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Accurate Theoretical Thermochemistry for Fluoroethyl Radicals Adam Ganyecz, Mihaly Kallay, and Jozsef Csontos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b12404 • Publication Date (Web): 10 Jan 2017 Downloaded from http://pubs.acs.org on January 14, 2017

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The Journal of Physical Chemistry

Accurate Theoretical Thermochemistry for Fluoroethyl Radicals ´ am Ganyecz, Mihály Kállay, and József Csontos∗ Ad´ MTA-BME Lend¨ ulet Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest P.O.Box 91, H-1521 Hungary E-mail: [email protected]

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Abstract An accurate coupled-cluster (CC) based model chemistry was applied to calculate reliable thermochemical quantities for hydrofluorocarbon derivatives including radicals 1-fluoroethyl (CH3 – CHF), 1,1-difluoroethyl (CH3 – CF2 ), 2-fluoroethyl (CH2 F – CH2 ), 1,2-difluoroethyl (CH2 F – CHF), 2,2-difluoroethyl (CHF2 – CH2 ), 2,2,2-trifluoroethyl (CF3 – CH2 ), 1,2,2,2-tetrafluoroethyl (CF3 – CHF), and pentafluoroethyl (CF3 – CF2 ). The model chemistry used contains iterative triple and perturbative quadruple excitations in CC theory, as well as scalar relativistic and diagonal Born–Oppenheimer corrections. To obtain heat of formation values with better than chemical accuracy perturbative quadruple excitations and scalar relativistic corrections were inevitable. Their contributions to the heats of formation steadily increase with the number of fluorine atoms in the radical reaching 10 kJ/mol for CF3 – CF2 . When discrepancies were found between the experimental and our values it was always possible to resolve the issue by recalculating the experimental result with currently recommended auxiliary data. For each radical studied here this study delivers the best heat of formation as well as entropy data.

Introduction In the last century, and especially in recent decades the average temperature of Earth is rising. This phenomenon is called global warming, and it is widely believed to be caused mainly by human activities. It can generate various changes in our environment, for example, because of rising sea levels many low-lying areas more susceptible to long-term flooding, and more extreme weather events such as heat waves, heavy rainfall with intermittent floods, and heavy snowfall can be expected. These developments can be a threat to our food security, making currently populated areas uninhabitable, and increase the displacement of people, increase the risk of extinction of several species, increase health problems and limit the water availability. 1 2


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The greenhouse gases are among the main causes of these effects. In 1987 the Montreal Protocol was signed to deal with chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), because they are not only greenhouse gases, but ozone depleting substances (ODSs). Therefore, since the 1990s CFCs and HCFCs have been replaced with ozone friendly alternatives, such as hydrofluorocarbons (HFCs) and perfluorocarbons (PFCs) for use as refrigerants, foam blowing agents, or propellant gases. Although HFCs have low ozone depleting potential, due to their long atmospheric lifetime and strong infrared absorption capability 2 their global warming potential is notable. 3 For instance, hydrofluoroethanes stay in the atmosphere for 1.5 to 47.1 years, while perfluoroethane (C2 F6 ) has an extremely high lifetime of about 10,000 years according to the most recent report of the Intergovernmental Panel on Climate Change (IPCC). 4 Furthermore, the radiative efficiencies of these molecules are approximately 6500-16500 times larger than that of the reference CO2 . 5 However, the concentration of these species is still considered to be low in the atmosphere, though they all continue to increase relatively rapidly, and their contributions to radiative forcing† are currently less then 1 % of the total well-mixed greenhouse gases. 4 Nonetheless, because of their popularity as replacements of ODSs and possible impact on climate change, they are covered by the Kigali Amendment to the Montreal Protocol, which was ratified this October by 197 parties. 6 HFC degradation in the atmosphere begin with H-atom abstraction by the OH radical to yield fluoroalkyl radicals, which reacts with O2 to form the corresponding peroxy radical. These peroxy radicals can react with NO, NO2 , or HO2 to give the proper alkoxy radicals, which can further degrade in various pathways. 7 It is important to know accurately the kinetic and thermodynamic parameters of these atmospheric reactions and corresponding species for the so-called chemistry-climate models 8 so that the models can provide detailed forecast on climate change. Usually these physicochemical quantities are available in databases, such as NIST-JANAF tables, 9 JPL, 10 Burcat’s compendium, 11 and the ATcT. 12 †

the difference between the incoming and outgoing radiation energies at the tropopause projected to the unit area of the Earth’s surface

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Nevertheless, in several cases discrepancies exist between the databases as well as some data are provided with large uncertainty. In this study, we provide benchmark quality thermochemical data by means of an accurate model chemistry for the following fluoroethane radicals: CH3 – CHF, CH3 – CF2 , CH2 F – CH2 , CH2 F – CHF, CHF2 – CH2 , CF3 – CH2 , CF3 – CHF, and CF3 – CF2 . Furthermore, the results obtained are compared to previously reported data, and a careful selection of the best available values is also presented.

Methods Quantum chemical calculations The present model chemistry is a slightly modified version of our previous thermochemical protocol, 13 which has been proven to provide accurate thermodynamic quantities including heats of formation at both 0 and 298 K for small- and medium-sized species (see refs 14 and 15, and references therein). A more detailed account can be found in ref 13; nevertheless, for the readers’ convenience a brief outline is given below. The equilibrium structures were obtained with the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] method using the cc-pVQZ basis set and correlating all electrons. The total energies, ETOT , for the species were calculated according to the following scheme

∞ ∞ ∞ ETOT = EHF + ∆ECCSD(T) + ∆ECCSDT + ∆ECCSDT(Q) + ∆Ecore + ∆EDBOC + ∆EREL . (1)

∞ In the above expression (i) EHF is the complete basis set (CBS) limit for the Hartree–Fock

(HF) energy, and it was determined by extrapolation from aug-cc-pVXZ 16 (X =T,Q,5) enX ∞ ∞ ergies using the extrapolation formula of Feller, 17 EHF = EHF + b · e−cX ; (ii) ∆ECCSD(T) is the

correlation energy extracted from CCSD(T) calculations and extrapolated to the basis set

4


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limit using aug-cc-pVXZ (X =Q,5) results with the formula of Helgaker and associates, 18 X ∞ ECC = ECC + B · X −3 ; (iii) ∆ECCSDT is defined as ECCSDT − ECCSD(T) , where ECCSDT and

ECCSD(T) are the correlation energies calculated, respectively, with the CC method with single, double, and triple excitations (CCSDT) 19 and the CCSD(T) method using the cc-pVTZ basis set; (iv) ∆ECCSDT(Q) = ECCSDT(Q) − ECCSDT is calculated with the cc-pVDZ basis set, where ECCSDT(Q) is the correlation energy obtained at the CCSDT level of theory with ∞ perturbative quadruples [CCSDT(Q)]; 20,21 (v) ∆Ecore is the core correlation contribution de-

fined as the difference between all-electron and frozen-core (FC) CCSD(T) energies, and it is extrapolated to the CBS limit using cc-pCVXZ (X =T,Q) basis set results and the extrapolation formula of Helgaker et al.; 18 (vi) ∆EDBOC , the diagonal Born–Oppenheimer correction (DBOC), which accounts for the deficiencies of the BO approximation, and it is calculated at the CCSD/cc-pCVTZ level; 22 (vii) the scalar relativistic contributions (∆EREL ) were considered at the CCSD(T)/cc-pCVTZ level of theory by determining the expectation values of the ∞ mass-velocity and one- and two-electron Darwin operators. For ∆ECCSD(T) , ∆ECCSDT , and

∆ECCSDT(Q) the FC approximation was utilized. For closed-shell and open-shell molecules, respectively, restricted and unrestricted HF orbitals were used in the calculations. The corresponding enthalpies are calculated as,

HT◦ =ETOT + EZPE +

RT 2 ∂Ω × + RT Ω ∂T

(2)

with EZPE as the zero-point vibrational energy (ZPE), and Ω, R, and T denote the molecular partition function, ideal gas constant, and the absolute temperature, respectively. EZPE = Harm Anharm Harm EZPE + ∆EZPE , where (i) EZPE was calculated at the CCSD(T)/cc-pVQZ level of theory Anharm using analytic second derivatives; 23 (ii) ∆EZPE , the anharmonic correction, was obtained

from frozen-core CCSD(T)/cc-pVTZ semi-quartic force field calculations. 24,25 Ω is calculated via the standard formulas of statistical thermodynamics within the ideal gas approximation and using the rigid rotor-harmonic oscillator (RRHO) approximation. 26

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Rotation barriers were also investigated around the C–C bond. The appropriate torsional angle was changed systematically from 0 to 360◦ by increments of 5◦ , and the obtained conformations were partially optimized keeping only the torsional angle fixed; the secondorder Møller–Plesset(MP2) method with cc-pVTZ basis set was utilized. To correct the errors of the harmonic oscillator model for this internal coordinate the one-dimensional hindered rotor model (1D-HR) was applied, 27,28 and the energy levels calculated were used to correct both the ZPE and the thermal correction values. The one-dimensional Schrödinger equation,

−

~2 d 2 Ψ + V (ϑ)Ψ = EΨ, 2Ir dϑ2

(3)

was solved using the Fourier grid Hamiltonian method. 29,30 Ir and V (ϑ) are the reduced moment of inertia and the potential obtained from the MP2/cc-pVTZ calculations, respectively. To get an analytical form of the potential V (ϑ) was expanded in a Fourier series, V0 X + {an cos nϑ + bn sin nϑ}, 2 n=1 10

V (ϑ) =

(4)

where V0 , an ’s, and bn ’s are fitted parameters. Ir was calculated at the equilibrium geometries using Pitzer’s approximation. 31,32 The CCSDT(Q) calculations were carried out with the mrcc 34 program, while all other results were obtained with Cfour. 35 The heats of formation were calculated using the elemental reaction approach. 13,15 For example, ∆f HT◦ (CH3-CHF) was calculated as 2 C + 12 F2 + 2 H2 = CH3 – CHF 1 ∆f HT◦ (CH3 −CHF) = HT◦ (CH3 −CHF) − 2HT◦ (Cgas ) − HT◦ (F2 )− 2

(5)

− 2HT◦ (H2 ) + 2∆f HT◦ (Cgas )

The reference states of the elements hydrogen and fluorine were taken to be H2 and F2 , 6


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as is standard in thermochemistry, and for carbon the gaseous atom was used as a reference state. For ∆f H0◦ (Cgas ) the ab initio value of ref 36, 711.65±0.32 kJ/mol was adopted, and the ◦ thermal correction was obtained from the NIST-JANAF tables 9 resulting in ∆f H298 (Cgas )

= 717.13 ± 0.32 kJ/mol. A size- and composition-dependent uncertainty measure for our heat of formation values was introduced and tested thoroughly in ref 13. It was found that associating 0.4 kJ/mol and 0.7 kJ/mol uncertainties, respectively, for every first- and second-row atom in a given molecule and summing these contributions a conservative estimate can be obtained for the 95% confidence interval of the heat of formation values calculated. Thus, every heat of formation value calculated here has a 95% confidence interval of 2.8 (7 × 0.4) kJ/mol. The 95% confidence interval, 1.5 JK−1 mol−1 , associated with our entropy data is based on a statistical analysis for a benchmark data set of 15 species including radicals. 13 The validity of these error estimates was further proven in ref 15 and references therein. Because the CCSD(T)/cc-pVQZ second derivative calculations were not feasible for CF3 – CHF, the uncertainty of its heat of formation and entropy data was increased, respectively, by 1 kJ/mol and 0.3 JK−1 mol−1 . Details of calculating conformationally averaged properties and their error measures can be found in ref 15.

Results and Discussion For each radical the potential energy curve (PEC) around the C–C bond is plotted in Fig 1. It can be observed that in radicals CH2 F – CH2 , CHF2 – CH2 , and CF3 – CH2 the internal torsional mode can be described as free rotation at 298 K. The barriers are low, the largest one is below 60 cm−1 (0.7 kJ/mol). For these radicals six minima can be seen which are the consequence of the interplay between the torsional mode of the C–C bond and the inversion mode of the radical center. The •CH2 radical center is almost planar, the •C – H – H – C dihedral angle is around 5◦ and the barriers for inversion are comparable to those of torsion,

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and consequently, during rotation inversion can occur duplicating the number of minima. Nevertheless, for CF3 – CH2 there is only one unique conformer, while for both CH2 F – CH2 and CHF2 – CH2 three distinct conformers exist: the unsymmetric global minimum along with its enantiomer pair, and a local minimum which possesses Cs symmetry. These findings are in consonance with previous ab initio 37 and experimental 38 results. Our PEC for CH2 F – CHF (Fig 1b) is comparable to that of Chen and associates (see Fig. 2., dashed curve, in ref 39). They identified three asymmetric minima along with their enantiomer pairs, however, it was suggested that one of them (at 75◦ in our Fig 1b) may not exist at higher level of theory. We can confirm their hypothesis i.e., the structure at 75◦ transforms, at both the MP2/cc-pVTZ and CCSD(T)/cc-pVTZ levels, to the global minimum without hindrance by inversion of the radical center; more precisely it transforms into the enantiomer pair of the starting global minimum conformer. Thus, two conformers exist (both have a distinct mirror image pair), the global and the local minimum, possessing, respectively, a synclinal and an antiperiplanar arrangement of the fluorine atoms. Fig 1c shows the PECs for the CH3 – CHF, CH3 – CF2 , CF3 – CHF, and CF3 – CF2 radicals. The curves have regular 3-fold structure with similar barrier heights. In these molecules the inversion of the •CHF and •CF2 radical centers does not occur during the torsional motion. One distinct conformer exists, and in the case of CH3 – CF2 and CF3 – CF2 it has Cs symmetry. The torsional mode is best described as a hindered rotation around the C–C axis.

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Table 1 lists the individual contributions of our protocol to the heats of formation at 0 ∞ ∞ ∞ K. It can be observed that the dominant contributions are those of ∆EHF , δECCSD(T) , δEcore , Harm ∞ Harm and δEZPE . The magnitude of both δECCSD(T) and δEZPE shrinks when the hydrogen ∞ atoms are replaced by fluorine atoms, while the δEcore contribution seems fairly constant

−10.4 kJ/mol on average. It is noteworthy that the CC contributions beyond CCSD(T), ∞ especially δECCSDT(Q) , increase with the number of fluorine atoms, and their sum can be

as large as 6 kJ/mol. Similarly, δEREL grows, as it is expected, with the number of core electrons, i.e., with the number of fluorine atoms, and reaches 5 kJ/mol for CF3 – CF2 . Thus, when the so-called chemical accuracy (1 kcal/mol or 4.2 kJ/mol) is sought, one definitely ∞ needs to take account of both the δECCSDT(Q) and the δEREL contributions.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 −1534.86 −1534.95 −1498.10 −1494.02 −1799.81

CHF2 – CH2 (Cs )

CHF2 – CH2 (C1 )

CH2 F – CHF (sc)

CH2 F – CHF (ap)

CF3 – CH2


11 1.28

1.18

1.29

0.72

0.61

0.92

0.98

0.82

0.72

0.69

0.61

δECCSDT

4.88

3.74

2.55

1.42

1.39

1.40

1.42

1.35

0.31

0.28

0.31

δECCSDT(Q)

−10.47

−10.56

−10.27

−10.52

−10.57

−10.18

−10.22

−10.71

−10.33

−10.16

−10.72

∞ δEcore

4.92

4.29

3.56

3.01

2.95

2.89

2.91

2.91

2.27

2.23

2.28

δEREL

52.25

59.88d

65.25

79.16

79.82

76.38

75.59

80.01

84.35

85.35

86.50

Harm δEZPE

−0.27

−0.85

−0.90

−1.45

−1.45

−1.24

−1.33

−1.16

−1.61

−2.38

−1.67

Anharm δEZPE

−0.31

−0.25e

−0.22

−0.10

−0.13

−0.12

−0.11

−0.25

−0.03

−0.02

−0.13

δEDBOC

−888.93

−688.49

−516.93

−230.14

−239.55

−271.81

−271.73

−287.70

−48.64

−47.95

−63.95

∆f H0◦ c

− 2∆ECCSD(T) (H2 ) (the ∆ and total energy values can be found in the Supporting Information)

Results obtained with the cc-pVTZ basis sets.

Results obtained with the cc-pVTZ basis sets using frozen-core approximation.

e

however, the hindered rotor corrections are excluded.

Please note that ∆f H0◦ (Cgas ) (2×711.65 kJ/mol) and the spin-orbit correction for the carbon atom (2×0.35 kJ/mol) are also included,

atoms, respectively.

Cs and C1 denote the point group of the conformer, while ap, and sc refer to the antiperiplanar and synclinal arrangements of the fluorine

1 2 ∆ECCSD(T) (F2 )

δ denotes the difference of the differences, for instance for CH3 – CHF, δECCSD(T) = ∆ECCSD(T) (CH3 −CHF) − 2∆ECCSD(T) (Cgas ) −

−156.29

−181.47

−202.38

−232.36

−238.08

−230.91

−230.12

−237.00

−257.95

−258.09

−263.38

∞ δECCSD(T)

d

c

b

a

−2208.93

−1547.68

CH3 – CF2

CF3 – CF2

−1290.37

CH2 F – CH2 (C1 )

−1988.46

−1289.86

CH2 F – CH2 (Cs )

CF3 – CHF

−1301.76

∞ ∆EHF

CH3 – CHF

speciesb

Table 1: Contributions to the calculated heats of formation at 0 Ka. All values are in kJ/mol.

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Table 2 shows the available thermochemical data for the species studied. It is well known that the experimental investigation of radical species is challenging, and our Table 2 also supports this claim: in two cases no experimental data could be found, and there is only one case, CH3 – CHF, where more than one experimental values are available. Furthermore, the experimental uncertainties are fairly large; in several cases they are considerably larger than the chemical accuracy. Previous theoretical findings, with a few exceptions, relied on fast but less accurate thermochemical protocols like Gn, 40–42 CBS 43–45 and their variants, or on second- or fourth-order MP perturbation theory. On the other hand, prior coupled-cluster studies used relatively small basis sets and did not go beyond the CCSD(T) method. Therefore, with one notable exception, it is fair to say that the methods applied here are more advanced and more reliable than those used in past studies. The exception is the focal-point approach of Feng and Allen, 46 who only studied the CH2 F – CH2 radical, therefore, detailed discussion of their result will be given latter in the proper subsection. Table 2: Summary of literature data for standard enthalpies (kJ/mol) and entropies (JK−1 mol−1 ) for fluoroethanes speciesa

∆f H0◦

CH3 – CHF

−62.3

−68.9

◦ b ∆f H298

◦ S298

notes and referencesc

−70.3 ± 8.4

ref 47

−78.2 ± 6.7

ref 48

−74.1 ± 4.6

ref 49

−72.4

274.0

MP2, ref 50

−69.6d

G2, mixed, ref 51

−79.4

CBS-4 ref 52

[−69.9, −78.2]

G2, G3, ref 53

−70.6

CCSD(T)/IB[(DT)], ref 54

−74.1

CCSD(T)/IB[(DT)], corrected, ref 54

−77.7 ± 8.4 −75.6 ± 4.9

274.0

G3B3, ref 11 BAC-MP4, ref 55

Continued on Next Page. . .

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Table 2 – Continued Speciesa

∆f H0◦ −64.0 ± 2.8

CH2 F – CH2

◦ b ∆f H298

−74.5 ± 2.8

◦ S298

272.4

−59.4 ± 8.4

notes and referencesc this study ref 47

−54.0d 279.7

MP2, ref 37

−52.8d

G2, mixed, ref 51

[−55.2, −63.6]

G2, G3, ref 53

−58.0 −61.1 ± 8.4

CCSD(T)/IB[(DT)] ref 54 278.8

−56.2 ± 5.8


−58.8d

CCSDT(Q), ref 46

Cs

−47.7 ± 2.8

−58.7 ± 2.8

278.0

this study

C1

−49.1 ± 2.8

−59.9 ± 2.8

278.5

this study

−59.7 ± 2.8

287.3

this studye

CH3 – CF2

−302.5 ± 8.4

ref 56

−302.5 ± 8.4

review, ref 57

−293.2

−302.5

290.3

MP2, ref 50

−293.2

−302.5

288.3

MP2, ref 11

−294.9

−304.8

CBS-4 ref 52

[−295.4, −307.5]

G2, G3, ref 53

−300.2 ± 5.1

CHF2 – CH2

BAC-MP4, ref 55

−287.7 ± 2.8

−297.6 ± 2.8

289.0

this study

−267.9

−277.2

297.8

MP2, ref 37

[−279.5, −290.8]

G2, G3, ref 53

−280.9 ± 6.4

BAC-MP4, ref 55

Cs

−271.8 ± 2.8

−281.7 ± 2.8

296.0

this study

C1

−272.1 ± 2.8

−282.1 ± 2.8

295.9

this study

−281.9 ± 2.8

305.1

this studye

−235.5

293.3

MP2, ref 39

CH2 F – CHF

−226.6

[−235.6, −249.4]

G2, G3 ref 53

−247.3 ± 5.4 sc

−239.5 ± 2.8

−248.0 ± 2.8

BAC-MP4, ref 55 298.4

this study


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Table 2 – Continued Speciesa ap

∆f H0◦ −229.8 ± 2.8

CF3 – CH2

◦ b ∆f H298

297.6

this study

−247.9 ± 2.9

299.1

this studye

−523.1 ± 5.7d

ref 58

−517.1 ± 8.4

review, ref 57

−523.1 ± 5.7d 298.9

ref 11

302.6

−531.3

G2, G3, ref 53

−525.5 ± 12.1

CCSD(T)/TZ, ref 59

−526.6 ± 6.7 −526.0 ± 2.8

BAC-MP4, ref 55 300.9

−691.1 ± 5.3d

CF3 – CHF −681.7

−688.3

−693.3

−700.4

326.2

CF3 – CF2

G2, G3, ref 53 BAC-MP4, ref 55 325.7

this study

−889.8 ± 5.4

ref 60

−891.2 ± 5.4

ref 61

−892.9 ± 4.2

review, ref 57

−885.6

−891.2

−895.8

−901.6

340.5

−901.92 ± 8.4

G2, G3, ref 53 341.0

−907.6 ± 6.7 −894.4 ± 2.8

MP2, ref 62 CBS-4, ref 52

[−896.6, −907.5]

−888.9 ± 2.8


−703.0 ± 6.5 −695.1 ± 3.8

this study ref 48

[−696.6, −722.6]

−688.6 ± 3.8


[−525.5, −543.1]

−517.3 ± 2.8


−238.3 ± 2.8

−524.3 −522.9

◦ S298


340.6

this study


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Table 2 – Continued Speciesa a

◦ b ∆f H298

∆f H0◦

◦ S298


Cs and C1 denote the point group of the conformer, while ap, and sc refer to the antiperiplanar and synclinal arrangements of the fluorine atoms, respectively.

b

Square brackets denote intervals for calculated results. That is, only the lowest and the highest values obtained with the corresponding method are indicated.

c

For experimental and evaluated data only the reference is listed, otherwise the computational method is indicated.

d

Recalculated here, see text.

e

Averaged value based on the Boltzmann distribution of the conformers; the entropy of mixing is also included for entropy values.

In the following, most relevant experimental and theoretical data for each species are summarized. CH3 – CHF In 1983 Martin and Paraskevopoulos investigated the kinetics of reactions that took place ◦ between OH radicals and fluoroethanes, 48 and for ∆f H298 (CH3-CHF) −78.2 ± 6.7 kJ/mol

was derived. Four years later Tschuikow and Salomon 49 studied the photobromation of C2 H5 Cl, and analyzing the kinetics and thermochemical data of related compounds they got ◦ a somewhat higher value, −74.1±4.6 kJ/mol, for ∆f H298 (CH3-CHF). Then, in 1996, an even

higher experimental value appeared when Miyokawa et al. 47 researched the photobromination ◦ of fluoroethane and determined −70.3 ± 8.4 kJ/mol for ∆f H298 (CH3-CHF).

Chen and his associates 50 using HF/6-31G(d) geometries and frequencies in conjunction ◦ with MP2/6-311G(d,p) energies [MP2/6-311G(d,p)//HF/6-31G(d)] determined ∆f H298 (CH3-CHF)

= −72.4 and ∆f H0◦ (CH3-CHF) = −62.3 kJ/mol. Burcat 11 adopted the latter results. Zachariah et al. 55 used bond additivity corrected fourth-order MP perturbation theory (BACMP4) to determine thermochemical data for C1 and C2 hydrofluorocarbons and oxidized hydrofluorocarbons. For CH3 – CHF they got −75.6 ± 4.9 kJ/mol at 298 K. Sekusak et al. 51 15



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used G2 calculations to investigate the reactivity of fluoroethane with the hydroxyl radi◦ cal, CH3 CH2 F + OH −−→ CH3 – CHF + H2 O, and got −60.3 kJ/mol for ∆f H298 (CH3-CHF). ◦ ◦ Please note that using the currently recommended value 10 for ∆f H298 (CH3CH2F) ∆f H298 (CH3-CHF)=

−69.6 kJ/mol can be obtained with their G2 reaction enthalpy. Lazarou et al. 54 used CCSD(T) calculations with double- and triple-ζ basis sets and extrapolated the results using the infinite basis (IB) method of Truhlar and coworkers. 63 They reported two values for ◦ ∆f H298 (CH3-CHF), −70.6 and −74.1 kJ/mol; the latter data was calculated applying an

empirical correction for the IB method. ◦ Our calculations resulted in ∆f H298 (CH3-CHF)= −74.5±2.8 kJ/mol (−64.0±2.8 kJ/mol ◦ ◦ (CH3-CHF)= 272.4 JK−1 mol−1 . Our computed ∆f H298 (CH3-CHF) is the at 0 K) and S298

most reliable value and is in line with the available experimental results. The agreement among the entropy values calculated (see Table 2) is reasonable, however, our computation level is more advanced. The other entropy calculations utilized HF/6-31G(d) and MP2/631G(d) frequencies and the internal rotation was corrected using the table of Pitzer and Gwinn, 64 while our internal rotor correction is based on the 1D-HR model. CH2 F – CH2 ◦ The only available experimental value, ∆f H298 (CH2F-CH2)= −59.4 ± 8.4 kJ/mol, is that

of Miyokawa and associates, who studied the kinetics of gas phase photobromination of CH3 – CH2 F. 47 Chen and his associates, 37 utilizing the MP2/6-311G(d,p)//HF/6-31G(d) level of theory, calculated the −9.8 kJ/mol for the reaction enthalpy of the CH2 F – CH3 + CF3 – CH2 −−→ CH2 F – CH2 + CF3 – CH3 reaction. With the help of auxiliary heat of formation data for ◦ CH2 F – CH3 , CF3 – CH2 , and CF3 – CH3 they obtained ∆f H298 (CH2F-CH2) = −44.6 kJ/mol.

Because this value seemed to be one of the outliers among the reported data we recalculated it using up-to-date auxiliary heat of formation values for CH2 F – CH3 and CF3 – CH3 from the JPL database, 10 along with the recalculated experimental value of ref 58 for CF3 – CH2

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◦ (−523.1 ± 5.7 kJ/mol, see below). This calculation resulted in ∆f H298 (CH2F-CH2)= −54.0

kJ/mol in line with other data. Building on the G2 method Sekusak et al. 51 studied the ◦ CH2 F – CH3 + OH −−→ CH2 F – CH2 + H2 O reaction and realized a ∆f H298 (CH2F-CH2) ◦ = −43.5 kJ/mol value, but when one uses the current value 10 for ∆f H298 (CH2FCH3), their ◦ ∆f H298 (CH2F-CH2) data shifts to = −52.8 kJ/mol. On the basis of the IB method Lazarou ◦ et al. 54 derived a ∆f H298 (CH2F-CH2) = −58.0 kJ/mol value. Most recently, using an accu-

rate CCSDT(Q) model chemistry, Feng and Allen 46 studied the reaction between CH2 – CH2 ◦ and F and suggested −55.2 kJ/mol for ∆f H298 (CH2F-CH2). ◦ ◦ Our calculations resulted in ∆f H298 (CH2F-CH2)(Cs )= −58.7±2.8 and ∆f H298 (CH2F-CH2)(C1 )=

−59.9 ± 2.8 kJ/mol. Although our error bar overlaps with that of ref 46, the 3.5 kJ/mol discrepancy seems fairly large and requires an explanation because the two computational approaches are similar. On the basis of their reported equilibrium geometry it is clear that the Cs conformer was studied in ref 46. Using their 0 K CH2 – CH2 + F −−→ CH2 F – CH2 reaction enthalpy, −186.7 ± 0.8 kJ/mol, with the appropriate auxiliary data ∆f H0◦ (F)= 77.29 ± 0.05 and ∆f H0◦ (CH2=CH2)= 61.0 ± 0.5 kJ/mol from the JPL database, 10 one can arrive at ∆f H0◦ (CH2F-CH2)= −48.4 ± 0.9 kJ/mol. This value agrees well with our data for the Cs conformer, ∆f H0◦ (CH2F-CH2)= −47.7 ± 2.8 kJ/mol. The 0.7 kJ/mol discrepancy is acceptable and it seems reasonable due to differences in the calculations. We also reproduced their calculations (see Table IV in ref 46) and obtained −44.57 kcal/mol for the CH2 – CH2 + F −−→ CH2 F – CH2 reaction enthalpy at 0 K. The minuscule, 0.06 kcal/mol difference is due to the different equilibrium structures; here all electron CCSD(T)/cc-pVQZ geometries were used, while in ref 46 the equilibrium structures were obtained at the FC CCSD(T)/aug-ccpVQZ level. When thermal corrections were added to each species, −45.55 kcal/mol was obtained for the reaction enthalpy at 298 K. With this reaction enthalpy and the auxiliary ◦ ◦ data of ∆f H298 (F)= 79.38±0.05 10 and ∆f H298 (CH2=CH2)= 52.4±0.5 10 kJ/mol one arrives ◦ at −58.8 kJ/mol for ∆f H298 (CH2F-CH2), which is in excellent agreement with our value,

−58.7 kJ/mol, for the Cs conformer. The latter indicates that the thermal correction used

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in ref 46 is probably incorrect. CH3 – CF2 In 1977 Pickard and Rodgers 56 studied the reaction of CH3 – CHF2 with iodine and they ◦ derived for ∆f H298 (CH3-CF2) a −302.5 ± 8.4 kJ/mol value. It can be seen in Table 2 that

previous theoretical results are consistent with the experimental data. ◦ Our calculations yielded ∆f H298 (CH3-CF2)= −297.6.5 ± 2.8 and ∆f H0◦ (CH3-CF2)= ◦ −287.7 ± 2.8kJ/mol. Our ∆f H298 (CH3-CF2) data is well inside the uncertainty range of

the only available experimental value and is in accord with other computational results. However, the model chemistry applied here is more reliable than those used previously and the uncertainty of our data is considerably smaller than that of the experiment. Prior entropy values, 290.3 and 288.3 JK−1 mol−1 , were reported, respectively, in refs 50 and 11. Because the calculation of Burcat 11 apparently used the data of ref 50 and the same methodology including Pitzer-Gwinn corrections 64 for the hindered rotor, one of the values must be erroneous. To resolve this issue we repeated the entropy calculations using the data in Table V of ref. 50, and obtained 288.4 JK−1 mol−1 , which seemed to support Burcat’s value. However, further investigation showed that there is a typo in Table V of ref 50, which was further propagated to Burcat’s database. The correct result for Ic is 16.2057·10−39 g cm2 instead of 10.2057 · 10−39 g cm2 . With this correction we could reproduce the entropy value of 290.3 JK−1 mol−1 . Nonetheless, our entropy value, 289.0 JK−1 mol−1 , was obtained in a more involved calculation and it is more reliable. CHF2 – CH2 The available data for CHF2 – CH2 is rather scarce. The MP2/6-311G(d,p)//HF/6-31G(d) computations 37 on a series of isodesmic-homodesmic reaction energies resulted in −277.2 and ◦ (CHF2-CH2) and ∆f H0◦ (CHF2-CH2). The various −267.9 kJ/mol, respectively, for ∆f H298 ◦ G2 and G3 values 53 spread between −279.5 and −290.8 for ∆f H298 (CHF2-CH2), while the

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◦ BAC-MP4 method in ref 55 provides ∆f H298 (CHF2-CH2) = −280.9 ± 6.4 kJ/mol.

In line with the HF/6-31G(d) findings of Chen and associates, 37 this study also confirms that three conformers exist for this radical: a symmetric Cs and an asymmetric C1 global minimum structure along with its enantiomer pair. It is also fair to say that the ◦ most accurate results are given here, namely, ∆f H298 (CHF2-CH2)= −281.7 ± 2.8 kJ/mol ◦ ◦ and S298 (CHF2-CH2)= 296.0 JK−1 mol−1 for the Cs conformer and ∆f H298 (CHF2-CH2)= ◦ −282.1 ± 2.8 kJ/mol and S298 (CHF2-CH2)= 295.9 JK−1 mol−1 for the C1 conformers.

CH2 F – CHF Similarly to its structural isomer CHF2 – CH2 no experimental investigation has been conducted to determine ∆f HT◦ (CH2F-CHF). The MP2/6-311G(d,p)//HF/6-31G(d) values of ◦ Chen et al. 39 are ∆f H298 (CH2F-CHF) = −235.48 and ∆f H0◦ (CH2F-CHF) = −226.56 kJ/mol.

In the study of Haworth et al. 53 variants of the G2 and G3 methods give values between −235.6 and −249.4 kJ/mol for the heat of formation of CH2 F – CHF at 298 K. In the BAC◦ MP4 paper of Zachariah and his associates 55 −247.3±5.4 kJ/mol is listed for ∆f H298 (CH2F-CHF).

Our calculations yielded, respectively, −238.3 ± 2.8 and −248.0 ± 2.8 kJ/mol for the heat of formation of the antiperiplanar and synclinal conformers at 298K. These are in line with the previous results, however, our data is more accurate. The only entropy value, 293.3 JK−1 mol−1 , is reported by Chen and his coworkers. 39 The correction for the torsional mode was calculated by direct summation of the energy levels obtained from a periodic potential function. 65 The potential was fitted to their HF/6-31G(d) PEC. They also found that the less accurate treatment as three-fold hindered rotation of the torsional mode resulted in only a slightly different value, 292.8 JK−1 mol−1 . Our entropy values for the conformers deviate by about 5 JK−1 mol−1 from their values. Since their reported molecular parameters, i.e., equilibrium structure, moments of inertia, harmonic frequencies are correct and reproducible the most likely reason for the discrepancy is that, by accident, they used a wrong symmetry number, two instead of one, during the calculation of entropy.

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CF3 – CH2 In 1974 Wu and Rodgers 58 studied the equilibrium of the CF3 CH3 +I2 =CF3 CH2 I+HI reaction and obtained 64.0±2.1 kJ/mol for the reaction enthalpy at 298 K. With the help of auxiliary bond dissociation energies and heat of formation values they derived −517.1 ± 5.0 kJ/mol ◦ for ∆f H298 (CF3-CH2). In 1982 McMillen and Golden 57 collected the available hydrocarbon ◦ bond dissociation energies, and reported ∆f H298 (CF3-CH2)= −517.1±8.4 kJ/mol. Burcat 11

also lists these values. On the basis of isodesmic and homodesmic reactions energies 37 calculated with the MP2/6-311G(d,p)//HF/6-31G(d) method an average value of −524.3 kJ/mol can be ob◦ tained for ∆f H298 (CF3-CH2) (see Table XI in ref 37). Espinosa-Garcia and Garcia-Bernaldez 59

tested an ONIOM-like integrated method 66 for calculating thermodynamic properties of radicals including CF3 – CH2 . They averaged the result of several models and got −525.5 ± ◦ 12.1 kJ/mol for ∆f H298 (CF3-CH2); their most accurate model is based on CCSD(T)/6-

311++G(2df,p) computations. Other theoretical studies reported similar values, consequently, the computational results deviate from the experimental data, and consistently predict the radical more stable at least by 8 kJ/mol. ◦ This study, in line with prior quantum chemical calculations, provides ∆f H298 (CF3-CH2)=

−526.0 ± 2.8 kJ/mol. It turned out that the discrepancy between the theoretical studies and the experimental work can be eliminated if currently accepted auxiliary values are used. ◦ Following the reasoning in ref 58 ∆f H298 (CF3-CH2) can be calculated as

◦ ◦ ◦ ◦ ∆f H298 (CF3 − CH2 ) = ∆r H298 + ∆f H298 (CF3 − CH3 ) − ∆f H298 (H) ◦ ◦ ◦ + D298 (CF3 CH2 − I) + D298 (HI) − D298 (I2 ),

◦ where ∆r H298 = 64.0±2.1 kJ/mol is the reaction enthalpy for the CF3 CH3 +I2 =CF3 CH2 I+HI ◦ ◦ ◦ reaction. With ∆f H298 (CF3-CH3)= −751.5±3.2, 10 ∆f H298 (H)= 218.0, 10 D298 (CF3 CH2 − I) = ◦ ◦ ◦ 235.6 ± 4.2, 58 D298 (HI) = 298.3, 58 and D298 (I2 ) = 151.5 58 kJ/mol ∆f H298 (CF3-CH2)=

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−523.1 ± 5.7 kJ/mol can be calculated in accord with the theoretical model chemistries. ◦ Similarly to the case of S298 (CH3-CF2) there are two entropy values, those of Burcat and

Chen and associates, 298.9 JK−1 mol−1 11 and 302.6 JK−1 mol−1 , 37 respectively. The first one is faulty because Burcat used one misprinted molecular parameter reported by Chen and coworkers (1.4637 · 10−39 g cm2 was reported but the correct value is 1.4637 · 10−38 g cm2 , see Table VI of ref 37). Anyway our entropy value of 300.9 JK−1 mol−1 is consistent with that of ref 37 but based on more accurate calculations. CF3 – CHF Martin and Paraskevopoulos 48 studied the reaction of OH and fluoroethanes and derived ◦ a −680.7 ± 9.6 kJ/mol value for ∆f H298 (CF3-CHF). They observed that the C-H bond

dissociation energies, DC−H , of alkanes and fluoroalkanes correlate with the logarithm of k/n, where k is the rate constant for the reaction and n is the number of hydrogens in the alkane or fluoroalkane. Thus, they estimated DC−H (CF3 CHF – H) to be 433.0 ± 4.2 kJ/mol ◦ ◦ at 298K, and using the auxiliary data, ∆f H298 (CF3-CH2F)= −895.8 ± 8.4 and ∆f H298 (H)= ◦ 218.0 kJ/mol, the above ∆f H298 (CF3-CHF) value was derived. It can be observed that ◦ all theoretical calculations predict the magnitude of ∆f H298 (CF3-CHF) considerably larger

than the experimental data. ◦ ◦ This study delivers ∆f H298 (CF3-CHF)= −695.1 ± 3.8 kJ/mol and S298 (CF3-CHF)=

325.7 JK−1 mol−1 . There is a fairly large, 14.4 kJ/mol, difference between our result and the experimental value. In addition, the error bars do not overlap. However, the source of the discrepancy can be easily identified, it is the auxiliary heat of formation data of CF3 – CH2 F. The currently accepted value, −906.2±3.2 kJ/mol, 10 differs by −10.4 kJ/mol from that used ◦ in ref 48. After recalculating ∆f H298 (CF3-CHF) with this auxiliary value one can arrive at

−691.1 ± 5.3 kJ/mol which agrees well with our result. The simple three-fold hindered rotation treatment of the torsional mode 39 resulted in 326.2 JK−1 mol−1 for the entropy. Our result agrees well with this value but it is expected to be more reliable because it is based

21



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on more accurate structural parameters and PEC. CF3 – CF2 In 1975 Chen et al. 60 collected the available thermochemical data for six fluoroethanes and ◦ reported −889.8 ± 5.4 kJ/mol for ∆f H298 (CF3-CF2). Wu and Rodgers 61 investigated the ◦ reaction between C2 F5 I and HI, and derived −891.2 ± 5.4 kJ/mol for ∆f H298 (CF3-CF2). ◦ The review of McMillen and Golden 57 listed −892.9 ± 4.2 kJ/mol for ∆f H298 (CF3-CF2).

The MP2/6-311G(d,p)//HF/6-31G(d) method yielded −891.19 at 298 K and −885.63 ◦ kJ/mol at 0 K for the heat of formation of CF3 – CF2 . 62 Burcat 11 reported ∆f H298 (CF3-CF2)= ◦ −901.92±8.4 kJ/mol based on G3B3 calculations. Zachariah et al. 55 calculated ∆f H298 (CF3-CF2)=

−907.6 ± 6.7 kJ/mol using the BAC-MP4 method. Zhang, 52 with the help of the CBS-4 ◦ method, obtained −901.57 kJ/mol for ∆f H298 (CF3-CF2) (−895.75 kJ/mol at 0 K). By ap-

plying G2 and G3 methods Haworth and her coworkers 53 had results between −896.6 and −907.5 kJ/mol for the heat of formation of CF3 – CF2 at 298 K. ◦ Our results, ∆f H0◦ (CF3-CF2) = −888.9 ± 2.8, ∆f H298 (CF3-CF2) = −894.4 ± 2.8 kJ/mol ◦ and S298 (CF3-CF2)= 340.6 JK−1 mol−1 , are in line with previous experimental and theoret-

ical investigations, and have the smallest uncertainties.

Conclusions Table 3 summarizes the best available theoretical and experimental thermochemical values for the species studied here. We believe this work provides the most reliable theoretical values for the 8 molecules considered in this study because the present model chemistry is more accurate than those utilized by previous studies, and in contrast with prior calculations, it also has a well-defined uncertainty measure. The importance of the excitations beyond the perturbative triples is noteworthy. The contribution to the heats of formation obtained from CCSDT(Q) calculations increases with the size of the radical, i.e., with the number

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of fluorine atoms, and it is as large as 5 kJ/mol for CF3 – CF2 . Relativistic corrections show a similar trend reaching their maximum, 5 kJ/mol, for CF3 – CF2 . Therefore, they seem to be unavoidable in thermochemical protocols seeking chemical accuracy. In those cases where conformer isomerism occurs for the radicals conformer specific values along with Boltzmann averaged quantities are also reported. Although previous investigators noted the presence of conformers and predicted the energy order for the conformers in line with our findings, thermodynamic functions were only reported for the most stable isomer. In this regard one exception is notable, i.e., an arrangement of CH2 F – CHF that was proven to be a conformer with the HF/6-31G(d) method 39 is not a minimum either at the MP2/ccpVTZ or CCSD(T)/cc-pVTZ level of theory. Although, originally, in the case of CF3 – CH2 and CF3 – CHF there were large discrepancies between our calculations and the experimental values, these were eliminated by updating the auxiliary data used in the original experimental report with currently recommended ones. Thus, it can be observed in Table 3 that our results agree well with the best experimental data but have smaller uncertainties attached.

Table 3: Best available enthalpies of formation at 0 and 298.15 K (in kJ/mol) as well as standard molar entropies at 298 K (in JK−1 mol−1 ) for fluoroethyl radicals computationa Speciesb

◦ S298

∆f H0◦

experiment ◦ ∆f H298

CH3 – CHF

272.4 ± 1.5

−64.0 ± 2.8

−74.5 ± 2.8

CH2 F – CH2 Cs

278.0 ± 1.5

−47.7 ± 2.8

−58.7 ± 2.8

CH2 F – CH2 C1

278.5 ± 1.5

−49.1 ± 2.8

−59.9 ± 2.8

287.3 ± 1.6c

−59.7 ± 2.8c

CH3 – CF2

289.0 ± 1.5

−287.7 ± 2.8

−297.6 ± 2.8

CHF2 – CH2 Cs

296.0 ± 1.5

−271.8 ± 2.8

−281.7 ± 2.8

CHF2 – CH2 C1

295.9 ± 1.5

−272.1 ± 2.8

−282.1 ± 2.8

305.1 ± 1.5c

−281.9 ± 2.8c

Continued on Next Page. . . 23


◦ ∆f H298

source

−74.1 ± 4.6

ref 49

−59.4 ± 8.4

ref 47

−302.5 ± 8.4

ref 56


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Table 3 – Continued Speciesa

◦ S298

∆f H0◦

CH2 F – CHF sc

298.4 ± 1.5

−239.5 ± 2.8

−248.0 ± 2.8

CH2 F – CHF ap

297.6 ± 1.5

−229.8 ± 2.8

−238.3 ± 2.8

299.1 ± 1.6c

◦ ∆f H298

◦ ∆f H298

source

−247.9 ± 2.9c

CF3 – CH2

300.9 ± 1.5

−517.3 ± 2.8

−526.0 ± 2.8

−523.1 ± 5.7d ref 58

CF3 – CHF

325.7 ± 1.8

−688.6 ± 3.8

−695.1 ± 3.8

−691.1 ± 5.3d ref 48

CF3 – CF2

340.6 ± 1.5

−889.9 ± 2.8

−894.4 ± 2.8

−892.9 ± 4.2

ref 57

a

This study

b

Cs and C1 denote the point group of the conformer, while ap, and sc refer to the antiperiplanar and synclinal arrangements of the fluorine atoms, respectively.

c

Conformationally averaged value; the entropy of mixing is also included for entropy values.

d

Recalculated here, see text.

Acknowledgement J.C. acknowledges the financial support of the János Bolyai fellowship of the Hungarian Academy of Sciences. We thank the NIIF Institute of Hungary for the generous grant of computer time on the HPC Infrastructure.

Supporting Information Available Total energies, geometries, frequencies, rotational constants, anharmonicity constants, G0 values, eigenvalues of the hindered rotor treatment. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Accurate Theoretical Thermochemistry for Fluoroethyl Radicals - The

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