ORIGINAL RESEARCH

Theoretical investigation of the atmospheric chemistry of methyldifluoroacetate: reaction with Cl atoms and fate of alkoxy radicalat 298 K

Ramesh Chandra Deka • Bhupesh Kumar Mishra

Received: 29 January 2014 / Accepted: 7 March 2014

� Springer Science+Business Media New York 2014

Abstract A theoretical study on the mechanism of the

reactions of methyl difluoroacetate (MDFA) CF2

HC(O)OCH3 with Cl atoms is presented. Two conformers

relatively close in energy have been identified for MDFA.

Geometry optimization and frequency calculations have

been performed at the MPWB1K/6-31?G(d,p) level of

theory, and energetic information is further refined by

calculating the energy of the species using G2(MP2) the-

ory. Transition states (TSs) are searched on the potential

energy surface involved during the reaction channels, and

each of the TSs is characterized by the presence of only one

imaginary frequency. The existence of TSs on the corre-

sponding potential energy surface is ascertained by per-

forming intrinsic reaction coordinate calculation. Our

calculations reveal that hydrogen abstraction from the

–CH3 group is thermodynamically and kinetically more

facile than that from the –CF2H group. Theoretically cal-

culated rate constants at 298 K using the canonical tran-

sition state theory are found to be in good agreement with

the experimentally measured ones. The atmospheric life-

time of CF2HC(O)OCH3 was estimated to be 16 years. The

atmospheric fate and the main degradation process of

alkoxy radical CF2HC(O)OCH2O are also discussed for the

first time. Our calculation indicates that the fluorine atoms

substitution has deactivating effect for the a-ester

rearrangement.

Keywords MDFA � Rate constant � Atmospheric

lifetime � Alkoxy radical � a-Ester rearrangement

Introduction

It is now a well-recognized fact that atomic chlorine

transported to the stratosphere on account of release of a

variety of chlorine containing compounds particularly

chlorofluorocarbons (CFCs) into the atmosphere is

responsible for the catalytic destruction of ozone in the

atmosphere [1]. Recently, hydrofluoroethers (HFEs) have

been the focus of intense attention as replacement materials

for CFCs and hydrochlorofluorocarbons (HCFCs) in

applications such as heat-transfer fluid in refrigeration

systems, cleaning agent in electronic industry, foam

blowing, and also for lubricant deposition [2]. The absence

of chlorine atoms in HFEs shows that such compounds

would have little impact on stratospheric ozone and that

they would possess a negligible ozone depleting potential

(ODP) [3]. The understanding of the degradation mecha-

nism of HFEs is an important area of recent research to

determine the impact of these compounds on atmospheric

pollution and global warming. Therefore, considerable

attention has been paid in recent years to perform experi-

mental and theoretical studies on the decomposition

kinetics of HFEs [4–11]. It is a well-known fact that

fluorinated esters (FESs) are the primary products of the

atmospheric oxidation of HFEs [12]. For instance, the

fluoroakylformates, C4F9OC(O)H and n-C3F7OC(O)H, are

the major degradation products of HFE-7100 (C4F9OCH3)

and HFE-7000 (C3F7OCH3), respectively [6, 7]. Similarly,

methyl trifluoroacetate, CH3OC(O)CF3, is the major deg-

radation product of OH-initiated oxidation of CH3

OCH(CF3)2 [8]. Recently, Bravo et al. [13] used density

functional theory to predict infrared spectra and calculate

radiative efficiencies (REs) and global warming potentials

(GWPs) for a number of FESs. Like most volatile organic

compounds, FESs containing C–H bonds are removed from

R. C. Deka � B. K. Mishra (&)

Department of Chemical Sciences, Tezpur University,

Napaam, Tezpur 784 028, Assam, India

e-mail: bhupesh@tezu.ernet.in

123

Struct Chem

DOI 10.1007/s11224-014-0425-3

the troposphere by reactions with atmospheric oxidants,

OH radicals being the most dominant oxidant [7]. Although

the reaction with OH radicals constitutes the main tropo-

spheric sink of HFEs, the chlorine atom plays an important

role in the atmospheric chemistry [14]. In fact, chlorine

atoms have been monitored in concentrations in the order

of 104 molecule cm-3 over the marine boundary layer [15].

Fluoroesters (FESs) may arise from both anthropogenic

and natural sources and produced in the atmosphere by

photochemical degradation and atmospheric oxidation of

HFEs [16]. These FES are removed from the troposphere

mainly by reaction with OH radicals. The degradation of

FESs produce environmentally burdened product like tri-

fluoroacetic acid (TFA), CO2, and COF2. TFA detected in

surface waters has no known sink apart from rainwater and

this species may impact on agricultural and aquatic systems

[17]. Thus, it is important to study the kinetics and

mechanistic degradation pathways of FESs for complete

assessment of atmospheric chemistry as well as explore the

impact of FESs on environment. Tanaka et al. [18] reported

that methyl difluoroacetate (MDFA)-based electrolyte

showed a greater ionic conductivity than an EC ? DMC-

based electrolyte. Recently, Zhao et al. [19] reported that

MDFA-based electrolyte is a promising electrolyte for

safer Li-ion batteries having the best electrochemical

properties and the highest thermal stability coexisting with

Li metal. Olivier et al. [20] took MDFA as the raw material

to obtain difluoroethanol on Rh/C catalyst by liquid-phase

hydrogenolysis. Recently, Zheng et al. [21] studied gas-

phase hydrogenolysis of MDFA leading to the formation of

1,1-difluoroethanol over Ru/C catalysts.

In this work, kinetic and mechanistic studies have been

performed for the reactions of Cl atoms with MDFA.

Blanco and Teruel [22] studied the hydrogen abstraction

reactions of MDFA by hydroxyl radicals using relative rate

technique method at 296 ± 2 K and atmospheric pressure

(750 Torr). The experimental rate constants were derived

as k (OH ? CF2HC(O)OCH3) = (1.48 ± 0.34) 9 10-13

cm3 molecule-1 s-1. In other reports, Blanco et al. [23]

studied the kinetics of the reactions of Cl atoms with

MDFA by the relative kinetic method at 298 ± 2 K and

atmospheric pressure (760 ± 10 Torr) and reported rate

constant as k (Cl ? CF2HC(O)OCH3) = (2.03 ± 0.65) 9

10-13 cm3 molecule-1 s-1. Very recently, Singh et al. [24]

performed a DFT study on the OH-initiated hydrogen

abstraction of CF2HC(O)OCH3 and reported a rate constant

of 1.35 9 10-13 cm3 molecule-1 s-1 at 298 K. They also

proposed that hydrogen abstraction by OH radicals from

the –CH3 group is thermodynamically and kinetically more

facile than that from the –CF2H group. To the best of our

knowledge, no theoretical study has been reported so far

for Cl-initiated hydrogen abstraction of MDFA. Thus, the

question arises: which is the major channel for the

CF2HC(O)OCH3 ? Cl reactions? Are the reaction mech-

anisms similar to those of the CF2HC(O)OCH3 ? OH

reactions? However, experimental studies provided only

the total rate constant and it is difficult to predict the

detailed mechanism, thermochemistry, and contribution of

each reaction channels toward overall rate constant. To the

best of our knowledge, this is the first detailed theoretical

study of the above-mentioned H-abstraction reactions of

MDFA.

Our calculation indicates that two reaction channels

from –CH3 groups and one reaction channel from –CF2H

are feasible for the MDFA ? Cl reactions as given below:

CF2HC Oð ÞOCH3 þ Cl! CF2HC Oð ÞOCH2 þ HCl

ð1a; bÞCF2HC Oð ÞOCH3 þ Cl! CF2C Oð ÞOCH3 þ HCl ð2Þ

The tropospheric degradation of MDFA is initiated by

attack of Cl atoms which leads to the formation of alkyl

radical CF2HC(O)OCH2. The latter reacts with atmo-

spheric O2 to produce peroxy radical, CF2

HC(O)OC(OO)H2. In a polluted atmosphere the peroxy

radicals thus formed may further react with other oxidizing

species such as NO2 and NO, which ultimately leads to the

formation of alkoxy radical CF2HC(O)OCH2O. The

chemistry of alkoxy radicals, thus generated has been a

subject of extensive experimental and theoretical investi-

gations as these species are interesting intermediates in the

atmospheric oxidation of halogenated hydrocarbons.

Blanco et al. [25] experimentally investigated the product

distribution and the mechanism of the Cl-initiated photo-

oxidation of MDFA using a 1,080 L environmental

chamber with in situ FTIR spectroscopy at (296 ± 2) K

and atmospheric pressure (760 Torr). Two loss processes

for that alkoxy radical were identified which include

a-ester rearrangement to produce fluoroacid and hydrogen

abstraction by reaction with O2 to produce the corre-

sponding fluoro-anhydride. No theoretical study has been

performed to elucidate the dissociative pathways of CF2

HC(O)OCH2O radical. This motivated us to investigate the

decomposition and reactivity mechanism of this radical on

a sound theoretical basis. During the recent past, consid-

erable theoretical studies have been performed on other

similar alkoxy radicals [26–31]. Thus, there are two

potential pathways for decomposition of alkoxy radical

which involve a-ester rearrangement and oxidation pro-

cesses. These are represented as follows:

CF2HC Oð ÞOCH2O� ! CF2HC Oð ÞOHþ CHO� ð3ÞCF2HC Oð ÞOCH2O� þ O2 ! CF2HC Oð ÞOCHOþ HO2

ð4Þ

Using the power of quantum chemistry methods, our

purpose is twofold: (i) gaining some insight into the fate of

Struct Chem

123

the alkoxy radicals, to analyze the mechanism of the

assumed oxidation with O2 which leads to the formation of

CF2HC(O)OCHO and HO2; and (ii) studying the impor-

tance of the other pathways that these radicals may

undergo. The thermochemical studies have been performed

to analyze the stability of all the species involved in the

reactions. This is the first computational study on the

a-ester rearrangement for alkoxy radical derived from

FESs.

Computational methods

Geometry optimization of the reactants, products, and

transition states (TSs) were made at the MPWB1K level of

theory [32] using 6-31?G(d,p) basis set. The 6-31?G(d,p)

basis set was used because the same basis set was used for

developing the model functional. The hybrid meta-density

functional, MPWB1K, has been found to give reliable

results for thermochemistry and kinetics [33, 34]. In order

to determine the nature of different stationary points on the

potential energy surface, vibrational frequency calculations

were performed using the same level of theory at which the

optimization was made. All the stationary points had been

identified to correspond to stable minima by ascertaining

that all the vibrational frequencies had real positive values.

The TSs were characterized by the presence of only one

imaginary frequency. To ascertain that the identified TSs

connect reactants and products smoothly, intrinsic reaction

coordinate (IRC) calculations [35] were performed at the

MPWB1K/6-31?G(d,p) level. As the reaction energy

barriers are very much sensitive to the theoretical levels,

the higher-order correlation corrected relative energies

along with the density functional energies are necessary to

obtain theoretically consistent reaction energies. Therefore,

a potentially high-level method such as G2(MP2) has been

used for single-point energy calculations. The G2(MP2)

[36] energy is calculated in the following manner:

E G2 MP2ð Þ½ � ¼ Ebase þ DE MP2ð Þ þ HLCþ ZPE;

where Ebase ¼ E QCISD Tð Þ=6-311G d,pð Þ½ �; DE MP2ð Þ ¼E MP2=6-311þG 3df;2pð Þ½ � � E MP2=6-311G d,pð Þ½ �; and

HLC (high-level correction) = -0.00481nb -0.00019na

(na and nb are the number of a and b valence electrons with

na C nb) and ZPE is zero-point energy.

In this method, the geometry and frequency calculations

were performed at MPWB1K/6-31?G(d,p) level. The ZPE

thus obtained was corrected with a scale factor of 0.951 to

partly eliminate the systematic errors [32]. This dual-level

calculation (G2(MP2)//MPWB1K/6-31?G(d,p)) is known

to produce reliable kinetic data [37–41]. All quantum

mechanical calculations were performed with the Gaussian

09 suite of program [42].

Results and discussion

The conformational landscape of MDFA was previously

investigated by Abraham et al. [43] by means of theoretical

tools. Geometry optimization of MDFA molecule predicts

two possible conformers (SC1 and SC2) and their structures

are shown in Fig. 1. The two conformers differ mainly in the

orientation of C1–F2 bond relative to the H–C–C–O back-

bone. The H4–C1–C2–O2 dihedral angle is 147.39� in the

SC1 conformer; whereas the same is 0.0� in the SC2 con-

former. This is in accord with the values reported by Abraham

et al. [43]. Since these two conformers are close in energy,

both of them (SC1 and SC2) need to be considered while

studying the reactions (R1–R2). However, for hydrogen

abstraction by Cl atoms, energetically same TSs were found

from both conformers of MDFA. Therefore, we have pre-

sented TSs geometry only from the most stable conformer

(SC1). There are two potential hydrogen abstraction sites of

CF2HC(O)OCH3, namely the –CH3 and –CF2H group.

However, as can be seen from the geometrical parameters and

stereographical orientation, the hydrogen atoms in the –CH3

group are not equivalent. One H-atom is different from the

other two in the –CH3 group. Three TSs are, therefore, located

for the CF2HC(O)OCH3 ? Cl reactions: two TSs for

H-abstraction from the –CH3 group and one TS for the same

from the –CF2H group. Therefore, three H-abstraction reac-

tion channels exist for the reactions studied here. The detailed

thermodynamic calculations performed at G2(MP2) and

MPWB1K/6-31?G(d,p) levels for reaction enthalpies and

free energies associated with reaction channels (1–2) are listed

in Table 1. The enthalpy of reaction (DrH�298) values recorded

in Table 1 for reaction channels (1–2) show that both the

reactions are significantly exothermic in nature and thermo-

dynamically facile. The free energy values show that all

reaction channels are exergonic (DG \ 0) and therefore

should be spontaneous in nature. The optimized geometries of

reactants, TSs, and products along with structural parameters

obtained at MPWB1K/6-31?G(d,p) level are shown in Fig. 1.

It can be seen from Fig. 1 that the optimized geometrical

parameters obtained at MPWB1K level of theory are in a

reasonable agreement with the values given in square bracket

reported by Abraham et al. [43]. TSs searched on the potential

energy surfaces of reactions (1–2) and are characterized as

TS1a, TS1b, and TS2, respectively. The search was made

along the minimum energy path on a relaxed potential energy

surface. Visualization of the optimized structures of TSs—

TS1a, TS1b, and TS2 for reactions (1–2) further reveals that

the length of the breaking C–H bonds is found to be longer in a

range of 22.41–27.95 % than the observed C–H bond length in

isolated CF2HC(O)OCH3; whereas the forming H���Cl bond

length is longer by 14.38–17.53 % than the H–Cl bond length.

The fact that the elongation of breaking bond is larger than that

Struct Chem

123

SC1

TS1OH TS2OH

TS2TS1aTS1b

CF2HC(O)OCH2O

TS4TS3

CF2C(O)OCH3

CF2HC(O)OCH2

SC2

Fig. 1 Optimized geometries of reactants, transition states, and products involved in the reaction channels (1–4) at MPWB1K/6-31?G(d,p) and

B3LYP/6-311G(d,p) (within bracket) methods. The values given in square brackets are taken from Ref. [43]

Struct Chem

123

of the forming bond indicates that the TS is product like i.e.,

the reaction will proceed via late TS.

Results obtained from frequency calculations for species

involved in reactions (1–2) are recorded in Table 2. All the

reactants and products were identified as stationary points

with zero imaginary frequency, while TSs—TS1a, TS1b, and

TS2 were identified as first-order saddle points with only one

imaginary frequency at 953i, 916i, and 1129i cm-1, respec-

tively. Visualization of the vibration corresponding to the

calculated imaginary frequencies shows a well-defined tran-

sition-state geometry connecting reactants and products dur-

ing transition. The existence of TSs on the potential energy

surface is further ascertained by IRC calculation performed at

the same level of theory using the Gonzalez–Schlegel steepest

descent path in the mass-weighted Cartesian coordinates with

a step size of 0.01 (amu1/2 bohr) [35]. The associated energy

barrier including zero-point energy correction for various

species and TSs involved in the reactions (1–2) at MPWB1K

and G2(MP2) levels are tabulated in Table 3. These results

show that energy barriers for H-atom abstraction by Cl atoms

from the –CH3 group are found to be 1.01 and

1.31 kcal mol-1 at G2(MP2), whereas these values are 1.42

and 1.59 kcal mol-1 at MPWB1K level. On the other hand,

the same from the –CF2H group (reaction 2) are 2.83 and

2.47 kcal mol-1, respectively, at G2(MP2) and MPWB1K/6-

31?G(d,p) level of theory. The barrier heights obtained from

the G2(MP2) results are only 0.17 to 0.36 kcal mol-1 higher

than that obtained at the MPWB1K level. The barrier height

values show that hydrogen abstraction by Cl atoms from the

–CH3 group of CF2HC(O)OCH3 is more facile than that from

the –CF2H group. Literature survey reveals that there are no

experimental data available for the comparison of the energy

barrier for the H-atom abstraction reaction of CF2HC(O)

OCH3 by Cl atoms. However, In order to ascertain the reli-

ability of the calculated values, we tried to compare our results

with the values calculated by Singh et al. [24] for the H-atom

abstraction reactions from –CH3 and –CF2H sites in CF2

HC(O)OCH3 ? OH reactions. The optimized geometries of

two TSs (TS1OH and TS2OH) are also given in Fig. 1. Our

calculated barrier heights amount to be 2.69 and

3.54 kcal mol-1 at G2(MP2)//MPWB1K/6-31?G(d,p) level

of theory for –CH3 and –CF2H sites, respectively, in

CF2HC(O)OCH3 ? OH reactions; whereas the same

obtained from the MPWB1K calculations amount to be 2.16

and 2.73 kcal mol-1. Thus, our calculated barrier heights at

Table 1 Thermochemical data for the calculated at G2(MP2) and

MPWB1K/6-31?G(d,p) (within parenthesis) level of theories

Reaction channels DrH�298 DrG�298

Reaction 1 -2.59 (-1.01) -5.25 (-3.67)

Reaction 2 -5.43 (-5.78) -7.85 (-8.20)

Reaction 3 -9.81 (-8.83) -17.52 (-17.05)

Reaction 4 -14.56 (-13.19) -24.67 (-23.68)

All values are in kcal mol-1

Table 2 Harmonic vibrational frequencies of reactants, products, and

transition states at MPWB1K/6-31?G(d,p) level of theory

Species Vibrational frequencies (cm-1)

SC1 28, 126, 139, 196, 293, 332, 422, 605, 770, 811,

913, 1119, 1181, 1192, 1206, 1244, 1388,

1415, 1453, 1517, 1527, 1530, 1924, 3148,

3229, 3239, 3279

SC2 24, 111, 142, 198, 321, 350, 444, 576, 655, 844,

974, 1076, 1183, 1207, 1236, 1242, 1337,

1409, 1471, 1517, 1523, 1529, 1943, 3149,

3188, 3240, 3278

TS1a 953i, 22, 43, 52, 154, 201, 290, 356, 415, 428,

511, 607, 764, 804, 885, 990, 1027, 1180,

1199, 1217, 1242, 1270, 1364, 1413, 1438,

1492, 1951, 3204, 3231, 3340

TS1b 916i, 30, 42, 53, 162, 213, 343, 358, 426, 450,

533, 569, 636, 829, 954, 1003, 1036, 1155,

1202, 1243, 1249, 1264, 1314, 1409, 1463,

1496, 1968, 3188, 3204, 3339

TS2 1129i, 37, 58, 102, 113, 161, 187, 254, 317,

376, 485, 610, 654, 855, 958, 1047, 1066,

1088, 1207, 1230, 1297, 1362, 1425, 1515,

1519, 1527, 1934, 3153, 3247, 3287

CF2HC(O)OCH2 29, 129, 156, 195, 264, 322, 350, 423, 605, 773,

791, 891, 1183, 1185, 1206, 1252, 1377,

1413, 1439, 1483, 1923, 3231, 3284, 3452

CF2C(O)OCH3 57, 111, 128, 179, 219, 317, 404, 520, 648, 718,

885, 1073, 1204, 1225, 1288, 1434, 1492,

1512, 1530, 1575, 1851, 3145, 3234, 3274

HCl 3084

CF2HC(O)OCH2O• 33, 63, 85, 184, 254, 299, 423, 562, 615, 756,

796, 836, 925, 1063, 1182, 1186, 1197, 1252,

1353, 1387, 1413, 1415, 1475, 1933, 3060,

3122, 3231

TS3 880i, 18, 84, 175, 216, 288, 422, 495, 506, 575,

615, 659, 889, 967, 1020, 1155, 1211, 1228,

1330, 1401, 1408, 1578, 1693, 1707, 1787,

3111, 3181

TS4 1,972i, 25, 47, 50, 123, 136, 172, 180, 307, 334,

384, 478, 539, 590, 604, 697, 857, 988, 1,025,

1,061, 1183, 1207, 1239, 1302, 1323, 1377,

1410, 1487, 1643, 1707, 1936, 3080, 3196

Table 3 Zero-point corrected relative energy, DE (kcal mol-1) for

the reactants, transition states, and products

Species G2(MP2) MPWB1K

CF2HC(O)OCH3 ? Cl 0.00 0.00

TS1a 1.01 1.42

TS1b 1.31 1.59

TS2 2.83 2.47

CF2HC(O)OCH2 ? HCl -3.15 -1.58

CF2C(O)OCH3 ? HCl -5.98 -6.33

Struct Chem

123

both levels are in good agreement with the reported values of

2.30 and 3.19 kcal mol-1 at G3B3//MPWB1K/6-31?G(d,p)

level of theory by Singh et al. [24]. Thus, the calculated energy

barriers for the title reactions studied here at G2(MP2)//

MPWB1K/6-31?G(d,p) can be relied upon. This gives us a

confidence that energy barrier calculated using G2(MP2)

method on the geometries optimized at MPWB1K/6-31?

G(d,p) yields reliable values for the hydrogen abstraction

channels considered in the present study. Moreover, an

intensive ab initio calculation performed in our previous study

[37] for a similar species, CF3C(O)OCH3 (MTFA), yielded a

value of 1.76 kcal mol-1 for hydrogen abstraction by Cl atoms

at G2(MP2)//MPWB1K/6-31?G(d,p) level. The lowering of

barrier heights in case of CF2HC(O)OCH3 is expected due to

replacement of more electronegative F atom in CF3C(O)OCH3

by H-atom in CF2HC(O)OCH3. A schematic potential energy

surface of the CF2HC(O)OCH3 ? Cl reactions obtained at the

G2(MP2)//MPWB1K/6-31?G(d,p) ? ZPE level is plotted

and shown in Fig. 2. In the construction of energy diagram,

zero-point corrected total energies as recorded in Table 3 are

utilized. These energies are plotted with respect to the ground-

state energy of CF2HC(O)OCH3 ? Cl arbitrarily taken as

zero. The values in parentheses shown in Fig. 2 are ZPE cor-

rected values obtained at MPWB1K/6-31?G(d,p) level. Spin

contamination is not important for the CF2HC(O)OCH3

because hS2i is found to be 0.76 at MPWB1K/6-31?G(d,p)

before annihilation that is only slightly larger than the expected

value of hS2i = 0.75 for doublets.

Fate of alkoxy radicals

The fate of alkoxy radical, CF2HC(O)OCH2O•, during its

thermal decomposition in the atmosphere is envisaged to

occur via reactions (3–4). The thermodynamic calculations

performed at G2(MP2) and MPWB1K/6-31?G(d,p) levels

for reaction enthalpies and free energies associated with

reaction channels (3–4) are listed in Table 1. Free energy

values show that both reactions are exergonic (DG \ 0)

and thus thermodynamic facile. Optimized geometries of

radicals, TSs, and products obtained at the MPWB1K/6-

31?G(d,p) level are shown in Fig. 1. TSs obtained on the

potential energy surfaces of reactions (3–4) are character-

ized as TS3 and TS4, respectively. The search was made

along the minimum energy path on a relaxed potential

energy surface. Harmonic vibrational frequencies of the

stationary points were calculated and are given in Table 2.

These results show that the reactant and products have

stable minima on their potential energy surface character-

ized by the occurrence of only real and positive vibrational

frequencies (Table 2). On the other hand, TSs are charac-

terized by the occurrence of only one imaginary frequency

obtained at 880i and 1972i cm-1, respectively. The exis-

tence of these TSs on the potential energy surface is further

ascertained by IRC calculation [35] performed at the same

level of theory. The associated energy barriers corre-

sponding to reactions (3–4) calculated at various levels are

recorded in Table 4. The associated energy barriers cor-

responding to reactions (3–4) determined from the data of

Table 4 show that the energy barriers for a-ester rear-

rangement are in the range of 13.14–17.41 kcal mol-1

depending upon the level of theory used during the cal-

culation, whereas the same for H-abstraction reaction of

CF2HC(O)OCH2O• radical with molecular O2 is in the

range of 10.14–13.84 kcal mol-1. Results show that the

G2(MP2) method yields a value of 13.14 and

10.14 kcal mol-1 for a-ester rearrangement and oxidation

by molecular O2, respectively. On the other hand, the

MPWB1K method yields corresponding values as 17.41

and 13.84 kcal mol-1. The corresponding energy barriers

calculated at MPWB1K/6-311?G(3df,2p) level is found to

be 16.22 and 12.64 kcal mol-1 as recorded in Table 4.

No experimental or theoretical data are available in the

literature to compare the energy barriers associated with

the decomposition channels of CF2HC(O)OCH2O• radical

considered during the present investigation. However, in

order to ascertain the reliability of the calculated values, we

tried to compare with the energy values calculated at

G2(MP2,SVP) and B3LYP/6-311G(2df,2p)//B3LYP/6-

31G(d,p) by Ferenac et al. [27] for structurally similar

alkoxy radical CH3C(O)OCH2O yielding the energy barrier

of 9.4 and 10.30 kcal mol-1, respectively, for the a-ester

rearrangement. The optimized geometrical parameters at

B3LYP/6-311G(d,p) level of theory for alkoxy radical and

TSs (TS3 and TS4) are also given in Fig. 1. The calculated

barrier heights at B3LYP/6-311G(2df,2p) and B3LYP/6-

311G(d,p) levels recorded in Table 4 reveal that the barrier

P2 = CF2C(O)OCH3

P1 = CF2HC(O)OCH2

1.31 (1.59)

TS2

R = CF2HC(O)OCH3

-5.98 (-6.33)

-3.15 (-1.58)

P1 + HCl

P2 + HCl

2.83 (2.47)

1.01 (1.42)0.00

R + Cl

TS1b

TS1a

Rel

ativ

e E

ner

gy

+ Z

PE

(kc

al m

ol-1

)

Fig. 2 Potential energy diagram of the CF2HC(O)OCH3 ? Cl reac-

tions at G2(MP2) level. The values in parentheses are ZPE corrected

total energies at MPWB1K/6-31?G(d,p) level. Energy values are in

kcal mol-1

Struct Chem

123

heights for a-ester rearrangement in CF2HC(O)OCH2O•

radical are higher than the calculated values for

CH2C(O)OCH2O radical by Ferenac et al. [27]. This

indicates that the fluorine atoms substitution that withdraws

electron density will strengthen the C–H bond which in

turn increases the activation energy for the a-ester rear-

rangement. This is in line with the fact of high yield of

CF2HC(O)OCHO assigned by Blanco et al. [25]. The cal-

culated energy barriers for reactions (3–4) clearly show the

dominance of hydrogen abstraction by molecular O2

pathways leading to the formation of formic difluoroacetic

anhydride CF2HC(O)OCHO over a-ester rearrangement

pathways.

Rate constants

The rate constants for reactions (1–2) are calculated using

canonical transition state theory (CTST) [44] given by the

following expression:

k ¼ rC Tð Þ kBT

h

QzTS

QR

exp�DE

RT; ð5Þ

where r is the symmetry number and C(T) is the tunneling

correction factor at temperature T. QzTS and QR are the total

partition functions for the transition states and reactants,

respectively. DE, kB, and h are the barrier height including

ZPE, Boltzmann’s, and Planck’s constants, respectively.

The partition functions for the respective TSs and reactants

at 298 K are obtained from the vibrational frequency cal-

culation made at MPWB1K/6-31?G(d,p) level. Barrier

heights were estimated from the energy difference including

ZPE between TSs and reactants. The partition functions for

the respective TSs and reactants at 298 K are obtained from

the vibrational frequencies calculation made at MPWB1K/

6-31?G(d,p) level. The translational partition function was

evaluated per unit volume. Most of the vibrational modes

were treated as quantum-mechanical separable harmonic

oscillators except for lower vibration modes. The tunneling

correction C(T) was estimated by the Eckart’s unsymmet-

rical barrier method [45]. The hindered rotor approximation

of Truhlar and Chuang [46] was used for calculating the

partition function of lower vibration modes. Using Truhlar’s

procedure [47], the qHIN/qHO ratio was found to be close to

unity. In the calculation of reactant electronic partition

function, the excited state of the 2P3/2 and 2P1/2 electronic

states of Cl atom are also included with 881 cm-1 splitting

due to spin–orbit coupling. As shown in Fig. 2, reactions

(1–2) pass through two different channels involving TSs—

TS1a, TS1b, and TS2, the contribution from each of these

two channels needs to be taken into account while calcu-

lating the total rate coefficient (kCl) for the CF2

HC(O)OCH3 ? Cl reactions. The total rate coefficient (kCl)

is, therefore, obtained from the addition of rate coefficients

for the two channels: kCl = k1a ? kx1b ? k2. At 298 K, our

calculated kCl value using G2(MP2) barrier heights is

1.95 9 10-13 cm3 molecule-1 s-1 which is in good agree-

ment with the experimental value of (2.03 ± 0.65) 9 10-13

cm3 molecule-1 s-1 reported by Blanco and Teruel [23]. The

rate coefficient of 1.85 9 10-13 cm3 molecule-1 s-1

obtained from the MPWB1K results is slightly lower than

the G2(MP2) and experimental values owing to greater

barrier height for hydrogen abstraction.

In general, tropospheric lifetime (seff) of MDFA can be

estimated by assuming that its removal from troposphere

occurs only through the reactions with Cl atoms. Then (seff)

can be expressed as [48]

seff ¼ sCl; ð6Þ

where (sCl) = (kCl 9 [Cl])-1. Using the 298 K value of

kCl = 1.95 9 10-13 cm3 molecule-1 s-1 and the global

average atmospheric Cl concentrations of 1.0 9 104 mol-

ecule cm-3 [49], the estimated atmospheric lifetime of

MDFA with respect to Cl atoms is found to be 16 years,

which almost produce the experimental values reported by

Blanco et al. [23].

Conclusions

The potential energy surface and reaction kinetics of the

H-abstraction reactions of CF2HC(O)OCH3 by Cl atoms

are investigated at G2(MP2)//MPWB1K/6-31?G(d,p)

level of theory. The barrier height for dominant pathway is

calculated to be 1.01 kcal mol-1 at G2(MP2) level. The

Table 4 Calculated barrier heights (ZPE corrected) for transition states involved in thermal decomposition of CF2HC(O)OCH2O radical at

various levels of theory

Reaction channels G2(MP2) MPWB1K/6-

311?G(3df,2p)

MPWB1K/6-

31?G(d,p)

B3LYP/6-

311G(2df,2p)

B3LYP/6-

311G(d,p)

TS3 (a-ester

rearrangement)

13.14 16.22 17.41 10.10 10.18

TS4 (reaction with O2) 10.14 12.64 13.84 5.44 5.02

All values are in kcal mol-1

Struct Chem

123

calculated rate constants of the H-abstraction reactions are

consistent with the available experimental values. Our

calculations suggest that the H-abstraction from the –CH3

group is more favorable than that from the –CF2H group

for CF2HC(O)OCH3 ? Cl reactions. The thermal rate

constant for the H-atom abstraction of CF2HC(O)OCH3 by

Cl atoms is found to be 1.95 9 10-13 cm3 molecule-1 s-1

at 298 K using canonical transition state theory which is in

good agreement with experimental data. The atmospheric

lifetime of CF2HC(O)OCH3 with respect to reaction with

Cl atoms is estimated to be 16 years. Our results also

confirm that the sole atmospheric fate for decomposition of

CF2HC(O)OCH2O radical in atmosphere is the reaction

with O2 that occurs with the lowest barrier height.

Acknowledgments The authors acknowledge the financial support

from the Department of Science and Technology, New Delhi in the

form of a project (SR/NM.NS-1023/2011(G)). BKM is thankful to

University Grants Commission, New Delhi for providing Dr. D. S.

Kothari Fellowship.

References

1. Farman JD, Gardiner BG, Shanklin JD (1985) Nature

315:207–210

2. Sekiya A, Misaki S (2000) J Fluor Chem 101:215–221

3. Ravishankara RA, Turnipseed AA, Jensen NR, Barone S, Mills

M, Howark CJ, Solomon S (1994) Science 263:71–75

4. Urata S, Takada A, Uchimaru T, Chandra AK (2003) Chem Phys

Lett 368:215–223

5. Singh HJ, Mishra BK (2010) J Mol Model 16:1473–1480

6. Wallington TJ, Schneider WF, Sehested J, Bilde M, Platz J,

Nielsen OJ, Christensen LK, Molina MJ, Molina LT, Wooldridge

PW (1997) J Phys Chem A 101:8264–8274

7. Ninomiya Y, Kawasaki M, Guschin A, Molina LT, Molina MJ,

Wallington TJ (2000) Environ Sci Technol 34(14):2973–2978

8. Chen L, Kutsuna S, Tokuhashi K, Sekiya A, Tamai R, Hibino Y

(2005) J Phys Chem A 109:4766–4771

9. Singh HJ, Mishra BK (2011) J Mol Model 17:415–422

10. Urata S, Takada A, Uchimaru T, Chandra AK (2003) Chem Phys

Lett 368:215–223

11. Singh HJ, Mishra BK, Rao PK (2010) Bull Korean Chem Soc

31:3718–3722

12. Nohara K, Toma M, Kutsuna S, Takeuchi K, Ibusuki T (2001)

Environ Sci Technol 35(1):114–120

13. Bravo I, Dıaz-de-Mera Y, Aranda A, Moreno E, Nutt DR, Mar-

ston G (2011) Phys Chem Chem Phys 13:17185–17193

14. Dalmasso PR, Taccone RA, Nieto JD, Teruel MA, Lane SI

(2006) Atmos Environ 40:7298–7303

15. Wingenter OW, Kubo MK, Blake NJ, Smith TW, Blake DR

(1996) J Geophys Res 101:4331–4340

16. Sulback AMP, Nielsen OJ, Wallington TJ, Hurley MD, DeMoore

GW (2005) J Phys Chem A 109:3926–3934

17. Jordan A, Frank H (1999) Environ Sci Technol 33(4):522–527

18. Tanaka T, Doi T, Okada S, Yamaki J (2009) Fuel Cells

09:269–272

19. Zhao L, Okada S, Yamaki J (2013) J Power Sources 244:369–374

20. Olivier B, Karol L WO, Patent 2,007,093,567

21. Zheng S-Z, Cao X-Y, Zhou Q, Wang S-H, Hua G-S, Lu J-Q, Luo

M-F, Wang Y-J (2013) J Fluor Chem 145:132–135

22. Blanco MB, Teruel MA (2007) Atmos Environ

41(34):7330–7338

23. Blanco MB, Bejan I, Barnes I, Wiesen P, Teruel MA (2008)

Chem Phys Lett 453:18–23

24. Singh HJ, Tiwari L, Rao PK, Mol Phys. doi:10.1080/00268976.

2013.868554

25. Blanco MB, Bejan I, Barnes I, Wiesen P, Teruel MA (2010)

Environ Sci Technol 44:2354–2359

26. Henon E, Bohr F, Gomex NS, Caralp F (2003) Phys Chem Chem

Phys 5:5431–5437

27. Ferenac MA, Davis AJ, Holloway AS, Dibble TS (2003) J Phys

Chem A 107:63–72

28. Singh HJ, Mishra BK, Gour NK (2010) Theor Chem Acc

125:57–64

29. Vereecken L, Peeters J (2009) Phys Chem Chem Phys

11:9062–9074

30. Singh HJ, Mishra BK, Rao PK (2012) Can J Chem 90:403–409

31. Singh HJ, Mishra BK (2011) J Chem Sci 123:733–741

32. Zhao Y, Truhlar DG (2004) J Phys Chem A 108:6908–6918

33. Zeegers-Huyskens T, Lily M, Sutradhar D, Chandra AK (2013) J

Phys Chem A 117:8010–8016

34. Chakrabatty AK, Mishra BK, Bhattacharjee D, Deka RC (2013) J

Fluor Chem 154:60–66

35. Hratchian HP, Schlegel HB (2005) J Chem Theory Comput

1:61–69

36. Curtiss LA, Raghavachari K, Pople JA (1993) J Chem Phys

98:1293–1298

37. Chakrabatty AK, Mishra BK, Bhattacharjee D, Deka RC (2013)

Mol Phys 111:860–867

38. Chandra AK (2012) J Mol Model 18:4239–4247

39. Mishra BK, Chakrabatty AK, Deka RC (2013) J Mol Model

19:3263–3270

40. Devi KhJ, Chandra AK (2011) Comput Theor Chem

965:268–274

41. Mishra BK, Chakrabatty AK, Deka RC (2014) Struct Chem

25:463–470

42. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA,

Cheeseman JR, Scalmani G, Barone V,Mennucci B, Petersson

GA, Nakatsuji H, CaricatoM, Li X, Hratchian HP, Izmaylov AF,

Bloino J, Zheng G, Sonnenberg JL, Hada M, EharaM, ToyotaK,

FukudaR, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O,

Nakai H, Vreven T, Montgomery JA Jr., Peralta JE, Ogliaro F,

Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN,

Kobayashi R, Normand J, Raghavachari K, Rendell K, Burant JC,

Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M,

Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts

R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C,

Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth

GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas

O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2010) Gaussian

09, revision B.01. Gaussian Inc., Wallingford

43. Abraham RJ, Tormenab CF, Rittner R (2001) J Chem Soc Perkin

Trans 2:815–820

44. Laidler KJ (2004) Chemical Kinetics, 3rd edn. Pearson Educa-

tion, New Delhi

45. Johnston HS, Heicklen J (1962) J Phys Chem 66:532–533

46. Truhlar DG, Chuang YY (2000) J Chem Phys 112:1221–1228

47. Truhlar DG (1991) J Comput Chem 12:266–270

48. Papadimitriou VC, Kambanis KG, Lazarou YG, Papagiannako-

poulos P (2004) J Phys Chem A 108:2666–2674

49. Spicer CW, Chapman EG, Finlayson-Pitts BJ, Plastridge RA,

Hubbe JM, Fast JD, Berkowitz CM (1998) Nature 394:353–356

Struct Chem

123