and Hydrogen Abstraction Reaction with OH Radical
ASIT K. CHANDRA,1,* TADAFUMI UCHIMARU,2 MASAAKI SUGIE,2 AKIRA SEKIYA2 1
Research Institute of Innovative Technology for the Earth (RITE), AIST Tsukuba Central 5, Tsukuba 305-8565, Japan
2
National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Tsukuba 305-8565, Japan
Received 7 June 2002; Accepted 6 August 2002
Abstract:
The conformational potential energy surfaces for mono- and difluoromethyl formate have been determined by using a modified G2(MP2) level of calculations. The structures and vibrational frequencies for the conformers of mono- and difluoromethyl formate have been reported. The hydrogen abstraction reaction channels between these two formates and OH radicals have been studied at the same level of theory. Using the standard transition state theory and taking into account the effect of tunneling across the reaction barrier, we have estimated the rate constant for hydrogen abstraction by OH radical. The effect of successive fluorine substitution for methyl hydrogen on the conformational stability and on the hydrogen abstraction rate has been analyzed.©2003 Wiley Periodicals, Inc. J Comput Chem 24: 396 – 407, 2003
Key words: fluorinated formate;ab initio; hydrogen abstraction; OH radical; rate constant
Introduction
The structure of methyl formate (MF) has been studied extensively both experimentally1,2 and theoretically,3–5 but the structures of
halomethyl formates are not as well known. Hotokka and Dahlqvist6
studied the conformational potential energy surfaces of chloromethyl formate and fluoromethyl formate (FMF), CH2FOCHO, by usingab
initiocalculations at the Hartree-Fock level. However, their study was restricted only to the rotation of the halomethyl group about the OOC bond, and other bond lengths and angles were not optimized. Later, Lopata and Kuczkowski7identified thesynconformer of FMF for the
first time in their laboratory as a decomposition product from vinyl fluoride ozonide and determined its structural parameters. They also predicted the possibility of existence of another conformer of FMF. In fact, it is well known8that alkyl formates can exist in two
conforma-tions,synandanti:
If R is hydrocarbon, thesynconformer is largely preferred to the
anti and the barrier to interconversion is around 10 kcal/mol.8
However, when R⫽CF3, the two conformers become closer in
energy and also the barrier to interconversion decreases. Thus, both the conformers of CF3OCHO exist in normal conditions. It is,
therefore, interesting to study how the stability of the two con-formers changes with the successive fluorine substitution while going from CH3OCHO (MF) to trifluoromethyl formate (TFMF),
CF3OCHO through FMF and difluoromethyl formate (DFMF),
CHF2OCHO. In the case of FMF and DFMF, the rotation of the
OCH2F andOCHF2groups, respectively, along the OOC bond
may generate more conformers than the two shown above. In the present work, we have calculated for the first time the structures and vibrational frequencies for all the conformers of FMF and DFMF by usingab initioMP2(full)/6-311G(d,p) method. More-over, the energies of all the species have been calculated by using high level G2(MP2) method. To the best of our knowledge, there is no experimental or theoretical report on the structure and
con-*Current address: Chemistry Group, Birla Institute of Technology and Science (BITS), Pilani 333 031, Rajasthan, India.
Correspondence to: T. Uchimaru; e-mail: [email protected]
This article includes Supplementary Material available from the authors upon request or via the Internet at ftp://ftp.wiley.com/public/journals/jcc/ suppmat/24/396 or http://www.interscience.wiley.com/jpages/0192-8651/ suppmat/v24.396.html
formational stability of DFMF. Our study provides accurate infor-mation about the structure, relative stability, and vibrational fre-quencies of the conformers of FMF and DFMF and those of the rotational barrier separating the two conformers.
Moreover, we have also studied the hydrogen abstraction re-actions of FMF and DFMF with OH radicals. Recent works9 –12
have shown formates as major products resulting from the oxida-tion of halogenated ether compounds in the atmosphere. The atmospheric impact of the resulting formates should, therefore, be included while considering the global warming potential of ha-loethers. Because hydrogen abstraction reaction with OH radicals is likely to be one of the major degradation channels for haloge-nated formates in the atmosphere,11,12it is important to understand
the reaction of formates with OH radicals. Knowledge of the rate constants is essential to evaluate the atmospheric lifetime of a compound. The kinetic data on hydrogen abstraction from for-mates are very limited. Very recently, we investigated the hydro-gen abstraction reaction: CF3OCHO⫹OH3CF3OCO ⫹H2O
usingab initioG2(MP2) theory.13In the present study, we also
investigate for the first time the kinetics and mechanism of the following hydrogen abstraction reactions of FMF and DFMF with OH radicals:
CH2FOCHO⫹OH 3 CH2FOCO⫹H2O (R1a)
CH2FOCHO⫹OH 3 CHFOCHO⫹H2O (R1b)
CHF2OCHO⫹OH 3 CHF2OCO⫹H2O (R2a)
CHF2OCHO⫹OH 3 CF2OCHO⫹H2O (R2b)
The result provides an indication of kinetics of these reactions and how the reactivity for hydrogen abstraction changes with the change in fluorine substitution.
Computational Details
Full geometry optimizations for all species were carried out at the MP2(full)/6-311G(d,p) level. Frequencies of all the stationary points were then calculated at the same level of theory. This computational level was chosen as a reasonable compromise be-tween speed and accuracy of calculations, which was based on our experience in the earlier studies.14,15After optimizing the
geom-etries, single point calculations of the energies were carried out at the QCISD(T)/6-311G(d,p) and MP2/6-311⫹G(3df,2p) levels of theory in order to determine accurately the relative stability of the various conformers of FMF and DFMF, and also to calculate the barrier height and thermochemistry of the reactions (R1) and (R2) at the G2(MP2)16level of theory. We should point out that the
G2(MP2) calculations in the present study were made with MP2(full)/6-311G(d,p) geometries and frequencies rather than the prescribed MP2(full)/6-31G(d) geometries and HF/6-31G(d) fre-quencies. In our previous work we employed this modified G2(MP2) procedure on the reaction between CF3OCHO and OH
radical.13This procedure produced very good results for hydrogen
abstraction from CF3OCHO. We also calculated the hydrogen
abstraction rate constant for the reaction between CH3OCHO and
OH by applying the same procedure, and the calculated value of 1.8⫻10⫺13cm3molecule⫺1s⫺1is found to be in good agreement
with the experimental value of (1.73 ⫾ 0.21) ⫻ 10⫺13 cm3
molecule⫺1s⫺1at 298 K.17Thus, we employed the same
modi-fication of the G2(MP2) procedure in the present study. The calculated harmonic vibrational frequencies were scaled by a fac-tor of 0.949618and the zero point energies (ZPEs) and vibrational
contribution to enthalpy were estimated from the scaled frequen-cies. Spin contamination is often a serious problem in treating open-shell systems with single configuration wave function. How-ever, in the present case, spin contamination was not high for either the radicals or transition states (TSs) for hydrogen abstrac-tion; the具S2典 value never exceeded 0.76 for the radicals and 0.78 for TSs. All calculations were performed with the GAUSSIAN98 suite of programs.19
Results and Discussion
Structures and Vibrational Frequencies
FMF and DFMF have two stable conformations based on the values of the C3OO1OC2OO4 torsional angle (see Figs. 1 and
2):synwhen the C3OO1OC2OO4 dihedral angle is around zero
and anti when the C3OO1OC2OO4 dihedral angle is around
180°. The same is true for the radicals generated after a hydrogen atom abstraction either from the carbonyl site or from the fluori-nated methyl group of FMF and DFMF. However, under thesyn
andantiarrangement of C3OO1OC2OO4, more than one
con-former may exist depending upon the C2OO1OC3OF6 torsional
angle for FMF and the C2OO1OC3OH6 torsional angle for
DFMF. Studying the rotation of the carbonyl group along the O1OC2 bond and the rotation of the fluoromethyl/difluoromethyl
group along the O1OC3 bond, we have identified two conformers
for FMF and four conformers for DFMF.
Table 1 presents the optimized geometrical parameters (see Fig. 1 for the definition) for both thesynandanticonformers of FMF and the radicals generated after hydrogen atom abstraction from both the carbonyl and fluoromethyl groups. Experimental geomet-rical parameters are available only for thesynconformer of FMF.7
Our calculated values are in excellent agreement with the experi-mental results. Our calculated value for the optimum C2OO1OC3
angle (114.9°) ofsyn-FMF is much lower than the value (122°) obtained from low level ab initio computations.6 Experimental
geometry is not available for theanti-FMF, probably because at room temperature almost 99% of FMF will be atsynconformation due to its lower energy (discussed later). The carbonyl oxygen atom (O4) deviates slightly from the C3OO1OC2 plane of FMF.
Such deviation from planarity was also noticed from the experi-mental results.7However, the energy change from the planar to the
equilibrium slightly nonplanar configuration is very small (⬍0.05 kcal/mol), indicating the flatness of the potential energy surface in this region. The C2OO1OC3OF6 dihedral angle (⬇80°)
indi-cates that the O1OC3OF6 plane is nearly perpendicular to the
C2OO1OC3 plane. This conformation is in clear contrast to those
observed for cis- and trans-fluoroacetic acid,20 cis- and trans
-fluoroacetyl fluoride,20 and
cis- and trans-1,3-difluoroacetone,21
group. The interaction that leads to this contrast can be explained in terms of anomeric effect resulting from the interaction between
noxygenand*
CForbitals of the CH2FOO system (see Fig. 3). This
interaction is most favorable when the O1OC3OF6 plane
be-comes nearly perpendicular to the C2OO1OC3 plane. Except for
the O1OC2OO4 and O1OC2OH5 angles, the bond lengths and
angles in the syn and anti-FMF are not much different. The O1OC2OO4 angle is more than 3° larger for the syn-FMF, whereas the O1OC2OH5 angle is smaller by nearly 4° in
com-parison to that in theanti-FMF. In the TS structure related to the interconversion of syn and anti conformers of FMF, the C3OO1OC2OO4 torsional angle becomes 99°. The dipole
mo-ments for thesynandanti-FMF are calculated to be 2.18 and 3.31 D, respectively, at the MP2(full)/6-311G(d,p) level. Our calculated dipole moment value forsyn-FMF (2.18 D) is close to the exper-imental value of 2.24 ⫾ 0.02 D.7 The C2
OO1 bond becomes
shorter and the C3OO1 bond becomes longer while going from
FMF molecule to the corresponding CH2FOCO radical. The
op-posite is true for the CHFOCHO radical. The O1OC2OO4 angle
in the CH2FOCO radical is more than 4° larger than that in the
corresponding parent molecule.
The optimized geometrical parameters for DFMF and the rad-icals generated due to hydrogen abstraction from it are given in
Table 2 (see also Fig. 2). The two conformers of DFMF where C3OO1OC2OO4 torsional angle is around 0°, but
C2OO1OC3OH6 torsional angles are 39.1° and 180.0°, are
namedsyn-1 andsyn-2, respectively. Similarly, the two conform-ers of DFMF under anti conformation (C3OO1OC2OO4 ⬃
180°) are designated as anti-1 (C2OO1OC3OH6 180.0°) and
anti-2 (C2OO1OC3OH6 41.6°). The same type of nomenclature
is used for designating the conformers of CHF2OCO radical. It is
interesting to note that in the most stable syn-1 conformer of DFMF the O1OC3OF8 plane makes an angle of 82° with the
C2OO1OC3 plane, which gives extra stabilization to the system
due to anomeric effect, as discussed before for FMF. The C2OO1OC3 angle insyn-2-CHF2OCHO is more than 3° larger
than that insyn-1-CHF2OCHO. The most significant differences
between the structures of thesynand anticonformers of DFMF can be observed for the O1OC2OO4 and O1OC2OH5 angles
(see Fig. 2). The values of O1OC2OO4 angles insyn-1 andsyn-2
conformers are nearly 5° higher than the values of the same angles inanti-1 and anti-2 conformers. The opposite trend can be ob-served for the O1OC2OH5 angle. As mentioned earlier, the
position of the H6 atom insyn-1 andanti-2 is different from the position of the same atom in syn-2 and anti-1 conformers of DFMF. In the former two conformers, the C2OO1OC3OH6
Figure 1. Schematic diagrams for the structures of both thesynandanticonformers of CH2FOCHO
Figure 2. Schematic diagrams for the structures of the four conformers of CHF2OCHO (DFMF) and the corresponding radicals generated for the hydrogen abstraction from the formyl group and theOCHF2
dihedral angle is around 40°, whereas the same angle amounts to 180° for the latter two conformers. In fact, syn-2 and anti-1 conformers of DFMF molecule haveCssymmetry. It is interesting
to compare the key geometrical parameters ofsynand anti con-formers of FMF and DFMF with those of MF and TFMF. The C2OO1 bond length increases and the C3OO1 bond length de-creases with the increase in fluorine substitution while going from MF to TFMF through FMF and DFMF. Successive fluorine sub-stitutions at the methyl position enhance the electron withdrawing ability of this group, and as a result an electron cloud is likely to shift from C2OO1 bonding region to the C3OO1 bonding region.
This makes the C2OO1 bond weaker and C3OO1 bond stronger with the successive fluorine substitution at the methyl position. The dipole moments for thesyn-1,syn-2,anti-1, andanti-2 con-formers of DFMF are calculated to be 1.48, 2.65, 2.13, and 3.04 D, respectively, at the MP2(full)/6-311G(d,p) level. The
C3OO1OC2OO4 torsional angle amounts to 90° for the TS
structure ofsyntoantiinterconversion in DFMF. Hydrogen ab-straction from the carbonyl group of DFMF yields CHF2OCO
radicals. Like the parent molecule, CHF2OCO radical has four
stable conformers. The optimized geometrical parameters for these conformers are given in Table 2. Thesyn-2 andanti-1 conformers of CHF2OCO radical remain inCs symmetry as its parent
mole-cule. Table 2 shows that the main structural changes in CHF2OCO
radicals include a shortening of the C2OO1 bond and lengthening
of the C3OO1 bond. The opposite trend is observed for
CF2OCHO radicals, which results from the methyl hydrogen
ab-straction of DFMF. In the case of CF2OCHO radical, the C2OO1
bond increases and C3OO1 bond decreases in comparison to those in parent DFMF molecule.
The vibrational frequencies for all the conformers of FMF and DFMF, and the radicals generated from them after hydrogen abstraction are given in Table 3. The calculated results cannot be compared with any other data, because no such data, experimental or theoretical, are available for these systems. The stretching frequency for the COH bond (3132 cm⫺1) in the formyl group of
syn-FMF is much higher than that for the same bond inanti-FMF (3042 cm⫺1), indicating that this C
OH bond is much weaker in
anti-FMF. The difference in the vibrational frequencies of the COH bond in the formyl group ofsyn-1 (3148 cm⫺1),syn-2 (3133
cm⫺1), and anti-1 (3129 cm⫺1) conformers of DFMF is rather
small. The carbonyl COO stretching frequency for syn-FMF
(1828 cm⫺1) is found to be lower by 34 cm⫺1 than that for
anti-FMF (1862 cm⫺1). The C2
OO4 bond length insyn-FMF is
somewhat longer (0.006 Å) than the same bond in anti-FMF, which indicates that the C2OO4 bond in the former is weaker than
Table 1. Optimized Geometrical Parameters for thesynandantiConformers of CH2FOCHO (FMF)
Molecules, CH2FOCO Radical, and CHFOCHO Radical at the MP2(full)/6-311G(d,p) Level.
Geometrical parameters
CH2FOCHO (FMF) CH2FOCO CHFOCHO
syn Expt.a anti syn anti syn anti
C2OO1 1.360 1.355 1.366 1.339 1.351 1.363 1.381
C3OO1 1.407 1.404 1.395 1.423 1.410 1.374 1.361
C2OO4 1.199 1.194 1.193 1.186 1.181 1.199 1.191
C2OH5 1.096 1.100 1.103 1.095 1.099
C3OF6/F5 1.364 1.369 1.369 1.358 1.361 1.327 1.342
C3OH7 1.087 1.082 1.087 1.090 1.090 1.085 1.083
C3OH8/H6 1.089 1.066 1.093 1.087 1.087
C2OO1OC3 114.9 115.8 114.7 114.6 113.9 116.0 115.4
O1OC2OO4 125.8 125.8 122.4 130.2 126.9 125.6 121.5
O1OC2OH5 108.2 108.5 112.4 107.9 112.3
O1OC3OF6/F5 109.8 109.6 110.1 109.7 109.7 109.5 113.7
O1OC3OH7 105.6 106.8 106.4 109.9 110.5 116.9 112.7
O1OC3OH8/H6 110.6 111.1 111.4 105.2 105.6
C3OO1OC2OO4 1.6 1.5 175.3 1.8 175.0 1.2 174.0
C2OO1OC3OF6/F5 80.5 83.9 77.9 77.1 81.9 ⫺164.0 64.9
C2OO1OC3OH7 ⫺162.0 ⫺164.0 ⫺164.1 ⫺42.4 ⫺37.9 ⫺32.1 ⫺163.0
aRef. 7.
Bond lengths and angles are given in Angstrom and degrees, respectively. See Figure 1.
in the latter. This is also reflected in the force constant values for the C2OO4 bond of syn-FMF (17.68 mDyne/Å) andanti-FMF
(19.76 mDyne/Å). The distance between O4 and H8 atoms (see Fig. 1) insyn-FMF amounts to 2.40 Å, which indicates the pres-ence of weak hydrogen bonding interaction between these two atoms. This hydrogen bonding interaction weakens the C2OO4
bond in syn-FMF. Interestingly, the carbonyl COO stretching
frequencies for thesyn- (1828 cm⫺1) andanti-FMF (1862 cm⫺1)
are almost the same as those calculated for the syn and anti
conformers of DFMF. The COH stretching frequencies for the
COH bond in the fluoromethyl group for thesyn- (3157 cm⫺1)
andanti-FMF (3117 cm⫺1) are higher than those observed for the
syn- (3228 and 3225 cm⫺1) and
anti-DFMF (3245 and 3169 cm⫺1).
Energetics
As mentioned before, FMF has two conformers,synandanti.The
synconformer is found to be lower in energy than the correspond-ing anticounterpart. The energy differences between these two conformers of FMF amount to 3.0 kcal/mol, at the G2(MP2) level of theory. DFMF has four stable conformers, and the G2(MP2) calculated energy differences between the most stablesyn-1 and the other three conformers are found to be 2.4, 2.4, and 4.0 kcal/mol forsyn-2,anti-1, andanti-2, respectively. These energy differences are much lower than those observed for MF, where at the same G2(MP2) level thesynconformer is 4.7 kcal/mol lower in energy than theanti-CH3OCHO. Thus the energy difference
between the two conformers comes down with the increase in fluorine substitution for the methyl hydrogen. In fact, the energy
difference between the two conformers of TFMF is only 1.1 kcal/mol.13 The barrier to interconversion (
syn 3 anti) is also found to reduce with increasing fluorine substitution at the methyl position. The G2(MP2) calculated barrier heights forsyn3anti
interconversion amount to 12.8, 9.8, and 7.1 kcal/mol, respec-tively, for MF, FMF, and TFMF. However, in the case of DFMF, thesyn-13anti-2 interconversion barrier (11.0 kcal/mol) is found to be much higher than thesyn-23anti-1 barrier (6.4 kcal/mol). Thesyn-1 3syn-2 andanti-13anti-2 interconversion barriers for DFMF are found to be 7.1 and 3.2 kcal/mol, respectively, at the G2(MP2) level. In the case of TFMF, the strong -accepting
influence of the CF3 group is known to be responsible for the
decrease in energy difference between the two conformers and the barrier separating the two.8,22The energy differences between the
conformers of FMF and DFMF indicate that the presence of the
anticonformer will be negligible in any sample of FMF or DFMF at room temperature (298 K). However, the population of anti
conformer will be significant at higher temperature and can be experimentally detected.
In contrast to FMF and DFMF molecules, theanticonformers of CH2FOCO and CHF2OCO radicals are found to be 1.5 to 2.7
kcal/mol lower in energy than the corresponding thesyn conform-ers. The reversal in the stability order of the two conformers of radicals in comparison to the stability order of the two conformers of FMF and DFMF molecules introduces a significant difference in the bond strength between the COH bonds at the carbonyl groups
of thesynandanti conformers of FMF and DFMF. The energy difference between theanti-1 andanti-2 conformers of CHF2OCO
is found to be rather small (0.1 kcal/mol), whereas the energy
Table 2. Optimized Geometrical Parameters for the Different Conformers of CHF2OCHO (DFMF)
Molecules, CHF2OCO Radical, and CF2OCHO Radical at the MP2(full)/6-311G(d,p) Level.
Geometrical parameters
CHF2OCHO (DFMF) CHF2OCO CF2OCHO
syn-1 syn-2 anti-2 anti-2 syn-1 syn-2 anti-1 anti-2 syn anti
C2OO1 1.364 1.377 1.383 1.371 1.342 1.353 1.367 1.354 1.377 1.386
C3OO1 1.393 1.388 1.374 1.381 1.410 1.404 1.389 1.397 1.370 1.358
C2OO4 1.198 1.193 1.191 1.192 1.186 1.182 1.178 1.180 1.193 1.189
C2OH5 1.095 1.096 1.096 1.101 1.094 1.098
C3OH6/H5 1.087 1.087 1.085 1.091 1.088 1.086 1.086 1.088
C3OF7 1.336 1.342 1.351 1.332 1.337 1.338 1.341 1.340 1.317 1.313
C3OF8/F6 1.342 1.342 1.351 1.348 1.329 1.338 1.341 1.332 1.324 1.332
C2OO1OC3 115.1 118.2 115.8 115.3 114.6 117.2 114.4 113.8 115.5 114.9
O1OC2OO4 125.6 126.5 120.8 121.9 129.9 130.7 125.4 126.6 125.5 121.1
O1OC2OH5 108.0 106.8 113.2 112.9 107.3 112.4
O1OC3OH6/H5 112.4 106.6 108.1 113.0 111.5 106.3 106.7 112.0
O1OC3OF7 106.2 111.1 110.9 107.0 109.2 110.5 110.7 109.0 109.3 110.3
O1OC3OF8/F6 109.4 111.1 110.9 109.7 106.0 110.5 110.7 106.5 113.3 113.4
C3OO1OC2OO4 0.0 0.0 180.0 175.4 ⫺1.0 0.0 180.0 176.4 1.2 174.0
C2OO1OC3OH6/H5 39.1 180.0 180.0 41.6 42.0 180.0 180.0 28.7 ⫺164.0 64.9
H6OO1OC3OF7 121.1 119.5 120.6 121.0 ⫺32.1 ⫺163.0
H6OO1OC3OF8 ⫺121.8 ⫺119.5 ⫺120.6 ⫺121.2
C2OO1OC3OF6 72.7 71.1
difference betweensyn-1 and syn-2 conformers amounts to 1.1 kcal/mol. Interestingly, the syn conformer is found to be more stable than the anti conformer for CHFOCHO and CF2OCHO
radicals, generated due to hydrogen abstraction from the fluorom-ethyl group of FMF and DFMF. The interconversion (syntoanti) barrier for CHFOCHO and CF2OCHO radicals is calculated to be
8.7 and 7.6 kcal/mol, respectively.
Reaction with OH Radical
There are two potential hydrogen abstraction sites in FMF and DFMF molecules, namely the formyl hydrogen and the hydrogen atom of the fluoromethyl group. Moreover, in principle, hydrogen abstraction from bothsynandanticonformers of FMF and DFMF should be considered. The free energy difference at 298 K between the syn and anti conformers of FMF is calculated to be 2.8 kcal/mol at the G2(MP2) level. It suggests that at 298 K only about 1% of FMF will exist asanticonformer. In the case of DFMF,
syn-1 is the lowest energy conformer, and the free energy differ-ences between syn-2, anti-1, and anti-2 conformers and syn-1 amount to 2.7, 2.4, and 3.5 kcal/mol, respectively. Thus at 298 K
about 1% of the DFMF molecule is likely to exist in syn-2 conformation, whereas about 1.5% of the molecule exists asanti-1 conformer. However, at higher temperature, the presence ofanti
conformer of FMF andsyn-2 and anti-1 conformers of DFMF cannot be neglected in any reaction sample of FMF or DFMF. For example, at 450 K, the percentage of anti conformer of FMF should be around 4%. The presence ofanti-2 conformer of DFMF can be neglected even at higher temperature. Thus, hydrogen abstraction from both thesyn and anticonformers of FMF and
syn-1,syn-2, andanti-1 conformers of DFMF should be taken into account while calculating the total hydrogen abstraction reaction rate of FMF and DFMF at a temperature significantly higher than the room temperature (298 K).
Six TSs (three TSs for each conformer of FMF) are identi-fied for hydrogen abstraction reactions of OH radicals with
syn-FMF and anti-FMF. Similarly, DFMF has two different hydrogen abstraction sites, and accordingly six TSs (two TSs for each of thesyn-1,syn-2, andanti-1 conformers) are found for reaction with OH radicals. Figures 4 and 5 illustrate the structures and key geometrical parameters of these TSs for the
Table 3. Unscaled Harmonic Vibrational Frequencies (in cm⫺1)
at the MP2(full)/6-311G(d,p) Level.
System in cm⫺1
syn-FMF (CH2FOCHO)
101, 245, 336, 553, 773, 1009, 1055, 1121, 1177, 1217, 1345, 1424, 1499, 1544, 1828, 3132, 3157, 3242
anti-FMF (CH2FOCHO)
107, 151, 357, 503, 692, 1042, 1049, 1116, 1156, 1231, 1341, 1447, 1498, 1552, 1862, 3042, 3117, 3229
syn -CH2FOCO
94, 272, 332, 545, 767, 990, 1120, 1156, 1198, 1332, 1489, 1546, 1883, 3152, 3246
anti -CH2FOCO
102, 225, 326, 492, 674, 1029, 1123, 1144, 1216, 1342, 1499, 1547, 1908, 3150, 3241
syn -CHFOCHO
76, 250, 300, 470, 794, 990, 1043, 1080, 1211, 1246, 1388, 1434, 1817, 3147, 3229
anti -CHFOCHO
116, 143, 322, 521, 695, 963, 1041, 1072, 1182, 1224, 1397, 1436, 1860, 3094, 3260
syn-1-DFMF (CHF2OCHO)
69, 218, 254, 459, 522, 662, 799, 1053, 1079, 1162, 1198, 1222, 1427, 1436, 1449, 1827, 3148, 3228
syn-2-DFMF (CHF2OCHO)
120, 204, 209, 487, 535, 606, 839, 1032, 1046, 1154, 1186, 1190, 1424, 1440, 1454, 1845, 3133, 3225
anti-1-DFMF (CHF2OCHO)
104, 161, 234, 482, 521, 598, 806, 1000, 1039, 1147, 1183, 1199, 1422, 1443, 1467, 1861, 3129, 3245
anti-2-DFMF (CHF2OCHO)
42, 124, 251, 431, 531, 616, 746, 1037, 1132, 1153, 1180, 1231, 1430, 1449, 1471, 1863, 3061, 3169
syn -1-CHF2OCO
64, 211, 302, 456, 518, 664, 782, 1056, 1137, 1188, 1234, 1430, 1446, 1886, 3213
syn -2-CHF2OCO
100, 195, 268, 488, 535, 610, 840, 1016, 1109, 1177, 1194, 1427, 1434, 1902, 3235
anti -1-CHF2OCO
111, 211, 217, 476, 517, 590, 806, 983, 1156, 1184, 1187, 1434, 1448, 1929, 3240
anti -2-CHF2OCO
40, 209, 258, 429, 518, 619, 720, 1127, 1136, 1178, 1220, 1431, 1444, 1913, 3212
syn -CF2OCHO
77, 191, 238, 453, 517, 670, 801, 1036, 1046, 1163, 1235, 1315, 1429, 1840, 3155
anti -CF2OCHO
hydrogen abstraction from FMF and DFMF. The S-FMF-TS1 and A-FMF-TS1 (see Fig. 4) are the TSs in which the hydroxyl radical attacks, respectively, the formyl hydrogen ofsyn- and
anti-FMF to form CH2FOCO radical and H2O [reaction (R1a)].
The other four TSs are associated with the hydrogen abstraction from theOCH2F group ofsyn-FMF (TS2 and
S-FMF-TS3) andanti-FMF (A-FMF-TS2 and A-FMF-TS3), resulting in the CHFOCHO radical and H2O [reaction (R1b)]. The
S1-DFMF-TS1, S2-S1-DFMF-TS1, and A1-DFMF-TS1 (see Fig. 5) are associated with the reaction (R2a) and correspond, respec-tively, to the hydrogen abstraction from the formyl group of
syn-1,syn-2, andanti-1 DFMF. The breaking COH bonds are
elongated in the TS by nearly 10%; on the other hand, the forming OOH bonds are longer by almost 33% than the normal
OOH bond length in water molecule. These structural features
indicate the formation of early TS, which is, of course, expected from Hammond’s postulate23due to the exothermic nature of
the reaction (discussed later). The other structural parameters do not change much while going from isolated molecules to TS. The distance between H(10) and O(1) atoms (see Figs. 4 and 5) in S-FMF-TS1 (2.67 Å), A-FMF-TS3 (2.61 Å), S1-DFMF-TS1 (2.68 Å), S2-DFMF-TS1 (2.67 Å), and A1-DFMF-TS2 (2.66 Å) is slightly shorter than the sum of van der Waals radii of these two atoms (2.72 Å).24Thus weak hydrogen bonding
interac-tions might be present in these TSs and reduce the barrier height for hydrogen abstraction. Meanwhile, strong hydrogen bonding interaction exists between H(10) and O(4) atoms (see Figs. 4 and 5) in S-FMF-TS2 and S1-DFMF-TS2, because the distance between these two atoms is much shorter than the sum of van der Waals radii of these two atoms. The hydrogen bonding interaction is also found to exist between H(10) and F(6) atoms of S-FMF-TS3 and A-FMF-TS2. The vibrational frequencies for all the TSs are given as supplementary information in Table S1. Each TS has one imaginary frequency, the normal mode of Figure 4. Optimized structures for the transition states of the hydrogen abstraction reaction of OH radical
which corresponds to the coupling of the breaking COH bond
and the forming OOH bond stretching vibrational modes.
The barrier heights for hydrogen abstraction reactions are given in Table 4. Owing to the lower COH bond strength, hydrogen
abstraction from the formyl group of FMF and DFMF is expected to have lower barrier heights than the barrier heights for hydrogen abstraction from the fluoromethyl group. However, the reaction
channel (R1b) through S-FMF-TS2 has a somewhat lower barrier (2.6 kcal/mol) than the barrier (2.9 kcal/mol) for hydrogen abstrac-tion from the carbonyl group (S-FMF-TS1) ofsyn-FMF, presum-ably due to the presence of strong hydrogen bonding interaction in S-FMF-TS2. The S-FMF-TS3 and A-FMF-TS3 are significantly higher in energy in comparison to other hydrogen abstraction reaction channels in FMF and, therefore, they are unlikely to make Figure 5. Optimized structures for the transition states of the hydrogen abstraction reaction of OH radical
withsyn-1, syn-2, and anti-1 conformers of CHF2OCHO (DFMF). Bond lengths and angles are in
any contribution to the total reaction rate. Similarly, the hydrogen abstraction reactions (R2b) from the OCHF2 group of syn-1,
syn-2, andanti-1 conformers of DFMF have much larger barrier height and should not make any contribution to the total reaction rate. It should be mentioned here that activation entropies (⌬S#)
are always more negative for the hydrogen abstractions (R2b) from theOCHF2group than the hydrogen abstractions (R2a) from the
formyl group. Thus, even the entropy factor is not favorable for the hydrogen abstraction from the OCHF2 group of DFMF. The
barrier height for hydrogen abstraction is seen to increase with successive substitution of methyl hydrogen by fluorine. For exam-ple, the barrier heights for hydrogen abstraction from the formyl group of syn-CH3OCHO, syn-CH2FOCHO, syn-1-CHF2OCHO,
and syn-CF3OCHO amount to 2.4, 2.9, 3.3, and 4.1 kcal/mol,
respectively. The heats of reaction calculated from the G2(MP2) results are given in Table 4. Hydrogen abstraction from the car-bonyl group is found to be much more exothermic than that from the fluoromethyl group of FMF and DFMF. This is because the energies for CHFCHO and CF2OCHO radicals are higher than the
energies of CH2FOCO and CHF2OCO, respectively. Among the
conformers of FMF and DFMF, heats of reaction are always higher for theanticonformer.
Rate Constants
Using simple standard transition-state theory (TST),25 the rate
constant for hydrogen abstraction reaction was calculated from the expression
where⌬E0#is the barrier height calculated from the energy
differ-ence (including the ZPEs) between the TS and the two reactants,
Tis the temperature, andQ’s are the respective partition functions. The⌫,kB, andhin eq. (1) stand for the transmission coefficient for tunneling, the Boltzmann constant, and Planck’s constant, respectively. The tunneling factor, ⌫, was calculated by using Eckart’s method for unsymmetrical one-dimensional potential bar-riers.26In the Eckart’s method, the tunneling factor is estimated as
an integrated sum of the energy dependent transmission probabil-ity,(E). The barrier heights given in Table 4 and the imaginary frequencies (scaled by 0.9496) for the TSs mentioned in Table S1 were used for tunneling correction. As described in the section of “Computational Details,” we observed during our studies on the hydrogen abstraction reactions of CF3OCHO and CH3OCHO that
the rate constants calculated from the TST equation in conjunction with the tunneling correction by Wigner’s method were somewhat lower than the corresponding experimental values. On the other hand, the rate constants calculated from the TST equation but with tunneling correction by Eckart’s method were in very good and satisfactory agreement with the experimental values.13Thus we
used the same procedure (i.e., TST with Eckart’s method of tunneling correction) for the present study. The partition functions were evaluated with the rigid-rotator and quantum harmonic ap-proximation27using the scaled frequencies at the
(U)MP2(full)/6-311G(d,p) level. The electronic partition function of the OH rad-ical was evaluated by taking into account the splitting of 139.7 cm⫺1in the2⌸ground state.28
It is evident from the barrier heights that bothsyn- andanti -FMF have two competitive hydrogen abstraction channels; one channel is originated from the formyl site (S-FMF-TS1 and A-FMF-TS1) and the other channel (S-FMF-TS2 and A-FMF-TS2) is from the fluoromethyl group, which both contribute to the total reaction rate. As discussed before, the contribution from theanti
conformer of FMF and DFMF will slowly rise with the increase in temperature and its contribution should also be accounted for in the total reaction rate. The total hydrogen abstraction rate constants (ktotal) for FMF and DFMF were, therefore, calculated from the weighted sum of the individual rate constants of each channel, as expressed in eqs. (2) and (3):
ktotal共FMF兲⫽wsynk共syn兲⫹wantik共anti兲 (2)
Table 4. Heats of Reaction and Barrier Heights for the Hydrogen
Abstraction Reaction ofsynandantiConformers of CH2FOCHO
(FMF), CHF2OCHO (DFMF), and CF3OCHO (TFMF) with
OH Radicals as Calculated at the G2(MP2) Level.
System ⌬E0#
CHF2OC*HO⫹OH (S1-DFMF-TS1) 3.33 ⫺17.7
C*HF2OCHO⫹OH (S1-DFMF-TS2) 4.25 ⫺12.5
CHF2OC*HO⫹OH (S2-DFMF-TS1) 2.87 ⫺19.0
C*HF2OCHO⫹OH (S2-DFMF-TS2) 5.70 ⫺15.0
CHF2OC*HO⫹OH (A1-DFMF-TS1) 2.59 ⫺21.7
C*HF2OCHO⫹OH (A1-DFMF-TS2) 6.25 ⫺13.3
Reactions for TFMF
CF3OCHO⫹OH (syn) 4.11 ⫺17.7
CF3OCHO⫹OH (anti) 3.00 ⫺21.3
Asterisk (*) indicates the hydrogen abstraction site (see Figs. 4 and 5). Heats of reaction [⌬Hr(298 K)] and barrier heights (⌬E0
#) are in kcal/mol.
Table 5. Total Rate Constants (in cm3molecule⫺1s⫺1) for Hydrogen
Abstraction Reactions between Formates and OH Radicals at 298 K.
ktotal共DFMF兲⫽wsyn-1k共syn-1兲⫹wsyn-2k共syn-2兲⫹wanti-1k共anti-1兲 (3)
wherewsynandwantiare the weight factors for thesynandanti
conformers calculated from the free energy difference between them. Thek(syn)andk(anti)are the individual hydrogen
abstrac-tion rate constants forsynandanticonformers, respectively, at a particular temperature. In the case of DFMF, the contribution from theanti-2 conformer is not considered in eq. (3), because the population ofanti-2 is negligibly small within the temper-ature region studied here. In the case of FMF,k(syn)and k(anti)
include contributions from both the hydrogen abstraction reac-tion channels (R1a) and (R1b). For DFMF, the hydrogen ab-straction takes place mainly from the formyl site [reaction (R2a)], because contribution for hydrogen abstraction from the
OCHF2site is much lower. For example, thek(R2a)is found to
be almost 18 times higher thank(R2b)at 298 K for the syn
-1-DFMF, while thek(R2a)/k(R2b)for theanti-1-DFMF amounts to 98. Thus k values for each conformer in eq. (3) primarily correspond to the rate constant for the hydrogen abstraction from the formyl group.
The calculated rate constant values for FMF and DFMF at 298 K are reported in Table 5. The values for CH3OCHO and
CF3OCHO are also given in Table 5 for comparison. It should be
noted here that even at room temperature both syn and anti
conformers of CF3OCHO contribute to the total reaction rate,
whereas contribution from theanticonformers is negligible for the other three formates at lower temperature. The branching ratio of the two reactions (R1a) and (R1b) of FMF can be calculated from the ratio of the two rate constant values [k(R1a)/k(R1b)] at any temperature. For example, thek(R1a)andk(R1b)amount to 4.8⫻ 10
⫺14and 1.1⫻10⫺14cm3molecule⫺1 s⫺1 at 298 K and this
produces a branching ratio of 4.4. Therefore, OH radical initiated hydrogen abstraction reaction predominantly (81%) takes place at the formyl hydrogen of FMF. The [k(R2a)/k(R2b)] value for DFMF
at 298 K is 18.8 and thus almost 95% of the reaction is from the carbonyl site of DFMF. The rate constant value is found to decrease with the increase in fluorine substitution at the methyl position. Figures 6 and 7 display Arrhenius plots for the hydrogen abstraction rate constants of FMF and DFMF in the temperature region of 250 to 450 K. Hydrogen abstraction rate from the carbonyl site ofsyn-FMF is always found to be larger than that from the fluoromethyl group. This is because of the lower pre-exponential factor for the latter. The entropy value for S-FMF-TS2 (83.5 cal/mol-K) is much lower than that for S-FMF-TS1 (88.4 cal/mol-K), due to the presence of strong hydrogen bonding inter-action in S-FMF-TS2. Thus the entropy of activation⌬S#is much lower for S-FMF-TS2 (⫺31.2 cal/mol-K) than that for S-FMF-TS1 (⫺26.3 cal/mol-K). As a result, the pre-exponential factor (which depends upon⌬S#exponentially) is much smaller for the reaction
channel through S-FMF-TS2. In the case of DFMF, hydrogen abstraction from the carbonyl group ofsyn-2 andanti-1 conform-ers is faster than that for thesyn-1 conformer. However, due to higher population, syn-1 always remains the main contributor toward the total hydrogen abstraction rate constant. Arrhenius expressions for the rate constants of FMF and DFMF within the temperature range of 250 – 450 K are found to be 8.3 ⫻
10⫺13exp(⫺773/T) and 8.0 ⫻ 10⫺13exp(⫺908/T) cm3
mole-cule⫺1s⫺1, respectively.
Figure 6. Arrhenius plot for the total and individual rate constants (in cm3 molecule⫺1 s⫺1) of the hydrogen abstraction reaction of OH
radicals withsynandanticonformers of CH2FOCHO (FMF). The total
rate constant is estimated from the weighted sum [eq. (2)] of the rate constants for thesynandanti-CH2FOCHO.
Figure 7. Arrhenius plot for the total and individual rate constants (in cm3 molecule⫺1 s⫺1) of the hydrogen abstraction reaction of OH
radicals with syn-1, syn-2, and anti-1 conformers of CHF2OCHO
(DFMF). The total rate constant is estimated from the weighted sum [eq. (3)] of the rate constants for the three conformers of CHF2OCHO
Summary
The structures and vibrational frequencies for both thesynandanti
conformers of FMF and DFMF have been reported for the first time. Thesynconformer is found to be lower in energy. However, the energy difference between thesynandanticonformers and the barrier to interconversion between them are found to decrease with the increase in fluorine substitution at the methyl position of formates. The energy differences between the most stablesynand
anticonformers of FMF and DFMF are calculated to be 3.0 and 2.4 kcal/mol at the G2(MP2) level. Thus the experimental detec-tion of anti-FMF and -DFMF may be possible at an elevated temperature. The kinetics and mechanism of the hydrogen abstrac-tion reacabstrac-tions of OH radical with FMF and DFMF have been studied. The reaction rate is always found to be higher for the hydrogen abstraction from the carbonyl site of theanticonformer, primarily due to the lower COH bond strength. However, owing
to much larger population, thesynconformer of FMF and DFMF is always found to be the main contributor to the total rate constant. Arrhenius expressions for the temperature dependent rate con-stants of FMF and DFMF are estimated to be 8.3 ⫻
10⫺13exp(⫺773/T) and 8.0 ⫻ 10⫺13exp(⫺908/T) cm3
mole-cule⫺1s⫺1, respectively.
Acknowledgments
A.K.C. thanks RITE, Japan, for providing him with a senior researcher position.
6. Hotokka, M.; Dahlqvist, M. G. J Mol Struct 1980, 63, 287. 7. Lopata, A. D.; Kuczkowski, R. L. J Am Chem Soc 1981, 103, 3304. 8. Wallington, T. J.; Schneider, W. F.; Sehested, J.; Bilde, M.; Platz, J.;
Nielsen, O. J.; Christensen, L. K.; Molina, M. J.; Molina, L. T.; Wooldridge, P. W. J Phys Chem A 1997, 101, 8264.
9. Christensen, L. K.; Wallington, T. J.; Guschin, A.; Hurley, M. D. J Phys Chem A 1999, 103, 4202.
10. Nohara, K.; Toma, M.; Kutsuna, S.; Takeuchi, K.; Ibusuki, T. Environ Sci Technol 2001, 35, 114.
11. Good, D. A.; Kamboures, M.; Santiano, R.; Francisco, J. S. J Phys Chem A 1999, 103, 9230.
12. Chen, L.; Kutsuna, S.; Nohara, K.; Takeuchi, K.; Ibusuki, T. J Phys Chem A 2001, 105, 10854.
13. Chandra, A. K.; Urata, S.; Uchimaru, T.; Sugie, M.; Sekiya, A. Int J Chem Kinet 2002, 34, 500.
14. Chandra, A. K.; Uchimaru, T. J Phys Chem A 2000, 104, 8535. 15. Chandra, A. K.; Uchimaru, T. J Phys Chem A 1999, 103, 10874. 16. Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J Chem Phys 1993, 98,
1293.
17. Le Calve´, S.; Le Bras, G.; Mellouki, A. J Phys Chem 1997, 101, 5489. 18. Scott, A. P.; Radom, L. J Phys Chem 1996, 100, 16502.
19. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery Jr, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clif-ford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Moro-kuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanay-akkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. GAUSSIAN98, Revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998.
20. Van Eijck, B. P.; Brandts, P.; Maas, J. P. M. J Mol Struct 1978, 44, 1. 21. Finnegan, D. J.; Gillies, C. W.; Suenram, R. D.; Wilson, E. B.;
Karlsson, H. J Mol Spectrosc 1975, 57, 363.
22. Schneider, W. F.; Nance, B. I.; Wallington, T. J. J Am Chem Soc 1995, 117, 478.
23. Hammond, G. S. J Am Chem Soc 1955, 77, 334. 24. Bondi, A. J Phys Chem 1964, 68, 441.
25. Eyring, H. J Chem Phys 1935, 35, 107.
26. Johnston, H. S.; Heicklen, J. J Phys Chem 1962, 66, 532.
27. McQuarrie, D. A.; Simon, J. D. Molecular Thermodynamics; Univer-sity Science Books: Sausalito, CA, 1999; pp 135–174.
