Thermochemical Properties Enthalpy, Entropy, and Heat Capacity of

Article pubs.acs.org/JPCA

Thermochemical Properties Enthalpy, Entropy, and Heat Capacity of C1−C4 Fluorinated Hydrocarbons: Fluorocarbon Group Additivity Heng Wang, Á lvaro Castillo, and Joseph W. Bozzelli* Department of Chemical Engineering, Chemistry, and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States S Supporting Information *

ABSTRACT: Enthalpies of formation for 14 C2−C4 fluorinated hydrocarbons were calculated with nine popular ab initio and density functional theory methods: B3LYP, CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, G4, G4(MP2)-6X, and W1U via several series of isodesmic reactions. The recommended ideal gas phase ΔH°f 298 (kcal mol−1) values calculated in this study are the following: −65.4 for CH3CH2F; −70.2 for CH3CH2CH2F; −75.3 for CH3CHFCH3; −75.2 for CH3CH2CH2CH2F; −80.3 for CH3CHFCH2CH3; −108.1 for CH2F2; −120.9 for CH3CHF2; −125.8 for CH3CH2CHF2; −133.3 for CH3CF2CH3; −166.7 for CHF3; −180.5 for CH3CF3; −185.5 for CH3CH2CF3; −223.2 for CF4; and −85.8 for (CH3)3CF. Entropies (S298 ° in cal mol−1 K−1) were estimated using B3LYP/6-31+G(d,p) computed frequencies and geometries. Rotational barriers were determined and hindered internal rotational contributions for S298 ° , and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curve. Thermochemical properties for the fluorinated carbon groups C/C/F/H2, C/C2/F/H, C/C/F2/H, C/C2/F2, and C/C/F3 were derived from the above target fluorocarbons. Previously published enthalpies and groups for 1,2-difluoroethane, 1,1,2-trifluoroethane, 1,1,2,2tetrafluoroethane, 1,1,1,2-tetrafluoroethane, 1,1,1,2,2-pentafluoroethane, 2-fluoro-2-methylpropane that were previously determined via work reaction schemes are revised using updated reference species values. Standard deviations are compared for the calculation methods.

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partially fluorinated hydrocarbons of C1 and C2. Berry2 et al. studied fluorinated C1 species with bromine using G2(MP2), CBS, and BAC-MP4 methods. Berry2 et al. reported that the negative errors in the calculated enthalpies by atomization methods were observed to be linearly dependent upon the number of C−F bonds in the molecule. Yamada6,8 et al. leveraged the isodesmic reaction method with literature data for highly fluorinated C2HXF6−X ethanes using MP2 and G2. Yamada6,8 et al. also updated the thermochemical enthalpy data of C/F/H groups needed for use of the Group Additivity Method,10 where they reported that interaction groups had to be used to correct for fluorine atoms when they occurred on adjacent carbons. Yamada and Berry7 together continued using G2MP2 to expand the data to C3 hydro-fluorocarbons. In 2000, Haworth4 et al. published a study on more than one hundred fluorinated C1 and C2 hydrocarbons, including stable molecules and radicals. They evaluated differences in enthalpy data between the values from isodesmic reaction versus atomization energies and recommended use of the G3 method data.

INTRODUCTION Fluorinated hydrocarbons are present in the atmosphere, hydrosphere, and lithosphere as a result of past use as solvents and propellants as well as past and current use as refrigerants and heat exchange fluids and in polymers. They were regarded as the replacement of greenhouse gas like chlorofluorocarbons because of their non or less adverse effects on the stratospheric ozone layer.1 They exist in the environment from pure compounds to partially oxidized intermediates resulting from environmental driven oxidation of the molecular structures. The fundamental thermodynamic and chemical properties of the fluorocarbons and their oxygenated breakdown intermediates are critical to understand in order to study their lifetimes and reactivity in biological processes and in the environment. Thermochemical properties are also needed in kinetic modeling and in equilibrium codes. There are several studies on the thermochemistry of fluorinated alkanes with one and two carbon atoms in the literature.2−9 In 1994, Chen3 et al. studied thermodynamic properties of CH2FCHF2 and CHF2CHF2 using RHF, MP2, and MP4 calculation methods. Zachariah9 et al. employed the BAC-MP4 method and expanded the database for thermochemistry of C/H/F/O species significantly as the data was needed for construction of a mechanism to model oxidation of © 2015 American Chemical Society

Received: April 24, 2015 Revised: June 10, 2015 Published: June 11, 2015 8202

DOI: 10.1021/acs.jpca.5b03912 J. Phys. Chem. A 2015, 119, 8202−8215

Article

The Journal of Physical Chemistry A Recently, Nagy5 et al. has used Weizmann-n methods (for total energies) and CCSD(T) (for conformer energies and rotational barriers) to study enthalpies on a series of multifluoro C2HXF6−X molecules. They did not report entropy and heat capacity data on monofluoro hydrocarbons or larger C3 and C4 fluorocarbons. In this study, we verify the standard enthalpy of formation for fluoromethane with that of the literature4,11−14 and use these molecules as reference species in isodesmic work reactions for fluorocarbons with a higher carbon content. We show and compare the performance of nine different ab initio, composite, and density functional calculation methods for accuracy, and we determine the ideal gas thermodynamic properties and compare our data with that from experiments. Our C1 and C2 fluorocarbons are used to calculate C3 and C4 related fluoro-hydrocarbons. We use between four and twenty-nine work reactions for error cancellation in the calculation enthalpy for each species. We re-evaluate group contribution values (for group additivity) for C/C/F/H2, C/C2/F/H, C/C/F2/H, C/ C2/F2, and C/C/F3 based on our calculated values. We use the previous calculated thermal enthalpies and enthalpies of work reactions of Yamada et al.6−8 with more accurate data for the reference molecules and show good agreement with current literature values. The data of this study and of Yamada et al.10 has been used to build group additivity terms for calculation of thermochemical properties of fluorocarbons, including interactions between fluorine atoms on adjacent carbons. Group additivity is a popular method for estimation of thermochemical properties on hydrocarbons and oxygenated hydrocarbons, but it is not widely used for fluorocarbons.

shown that this method presents a mean absolute error of 0.0023 Å and a maximum absolute error of 0.0045 Å for a set of 19 molecules that include atoms of the first row (including HF, F2, and HOF).27 Geometry optimization is carried out with Gaussian09, 28 and frequency and single point energy calculations for fluoromethane were carried out with GAMESS.29−32 Density Functional Theory and Composite Calculations for Fluorinated Hydrocarbons C1−C4 via Series of Isodesmic Reactions. All calculations for the C 1 −C 4 fluorocarbons, (excluding CH3F as above) are performed using the Gaussian 0928 program. Structures, vibration frequencies, zero-point vibrational and thermo energies, and internal rotor potentials are initially analyzed with the hybrid density functional theory (DFT) method B3LYP. This method combines the three-parameter Becke exchange functional B3,33 with the Lee−Yang−Parr correlation functional, LYP,34 and is used here with the 6-31G+(d,p) basis set. B3LYP/6-31G+(d,p) is chosen because it is computational, economical and, thus, possibly applicable to larger molecules. Energies are further refined using the procedures of the complete basis method developed by Petersson and co-workers, CBS-QB3.35 It utilizes B3LYP/6-311G(2d,d,p) level of theory to calculate geometries and frequencies followed by single-point calculations using the CCSD(T) MP4(SDQ), and MP2 level. The CBS-APNO36 method performs an initial geometry optimization and frequency calculation at the HF/6-311G(d,p) level, followed by a higher-level QCISD/6-311G(d,p) geometry optimization. A single-point energy calculation is then performed at the QCISD(T)/6-311++G(2df,p) level, followed by extrapolation to the complete basis set limit. In 2007, two new hybrid meta exchange-correlation functional, M06 and M06-2X, were reported.37 A third new hybrid density functional method, that includes 100% long-range exact exchange and 16% of exact short-exchange, called ωB97X,38 was developed in 2008. These three modified DFT calculation levels are further used and evaluated in this fluorocarbons study. We also utilized the W1U39 theory, a modification of W140 (Weizmann 1), as fluorine is in the first row of the periodic table. W1U theory is an unrestricted coupled cluster spin contamination corrected [UCCSD(T)] method. Due to the large computational requirements of the CCSD(T)-FC \AugH−CC-pVTZ+2df and CCSD-FC\AugH-CC-pVQZ+2df energy calculations in the W1U method, this method is not applicable to the larger molecules used in this study. Gaussian-4 theory (G4)41 is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. This method performs an initial geometry optimization and frequency calculation at the B3LYP/6-31G(2df, p) level, followed by a series of single point correlation energy calculations started from CCSD(T), MP4SDTQ, until MP2-Full. With regard to the computational time cost of the G4 composite calculation methods, a cost-effective improvement to G4 had been presented in 2011, called G4(MP2)-6X.42 This calculation method is reported to have a cost comparable to that of G4(MP2) but performance approaching that of G4. Enthalpy of Formation Calculations. The basic requirement of an isodesmic reaction is that the number of each bond type is conserved in products and reactants, which leads to the cancellation of systematic errors in the molecular orbital calculations.43 The careful choice of the isodesmic reactions

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COMPUTATIONAL METHODS Ab Initio Calculation for Fluoromethane via Atomization Reaction. We consider fluoromethane as core reference species in our isodesmic reactions; hence, it is important that the standard enthalpy of formation of fluoromethane we use is accurate. In addition to evaluating data in the literature, we have calculated the enthalpy of formation of fluoromethane using extrapolated CCSD(T)15−18 energies with atomization reactions. The accurate calculation of electronic energies requires the extrapolation of the calculated values to the basis set limit, and that the Hartree−Fock (self-consistent field) energies and the correlation energies converge to this limit differently.19 HFSCF energies are calculated with the augmented correlation consistent basis set (X= T, Q, 5),20−22 and extrapolated as −bX suggested by Feller,23 EXHF = E∞ , with EXHF being the HF + ae three calculated HF-SCF energies using the aug-cc-pVXZ basis sets. The E∞ HF extrapolated energy and parameters a and b can then be calculated with X as the cardinal number of the basis set (T:3, Q:4, and 5). CCSD(T) correlation energies where calculated with the aug-cc-pVXZ (X = Q, 5), and extrapolated following the atomic partial wave expansion of Helgaker et al.,24 −3 X EXcorrCCSD(T) = E∞ corrCCSD(T) + AX , where EcorrCCSD(T) are the CCSD(T) correlation energies using the aug-cc-pVXZ basis sets. The E∞ corrCCSD(T) and parameter A can then be calculated with simple algebra as for the HF-SCF energies. Enthalpies of formation where then calculated using atomization reactions, with Ruscic’s active thermochemical tables for the experimental atomic enthalpies: H = 51.63 ± 0.00 kcal/mol; C = 170.12 ± 0.05 kcal/mol; F = 18.45 ± 0.06 kcal/mol,25,26 and they include thermal corrections for enthalpy. Molecular geometries where calculated using CCSD(T)/cc-pVTZ because it has been 8203


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The Journal of Physical Chemistry A Table 1. Isodesmic Reactions and Enthalpy of Formation for Fluoroethane from the Selected Calculation Method ΔH°f, 298a

CH3CH 2F + CH4 → CH3F + CH3CH3

−65.28b

a1

CH3CH 2F + CH3CH3 → CH3F + CH3CH 2CH3

−65.51

b

a2

CH3CH 2F + CH3CH 2CH3 → CH3F + CH3CH 2CH 2CH3

−65.41c

a3

CH3CH 2F + CH3OH → CH3F + CH3CH 2OH

−65.50

a4

b

−1 b

Unit in kcal mol . Average of enthalpy of formation of fluoroethane over seven selected calculation methods (CBS-QB3, CBS-APNO, M06, M062X, ωB97X, G4, and W1U). cAverage of enthalpy of formation of fluoroethane over six selected calculation methods (CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, and G4). a

Figure 1. Standard deviation range of each calculation method.

average: the average of all calculated ΔH°f 298 values from all of the nine calculation levels on the isodesmic reactions. We use fluoroethane as an example: the method average under B3LYP is the average of four values determined by the four isodesmic reactions using B3LYP, −65.92 kcal mol−1. The selected method averages for fluoroethane are CBS-QB3 (−65.28), CBS-APNO (−65.28), M06 (−65.68), M06-2X (−65.42), ωB97X (−65.76), W1U (−65.32), G4(−65.21), and G4(MP2)-6X(−65.25) kcal mol−1. The overall average for fluoroethane is the average of all calculated ΔHf°298 values from the nine methods over the set of isodesmic reactions, −65.46 kcal mol−1. The selected average for fluoroethane, which we recommend for the enthalpy of formation values (from CBSQB3, CBS-APNO, M06, M06-2X, ωB97X, G4, and W1U methods over the set of isodesmic reactions) is −65.42 kcal mol−1. These averaging methods are used for the 14 target molecules of this study. The method average enthalpy of formation is initially determined for each method. We then calculate the selected method average enthalpy of formation from the seven method calculation set. We note that in order to have good cancelation of error in the work reactions, we use one of the smaller fluorocarbons, as reference species for larger target molecules. Here, the method, selected, and overall average enthalpy of formation of the target is then determined using the respective “method, selected, and overall” average enthalpy of formation of the reference fluorocarbon. The isodesmic reactions used for each of the C2−C4 fluorinated hydrocarbons and their enthalpies of formation are illustrated in Table S1−S14 of the Supporting Information. The

allowed evaluation of enthalpies of formation to accuracies approaching the sum of the uncertainties of the other−often experimental−values involved in the isodesmic reactions. Taking fluoroethane as an example, the following four isodesmic reactions (Table 1) are selected to determine the ΔH°f 298 of the target molecule, fluoroethane. Since the ΔH°f 298 values of all species but fluoroethane in a1− a4 (Table 1) are known, the ΔH°f 298 of the target species fluoroethane, is obtained from this data and the calculated ΔHrxn, ° 298. We have calculated thirty-five ΔHf°298 values (from nine different calculation levels on each of the four isodesmic reactions, a1−a4) are determined for the unknown target molecule, fluoroethane. Several of our evaluated fluorinated hydrocarbons are further used in some of the isodesmic reactions, as reference species so that we can achieve error cancellation. The nine computation methods combined with up to twenty-nine work reactions provide several methods to formulate averages for evaluation of the standard enthalpy of formation on the target molecules. (i) Method average: uses the average of the calculation method values for each target molecule over the series of isodesmic reactions. (ii) Selected average: reports the average ΔH°f 298 values from the selected set of seven calculation methods (CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, G4, and W1U) from the respective isodesmic reaction sets. B3LYP and G4(MP2)-6X are excluded based on the large standard deviation range as shown in Figure 1. The selected average enthalpy values are the recommended values and those which have been reported below. (iii) Overall 8204


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The Journal of Physical Chemistry A

entropies and heat capacities are calculated using the geometry, symmetry, frequencies, and moments of inertia of the B3LYP/ 6-31+G(d,p) optimized structures. The calculations use standard formulas from statistical mechanics for the contributions of translation, external rotation, and vibrations using the “SMCPS”46 program. This program utilizes the rigid-rotorharmonic oscillator approximation from the frequencies along with moments of inertia from the optimized structures. Contributions from internal rotors using the program “Rotator” are substituted for contributions from the corresponding internal rotor torsion frequencies. The Rotator program calculates the thermodynamic functions from hindered rotations with arbitrary potentials based on the method developed by Krasnoperov, Lay, and Shokhirev.47 This technique employs expansion of the hindrance potential in the Fourier series, calculation of the Hamiltonian matrix in the basis of the wave functions of free internal rotation, and subsequent calculation of energy levels by direct diagonalization of the Hamiltonian matrix. All potential curves of rotational barrier versus dihedral angle are fit by a cosine curve. In this work, the torsional potential calculated at discrete torsional angles is represented by a truncated ten-parameter Fourier series of the following form:

reference species in the isodesmic reactions are listed in Table 2 along with the uncertainties. We note that we use standard Table 2. ΔHf 298° for Reference Species in The Isodesmic Reactions species CH4 CH3CH3 CH3CH2CH3 CH3CH2CH2CH3 CH3OH CH3CH2OH (CH3)3CH CH3CH(CH3)CH2CH3 CH3F a

enthalpya (kcal mol−1) −17.78 −20.03 −25.02 −30.02 −48.16 −56.21 −32.07 −36.74 −56.54

± ± ± ± ± ± ± ± ±

0.10 0.10 0.12 0.17 0.07 0.10 0.17 0.24 0.07b

Pedley.44 bGoos.13

enthalpy of formation for methanol determined by Pedley44 as −48.16 ± 0.07 kcal mol−1 and not the value recommended in the NIST Web book45 (−49.0 ± 3.0 kcal mol−1). Our calculation for the enthalpy of methanol, −48.15 kcal mol−1, is in Table S15 of the Supporting Information. The uncertainty for the target molecules incorporates: (i) uncertainty of the work reaction calculation method, (ii) the number of work reactions, and (iii) uncertainty of the reference species. Uncertainty of the work reaction computational method was derived from analysis of the calculated ΔHrxn for a series of 12 work reactions vs ΔHrxn of evaluated literature data. Table S19 of the Supporting Information shows the standard deviation (std) for the 12 work reactions was 0.69 kcal mol−1. This std value was then used in a Student’s t test for the number of work reactions used for each fluorocarbon at the 95% confidence limit. Separately, the sum of three reference species uncertainties for each work reaction of the target molecule was calculated. The std of the two values: (a) calculation method, Student’s t test value and (b) sum reference species uncertainty. The average value of this std over the set of work reactions was calculated and reported as the uncertainty for that species. As an example, four work reactions were used for fluoroethane. The Student’s t test using the std of the 12 reference reactions 0.69, applied for four reactions, resulted in a Student’s t test uncertainty of 1.09 for the work reaction method. The sum or the uncertainties over the three reference species for each of the four work reactions was 0.1, 0.1, 0.2, and 0.1 kcal mol−1. Calculation of the std of these two values, the (a) reaction and t test method and (b) the sum species uncertainty was 1.1, 1.1, 1.2, and 1.1 (four work reactions), resulting in an average uncertainty of 1.1 kcal mol−1. The calculated computational method uncertainty for each molecule is ± 1.09 for CH3CH2F, ± 0.72 for CH3CH2CH2F, ± 0.72 for CH3CHFCH3, ± 0.53 for CH3CH2CH2CH2F, ± 0.46 for CH3CHFCH2CH3, ± 0.64 for CH2F2, ± 0.49 for CH2CHF2, ± 0.42 for CH3CH2CHF2, ± 0.42 for CH3CF2CH3, ± 0.40 for CHF3, ± 0.34 for CH3CF3, ± 0.30 for CH3CH2CF3, ± 0.26 for CF4, and ±1.09 for (CH3)3CF. Entropy, Heat Capacity, and Internal Rotor Analysis for 14 Fluorinated Hydrocarbons. Entropy and heat capacity contributions as a function of temperature are determined from the calculated structures, moments of inertia, vibration frequencies, symmetry, electron degeneracy, number of optical isomers, and the known mass of each molecule. The

10

V (⌀ ) = a 0 +

10

∑ a 0 cos(i⌀) +

∑ bj cos(j⌀)

i=1

j=1

(1)

The values of the coefficients ai and bj are calculated to provide the minima and maxima of the torsional potentials with allowance for a shift of the theoretical extreme angular positions. Vibrational frequencies are scaled by a factor of 0.964 for the B3LYP/6-31+G(d,p) calculation method for the use in calculation of standard entropy and heat capacity based on the computational chemistry comparison and benchmark database.48 Group Additivity. Group additivity10 is a straightforward and reasonably accurate calculation method to estimate thermodynamic properties of hydrocarbons and oxygenated hydrocarbons;49 it is particularly useful for application to larger molecules and in codes or databases for the estimation of thermochemical properties in reaction mechanism generation. Selection of values for the initial groups in a series is critical to development of a group additivity scheme for accurate property estimation. In this study, we update several fluorocarbon alkane groups from our previous research6,8 and develop several new fluorocarbon alkane groups derived from use of thermodynamic property data. Data for the C/C/F/H2 group is derived from fluoroethane, 1-fluoropropane, and 1-fluorobutane. There are no other halogens or bulky groups/fragments on the carbon atoms adjacent to the carbon atoms containing the fluorine in the defining group. The enthalpy of formation and heat capacities of C/C/F/H2 is calculated by the average from the following: (CH3CH 2F) = (C/C/H3) + (C/C/F/H 2)

(b1)

(CH3CH 2CH 2F) = (C/C/H3) + (C/C2 /H 2) + (C/C/F/H 2)

(b2)

(CH3CH 2CH 2CH 2F) = (C/C/H3) + 2(C/C2 /H 2) + (C/C/F/H 2) 8205

(b3)


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The Journal of Physical Chemistry A The standard entropy of C/C/F/H2 is calculated from

Table 4. CarbonFluorine Bond Length for C2−C4 Fluorinated Hydrocarbons at the B3LYP/6-31+G(d,p) and QCISD/6-311G(d,p) Levels of Theory

(CH3CH 2F) = (C/C/H3) + (C/C/F/H 2) − R ln(σ ) (c1)

bond length (C−F) (Å)

(CH3CH 2CH 2F) = (C/C/H3) + (C/C2 /H 2) + (C/C/F/H 2) − R ln(σ )

CH3CH2F CH3CH2CH2F CH3CHFCH3 CH3CH2CH2CH2F CH3CHFCH2CH3 CH2F2 CH3CHF2 CH3CH2CHF2 CH3CF2CH3 CHF3 CH3CF3 CH3CH2CF3 CF4 (CH3)3CF

(c2)

(CH3CH 2CH 2CH 2F) = (C/C/H3) + 2(C/C2 /H 2) + (C/C/F/H 2) − R ln(σ )

(c3) −1

−1

where R = 1.987 cal mol K and σ is symmetry number, which is 3 for fluoroethane, 1-fluoropropane, and 1fluorobutane. The groups C/C/F/H2, C/C2/F/H, C/C/F2/H, C/C2/F2, and C/C/F3 are also updated in the basis of the well-known accuracy and validity of group additivity for hydrocarbons. We note for halocarbons with halogen atoms on adjacent atoms interaction terms6 are needed to account for intermolecular interactions.

c

RESULTS AND DISCUSSION Enthalpy of Fluoromethane. Table 3 shows the calculation for enthalpy of fluoromethane via atomization reaction.

lit.b

Δb (this study, lit.)

CH3F

−56.3

−56.0 −56.3(G3[MP2(full)])d −56.9 (G3)d −56.54 ± 0.07e −56.62 ± 0.48f −57.1 ± 0.2g

−0.3 0.0 0.6 0.2 0.3 0.8

c

1.4104 1.4116 1.4219 1.4122 1.4231 1.3705a 1.3808b 1.3810a 1.3914a 1.3476a 1.3583a 1.3591a 1.3329a 1.4335

1.3892 1.3911 1.3978 1.3912 1.3997 1.355a 1.3629a 1.3635a 1.3716a 1.3336a 1.3425a 1.3433a 1.3329a 1.4068

Average of all C−F bonds in the molecule. bB3LYP/6-31+G(d,p). QCISD/6-311G(d,p).

bond lengths optimized by QCISD are approximately 1.5% shorter than optimized by B3LYP. The data also show that primary C−F bonds are shorter than secondary C−F bonds. Enthalpies of Formation of C2−C4 Target Molecules. Isodesmic reaction schemes were used to determine enthalpy of formation of C2−C4 fluorinated hydrocarbons. The work reactions are chosen to have similar bonding on the reactant and product sides in order to have good cancellation of calculation error across the reactions. Table 5 lists the method average, the selected average, and the overall average standard enthalpies for each target molecule. The B3LYP/6-31+G(d,p) and G4(MP2)-6X are consistently a factor of 2 higher in standard deviation in standard heat of reaction and were excluded from the selected method. Table 5 also compares the literature enthalpy values for each of the fluorinated hydrocarbons. Our recommended values for CH 3 CH 2 F, CH 2 F 2 , CH 3 CHF 2 , CH 3 CH 2 CHF 2 , CHF 3 , CH3CF3, CH3CH2CF3, and CF4 agree with reference data within their uncertainty, when uncertainty was reported. There are several species with a larger difference from the literature values. Our enthalpy of formation of CH3CHFCH3 gives a 5.11 kcal mol−1 lower enthalpy than the value recommended by Pedley.44 Our suggestion enthalpy of CH3CH2CH2F is near 2.60 kcal mol−1 lower energy than Stull,50 Frenkel,51 and Yamada’s6,8 values. Our determination for enthalpy of CH3CF2CH3 shows a 3.45 kcal mol−1 lower enthalpy than the value presented by Williamson.52 Our evaluation of (CH3)3CF is 7.31 kcal mol−1 lower energy than Yamada.6 (Selected and overall values are shown to two decimal places for comparisons; they should be rounded to one decimal for application.) Table 6 illustrates the trends in adding carbon atom and separately adding fluorine atoms. In the CXH(2X+1)F, CXH(2X)F2, and CXH(2X−1)F3 (x ≥ 2) systems, adding one more −CH2− group lowers the enthalpy of formation approximately 4.9 kcal mol−1, as is the case throughout hydrocarbon group additivity. The following enthalpy changes are observed for substitution of a fluorine atom for a hydrogen atom on a normal C2 and higher mono- and difluoro carbons. Substitution on a primary

Table 3. Enthalpies of Formation for Fluoromethane this worka,b

QCISDc

a

■

compound

B3LYPb

See Methods for details. bUnits in kcal mol−1. cChase.11 dHaworth.4 Goos.13 fCsontos.12 gKormos.14

a e

Goos et al.13 report an evaluated enthalpy for fluoromethane of −56.54 kcal mol−1, with uncertainty of ±0.07; this value is 0.24 kcal mol−1 lower energy than the extrapolated CCSD(T) value calculated in this study. We have used the value of Goos et al. as a reference species value in our work reactions. Geometries and Frequencies. The optimized geometries at the B3LYP/6-31+G(d,p) density functional calculation level for CH3CH2F, CH3CH2CH2F, CH3CHFCH3, CH3CH2CH2CH2F, CH3CHFCH2CH3, CH2F2, CH3CHF2, CH3CH2CHF2, CH3CF2CH3, CHF3, CH3CF3, CH3CH2CF3, CF4, and (CH3)3 CF are presented in the Supporting Information. The Cartesian coordinates (Table S16 of the Supporting Information), vibrational frequencies (Table S17 of the Supporting Information), and moments of inertia (Table S18 of the Supporting Information) are also listed. The structures are shown in Figures S1−S14 of the Supporting Information. Trends in C−F single bond lengths are illustrated in Table 4, which includes bond lengths from QCISD/6-311G(d,p) optimized geometries in the CBS-APNO calculations. Using data in Table 4, we compare the B3LYP calculation to the higher-level QCISD calculations. The B3LYP geometries and frequencies follow the same trends as the QCISD, and the C−F 8206


8207

selected avg overall avg

selected avg overall avg method avg std literature

−119.61 (10) 0.40

−106.64 (7) 0.30

−79.42 (11) 0.48

selected avg overall avg method avg std


−74.80 (9) 0.34

−74.96 (6) 0.41

−70.08 (6) 0.41

−65.68 (4) 0.51

selected avg overall avg method avg std



selected avg overall avg method avg stdb literature

B3LYP

CBS-APNO

M06

M06-2X

ωB97X W1U

G4

CH3CH2F −65.42 ± 1.11 [0.25]b (27)c −65.46 [0.36] (35) −65.04 (4) −65.04 (4) −65.44 (4) −65.18 (4) −65.52 (4) −65.08 (3) −64.97 0.09 0.09 0.15 0.25 0.23 0.18 0.12 −62.90 ± 0.40,d −62.5,e −64.51,f −66.10 ± 1.00,g −65.70 (G3),h −65.20 (G3[MP2(full)]),h −65.06,i −65.20,j −66.5 ± 0.4v CH3CH2CH2F −70.24 ± 1.30 [0.21]b (41)c −70.19 [0.32] (53) −70.07 (6) −69.93 (6) −70.16 (6) −70.00 (6) −70.15 (6) −69.89 (5) −69.76 0.07 0.07 0.11 0.20 0.20 0.14 0.10 −68.33 ± 0.55,j −67.20,e −67.83,k −67.37l CH3CHFCH3 −75.26 ± 1.30 [0.20]b (41)c −75.13 [0.45] (53) −75.02 (6) −74.93 (6) −75.35 (6) −74.96 (6) −75.25 (6) −74.77 (5) −74.89 0.07 0.07 0.11 0.20 0.20 0.14 0.10 −70.15 ± 0.36,j −75.4 ± 0.5v CH3CH2CH2CH2F −75.17 ± 1.28 [0.21]b (54)c −75.10 [0.32] (72) −75.05 (9) −74.92 (9) −74.95 (9) −74.85 (9) −74.95 (9) −74.99 0.09 0.08 0.08 0.18 0.18 0.13 CH3CHFCH2CH3 −80.25 ± 1.28 [0.22]b (66)c −79.99 [0.49] (88) −80.16 (11) −79.95 (11) −80.24 (11) −79.86 (11) −79.94 (11) −80.03 0.08 0.08 0.12 0.20 0.22 0.11 CH2F2 −108.07 ± 1.46 [0.52]b (47)c −107.97 [0.72] (61) −107.46 (7) −108.09 (7) −107.16 (7) −107.50 (7) −107.39 (7) −107.78 (5) −107.77 0.04 0.04 0.06 0.12 0.15 0.07 0.07 −108.08 ± 0.22,j −107.71,m −108.40 (G3),h −107.90 (G3[MP2(full)]),h −107.67 ± 0.48u CH3CHF2 −120.87 ± 1.62 [0.30]b (68)c −120.68 [0.50] (88) −120.25 (10) −120.68 (10) −120.47 (10) −120.46 (10) −120.42 (10) −120.27 (8) −120.21 0.05 0.05 0.11 0.16 0.18 0.11 0.08 −118.79 ± 2.01,j −119.70 ± 0.07,d −118.80,e −119.29,f −121.30 (G3),h −120.90 (G3[MP2(full)]),h −120.22 ± 0.76,n −120.77 ± 1.05o CH3CH2CHF2 −125.82 ± 1.65 [0.47]b (78)c −125.51 [0.66] (104)

CBS-QB3

(10)

(7)

(11)

(9)

(6)

(6)

(4)

−119.45 (10) 0.40

−107.72 (7) 0.26

−78.48 (11) 0.49

−74.43 (9) 0.32

−73.83 (6) 0.48

−69.51 (6) 0.48

−65.01 (4) 0.55

G4(MP2)-6X

Table 5. Selected Average (Recommended), the Method Average from each Calculation Method and the Overall Average Enthalpy of Formation for 14 Fluorinated Hydrocarbons and the Differences between the Calculation vs Experimental/Literature Reference Values

The Journal of Physical Chemistry A Article


8208

k

−215.77 (29) 0.21

−180.96 (23) 0.29

−176.43 (18) 0.33

−162.81 (14) 0.27

−131.10 (13) 0.40

−124.07 (13) 0.40

B3LYP

CBS-APNO

M06

M06-2X

ωB97X W1U

G4

CH3CH2CHF2 −125.18 (13) −125.47 (13) −125.30 (13) −125.23 (13) −125.07 (13) −125.93 (13) 0.05 0.05 0.11 0.16 0.18 0.08 −123.66l CH3CF2CH3 −133.25 ± 1.65 [0.34]b (78)c −132.72 [0.87] (104) −132.73 (13) −132.89 (13) −133.34 (13) −132.77 (13) −132.62 (13) −132.47 (13) 0.05 0.05 0.11 0.16 0.18 0.08 −129.80 ± 3.00p CHF3 −166.71 ± 1.97 [0.73]b (93)c −166.24 [1.03] (121) −165.61 (14) −167.36 (14) −165.43 (14) −165.59 (14) −165.09 (14) −166.53 (9) −166.40 (14) 0.04 0.03 0.06 0.11 0.14 0.06 0.06 −166.20 ± 0.65,j −166.72 ± 0.64,q −166.60,m −165.10,r −167.10 (G3),h −166.90 (G3[MP2(full)]),h −166.09 ± 0.48u CH3CF3 −180.51 ± 2.05 [0.51]b (119)c −179.87 [0.89] (155) −179.61 (18) −180.85 (18) −179.92 (18) −179.76 (18) −179.03 (18) −179.75 (11) −179.81 (18) 0.05 0.04 0.08 0.15 0.16 0.10 0.07 −177.96 ± 0.41,j −178.20 ± 0.38,d −178.94 ± 0.76,s −178.20,e −178.47,f −181.30 (G3),h −181.00 (G3[MP2(full)]),h −179.61 ± 0.76n CH3CH2CF3 −185.48 ± 2.15 [0.56]b (138)c −184.73 [0.95] (184) −184.80 (23) −185.76 (23) −184.92 (23) −184.59 (23) −183.76 (23) −184.89 (23) 0.04 0.04 0.08 0.13 0.14 0.06 −183.09l CF4 −223.15 ± 2.52 [0.94]b (189)c −222.12 [1.31] (247) −221.67 (29) −224.78 (29) −221.40 (29) −221.48 (29) −220.05 (29) −223.12 (15) −223.03 (29) 0.03 0.03 0.04 0.09 0.11 0.05 0.05 −223.14 ± 0.33,j −223.00 ± 0.40,q −221.00 ± 6.00,m −223.10 ± 1.10,g −223.90 (G3),h −223.70 (G3[MP2(full)]),h −223.18 ± 0.31u (CH3)3CF −85.75 ± 1.71 [0.11]b (4)c −85. 75 [0.11] (4) −85.83 (4) −85.75 (4) −85.6 (4) 0.10 0.11 0.07 −81.2, −78.2,t −86.0 ± 2.0v

CBS-QB3

−220.14 (29) 0.16

−182.34 (23) 0.32

−177.58 (18) 0.32

−165.30 (14) 0.21

−130.06 (13) 0.43

−124.01 (13) 0.43

G4(MP2)-6X

Units in kcal mol−1. bStandard deviation in square brackets. cNumber of isodesmic reactions used in method average in parentheses. dChen.53 eStull.50 fBerry.2 gLuo.54 hHaworth.4 iBakowies.55 jPedley.44 Frenkel.51 lYamada.7 mChase.11 nNagy.5 oZachariah.9 pWilliamson.52 qKolesov.56 rLord.57 sKolesov.58 tYamada6 (calculated value −81.2, revised to −78.2, see rerevised below). uCsontos.12 vKormos.14

a







method avg std literature

Table 5. continued

The Journal of Physical Chemistry A Article


Article


Table 6. Change in the Enthalpy of Formation by Inserting One CH2 Group in the Carbon Chain, and in Replacing an H Atom with a Fluorine Atom

a

compound (# of C)

ΔH°f 298a

CH3CH2F (2) CH3CH2CH2F (3) CH3CH2CH2CH2F (4) CH3CHFCH3 (3) CH3CHFCH2CH3 (4) CH3CHF2 (2) CH3CH2CHF2 (3) CH3CF3 (2) CH3CH2CF3 (3)

−65.42 −70.24 −75.17 −75.26 −80.25 −120.87 −125.82 −180.51 −185.48

Δa,b 4.82 4.93 4.99 4.95 4.97

−1 b

compound (# of F)

ΔH°f 298a

CH2F2 (2) CHF3 (3) CF4 (4) CH3CH2F (1) CH3CHF2 (2) CH3CF3 (3) CH3CH2CH2F (1) CH3CH2CHF2 (2) CH3CH2CF3 (3) CH3CHFCH3 (1) CH3CF2CH3 (2)

−108.07 −166.71 −223.15 −65.42 −120.87 −180.51 −70.24 −125.82 −185.48 −75.26 −133.25

Δa,b 58.64c 56.44c 55.45c 59.64c 55.58c 59.66c 57.99d

Units in kcal mol . Insertion of CH2 (difference between rows). Adding one fluorine atom to a primary carbon. To a secondary carbon. c

d

to tetrafluorocarbon, the enthalpy of formation decreases 56.4 kcal mol−1. We utilize and discuss these trends further below, where we develop and revise groups for use in fluorocarbon group estimation for thermochemical properties. Specifically, we use these −CH2− insertion and F/H substitution trends to estimate the enthalpy of formation values for several fluoroalkanes: 1-fluoropentane, 2-fluoropentane, 1,1difluorobutane, 1,1,1-trifluorobutane, 1,1-difluoropentane, 1,1,1-trifluoropentane, 2,2-difluorobutane, and 2,2-difluoropentane in Table 7. We compare the data from these trends to values from group additivity. We recommend use of group additivity for thermochemical property estimation, as these trend values are limited to normal alkyl fluorocarbons and cannot be used when the fluorine atoms are on adjacent carbon groups (see group additivity below). Internal Rotor Potential Energy Diagrams. Potential energy profiles for internal rotations in each molecule are calculated at the B3LYP/6-31+G(d,p) density functional level. The potential energy as a function of dihedral angle is calculated by scanning the torsion angles from 0° to 360° at 10° intervals, while allowing the molecule’s remaining structural parameters to be optimized. Ten-parameter Fourier series

Table 7. Enthalpy of Formation for C5 Fluorinated Hydrocarbons Estimated Using the CH2 Insertion and F/H Substitution Trends, and Comparison to Group Additivity (kcal mol−1) molecules

based on trend

group additivity

CH3CH2CH2CH2CH2F CH3CHFCH2CH2CH3 CH3CH2CH2CHF2 CH3CH2CH2CF3 CH3CH2CH2CH2CHF2 CH3CH2CH2CH2CF3 CH3CF2CH2CH3 CH3CF2CH2CH2CH3

−80.07 −85.25 −130.82 −190.48 −135.82 −195.48 −138.25 −143.25

−80.28 −85.26 −130.70 −190.50 −135.70 −195.50 −138.25 −143.25

fluoro-methyl group, where the fluorine atoms are on the same carbon: (i) the enthalpy of formation decreases 55.5 kcal mol−1 from monofluorocarbon to difluorocarbon; (ii) from difluorocarbon to trifluorocarbon, the enthalpy of formation decreases 59.7 kcal mol−1. Substitution of a fluorine atom for a hydrogen atom on a secondary carbon group (conversion of a CHF group to a difluorocarbon CF2 group) lowers the enthalpy 58.0 kcal mol−1. For methane converting from a trifluorocarbon

Figure 2. Potential energy profiles of the C−CCCF, CC−CCF, and CCC−CF internal rotors for 1-fluorobutane (symbols). The solid line is the fit of the Fourier series expansions. 8209


Article


Table 8. Ideal Gas Phase Entropy and Heat Capacity Obtained by B3LYP/6-31+G(d,p) Calculation, Comparison with Literature S298 ° b CH3F

CH3CH2F

CH3CH2CH2F

CH3CHFCH3

CH3CH2CH2CH2F

CH3CHFCH2CH3

CH2F2

CH3CHF2

CH3CH2CHF2

CH3CF2CH3

CHF3

CH3CF3

CH3CH2CF3

CF4

a

TVR Rodgers et al.e Csontosl TVR internal rotorc totald Stull et al.f Chen et al.g Yamada et al.h TVR internal rotor total Stull et al.f Frenkel et al.i Yamada et al.j TVR internal rotor total Yamada et al.k Stull et al.f Frenkel et al.i TVR internal rotor total TVR internal rotor total TVR Rodgers et al.e Csontosl TVR internal rotor total Stull et al.f Chen et al.g Yamada et al.h TVR internal rotor total Yamada et al.j TVR internal rotor total Frenkel et al.i TVR Rodgers et al.e Csontosl TVR internal rotor total Stull et al.f Chen et al.g Yamada et al.h TVR internal rotor total Yamada et al.j TVR Rodgers et al.e Csontosl

53.25 53.25 53.18 59.21 4.20 63.41 63.22 63.34 63.23 63.60 9.10 72.70 72.84 72.84 73.39 61.97 8.68 70.65 70.24 69.82 70.03 67.59 16.75 84.34 65.94 14.55 80.49 57.65 58.94 58.87 63.31 4.25 67.55 67.52 67.50 67.34 67.43 10.55 77.98 77.51 64.17 8.82 72.99 72.38 62.20 62.04 61.95 64.53 4.31 68.84 68.66 68.67 68.59 68.34 10.72 79.06 78.79 62.73 62.46 62.36

Cp300b

Cp400

Cp500

Cp600

Cp800

Cp1000

Cp1500

8.97 8.99

10.50 10.56

12.17 12.26

13.72 13.84

16.28 16.46

18.25 18.45

21.37 21.56

12.00 2.06 14.06 14.17 14.28 14.23 14.84 4.25 19.09 19.83 19.71 19.70 15.77 4.19 19.97 20.18 19.68 20.00 17.77 6.90 25.67 18.73 7.35 26.07 10.34 10.28

15.22 2.15 17.37 17.57 17.71 17.69 19.68 4.10 23.78 24.55 24.65 24.74 20.51 4.26 24.78 25.31 24.72 25.19 24.17 6.69 30.85 25.02 6.99 32.01 12.26 12.22

18.38 2.09 20.46 20.72 20.86 20.92 24.34 3.79 28.12 28.99 29.18 29.35 25.01 4.07 29.08 29.85 29.27 29.71 30.29 6.29 36.58 30.99 6.48 37.47 14.12 14.10

21.17 1.97 23.14 23.44 23.56 23.69 28.41 3.47 31.88 32.82 33.02 33.27 28.94 3.80 32.75 33.68 33.14 33.51 35.63 5.85 41.48 36.18 5.97 42.15 15.71 15.72

25.66 1.73 27.38 27.76 27.82 28.06 34.88 3.00 37.88 38.88 39.04 39.38 35.21 3.31 38.52 39.61 39.14 39.39 44.10 5.08 49.18 44.44 5.12 49.56 18.14 18.22

29.02 1.54 30.56 30.98 31.00 31.27 39.70 2.70 42.41 43.37 43.42 43.82 39.91 2.95 42.86 43.96 43.55 43.81 50.38 4.54 54.92 50.59 4.54 55.13 19.87 19.98

34.30 1.28 35.58

14.22 2.07 16.29 16.31 16.31 16.37 17.17 4.38 21.54 21.64 18.56 4.20 22.75 22.87 12.38 12.27

17.73 2.15 19.88 19.93 19.93 20.07 22.22 4.38 26.60 26.89 23.55 4.22 27.77 28.22 14.69 14.61

20.93 2.09 23.01 23.07 23.08 23.32 26.88 4.18 31.05 31.51 28.01 4.00 32.01 32.52 16.65 16.59

23.64 1.97 25.61 25.68 25.70 26.01 30.85 3.91 34.76 35.35 31.77 3.73 35.49 36.34 18.19 18.16

27.82 1.72 29.54 29.69 29.70 30.06 37.01 3.41 40.42 41.18 37.59 3.24 40.83 41.76 20.34 20.35

30.83 1.54 32.37 32.56 32.57 32.92 41.48 3.04 44.52 45.33 41.85 2.90 44.74 45.64 21.73 21.76

35.42 1.28 36.69

16.82 2.09 18.91 18.83 18.84 18.94 19.77 4.38 24.16 24.32 14.92 14.59

20.63 2.14 22.77 22.75 22.75 22.89 25.11 4.37 29.48 29.77 17.56 14.65

23.82 2.06 25.89 25.90 25.90 26.11 29.76 4.16 33.91 34.32 19.52 17.30

26.40 1.93 28.33 28.38 28.38 28.65 33.59 3.88 37.47 37.99 20.93 20.74

30.18 1.69 31.86 31.98 31.98 32.29 39.35 3.37 42.72 43.41 22.72 22.58

32.79 1.51 34.29 34.45 34.44 34.75 43.42 3.00 46.41 47.15 23.71 23.61

36.62 1.26 37.87

± 0.36

35.90 36.16 47.19 2.34 49.53

50.57 47.26 2.48 49.75 50.61

60.08 3.80 63.88 60.15 3.79 63.94 22.42 22.54

± 0.36

36.90 37.16 48.29 2.53 50.82 51.47 48.42 2.45 50.87 51.42 23.59 23.63

± 0.36

38.00 38.26 49.47 2.51 51.98 52.55 24.83 24.78

± 0.36 8210


Article

The Journal of Physical Chemistry A Table 8. continued S298 ° b (CH3)3CF

TVR internal rotor total Yamada et al.j

67.54 13.29 80.83 74.32

Cp300b

Cp400

Cp500

Cp600

Cp800

Cp1000

Cp1500

25.39 6.32 31.71 26.53

31.85 6.29 38.14 32.87

37.73 5.92 43.65 39.10

42.79 5.49 48.28 44.02

50.81 4.76 55.56 51.47

65.80 4.26 61.06 56.89

66.20 3.63 69.83 65.20

a Sum of contributions from translations, vibrations, and external rotations. bUnits in cal mol−1 K−1. cContributions from internal rotors. dSum of TVR and internal rotors. eRodgers.59 fStull.50 gChen.53 hYamada.8 iFrenkel.51 jYamada.6 kYamada.7 lCsontos.12

Table 9. Composition of Groups for Ten C2−C4 Fluorocarbons group group group group

1 2 3 4

group 1 group 2 group 3

CH3CH2F

CH3CH2CH2F

CH3CHFCH3

C/C/H3 C/C/F/H2

C/C/H3 C/C2/H2 C/C/F/H2

C/C/H3 C/C2/F/H C/C/H3

CH3CHF2

CH3CH2CHF2

CH3CF2CH3

C/C/H3 C/C/F2/H

C/C/H3 C/C2/H2 C/C/F2/H

C/C/H3 C/C2/F2 C/C/H3

CH3CH2CH2CH2F C/C/H3 C/C2/H2 C/C2/H2 C/C/F/H2 CH3CF3

CH3CHFCH2CH3 C/C/H3 C/C2/F/H C/C2/H2 C/C/H3 CH3CH2CF3

C/C/H3 C/C/F3

C/C/H3 C/C2/H2 C/C/F3

Table 10. Standard Molar Enthalpy and Entropy Values and Heat Capacities (300−1500K) for Benson60 Group Additivity C/C/H3c C/C2/H2c C/C/F/H2d C/C/F/H2e C/C/F/H2f avg C/C/F/H2n C/C2/F/Hg C/C2/F/Hh avg C/C2/F/Hn C/C/F2/Hi C/C/F2/Hj avg C/C/F2/Hn C/C2/F2k C/C2/F2n C/C/F3l C/C/F3m avg C/C/F3n

ΔH°f 298a

S298 ° b

Cp300b

Cp400

Cp500

Cp600

Cp800

Cp1000

Cp1500

−10.00 −5.00 −55.42 −55.24 −55.17 −55.28 −52.90 −55.26 −55.25 −55.26 −50.20 −110.87 −110.52 −110.70 −109.70 −113.25 −104.90 −170.51 −170.48 −170.50 −168.20

30.30 9.40 35.23 35.06 37.30 34.86 35.00 12.17 12.57 12.37 13.58 39.34 40.31 39.83 39.11 14.50 17.30 40.61 41.37 40.99 42.55

6.19 5.50 7.77 7.27 7.32 7.45 8.04 7.49 8.07 7.78 7.62 9.95 9.67 9.81 10.18 10.24 10.49 12.55 12.27 12.41 12.75

7.84 6.95 9.37 8.81 8.90 9.03 9.85 8.94 9.21 9.08 9.51 11.83 11.57 11.70 12.23 11.92 12.54 14.72 14.45 14.59 15.05

9.40 8.25 10.90 10.28 10.45 10.54 11.52 10.12 10.23 10.18 10.91 13.40 13.16 13.28 13.92 13.03 13.72 16.26 16.02 16.14 16.71

10.79 9.35 12.20 11.56 11.78 11.85 12.90 11.01 11.04 11.03 11.93 14.62 14.40 14.51 15.22 13.74 14.76 17.33 17.10 17.22 17.86

13.02 11.07 14.25 13.65 13.86 13.92 15.04 12.36 12.31 12.34 13.35 16.37 16.16 16.27 17.04 14.65 15.72 18.69 18.46 18.58 19.27

14.77 12.34 15.71 15.19 15.35 15.42 16.50 13.23 13.14 13.19 14.27 17.49 17.29 17.39 18.15 15.10 16.10 19.40 19.18 19.29 19.98

17.58 14.20 17.97 17.70 17.84 17.84 18.58 14.54 14.52 14.53 15.52 19.07 18.98 19.03 19.58 15.66 16.26 20.23 20.13 20.18 20.68

Units in kcal mol−1. bUnits in cal mol−1 K−1. cCohen.60 dDerived from fluoroethane. eDerived from fluoropropane. fDerived from fluorobutane. Derived from 2-fluoropropane. hDerived from 2-fluorobutane. iDerived from 1,1-difluoroethane. jDerived from 1,1-difluoropropane. kDerived from 2,2-difluoropropane. lDerived from 1,1,1-trifluoroethane. mDerived from 1,1,1-trifluoropropane. nYamada.6

a g

expansions to represent the energy versus rotation angle have been calculated for each of the internal rotors, according to eq 1. Figure 2 shows the potential energy profiles of the three C−C internal rotors in 1-fluorobutane. The nonuniformity in foldness is due to different gauche interactions, c-cc-cf and cc-cc-f. The energy profiles for all target molecules with internal rotors are included in Figures S15−S25 of the Supporting Information. Entropy and Heat Capacity. The entropy and heat capacity results using B3LYP/6-31+G(d,p) geometries and frequencies are summarized in Table S16 and S17 of the Supporting Information. TVR represents the sum of the contributions from translations, vibrations, and external rotations. IR indicates the contribution from hindered internal rotation,

which replaces the torsion frequency contributions for these internal rotors in the TVR heat capacity and entropy data. Table 8 lists the entropies and heat capacities compared with literature. Our values agree well with the literature data. Group Additivity. Group additivity is particularly useful for large molecules where high-level ab initio or density functional calculations are not practical. It represents a molecule’s thermochemical properties as the sum of the thermochemical properties of a series of groups. The groups for each target molecule are shown in Table 9. The group additivity contributions for 1-fluoroproane are CH3CH 2CH 2F = C/C/H3 + C/C2 /H 2 + C/C/F/H 2 (d1) 8211


Article

The Journal of Physical Chemistry A Table 11. Re-evaluation of the Enthalpy of Formation from Previous Study

Table 13. Re-evaluated Enthalpies of Formation of Fluorine(s)−Fluorine(s) Interaction Terms

ΔHf,298b

ΔHf,298b

isodesmic reactiona

revisedc

Yamada 1999d

this studye

CH3CH2CH2F + CH3CH3 = CH3CH2CH3 + CH3CH2F CH3CH2F + CH4 = CH3F + CH3CH3 CH3CHFCH3 + CH3CH3 = CH3CH2CH3 + CH3CH2F (CH3)3CF + CH3CH2CH3 = (CH3)3CH + CH3CHFCH3

−70.39

−67.46

−70.24

−66.37 −75.48

−65.61 −72.55

−65.42 −75.26

−85.80

−78.20

−85.75

interaction terms F/F 2F/F 2F/2F 3F/F 3F/2F

a

this study

Yamada 1999c

Yamada 1998d

2.6 5.2 9.3 7.4 13.4

3.1 5.7 9.8 7.8 13.8

−0.8 4.8 9.3 7.0 13.9

“/” indicates interaction for fluorine atoms adjacent carbons on an alkane. bUnits in kcal mol−1. cYamada et al.6 dYamada et al.8 a

Isodesmic reaction from Yamada.6 bUnits in kcal mol−1. Bold (target species). cHeat of formation of target molecules calculated with Yamada’s6 calculated thermal energy and values for reference species from this current study. dYamada.6 eHeat of formation of target molecules selected in this study. a

between the revised values and data of the current study are less than 1 kcal mol−1. We further estimate the standard enthalpy of five multifluorinated ethanes in the Yamada et al. articles that were not included in this study but were reported previously using work reaction analysis.6 The thermal energy of the reactions from the previous study [G2(MP2)] was used to calculate the enthalpy of isodesmic reaction, and the enthalpies of formation for reference species are from this study. We reinforce the need for fluorine−fluorine non-nearest neighbor interaction (NNi) groups described previously6,8 to be included in the group additivity estimation of fluorocarbons when fluorines are present on adjacent central atoms. We use the group values in Table 9 and the re-evaluation of the heat of formation of the target molecules in Table 12 to re-evaluate the fluorine/fluorine interaction terms. All enthalpies are in kcal mol−1.

The additivity contributions for groups C/C/H3 and C/C2/ H2 are known as −10.00 and −5.00 kcal mol−1, respectively.60 The group C/C/F/H2 is less well-known, however, and has been calculated here, with the results provided in Table 10. ( −70.24) = (− 10.00) + (− 5.00) + (C/C/F/H 2)

(d2)

Thus, the group additivity contribution of C/C/F/H 2 = ( −70.24) − (− 10.00) − (− 5.00) = −55.24 kcal mol−1

(d3)

On the basis of the estimation of each fluorinated groups, we estimate up to C5 fluorinated hydrocarbon system which is illustrated in Table 7. Monofluoro to Pentafluoro Ethanes Comparisons and Revaluation of Groups for fluorocarbons with fluorine atoms on adjacent carbons. T. Yamada et al. used isodesmic work reactions in an earlier study to determine standard enthalpies of monofluoro- to pentafluoro- ethanes.6,8 At that time, accurate data for the reference species was limited. We revisit their work reaction analysis using reference values from this study and the previously reported, “calculated thermal reaction enthalpies”, to re-evaluate the heat of formation of the higher multifluoro ethanes. We compare and try to improve the accuracy of our data in previous studies.6,8 Current values (this study) are compared with the reported values of ref 6 and recalculated values from Yamada et al. using reference species data from this study with the previous “calculated thermal reaction enthalpies”. Table 11 illustrates the re-evaluations of fluoroethane, 1-fluoropropane, and 2-fluoropropane. Heats of formation for these three molecules show agreement with current study, where the differences in standard enthalpies

CH 2FCH 2F = C/C/F/H 2 + C/C/F/H 2 + F/F

( −107.96) = ( − 55.28) + (− 55.28) + F/F CHF2CH 2F = C/C/F2 /H + C/C/F/H 2 + 2F/F

( −160.77) = ( − 110.70) + (− 55.28) + 2F/F

CHF2CHF2 = C/C/F2 /H + C/C/F2 /H + 2F/2F ( −212.13) = ( − 110.70) + (− 110.70) + 2F/2F CF3CH 2F = C/C/F3 + C/C/F/H 2 + 3F/F

( −218.35) = ( − 170.50) + (− 55.28) + 3F/F CF3CHF2 = C/C/F3 + C/C/F2 /H + 3F/2F

( −267.79) = ( − 170.50) + (− 110.70) + 3F/2F (CH3)3 CF = C/C/H3 + C/C/H3 + C/C/H3 + C/C3/F

Table 12. Enthalpies of Formation: Difluoro- to Pentafluoro- Ethanes ΔHf,298b isodesmic reaction

a

CH2FCH2F + CH3CH3 = CH3CH2F + CH3CH2F CHF2CH2F + CH3CH3 = CH3CHF2 + CH3CH2F CHF2CHF2 + CH3CH3 = CH3CHF2 + CH3CHF2 CF3CH2F + CH3CH3 = CF3CH3 + CH3CH2F CF3CHF2 + CH3CH3 = CF3CH3 + CH3CHF2

this study

c

d

Yamada 1999

Yamada 1998e

Berry 1998f

Haworth 2000g

−102.7 −156.9 −209.6 −213.3 −264.1

−106.6 −157.8 −210.1 −214.1 −264.0

−105.9 −158.5 −209.1 −215.6 −264.3

−107.3 −161.1 −212.5 −219.0 −268.2h

−107.96 −160.77 −212.13 −218.35 −267.79

a Isodesmic reaction from Yamada,6 reference species this study. bUnits in kcal mol−1. cHeat of formation of target molecules calculated with Yamada’s6 total energy and reference species values from this study. dYamada et al.6 eYamada et al.8 fBerry et al.2 gHaworth et al, G3 calculation method.4 hHaworth et al, G3[MP2(full)] calculation method.4 Bold−target molecule, values of this study, recommended.

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( − 85.75) = ( − 10.00) + ( − 10.00) + ( − 10.00) + (C/C3/F)

Enthalpies of formation for the five multifluoro-ethanes are shown and compared with previously reported values in Table 12. The re-evaluated F/F enthalpy interaction terms are presented in Table 13 and are compared with previous studies. C/C3/F group is reviewed as of −55.75 kcal mol−1, which present significant different value comparing with Yamada’s paper (−48.2 kcal mol−1).

■

SUMMARY AND CONCLUSIONS Thermodynamic properties of 14 C1 to C4 fluorocarbons with one to three fluorine atoms on a carbon atom of the molecule are calculated using density functional and ab initio methods with isodesmic reaction schemes for cancellation of calculation errors. Standard enthalpies of formation are determined from the average of CBS-QB3, CBS-APNO, M06, M06-2X, ωB97X, G4, and W1U calculation levels and multiple work reactions. Entropies and heat capacities are determined with B3LYP/631+G(d,p) optimized geometries and frequencies. Hindered internal rotation contributions to entropy and heat capacity are calculated by intramolecular torsion potential curves at the B3LYP/6-31+G(d,p) level, with an entropy correction for mixing of rotational conformers. For C2 and higher compounds, adding the second fluorine atom to the primary carbon site leads to about 55 kcal mol−1 energy decrease, whereas adding the third fluorine atom to the primary carbon site reduces the standard enthalpy 59 kcal mol−1. Adding the second fluorine atom to the secondary carbon site lowers the enthalpy 58 kcal mol−1. All calculation methods in the SELECTED set appear to work well for work reaction analysis methods for enthalpies of formation of fluorinated hydrocarbons. ASSOCIATED CONTENT

S Supporting Information *

Table S1−S14 show isodesmic reactions for 14 C2−C4 target molecules and the method average and selected average for each species. Table S15 lists the enthalpy of formation for methanol. Table S16, S17, and S18 presents a detailed geometry for each target molecule, frequencies, and moments of inertia under B3LYP/6-31+G(d,p), respectively. Table S19 lists the isodesmic reactions which were used to determine the computational method uncertainty. Figure S1−S14 presents the structure of 14 target molecules under B3LYP/6-31+G(d,p). Figure S15−S25 shows potential energy profiles for all target molecules with internal rotors. Complete author names are listed for ref 24, Gaussian09 program. Figure 1 illustrates the standard deviation range of each calculation method. Figure 2 illustrates the potential energy profiles of the C-CCCF, CCCCF, and CCC-CF internal rotors for 1-fluorobutane (symbols). The solid line is the fit of the Fourier series expansions. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpca.5b03912.

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C/C3/F = −55.75

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 8213


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Thermochemical Properties Enthalpy, Entropy, and Heat Capacity of

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