| Краткое содержание: | Introduction
Carboxylic acids are important constituents of the atmosphere
and can be found in gaseous phase and in particulate matter,
such as fog, clouds, rainwater, snow, and ice.1 Carboxylic acids
together with carbonyl compounds account for a major fraction
of the total organic carbon in fog, cloud, and precipitation,1 and
contribute considerably to ambient and precipitation acidity.2
Carboxylic acids originate from primary anthropogenic sources,
such as emissions from wood bu
ing and vehicle exhausts, and
from biogenic sources, such as soil and vegetation, as well as
from secondary reactions.1 In addition to dry and wet deposition,
atmospheric carboxylic acids can be removed through photochemical
oxidation by hydroxyl radicals. The lifetime of
carboxylic acids in the atmosphere may vary from several hours
to more than one week.1 The oxidation of organic acids follows
a free-radical mechanism in which the initial step is hydrogen
abstraction by hydroxyl radicals. This initial step determines
the lifetime and, to a large extent, the fate of the oxidation of
carboxylic acids.
Experimental studies conclude that hydroxyl radicals preferentially
attack the acid hydrogen atom for small carboxylic
acids, such as formic and acetic acid.3-6 For larger carboxylic
acids, a change in selectivity is observed. Electron paramagnetic
resonance studies indicate that abstraction of a -hydrogen atom
is the dominant mechanism for propionic and butyric acid,7
while abstraction at both the - and γ-position was reported
for butyric and valeric acid.8 This change in selectivity has been
rationalized by the higher calculated frontier orbital electron
density at the - and γ-positions in larger organic acids.8
Theoretical studies of the initial hydrogen abstraction from
organic acids by hydroxyl radicals focus mainly on formic9-11
and acetic acid.11-13 In agreement with experimental data,
abstraction of the acid hydrogen was found to be the dominant
mechanism for both acids. Interestingly, the observed dominance
of the acid channel at 298 K is caused by the enhancement of
the reaction rate for the acid channel by quantum mechanical
tunneling and not by a lower activation barrier.9,11 Our previous
study11 showed that state-of-the-art first principles calculations
can begin to predict rate coefficients for reactions between small
organic acids and hydroxyl radicals with chemical accuracy (i.e.,
typically within a factor of 4 of experimental data at 298 K)
and that the selectivity between the acid and the C-H channels
can be calculated reliably. Quantum mechanical tunneling is,
however, very important for the acid channel at temperatures
below 400 K, and the small curvature tunneling (SCT) method14
which accounts for the curvature of the reaction path and
approximately incorporates tunneling paths other than the
minimum energy path (MEP), is required for accurate results.
In this study, we use first principles calculations to investigate
the initial step in the oxidation of carboxylic acids via hydrogen
abstraction by hydroxyl radicals, to begin to provide a more
detailed understanding of the degradation mechanism of carboxylic
acids in the troposphere. Our main objective is to
quantify and rationalize the selectivity between the possible
pathways. Valeric acid, C4H9COOH, was selected as a representative
linear carboxylic acid and allows quantifying the
selectivity among the acid, R-, -, γ-, and methyl channel
(Scheme 1).
* To whom correspondence should be addressed. Phone: +65 6516 5826.
Fax: +65 6779 1936. E-mail: chesm@nus.edu.sg.
† Department of Chemical and Biomolecular Engineering.
‡ Division of Environmental Science and Engineering.
7852 J. Phys. Chem. A 2009, 113, 7852–7860
10.1021/jp8090792 CCC: $40.75 2009 American Chemical Society
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Published on June 15, 2009 on http://pubs.acs.org | doi: 10.1021/jp8090792
2. Computational Methods
In our previous study of the reaction of formic and acetic
acid with hydroxyl radicals,11 a computational procedure was
developed to predict rate coefficients for this family of reactions
with chemical accuracy; that is, within a factor 2-4 of
experimental data. The procedure is briefly summarized below.
Standard enthalpies of formation for the reactants, complexes,
transition states, and products are calculated using the complete
basis set CBS-QB3 method.15 This method was found to predict
activation barriers and reaction energies for hydrogen abstraction
from formic and acetic acid by hydroxyl radicals within 3 kJ/
mol11 and standard enthalpies of formation of hydrocarbons with
a mean absolute deviation of 2.5 kJ/mol.16 Within the CBSQB3
method, geometries are optimized at the B3LYP/6-
311G(d,p) level of theory. For this family of reactions,
geometries optimized at the B3LYP/6-311G(d,p) level of theory
are essentially similar to geometries optimized using a larger
cc-pVTZ basis set and fairly similar to QCISD/6-311++G(d,p)
geometries.11 Intrinsic reaction coordinate calculations17 were
performed to confirm the reaction paths.
In the high-pressure-limit regime, reaction rate coefficients
were calculated using the microscopic formulation of transition
state theory:
where kB is the Boltzmann constant, h is the Planck constant,
and QR(T) and QTS(T) are the reactant and transition state
partition functions, respectively. The activation barrier at 0 K,
ΔE0(0 K), is the energy difference between the transition state
and the reactants at 0 K, including the zero point energy (ZPE),
and was calculated with the CBS-QB3 method. The tunneling
correction factor κ(T) accounts for tunneling effects on the
reaction rate. Partition functions Q(T) were calculated using
standard formulas from statistical thermodynamics.18 Inte
al
rotation partition functions were obtained using the onedimensional
hindered rotation approximation.19 Rotational potentials
were calculated as a function of the torsion angle at
10° intervals using the B3LYP/6-311G(d,p) method. A 0.9679
scaling factor20 was used for frequencies that enter the vibrational
partition function, and the ZPE was calculated within the
CBS-QB3 method. Only the ground state was used to calculate
the electronic partition function, except for the hydroxyl radical
for which the first excited state, located 1.7 kJ/mol above the
ground state,21 was taken into account. All the first principles
calculations were performed with the Gaussian03 computational
package.22
Tunneling correction factors κ(T) were calculated using the
small curvature tunneling method, as implemented in the Polyrate9.723
and the Gaussrate9.724 programs, following the approach
outlined earlier.11 Tunneling calculations are done on
the vibrationally adiabatic ground-state potential energy surface
and require an accurate description of the energy variation along
the reaction path; in particular, near the transition state.
Depending on the tunneling approximation, a larger range of
the potential energy surface needs to be calculated. Since the
CBS-QB3 method was found to provide accurate reaction and
activation energies at a reasonable computational cost, geometries
along and curvatures orthogonal to the minimum energy
path were calculated at the B3LYP/6-311G(d,p) level of theory,
whereas the energy variation along the MEP was described using
the CBS-QB3 method. This approach is consistent with the
approach described by Malick et al.25 and Saeys et al.26 and
has been implemented using the dual-level VTST-ISPE method
in the Polyrate9.7 program.27 The Page-McIver method28 was
used to follow the reaction coordinate. The reoriented dividing
surface algorithm29 was used to calculate frequencies along the
reaction path. In addition, the low real frequency was interpolated
with the IVTST0FREQ scheme23 to avoid imaginary
frequencies. For the acid, R1, R2, , γ, methyl1, and methyl2
channels, the MEPs were mapped with a 0.53 pm step size for
reaction coordinates s from -0.69 to +0.98 Å, from -1.19 to
+0.29 Å, from -1.24 to +0.24 Å, from -1.52 to +0.24 Å,
from -1.52 to +0.29 Å, from -1.19 to +0.24 Å, and from
-0.95 to +0.19 Å, respectively, where s ) 0 indicates the
B3LYP/6-311G(d,p) transition state. The Hessians were recalculated
every nine steps. CBS-QB3 energies were calculated
for the saddle points, for complexes on the reactant and product
side, and for additional points at s ) -0.43, -0.24, -0.11,
0.16, 0.36, and 0.98 Å (acid); s)-1.19, -0.71, -0.43, -0.29,
-0.14, 0.05, 0.10, 0.14, 0.19, 0.24, and 0.29 Å (R1); s)-1.24,
-1.14, -0.90, -0.67, -0.43, -0.29, -0.14, 0.05, 0.10, 0.14,
0.19, and 0.24 Å (R2); s ) -1.52, -0.90, -0.57, -0.14, 0.05,
0.10, 0.14, 0.19, and 0.24 Å (); s ) -1.52, -1.29, -0.57,
-0.43, -0.29, -0.14, 0.05, 0.10, 0.14, 0.19, 0.24, and 0.29 Å
(γ); s)-1.19, -0.95, -0.71, -0.43, -0.29, -0.14, 0.05, 0.10,
0.14, 0.19, and 0.24 Å (methyl1); and s)-0.95, -0.71, -0.43,
-0.29, -0.14, 0.05, 0.10, 0.14, and 0.19 Å (methyl2) along
the MEPs. The tunneling correction factors were also calculated
with the computationally efficient Eckart method because Eckart
tunneling factors were found to agree well with more accurate
SCT factors for the C-H channels in formic and acetic acid.11
The Eckart tunneling factor is obtained by fitting an Eckart
potential to the potential energy profile using the B3LYP/6-
311G(d,p) curvature at the transition state, and the zero point
energy inclusive CBS-QB3 energy barrier and reaction energy.
The tunneling factor is then obtained using standard expressions.
30
Reactions between carboxylic acids and hydroxyl radicals
proceed through a hydrogen-bonded prereactive complex.9-13
First, a chemically activated prereactive complex* is formed,
which can undergo stabilization through collisions, where is
the collisional stabilization efficiency, ks is the collisional
stabilization rate coefficient, and [M] is the bath gas concentration;
dissociate back to the reactants, k-1; or react to form the
products, k2.
At the high-pressure limit, the prereactive complexes obey a
Boltzmann equilibrium population, and the pseudoequilibrium
assumption can be used for the formation of the prereactive
complexes above 230 K.11 Indeed, at 298 K, collision theory
gives 2 × 107 m3/(mol s) for k1, and using calculated equilibrium
coefficients of between 6.5 × 10-4 and 1.4 × 10-2 m3/mol for
the formation of the prereactive complexes, k-1 is calculated to
be between 1.1 × 109 and 2.5 × 1010 s-1. For the reaction
between valeric acid and hydroxyl radicals, k2 is at least 1-2
orders of magnitude smaller than k-1 at 298 K, and the
pseudoequilibrium assumption is valid. However, consistent with
the higher activation barrier, the difference between k-1 and k2
SCHEME 1
k ) k(T)
kBT
h
QTS(T)
QR(T)
e(-ΔE0(0K)
RT ) (1)
Hydrogen Abstraction from Organic Acids J. Phys. Chem. A, Vol. 113, No. 27, 2009 7853
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decreases at lower temperatures. Below 230 K, k-1 becomes
smaller than k2, and the pseudoequilibrium approximation no
longer holds. Using the pseudoequilibrium assumption for the
formation of the prereactive complexes, the reaction rate
coefficient can be written as11
where QTS(T) and ETS are the partition function and the energy
at 0 K for the transition state, and QR(T) and ER are the partition
function and the energy at 0 K for the separated reactants. κ(T)
is the tunneling correction factor for the hydrogen transfer
reaction, step 2 in Scheme 2.
The above calculations are based on transition state theory.
At 1 atm and 298 K, the high-pressure-limit assumption may
not be valid, and the reaction may be partially chemically
activated. Indeed, at low pressures, the collision frequency with
bath gas molecules is too low to stabilize the chemically
activated prereactive complexes before they undergo further
reactions. The effect of pressure on the overall rate coefficients
at 298 K was evaluated using the three-frequency version of
quantum Rice-Ramsberger-Kassel theory31 with the modified
strong-collision approximation (QRRK-MSC)32 using
CHEMDIS.33 The MSC approximation assumes that collision
either stabilizes the activated complex completely or not at all.36
Both the chemically activated and thermally activated mechanism
are considered in the simulations. Though the effect of
the bath gas pressure on the rate coefficient could be treated
more accurately using the master equation approach,34 reasonable
agreement between QRRK-MSC estimates and master
equation calculations has been reported.35 The high-pressurelimit
rate coefficients k1(T) and k2(T) were calculated as above,
while k-1(T) was obtained from the equilibrium constant. Within
CHEMDIS, the rate coefficients are described by four parameter
expressions, ATn exp(-RT) exp(-Ea/RT). Lennard-Jones parameters
for the prereactive complexes, σ ) 5.85 Å2 and ε )
327 K, were taken from literature values for n-pentane.37 N2
was used as the bath gas. Tunneling corrections are not included
in the QRRK-MSC simulations, and the final rate coefficients
were obtained by multiplying the pressure-dependent rate
coefficients with the corresponding SCT factors, κi(298).
Hydrogen bonds in the different transition states play an
important role in determining the rate and selectivity of the initial
hydrogen abstraction from organic acids by hydroxyl radicals.
To characterize and quantify the strength of the hydrogen bonds,
a natural bond orbital (NBO) analysis was performed at the
B3LYP/6-311G(d,p) level of theory using the NBO3.1 package,
38 as implemented in Gaussian03. |
