THEORETICAL INVESTIGATION OF LARGE AMPLITUDE MOTION IN THE METHYL PEROXY RADICAL Gabriel Just, Anne McCoy and Terry Miller The Ohio State University

Motivations Peroxy radicals (RO 2 ) are key intermediates in the oxidation of hydrocarbons. Hence obtaining spectral signatures for these radicals is crucial in order to extend our understanding of these radicals. Understanding the unusual spectral features observed in our two most recent studies 1,2,3 of the methyl peroxy Near-IR electronic transition. 1 MH06 2 RF09 3 RF10

What are these unusual spectral features ? Room temperature CRDS spectrum of CH 3 O ν 8 is the COO bend ν 12 is the CH 3 torsion

Mapping both electronic states 1131 cm cm -1 We found that a value of N=2 suffices to fit the 13 computed points with and RMS errors of 0.45 cm -1 for the ground state and 2.2 cm -1 for the excited state (B3LYP/6-31+G(d)) S is the Scaling factor for the potential y represent either the X or the A state

Method/Basis SetBarrier height for the ground electronic state (cm -1 ) Barrier height for the first excited electronic state (cm -1 ) ROHF/6-31+G(d) UHF/6-31+G(d) CCSD/6-31+G(d) QCISD(T)/6-311G(d,p) MP2/6-311G(d,p) MP2/6-311+G(d,p) MP2/6-311G(2df,p) MP2/6-311+G(3df,2p) MP4/6-311G(d,p) MP4/6-311+G(d,p) MP4/6-311G(2df,p) G G2MP G B3LYP/6-31+G(d) Barrier Height G2 T 00 = 7375 cm -1 Experiment : 7382 cm -1

Hamiltonian The rotation-vibration Hamiltonian can be written in the PAM 1 as This hamiltonian was used in the case of methanol which has only one plane of symmetry as methyl peroxy. In the case of CH 3 O 2 the c component of ρ vanishes by symmetry. 1 C. C. Lin and J. D. Swalen, Rev. Mod. Phys. 31, 841 (1959) Internal Rotation Rotation of the whole molecule F play the role of the reduce mass for the internal rotor. ρ is the angle between the principal axis and the methyl rotor axis

Simplifying the Hamiltonian Using the ρ axis method (RAM) 1,2 1 E.Herbst, J.K.Messer, F.C.DeLucia and P.Helminger, J. Mol. Spectrosc. 108, 42 (1984) 2 J.T.Hougen, I. Kleiner and M. Godefroid, J. Mol. Spectrosc. 163, 559 (1994) A R, B R, C R, D R are fixes to theab-initio values. Rather than using the ab initio F value obtained by the B3LYP calculation, we multiply it by This value was chosen after the evaluation of the F value for the different level of theory, and we notice variations in the F value

Calculating the eigenvalues and eigenfunctions Now that we have an expression for the Hamiltonian in the RAM. We can use the following analytical form of the potential in order to calculate the eigenvalues and eigenfunctions for both electionic states associated with the CH 3 torsional motion. We found that a value of N=2 suffices to fit the 13 computed points with and RMS errors of 0.45 cm -1 for the ground state and 2.2 cm -1 for the excited state

Eigenfunctions and Eigenvalues In order to calculate the eigenvalues and eigenfunction associated with the chosen Hamiltonian, we used a Fourier basis. The eigenfunction can then be generally written as : Where n takes on all positive and negative integer values, σ =0,±1. The integer index j labels eigenvalues of the same value of |σ| in increasing order of energy. For K=0 σ=0 defines A 1 or A 2 states and σ=±1 defines E states The general solution of the eigenvalues are given by:

A convenient way to label the torsional eigenvalues and eigenfunctions is to invoke the G 6 molecular symmetry group which is isomorphic to C 3v The eigenfunctions transforms as either A 1, A 2 or E. Near the bottom of the well, the A 1 and A 2 states alternatively combine with an E state to form the nearly 3-fold degenerate eigenvalues. Well above the barrier, A 1 and A 2 become nearly degenerate and, along with the E eigenfunction form a doubly degenerate free rotor function. Labeling of the eigenvalues

Correlation between low and high barrier We truncated the potential by including only the first 2 terms. In order to remove dependence on F y, we replace V 0 y and V 3 y by bF y So, the barrier of free rotation becomes only bF y. E j is define as the reduce energy and is obtain by deviding the resulting eigenvalues by F y.

K and A/E Splitting The fact that ≠0 leads to a splitting of the otherwise nearly degenerate K –levels for this asymmetric top in the near prolate limit. Hence, we can analyze this further by calculating the energies using H 1 plus only the first term of H 2 j=0 j=1 j=2 K Splitting A/E Splitting for positive and negative K

Summarizing for K=0 CH 3 O 2 CD 3 O 2

Spectral simulation We are only considering the Q-branch for each transition. The intensities are evaluated using the calculated Franck-Condon factors at K=0 and by assuming a ground state Boltzmann population distribution at 300K. Since the A/E splitting depends on the value of K, we include all thermally populated K-levels in our calculation. The nuclear spin weighting of 1:1:1 for the transitions originating from A 1 :A 2 :E levels for CH 3 O 2 and 11:11:16 for CD 3 O 2 was applied.

CH 3 O Exp Sim

CD 3 O 2 Exp Sim

cm

Conclusion We simulate successfully the room temperature spectrum obtain by E. Sharp and P. Rupper with a somewhat simple model and we now have a better understanding of the nature of the unexpected spectral feature that they observed in their room temperature CRDS spectra. Based on the calculation, the data fit with barrier for the CH 3 torsional mode of 321 cm -1 for the ground electronic state and 1131 cm -1 for the first excited electronic state. This work also allowed us a better understanding of the jet cooled spectra of these same radicals (RF09, RF10)

Acknowledgments Miller’s group: –Erin Sharp TB03, TB04, TB05 –Patrick Rupper MH06, RF09 –Ming-Wei Chen RF01 –Jinjun Liu RF02 –Shenghai Wu RG02 –Patrick Dupré RF10 FA05 –Dmitry Melnik –Terry Miller McCoy’s group: –Anne McCoy TH01 –Sara Ray WF08 –Samantha Horvath TH02 –Charlotte Hinkle FC07 Funding $$$: –NSF

Thank you!