~ ~ 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

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

Experimental protocol Production (R=C2H5): Detection: (a) Rotationally resolved HCl vibrational overtone @ 1.8mm Rotationally unresolved A-X RO2 transition @ 1.3 mm ~ ~ hn (a). D.G. Melnik, R. Chhantyal-Pun and T.A.Miller, J. Phys. Chem., 114, 11583 (2010)

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

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

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?

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%

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

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, 184303 (2009)

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)

Simulations of rovibronic spectra Rotational constants(cm-1) G-conformer T-conformer A B C X state 0.59099 0.18899 0.16299 1.1018 0.14766 0.13725 A state 0.55305 0.19250 0.16239 1.06663 0.14844 0.13715 |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 20112111 Dn 88.2 184.5 50.9 Int 0.26 0.099 0.129

Experimental and simulated spectra of C2H5O2 Simulation

Experimental value of |me| vs. quantum chemical calculations Geometry calc. A, cm-1 B, C, TDM |me|, 10-2 D MP2/ 6-31G(d) 0.59373 [-0.46%] 0.19055 [-0.83%] 0.16459 [-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) 0.58430 [1.14%] 0.18845 [0.29%] 0.16231 [0.40] 2.52 2.02 EOM-CCSD/6-31G(d) 3.31 UB3LYP 0.60628 [2.58%] 0.18481 [-2.21%] 0.16160 [-0.85] 2.42 1.78 3.17 Exp 0.59099 0.18899 0.16299 2.04(7)

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.

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

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