Introduction

Pinenes are a class of bicyclic molecules emitted by conifers and marine flora. These molecules constitute 6% of all biogenically derived volatile organic compound emissions in the atmosphere. Experimental research demonstrates that pinenes react with hydroxyl radicals via addition across the double bond. These, in turn, react with ambient oxygen to create pinene hydroxy-peroxy radicals. These species are stabilized by complexation with a water molecule. These reactions play a fundamental role in atmospheric chemistry. R-alpha and S-alpha pinene geometry optimizations for various stereoisomers of each radical and radical water complex were determined computationally at the B3LYP/6-311++G(2d,2p) method and basis set. Basis set superposition error was corrected using the counterpoise method. These calculation results were used to determine partition functions and calculate stereoisomer-specific equilibrium constants. The present work focuses on deducing Boltzmann-weighted average global equilibrium constants for the hydroxy-peroxy pinene-water complexes based on the stereoisomer-specific results.

Methods

Gaussian 092 was employed to determine binding energies and vibrational frequencies for radicals and radical-water complexes at the B3LYP/6-311G++(2d,2p) level. Partition functions were corrected for hindered internal rotors and Morse oscillators within each radical-water species. Radicals and radical-water complexes that may have a significant thermal population (typically < ~ 3 kTabove the lowest ground state energy) are used to calculate a Boltzmann-weighted average equilibrium constant of complexation for the radical-water complex. Our results for R-a-pinene radical-based complexes are shown in this work.

References

Computational Study of Isoprene Hyroxyalkyl Peroxy Radical-Water Complexes (CSH8(OH)O2-H20), Jared Clark, Seth T. Call, Daniel E. Austin, Jaron C. Hansen. The Journal of Physical Chemistry 2010 114 (23), 6534-6541.

Gaussian 09, Revision D.01,M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Wallingford CT, 2004.

Computational Study of Hexanal Peroxy Radical-Water Complexes, Emily Burrell, Jared C. Clark, Mathew Snow, Heidi Dumais, Seong-Cheol Lee, Brad J. Nielson, Derek Osborne, Lucia Salamanca-Cardona, Logan Zemp, Ryan S. Dabell, Jaron C. Hansen. International Journal of Quantum Chemistry. DOI: 10.1002/qua.23220

Determination of Boltzmann-Weighted Equilibrium Constantsfor Pinene-Based Hydroxy-PeroxyRadical-Water Complexes

Elizabeth Buchmiller, Michael Goytia, Tyler Southam, Paul Spiel, Kelly Wilson, Fan YangRyan S. DaBell, BYU-Idaho Department of Chemistry

and JaronC. Hansen, BYU Department of Chemistry and Biochemistry

Results Discussion

With BSSE corrected energies, representative equilibria have been determined for steroisomers of R-a-pinene and S-α-pinene derived radical-water complexes. The global equilibrium constants for each steroisomerand the Boltzmann-weighted average equilibrium constant are shown in Figure 1 for R-α-pinene and Figure 2 for S-α-pinene. K is noticeably lower for the pinene-based complex than for either the hexanal3 or isoprene-based1 complexes. This is likely due to the steric hindrance of the bicyclic ring and the bulky methyl groups in pinene that restrict the optimization of the water-radical hydrogen bond angle. Optimal hydrogen bond angles approach 180o,1 and bond angles for R-a-pinene and S-α-pinene, hexanal, and isoprene radical-water complexes are typically ~163o, 169o, and ~175o, respectively.1,3 Thus, decreasing the bond angle between the water and hydroxymoiety means that pinene-based radicals are much less likely to form a water complex than either hexanal- or isoprene-based radicals, as indicated by the respective Kvalues.

Future work will focus on calculating equilibrium constants for the remaining pinene-based radical-water complexes.

Figure 2: Natural log of S-α-Pinene complexes versus temperature. Solid line corresponds to Boltzmann weighted equilibrium constant

Figure 1: Natural log of R-α-Pinene complexes versus temperature. Solid line corresponds to Boltzmann weighted equilibrium constant

Complex Keq /10-21 Keq[H2O]=[Complex]/[Radical] (mol %)R-α-PineneS-α-Pinene

0.02040.3124

0.001760.00764

2-hydroxy-3-peroxy hexanal 0.427 0.03682-peroxy-3-hydroxy hexanal 1.21 0.104

Isoprene hydroxyalkyl Peroxy 10.4-260. 0.8-20.0

Table 2: Equilibrium constants at the Keq[H2O] ratio calculated for the formation of different complexes at the B3lYP/6-311++ G(2d,2p) level at 300 K. K eq is reported as cm3 molecule-1

-56

-54

-52

-50

-48

-46

-44

-42

200 220 240 260 280 300

lnKe

q

Temperature (K)

R-α-Pinene S-α-Pinene Isoprene Hydroxyalkyl PeroxyBond Length Angles Bond Length Angles Bond Length Angles

OH(hyd)-O(water) 1.89-1.96 164.9-172.5 1.89 164.9 1.87-1.97 156.4-176.3

OH(water)-O(hyd) 1.92 165.6 1.90-2.05 162.9-175.6

O1 (peroxy)-HO (water) 3.05 107.1 2.18-2.22 162.2-168.9O2(peroxy)-HO(water) 1.94-2.06 139.2-163.0 1.94-2.39 144.0-163.0 1.97-2.17 136.1-172.2

Table 1: Hydrogen bond length and angle ranges in different stereoisomers of pinene complexes and isoprene hydroxyalkyl peroxy

-55

-53

-51

-49

-47

-45

-43

-41

200 220 240 260 280 300

lnK eq

Temperature (K)