Ab Initio Reaction Path Analysis for the Initial Hydrogen Abstraction from Organic Acids by Hydroxyl Radicals

Краткое содержание

Wenjie Sun,† Liming Yang,‡ Liya Yu,‡ and Mark Saeys*,†

Department of Chemical and Biomolecular Engineering, 4 Engineering DriVe 4, National UniVersity of

Singapore, Singapore 117576, DiVision of EnVironmental Science and Engineering, 9 Engineering DriVe 1,

National UniVersity of Singapore, Singapore 117576

ReceiVed: October 14, 2008; ReVised Manuscript ReceiVed: May 5, 2009

Hydrogen abstraction from organic acids by hydroxyl radicals is the initial rate- and selectivity-determining

step in the photochemical oxidation of organic acids in the troposphere. To quantify the rate and selectivity

of these reactions, the abstraction of hydrogen atoms at the acid, R, _, γ, and methyl positions was studied

for valeric acid, C4H9COOH, using first principles calculations. At the high-pressure limit, an overall rate

coefficient at 298 K of 4.3 . 106 m3/(mol s) was calculated. The dominant pathways are abstraction at the

_; the γ; and, to a lesser extent, the acid positions; with a selectivity of 55, 28, and 8%, respectively. This

differs from the high selectivity for the acid channel for formic and acetic acids and from the thermodynamic

preference for abstraction at the R position, but it is consistent with the experimentally observed preference

for the _ and the γ positions in larger organic acids. The rate and selectivity are controlled by the strength

of hydrogen bonds between the acid group and the hydroxyl radical in the different transition states and do

not correlate with the stability of the products. Natural bond orbital analysis was used to quantify the nature

and strength of the hydrogen bonds. At 298 K and below 0.1 atm, the collision frequency is insufficient to

stabilize the prereactive complexes, and the reaction becomes chemically activated. However, the reaction

rate and the selectivity are largely unaffected by this mechanistic change.

1. 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

Published on Web 06/15/2009

Downloaded by AUSTRIA CONSORTIA on July 6, 2009

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 A, from -1.19 to

+0.29 A, from -1.24 to +0.24 A, from -1.52 to +0.24 A,

from -1.52 to +0.29 A, from -1.19 to +0.24 A, and from

-0.95 to +0.19 A, 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 A (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 A (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 A (R2); s ) -1.52, -0.90, -0.57, -0.14, 0.05,

0.10, 0.14, 0.19, and 0.24 A (_); 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 A

(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 A (methyl1); and s)-0.95, -0.71, -0.43,

-0.29, -0.14, 0.05, 0.10, 0.14, and 0.19 A (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.