1. 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-β, S-β, R-α, and S- α
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 (BSSE) was
corrected using the counterpoise method.
Boltzmann-weighted average global equilibrium
constants for the pinene radical-water
complexes were calculated.
The current work examines the effects of bond
length, bond angle, and second-order
perturbation energy on the hydrogen bonding.
Natural Bonding Orbital (NBO) analysis provides
a framework for this analysis.
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 kT above the lowest ground state
energy) are used to calculate a Boltzmann-
weighted average equilibrium constant of
complexation for the radical-water complex. NBO
analysis is used to characterize hydrogen bonding
between the radicals and water.
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
Examininghydrogen-bondinteractionsofpinene-basedhydroxy-peroxy
radical-watercomplexesusingnaturalbondingorbitalanalysis.
TylerSoutham,TimothyRose,MichaelGoytia,FanYang
RyanS.DaBell,BYU-IdahoDepartmentofChemistry
andJaronC.Hansen,BYUDepartmentofChemistryandBiochemistry
Results Discussion
As shown in Table 1, hydrogen bond lengths
are in the 1.88-2.21 Å range. Dominant
hydrogen bond lengths are in the 1.88-1.95 Å
range, with secondary bond lengths being
approximately 2.0-2.2 Å. Previous research
demonstrates that optimal hydrogen bond
angles approach 180o,1 and our primary H-
bond angles lie in the 159o-172o range,
consistent with this expectation. Table 1 also
includes BSSE corrected binding energies, in
the range of -4.9 to -7.6 kcal/mol. The
variations in these binding energies between
stereoisomers within a specific family of
complexes are illustrated in Figure 2.
Natural bonding orbital analysis yielded the
2nd order perturbation energies (E(2)) of
specific water-radical hydrogen bond
interactions shown in Table 1. Combining
perturbation energies with the hydrogen
bond geometries is a valuable tool in
understanding the specific intermolecular
interactions within these complexes.
Figure 1 highlights a proportional relationship
observed between PNBO off-diagonal matrix
elements for the hydrogen bond interactions
and the E(2) energy. PNBO off-diagonal
matrix elements are typically considered to
approximate the the overlap integral
between the two interacting NBOs,3 and this
relationship tends to support that assertion,
demonstrating that increased overlap results
in an improved hydrogen bond interaction.
Figure 2: Relative stereoisomer energies of radicals and complexes
derived from pinenes. (a) R-α pinene, (b) S-α pinene, (c) R-β pinene,
(d) S-β pinene
Table 1. Common characteristics for various hydrogen-bond interactions between water and related steroisomers derived from pinene
-7
-6
-5
-4
-3
-2
-1
0
1
2
(kcal/mol)
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
(kcal/mol)
-7
-6
-5
-4
-3
-2
-1
0
1
2
(kcal/mol)
-7
-6
-5
-4
-3
-2
-1
0
1
2
(kcal/mol)
Figure 2a
Figure 2dFigure 2c
Figure 2b
Root pinene
# of
stereoisomers
BSSE binding energies
(kcal/mol) H-bond lengths (Å)
H-bond angles
(degrees)
E(2) interaction energies
(kcal/mol) (PNBO matrix elements)2
R-α 4 -5.4 to -7.6 1.89 - 2.06 158.0 - 172.5 0.04 - 5.22 0.0022 - 0.075295
S-α 4 -5.6 to -7.2 1.90 - 2.06 138.5 - 171.7 0.19 - 4.65 0.000864 - 0.061306
R-β 3 -5.4 to -6.3 1.89 - 2.21 132.3 - 171.2 0.34 - 4.68 0.003125 - 0.082656
S-β 3 -4.9 to -6.3 1.88 - 2.21 132.5 – 171.9 0.34 - 5.66 0.006757 - 0.082025
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4 5 6
AbsoluteHFPNBOMatrixElement
E(2) (kcal/mol)
Figure 1: Absolute PNBO matrix element values as a function of second-
order perturbation energy for water-radical hydrogen bond interactions
in pinene-based radical-water complexes.