This study computationally characterized hydrogen bond interactions between pinene-based hydroxy-peroxy radicals and water molecules. Geometry optimizations and natural bonding orbital analyses were performed at the B3LYP/6-311++G(2d,2p) level of theory. Primary hydrogen bonds ranged from 1.88-1.95 Angstroms in length with angles of 159-172 degrees. Secondary hydrogen bonds were approximately 2.0-2.2 Angstroms in length. Binding energies were determined and correlated with hydrogen bond lengths and second-order perturbation energies from natural bonding orbital analysis.

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 was corrected
using the counterpoise method. These
calculation results were used to determine
partition functions and calculate Boltzmann-
weighted average global equilibrium constants
for the hydroxy-peroxy pinene-water complexes.
The current work focuses on characterizing the
hydrogen bond based on geometry data and
Natural Bonding Orbital (NBO) 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
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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
DeterminationofBoltzmann-WeightedEquilibriumConstants
forPinene-BasedHydroxy-PeroxyRadical-WaterComplexes
ElizabethBuchmiller,MichaelGoytia,TylerSoutham,PaulSpiel,KellyWilson,FanYang,TimothyRose
RyanS.DaBell,BYU-IdahoDepartmentofChemistry
andJaronC.Hansen,BYUDepartmentofChemistryandBiochemistry
Results Discussion
With BSSE corrected energies, representative
equilibria have been determined for
steroisomers of R-β-pinene and S-β-pinene
derived radical-water complexes. As shown in
Table 2, dominant hydrogen bond lengths are
in the 1.88-1.95 Angstrom range, with
secondary bond lengths being approximately
2.0-2.2 Angstroms. Previous research
demonstrates that optimal hydrogen bond
angles approach 180o,1 and the primary H-
bond angles pinene based radical-water
complexes are consistent with this
expectation, lying in the 159o-172o range.
Table 2 also illustrates that bond length,
rather than bond angle, affects the binding
energy of the complex more.
Natural bonding orbital analysis yielded the
2nd order perturbation energies shown in
table 2. These values contribute to the
binding energy of the complexes. Combining
perturbation energies with the hydrogen
bond geometries should yield an
understanding of the binding energy of each
complex. However, a direct correlation
between perturbation energy and binding
energy is not entirely evident.
Figure 2: Water complexing with an R-β
pinene “outside the cage.”
Figure 1: Water complexing with
pinene “inside the cage.”
Table 2: Hydrogen bond angles and lengths for some representative pinene stereoisomers. Significant H-bond interactions are bolded.
Pinene
Root
Stereoisomer
Complex
Type
Binding
Energy
(kcal/mol)
H-bond Length (angstrom) H-bond Angle (degree)
O1-H2O O2-H2O OH-OH2 HO-H2O O1-HO O2-HO O1-H2O O2-H2O OH-OH2 OH-OH2 HO-H2O HO-H2O O1-HO O2-HO
R-β 1oh2oor HO-H2O -6.3 - - - 1.88708 - 1.98348 - - - - 119.630 169.133 - 135.137
1oh2oos HO-H2O -6.0 - - - 1.89788 - 2.02716 - - - - 126.510 159.723 - 133.999
1oo2ohs O1-H2O-HO -5.4 2.20975 - 1.94922 - - - 132.323 - 171.244 118.304 - - - -
S-β 1oh2oor O2-H2O-HO -4.9 - 2.01713 1.91569 - - - - 139.481 171.889 116.389 - - - -
1oh2oos HO-H2O -6.6 - - - 1.88416 - 1.97944 - - - - 119.230 169.162 - 135.416
1oo2ohr O1-H2O-HO -5.4 2.20972 - 1.95140 - - - 132.472 - 171.218 118.630 - - - -
R-α 2ohr3oor O2-H2O-HO -7.6 - 1.96536 1.937 - - - - 158.037 165.427 124.525 - - - -
2ohr3oos O2-H2O-HO -6.3 - 2.06295 1.95495 - - - 139.163 - 172.478 114.332 - - - -
2oor3ohr O2-H2O-HO -5.4 - 1.94377 1.89355 - - - - 162.956 164.852 123.749 - - - -
2oor3ohs HO-H2O -5.4 - - - 1.92317 - 1.93472 - - - - 111.092 165.636 - 131.362
S-α 2ohr3oos O2-H2O-HO -6.2 - 2.05851 1.95215 - - - - 138.511 171.697 113.217 - - - -
2ohs3oos O2-H2O-HO -7.2 - 1.96536 1.93700 - - - - 158.037 165.427 124.525 - - - -
2oor3ohr HO-H2O -5.6 - - - 1.89868 - 2.51409 - - - - 117.679 167.36 - 118.257
2oos3ohs O2-H2O-HO -7.2 - 1.94377 1.89353 - - - - 162.95 164.858 123.754 - - - -
Table 1: Second order perturbation energies obtained from NBO analysis. Bolded
numbers correspond to bolded entries in Table 2.
Pinene
Root
Stereoisomer Binding Energy
(kcal/mol)
2nd Order Perturbation Energy (kcal/mol)
O1-H2O O2-H2O OH-OH2 HO-H2O
R-beta 1oh2oor -6.3 - - - 8.45
1oh2oos -6.0 - - - 8.79
1oo2ohs -5.4 0.74 - 9.36 -
S-beta 1oh2oor -4.9 - 3.21 11.29 -
1oh2oos -6.6 - - - 8.29
1oo2ohr -5.4 0.74 - 9.26 -
R-Alpha 2ohr3oor -7.6 - 4.91 8.43 -
2ohr3oos -6.3 - 2.54 9.14 -
2oor3ohr -5.4 - 6.88 10.43 -
2oor3ohs -5.4 - - - 7.02
S-alpha 2ohr3oos -6.2 - 2.55 9.30 -
2ohs3oos -7.2 - 8.45 - -
2oor3ohr -5.6 - - - 8.29
2oos3ohs -7.2 - 8.45 - -