharmonic correction
factor
Accuracy estimate for the “weak
anharmonicity approximation”
~ 5%

8. Absorption profile, A(n), calculation
Vibrational band intensity
Rotational profile of
the vibrational band
A(n)
SpecView: TC06, 56th MSS, 2001

9. Information required to calculate Q(T) and A(n)
Vibrational level energies of X state
Vibrationl level energies of A state
Franck-Condon factors for the
contributing bands
Rotational constants for contributing
bands
Orientation of TDM with respect to
principal molecular axes
Sources:
a. Quantum chemistry calculations
b. High-resolution jet-cooled
measurements(a)
(a) G. P. M. Just et al., J. Chem. Phys., 131, (2009)

10. Vibrational level structure calculations
Quantum chemistry calculations:
1. Gaussian (UB3LYP/aug-cc-pVTZ):
equilibrium geometries
normal modes
harmonic frequencies
fundamental frequencies
for n1-n20
potential scan for CCOO
torsion (n21)
MolFC:
Franck-Condon factors
The level structure for the n21 band
obtained by solving Schroedinger
equation .
G-conformer
T-conformer
mode n0 c
n15
991.4
0.015
1012
n16
841.6
0.012
837.6
n17
797.4
0.009
804.1
-0.002
n18
523.4
0.007
500.5
0.005
n19
361.0
0.011
306.7
-0.007
n20
225.4
-0.046
219.0
-0.088
n21
109.3
0.092
78.7
0.021
Conf.(a) gc
Ec , cm-1 G 2 T 1 81
(a) P. Rupper et al., J.Phys.Chem. A, 111, 832 (2007)

11. Simulations of rovibronic spectra
Rotational constants(cm-1)
G-conformer
T-conformer A B C
X state
1.1018
A state
|ma/m|2
0.229
0.499
0.272
1.0
Vibrational bands: G-conformer (Dn are relative to the origin at 7592 cm-1)
Band
000
2111
2011
1911
2112
2110
2101
2123
2124
2022 Dn
21.0
-11.8
-22.3
-28.4
140.9
-77.1
39.5
27.9
17.1
-64.0
Int.
0.65
0.23
0.20
0.12
0.22
0.11
0.094
0.078
0.069
0.058
0.055
T-conformer (Dn are relative to the origin at 7362 cm-1)
Band
2122
2133 Dn
88.2
184.5
50.9
Int
0.26
0.099
0.129

12. Experimental and simulated spectra of C2H5O2
Simulation

13. Experimental value of |me| vs. quantum chemical calculations
Geometry
calc. A,
cm-1 B, C,
TDM
|me|, 10-2 D
MP2/
6-31G(d)
[-0.46%]
[-0.83%]
[-0.98%]
UCIS/6-31G(d)
2.61
UCIS/
aug-cc-pVTZ
2.04
EOM-CCSD/
3.43
2.80
CCSD/
6-31+G(d)
[1.14%]
[0.29%]
[0.40]
2.52
2.02
EOM-CCSD/6-31G(d)
3.31
UB3LYP
[2.58%]
[-2.21%]
[-0.85]
2.42
1.78
3.17
Exp
2.04(7)

14. Summary
Complicated rovibrational structure of the electronic transition requires
detailed analysis which can be done by using the results of high resolution
spectra and quantum chemistry calculations.
The electronic TDM of the G-conformer of C2H5O2 has been
experimentally measured,
The values of TDM predicted using quantum chemistry calculations are
generally consistent with the experiment although vary significantly
over the variety of used methods.

15. Acknowledgements
Colleagues:
Dr. Gabriel Just,
Dr. Phillip Thomas,
Dr. Jinjun Liu,
Ming-Wei Chen,
Terrance Codd,
Neal Kline
Rabi Chhantyal-Pun
OSU
DOE
The Ohio Supercomputer Center

17. Weak anharmonicity approximation 1st order anharmonicity
Harmonic oscillator
Simulation:
n21=79 cm-1
c21=0.021
Weak anharmonicity
approximation
1st order anharmonicity