High Accuracy Quantum Chemical and Thermochemical Network Data

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High Accuracy Quantum Chemical and Thermochemical Network Data for the Heats of Formation of Fluorinated and Chlorinated Methanes and Ethanes Adam Ganyecz, Mihaly Kallay, and Jozsef Csontos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00614 • Publication Date (Web): 25 Jun 2018 Downloaded from http://pubs.acs.org on June 26, 2018

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The Journal of Physical Chemistry

High Accuracy Quantum Chemical and Thermochemical Network Data for the Heats of Formation of Fluorinated and Chlorinated Methanes and Ethanes ´ 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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The Journal of Physical Chemistry 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

Abstract Reliable heats of formation are reported for numerous fluorinated and chlorinated methane and ethane derivatives by means of an accurate thermochemical protocol, which involves explicitly correlated coupled-cluster calculations augmented with anharmonic, scalar relativistic, and diagonal Born–Oppenheimer corrections. The theoretical results, along with additional experimental data, are further enhanced with the help of the thermochemical network approach. For 28 species, out of 50, this study presents the best estimates, and discrepancies with previous reports are also highlighted. Furthermore, the effects of the less accurate theoretical data on the results yielded by thermochemical networks are discussed.

Introduction Climate change, which is probably caused by greenhouse gases (GHG) and ozone depleting agents as a byproduct of human activities, is one of the most paramount challenges to overcome in the 21st century. 1 Because chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) are ozone depleting agents, they have been covered by the Montreal Protocol, 2 and consequently, they have been replaced with ozone friendly alternatives, such as hydrofluorocarbons (HFCs) and perfluorocarbons (PFCs) in the chemical industry. However, these substances have considerably larger contribution to global warming than CFCs and HCFCs. HFCs and other GHGs are subject of the Kyoto Protocol. 3 To prolongate its impacts, because the second commitment period for it ends in 2020, the Paris Agreement was negotiated and adopted by the representatives of 196 parties in 2015. 4 To study and understand the effects of anthropogenic activities using the so-called chemistry-climate models, accurate kinetic and thermodynamic data for atmospherically important reactions and corresponding species are inevitable. 5,6 Several databases already contain substantial information (JPL, 7 NIST-JANAF, 8 Gurvich, 9 ATcT 10 ), however, some data is still inaccurate and discrepancies also exist among these databases. These variations 2


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are due to the fact that the chemistry of the troposhere and stratosphere is dominated by free radical reactions, and these open-shell systems pose a challenge to the experimental and theoretical investigations. Nevertheless, high accuracy calculations have become the method of choice especially for radical species because they can yield competitive, and, in some cases, even superior data to experiments. In most theoretical studies, various composite model chemistries have been utilized to determine thermochemical values. An incomplete list of frequently used computational methods includes the Gn theories, 11–13 the CBS 14–18 (complete basis set) models, the ccCA 19–21 (correlation consistent composite approach), the Weizmann-n, 22–24 and the HEAT 25–27 protocols, the focal point analysis of Allen and Császár 28,29 and the procedure of Feller, Peterson, and Dixon (FPD). 30,31 In recent years, due to their favourable price/performance ratio, many of these protocols incorporated explicitly correlated variants of the second-order Møller–Plesset (MP2) and coupled-cluster (CC) theories. 32–41 Nevertheless, the thermochemical quantites can be further improved using the thermochemical network approach (TNA). First applications of the TNA appeared in 1969 by Guest et al. 42 and Syverud. 43 In 1998, Ruscic and associates, 44 based on the work of Syverud, revived the idea of the TNA, which later led to the definition of active thermochemical tables (ATcT) bringing important novel features like iterative reweighting and the concept of the global TN. 45 Since its introduction in 2004, the thermochemical data provided by the ATcT have been widely used as benchmark data. 46–49 Although the ATcT database contains numerous experimental determinations, it predominantly consists of theoretical data. 10,50 The work of Császár and Furtenbacher is also noted here, who only used quantum chemical results in their TNA called NEAT (network of computed reaction enthalpies to atom-based thermochemistry). 51 The TNA has several advantages compared to sequential thermochemistry. 45,46 In the latter, following the “standard order of elements”, the most accurate determination (or the weighted average of the reliable ones) is chosen to calculate the corresponding thermodynamic

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quantity, and then this value is settled permanently and used for the calculation of the next line of species. There are several problems with this method: (i) the error is propagated through all the subsequent steps, and there is no feedback to the preceding determinations; (ii) only one (or a small group) of results is used for the determination; (iii) to take account of new findings, every step should be done again. Using the TNA one can mitigate these issues, by simultaneously determining the required data using all information that is provided in the network. Furthermore, if new information becomes available, the whole network can be updated easily and effortlessly. Because of the importance of thermochemical data in modeling of climate change, the goal of this study is to provide accurate and consistent heat of formation values for numerous HCFCs, CFCs, HFCs, PFCs, and chlorocarbons, as well as, for the related radicals using accurate model chemistries combined with experimental data in a TN. Beside that, we want to emphasize the importance of the quality of the input data in TNAs, and test how the theoretical input data, obtained with various model chemistries, influences the end result of a TN.

Methods Model chemistries To provide theoretical data for the TNA, various model chemistries were utilized. In addition to the well-known and widely used G3, 12 G4 13 and CBS-Q 17 models, two high-accuracy HEAT-like protocols were also applied. The first is the so-called diet-HEAT protocol which has been proven to provide accurate thermodynamic quantities including heats of formation at both 0 and 298 K for several small- and medium-sized species, 52–56 and the second one is the recently developed diet-HEAT-F12 method. 41 Although more detailed accounts of these protocols can be found in refs 52 and 41, for the readers’ convenience, a brief summary of the computational steps is given in Table 1. 4


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The enthalpies are calculated as

HT◦ =ETOT + ∆EZPE +

RT 2 ∂Ω × + RT Ω ∂T

(1)

where ETOT , ∆EZPE , Ω, R, and T denote the total electronic energy, the zero-point vibrational energy (ZPE), the molecular partition function, the ideal gas constant, and the absolute temperature, respectively. Ω is calculated via the standard formulas of statistical thermodynamics within the ideal gas approximation and using the rigid rotor-harmonic oscillator (RRHO) approximation. 57 The correction for inversion mode and hindered rotation are adopted from previous works, where it was necessary. 52,56,58 The heats of formation were calculated using both the atomization and the elemental reaction approach. 52,56 For example, using the atomization reaction, ∆f HT◦ (CH3 −CHF) can be calculated as, CH3 −CHF −−→ 2 C + 4 H + F

∆f HT◦ (CH3 −CHF) = 2∆f HT◦ (Cgas ) + 4∆f HT◦ (H) + ∆f HT◦ (F)

(2)

− 2HT◦ (Cgas ) − 4HT◦ (H) − HT◦ (F) + HT◦ (CH3 −CHF). On the other hand, with the elemental reaction approach, ∆f HT◦ (CH3 −CHF) can be obtained as, 2 C + 12 F2 + 2 H2 −−→ CH3 −CHF 1 ∆f HT◦ (CH3 −CHF) = HT◦ (CH3 −CHF) − 2HT◦ (Cgas ) − HT◦ (F2 ) 2

(3)

− 2HT◦ (H2 ) + 2∆f HT◦ (Cgas )

The reference state of the elements H2 and F2 was defined as it is standard in thermochemistry, and for carbon the gaseous atom was used as a reference state. The experimental 5



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heat of formation values utilized during the atomization approach are listed in Table 2. For ∆f H0◦ (Cgas ) the ab initio value of ref 59, 711.65 ± 0.32 kJ/mol was adopted and the ther◦ (Cgas ) = mal correction was obtained from the NIST-JANAF tables 8 resulting in ∆f H298

717.13 ± 0.32 kJ/mol. The G3, G4, and CBS-Q composite chemistries were calculated with the Gaussian 09 60 program. The explicitly correlated calculations were obtained with the Turbomole 7.1 package, 61,62 the CCSDT(Q) calculations were carried out with the mrcc 63 program, while all other results were obtained with cfour. 64

The Thermochemical Network Our local TN is built on 77 experimental and 209 theoretical reaction enthalpies listed in the Supporting Information. Note that generally, experimental values were taken from the literature without any additional revision or reinterpretation. Nevertheless, all data used had been already thoroughly reviewed by experts of the field. For more details, the reader is referred to Table S2. Only a brief description of the solution of the TN is given here, a more detailed account can be found in ref 65. One can write the standard reaction enthalpy ◦ , for a given reaction as at 298 K, ∆r H298

◦ ∆r H298 (i)

=

n X

◦ νij ∆f H298 (j) + (i)

(4)

j

◦ ◦ where (i) is the uncertainty of ∆r H298 (i), ∆f H298 (j) is the heat of formation of the species

j at 298 K, and νij is its corresponding stoichiometric number. Because the TN includes i = 1, . . . , m reactions it can be conveniently expressed as a matrix equation:

y = Xβ + ,

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(5)

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where X is the so-called stoichiometric matrix with the regressor variables (νij ), β con◦ (j), the vector y is constructed from the tains the unknown regression coefficients, ∆f H298 ◦ (i) values, and the elements of , (i), provide the uncertainties in the reaction en∆r H298

thalpies. Eq. 5 represents a multiple linear regression problem, 66–68 and the iteratively reweighted least squares (IRLS) method 69 was used to obtain its solution. In each step of the IRLS ˆ is generated for β. In the WLS iteration a weighted least squares (WLS) estimator, β, method the transformed form of Eq. 5 is used: 1

1

1

W 2 y = W 2 Xβ + W 2 ,

(6)

ˆ (k) , which is the WLS estimator where W is the diagonal matrix of the weights. To obtain β for β in the k th step, the minimum of the objective function L is determined,

(k)

L

=

m X

(k)

Wii i 2 = (y − Xβ)T W(k) (y − Xβ).

(7)

i=1

ˆ (k) , whose elements are the heat of formation values yielded by the TN in the The vector β k th iteration, can be calculated as: ˆ (k) = (XT W(k) X)−1 XT W(k) y. β

(8)

(k) (k) The variance of βˆj , Vβˆ , is determined according to the subsequent equation: 70 j

(k)

(k)

Vβˆ = Cjj , where C(k) ≈ j

1 (k) (k) Lmin (XT W X)−1 . m−n

(k)

(9)

C(k) is the covariance matrix and Lmin denotes the minimum of L(k) . The 95% confidence

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(k) ◦ (j)(k) , can be written as, interval for βˆj , i.e., for ∆f H298

(k) βˆj ± t0.025,m−n

q

(k)

Cjj

(10)

where t0.025,m−n is the appropriate t-value of the Student’s t-distribution with m − n degrees of freedom. During the iterative solution the heats of formation of several species were set to their known and accurate value, leading to a so-called local TN. These values can be found in Table 2. To analyze the results of our networks, two metrics will be used. The first is the residual (y − yˆ), the second is the DFBETA and its standardized version, SDFBETA. 71 These wellknown metrics in regression diagnostics show how the fitted parameters (heats of formation) change if an observation (a heat of reaction data) is excluded from the network. DFBETA shows the real change in the fitted parameter, while SDFBETA is divided with the standard √ deviation. For a large number of data if SDFBETA is larger than 2/ n, where n is the number of data points, then the observation has a high influence on the fitted parameter. From now on the networks will be named by the model chemistry used for the theoretical reactions, i.e. if diet-HEAT-F12 calculations are used in the network, then it is called dietHEAT-F12-network, if G3, then G3-network, etc.

Results diet-HEAT vs. diet-HEAT-F12 Table 3 shows a representative subset of heat of formation values obtained with the conventional diet-HEAT and diet-HEAT-F12 protocols (for a full list see the Supporting Information). It can be seen that for larger systems, the difference between diet-HEAT and diet-HEAT-F12 is increasing. The largest difference, 6.4 kJ/mol, is obtained for C2 F6 . Af8


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ter comparing the contributions, the main reasons for this discrepancy are found to be the HF and CCSD(T) contributions. Sylvetsky et al. 36 observed similar problems and reported that using even as large as 6Z basis sets, the basis-set superposition error (BSSE) is still considerable. To clarify this issue, counterpoise calculations were conducted for CF4 and C2 F6 , and the BSSE corrected contributions were compared to the original ones using the same CCSD(T)/cc-pVQZ geometry. Table 4 shows these results. When considering CF4 and conventional calculations, the difference between the uncorrected and BSSE corrected results is 0.65 and 1.27 kJ/mol, respectively, for the extrapolated HF and CCSD(T) contribution. However, for the explicitly correlated contributions these differences, 0.14 and 0.06 kJ/mol, are almost negligible. Similar tendency was obtained for C2 F6 , i.e., the discrepancies between the BSSE corrected and uncorrected conventional results were 1.08 and 2.04 kJ/mol for the HF/CBS and CCSD(T)/CBS contributions, respectively; while the corresponding differences with the F12 method were 0.34 and 0.14 kJ/mol. Another observation is that, in line with previous studies 41,72 the convergence of conventional HF and CCSD(T) energies is much slower than that of the CABS corrected HF and CCSD(F12*)(T). Thus, one can conclude that most of the differences between the two protocols come from the BSSE, while the remainder is due to the not fully converged CCSD(T) contribution. Therefore, one can regard the diet-HEAT-F12 protocol to be superior to the conventional diet-HEAT one.

Analysis of the diet-HEAT-F12-network Using the aforementioned 77 experimental data and 209 theoretical reactions treated with the diet-HEAT-F12 protocol, a thermochemical network is constructed, referred to as dietHEAT-F12-network. The experimental values are mostly from reviews and collections of Cox, 73 Rodgers, 74 Chen, 75 NIST-JANAF, 8 and Manion. 76 In addition several data are derived from different kinetic measurements. Although these are not direct measurements, they were still inserted in our network, because these are also information about the investigated species, especially for the radicals. The reactions considered in this network can be found 9



in the Supporting Information along with the descriptions, how the data was obtained. For ease of convenience, the reactions discussed in the text are listed in Table 5. Table 6 lists the species whose heat of formation is highly influenced by at least one reaction, i.e., the √ SDFBETA value is larger than the accepted limit of 2/ n, and the DFBETA number is larger than 0.5 kJ/mol. Even though this latter limit is arbitrary, it indicates well the highly influential points for our TN. In the case of CH2 F2 , our calculation, reaction 132, is the most influential data. The error bar is smaller than the largest DFBETA for this species, i.e., when deleting the most ◦ (CH2 F2 ) is changed by −0.682 kJ/mol, while its uncertainty influential reaction, 132, ∆f H298

is ±0.671 kJ/mol. For CF4 the most influential data are the currently accepted value of Greenberg and Hubbard, 77 reaction 17, the data of Scott et al., 78 reaction 49, and the results of Domalski, 79 reaction 24. Initially the network contained the result of Neugebauer and Margrave, 80 i.e., the hydrogenation and decomposition of C2 F4 , reactions E3, E4 and E5 (these can be found in the Supporting Information). However, reaction E3 had a DFBETA of 1.2 kJ/mol, along with a −13.2 kJ/mol residual, which means that this is an unreliable data with high influence on the results, therefore it was removed. This removal led to a change from −934.7 to −933.5 kJ/mol for the heat of formation of CF4 . Our calculations and numerous experiments, reactions 48, ◦ 50, 52, 81, 127, and 214, indicate a lower value for ∆f H298 (CF4 ), while only experiments

of Greenberg and Domalski agree well with the currently accepted higher value. Although our network result is close to the currently accepted value of Greenberg, our diet-HEATF12 calculations (−936.2 kJ/mol) advocate a lower value along with some more complicated experiments, therefore we suggest further investigations for the heat of formation of CF4 . [C2 F4 ]n was used to determine the heat of formation of CF4 by Waddington and associates, 78,81 Cox and coworkers, 82 Wood et al., 83 and Domalski. 79 Because these reactions were part of our network, it was inevitable to also fit the heat of formation of [C2 F4 ]n . How◦ ◦ ever, ∆f H298 ([C2 F4 ]n ) is highly correlated with ∆f H298 (CF4 ) and shows similar uncertainty

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in the DFBETAs. If either link between [C2 F4 ]n and CF4 , reactions 49 and 52 or reactions 17 and 24 (which define the value of CF4 ), is excluded, the heat of formation of [C2 F4 ]n decreases with at least 3 kJ/mol. This instability also calls for the further investigation of the CF4 thermochemistry. ◦ The value of ∆f H298 (CH3 Cl) is dominated by the flame calorimetry result of Fletcher

and Pilcher, 84 reaction 21. The results of Lacher et al. 85,86 were excluded from the network (reactions E1 and E2), as suggested by Manion, 76 due to their inconsistency with other data. If both hydrogenation results were in the network, they would shift not only the heat of formation of CH3 Cl but that of CH2 Cl as well. Our diet-HEAT-F12 result for CH3 Cl, −83.2 kJ/mol, is closer to the value of Fletcher and Pilcher, −81.9 kJ/mol, than to those of Lacher, −85.7 and −86.4 kJ/mol. The most influential reaction on the heat of formation of CCl3 is obtained from the CCl4 bomb calorimetry experiments of Hu and Sinke, 87 reaction 43, along with the diet-HEAT-F12 calculation (reaction 136). The heat of formation of CHCl3 is mostly determined by the measurements of Hu and Sinke, 87 reaction 36. The heat of formation of CCl4 is predominated by the most accurate experimental result obtained from the bomb calorimetry experiments of Hu and Sinke, 87 reaction 43. Our diet-HEAT-F12 calculation, based on the formation from elements, reaction 137, supports this value, −95.5 kJ/mol. However, DFBETAs show, that if one discards the result of Hu and Sinke, the heat of formation raises by 4.3 kJ/mol, and this elevation is considerably ◦ larger than the 0.4 kJ/mol error bar predicted by the network. Furthermore, ∆f H298 (CCl4 )

shifts towards the result yielded by the diet-HEAT-F12 atomization reaction, −90.4 kJ/mol, reaction 91. These suggest that there may be a problem with the results of Hu and Sinke. ◦ For the determination of ∆f H298 (CHFCl2 ) only theoretical reaction is available in our

network, and mostly dominated by reaction 149, its formation from elements. CFCl3 has two reactions with high DFBETA: measurements of Hu and Sinke 87 on CCl4 ,

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reaction 43, and the results of Mears and Stahl, 88 reaction 65, which connects the two species. ◦ (CFCl3 ), is supported by the elemental dietThe current −289.4 kJ/mol value for ∆f H298

HEAT-F12 result of −290.0 kJ/mol, reaction 151, due to the connection of CFCl3 to CCl4 , ◦ independent reactions of CCl4 are needed for a more established ∆f H298 (CFCl3 ) data.

The heat of formation value for CF2 Cl2 is influenced by CCl4 , reaction 43, through experiments of Petersen and Pitzer, 89 reaction 26, along with our calculation, reaction 152. However the DFBETAs are smaller than the assgined error bar, therefore the result seems well established. The only reaction with large DFBETA for CF3 Cl is our calculation, reaction 153. As it can be seen, in the cases of CH2 F2 , CF4 , [C2 F4 ]n , CH3 Cl, CCl3 , CHCl3 , CCl4 , and CFCl3 , the uncertainty of the results is smaller than the corresponding largest DFBETA value, which makes the accuracy of these results questionable. Therefore, to address this issue, for these species the error bars are raised to match the largest DFBETA data.

Effect of the accuracy of theoretical data on the network First, let us compare the raw diet-HEAT-F12 results with the diet-HEAT-F12-network data. Figure 1 shows that the results are consistent with each other, and the network considerably reduced the uncertainty of the heats of formation. Only four diet-HEAT-F12 result from ◦ ◦ ◦ ◦ the 50, ∆f H298 (CF4 ), ∆f H298 (CH3 Cl), ∆f H298 (CHCl3 ), and ∆f H298 (CF2 Cl2 ), are outside

of the 95% confidence interval provided by the network, and this is consistent with the statistical nature of the measure. In addition, these cases were discussed previously because of their high DFBETA values. Similar conclusion can be drawn from the comparision of the conventional diet-HEAT and diet-HEAT-network results (see Figure 2). However, if one compares these data with the diet-HEAT-F12 network, it can be seen that, unless accurate experimental data is available, heats of formation obtained by the conventional diet-HEAT or diet-HEAT-network are higher than those yielded by the diet-HEAT-F12 network. This issue, as discussed above, is the consequence of the difference in the conventional and explicitly 12


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Figure 1: The differences between the heats of formation obtained from the diet-HEAT-F12network and those yielded by raw diet-HEAT-F12 calculations. The error bars represent the 95% confidence intervals. correlated CCSD(T) contributions. The difference, as we saw in the previous subsection, increases with the size of the species, and for larger systems the error bars do not overlap. It can be observed for the diet-HEAT-network that CF4 has no reaction with DFBETA being ◦ larger than 0.5 kJ/mol, while ∆f H298 ([C2 F4 ]n ) is still marked by the DFBETA test. The

reason is that the diet-HEAT calculations support the results of Greenberg and Hubbard, therefore the less accurate reactions are weighted down. Nevertheless, because the BSSE deteriorates the diet-HEAT results, this value must be handled with caution. In the case of CH3 Cl, CCl3 , CHCl3 CCl4 , CFCl3 , CF2 Cl2 , and CF3 Cl the trends are similar to those discussed in the previous section for the diet-HEAT-F12-network.

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Figure 2: The differences between the heats of formation obtained from the diet-HEAT-F12network and those provided by the raw diet-HEAT calculations and the diet-HEAT-network. The error bars represent the 95% confidence intervals. To assess the importance of the input data quality, all calculated heats of reactions were replaced with data obtained from G3, G4, and CBS-Q calculations. The numerical results can be found in the Supporting Information, while, as a representative example, Figure 3 compares the G4 and G4-network results to those yielded by the diet-HEAT-F12-network. As a consequence of inaccurate input data, the G4-network and the diet-HEAT-F12-network differ significantly, i.e., the error bars for about half of the molecules do not overlap. Two cases can be distinguished. In the first case, the computed reaction energies yielded by the G4 and diet-HEAT-F12 model chemistries disagree considerably and no accurate experimental data is available for the given species. Consequently, the diet-HEAT-F12-network results

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Figure 3: The differences between the heats of formation obtained from the diet-HEAT-F12network and those provided by the raw G4 calculations and the G4-network. The error bars represent the 95% confidence intervals. For the sake of visibility the large error bars are not shown for the G4 values. closely follow the raw diet-HEAT-F12 calculations, while the G4-network results are guided by the G4 data. Most fluoroethyl radicals belong to this class. In the second case, seemingly accurate experimental data are available, but these are not consistent with the diet-HEATF12 calculations. CH2 CHF is such an example for this class. In this class, the experimental results outweight the poor quality G4 data, and this phenomenon leads to a very different network result with considerably smaller error bar for the affected species than for the rest of the G4-network. It is also noted that the DFBETAs for the G4-network components are higher in almost all cases than those obtained for the diet-HEAT and diet-HEAT-F12 networks. Similar conclusions can be drawn from the G3 and CBS-Q networks. Due to 15



Figure 4: Distribution of the differences for the various protocols and networks; the reference data is from the diet-HEAT-F12-network. Dashed lines show the fitted normal distributions. their appreciably large uncertainties, these low-level model chemistries cannot help to decide which experimental data should be favored or improved. Figure 4 summarizes the previous findings, i.e., it shows the performance of the various model chemistries and corresponding networks when they are compared to the diet-HEATF12-network results. The general tendency is that the use of the TNA makes the distribution less spreaded out in comparison to the raw theoretical data, i.e., the G4-network distribution is narrower than the G4 one. Similarly, although less strikingly, the variance for the dietHEAT-network differences is less than that for the raw diet-HEAT data. Also, the peaks of the network distributions shift toward the reference distribution. On averge, the results based on the G4 and diet-HEAT model chemistries, respectively, underestimate and overestimate

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the diet-HEAT-F12 network values. Table 7 shows the error statistics of the protocols and the corresponding networks used; reference values are provided by the diet-HEAT-F12-network. Including the computational results into a TN always improves the error statistics. It can also be observed that the less accurate the model chemistry is, the larger the benefit of the TN approach is. However, networks built from low-quality computational data can yield misleading results as discussed above. Therefore, it is always crucial to properly check the input data, especially when the experimental data is scarce.

Comparison with literature values In Table 8, the results for the diet-HEAT, diet-HEAT-F12 and diet-HEAT-F12-network are shown, along with heats of formation extracted from the literature. A comprehensive collection of literature data and its thorough discussion can be found in our previous works, 52,56,58 therefore, data from the current version of the ATcT, 10 and JPL 7 databases are shown. Other accurate experimental determinations are listed only if they recommend values different from those of JPL and/or ATcT.

Fluoroethyl radicals Before our previous work on the topic, 58 the thermochemical data had been fairly inaccurate for these species. The results of the present study differ slightly from our previous data. As aformentioned, the discrepancies are due to the BSSE and to the not fully converged CCSD(T) contributions. Because these issues were resolved by the diet-HEAT-F12 model chemistry, the diet-HEAT-F12-network results are considered to be the most reliable for these species.

17



Fluoroethanes The current JPL version promotes our previous diet-HEAT results. 56 The ATcT website lists only CH3 −CH2 F, CH3 −CHF2 , CH2 F−CH2 F, and C2 F6 among the fluoroethanes. According to the available information provided by the website, the ATcT results for these species are dominated by our diet-HEAT values as well as by low-level model chemistries (G3X, G4, CBS-n). Therefore, for species with fewer than 3 fluorine atoms, the differences among the ATcT, JPL, and our present results is less than 2 kJ/mol. For larger species the discrepancy between our recommended diet-HEAT-F12-network results and those of JPL and ATcT can be explained by the difference between the conventional diet-HEAT and diet-HEAT-F12 protocols. As pointed out above, the latter protocol is more reliable, therefore, the results presented here are superior to the previous data.

Fluoromethanes Our heat of formation result for CF, CF2 , and CF3 yielded by the diet-HEAT-F12-network is in line with the previous data. The ATcT results are based on our previous diet-HEAT data and on other high-level calculations, which leads to a 1.1 kJ/mol difference between the two network results for CF3 . As discussed above, for CF4 there is an experimental data obtained by Greenberg and Hubbard, 77 −933.2 ± 0.75 kJ/mol, which is also supported by Domalski, 79 and various highlevel calculations 90 including our diet-HEAT result. However, our diet-HEAT-F12 protocol gives a lower value, −936.19 ± 2.24 kJ/mol. Including these experimental and calculated data in our diet-HEAT-F12-network −933.53 ± 0.46 kJ/mol can be obtained. Nevertheless, the DFBETA values show that the latter result might be biased and further investigation is needed for a well-established result. The ATcT data is dominated by the aforementioned experiment of Greenberg and Hubbard 77 and high-level calculations. The main difference between our TN and ATcT is probably how the HF · nH2 O reaction energies were used. The formation enthalpy of hydrated HF (HF · nH2 O) is a key value in fluorine bomb calorimetry 18


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measurements. Before the experiments of Johnson and associates, 91 it was derived from the heat of vaporization and solution of HF. However, the enthalpy of vaporization of HF is subject to error, because HF(g) is far from being an ideal gas, and corrections are needed. To overcome this problem, in ref 91 HF(l) was used as a reference state and later its heat of formation was determined by the direct combination of the elements in a fluorine-bomb calorimeter. 92 These results were also corroborated by several complex Hess cycles of fluorine containing species, therefore, we used their data in our network. In the ATcT the problematic heat of vaporizations seem to be over-represented, 93,94 and ATcT also contains the results of King and Armstrong 95 who made similar experiments to those conducted by Johnson and coworkers, but the corrosion of the used monel was experienced. Although the effect of corrosion was considered their result is still subject to bias. 91 Nonetheless, for the differences between the various aqueous states, ATcT utilizes both Parker’s data 96 and that of Johnson and associates. 91 Nevertheless, when considering the contributions listed on the ATcT website, one can ◦ see the most influential data for ∆f H298 (HF · nH2 O) is the result of Cox 82 (reaction 50),

closely followed by the questionable heats of vaporization 93,94 and the results of King and Armstrong. 95 It can be also seen, that the ATcT heat of formation of CF4 is determined from reaction 17 and 24 along with high-level calculations. However the latter calculations are affected by the BSSE. If the above results 82,93–95 were used in our TN it was observed that ◦ (CF4 ) shifts the heat of formation of aqueous HF through the seemingly accurate ∆f H298

reaction 50, resulting false agreement with the corrupted heats of vaporization of HF. ◦ However, there is a 1.1 kJ/mol overall difference between the ∆f H298 (HF · nH2 O) value of

the ATcT and that of Johnson and associates and the error bars does not overlap. Furthermore, our findings indicate that the currently accepted heat of formation of CF4 may be less ◦ reliable than it is considered. Thus the agreement between our and the ATcT ∆f H298 (CF4 )

value seems to be fortuitous. ◦ In the case of ∆f H298 (CH2 F2 ), the currently accepted result, −452.7 ± 0.8 kJ/mol, is

19



reported by Rodgers 74 on the basis of bomb calorimetry experiments, 97 reaction 23. Our dietHEAT and diet-HEAT-F12 calculation led to slightly higher values, and the diet-HEAT-F12network yielded −451.66 ± 0.68 kJ/mol. ATcT using high-level calculations 33,98,99 and this experimental data give −450.73 ± 0.36 kJ/mol. The reason for the non-negligible difference is probably that ATcT relies on different values for the heats of formation of HF · nH2 O. Also several computational results in the ATcT are affected by the BSSE (diet-HEAT, 52 W4, 99 G3-variants). This problem is partly compensated by the inclusion of data of Klopper, 33 who used a similar explicitly correlated protocol to diet-HEAT-F12, but this cannot completely vanish the bias of other calculations. Other species are in line with experimental data. The ATcT values for CHF, CHF3 , and CH3 F are mostly based on our previous diet-HEAT and the explicitly correlated calculations of Klopper. 33 The considerable difference for CHF3 , 1.58 kJ/mol, between the diet-HEATF12-network and ATcT can be connected to the issue of CF4 and CH2 F2 , viz. the reactions with these species are listed as largest contributors in the ATcT.

Chloromethanes In the cases of CCl, CCl2 , CHCl, and CH2 Cl, there is neither accurate experimental data nor ATcT value available. Our diet-HEAT-F12-network values can be regarded as the most reliable data. For the heat of formation of CCl3 our 71.86±1.60 kJ/mol agrees well with the value of 71.1 ± 2.5 kJ/mol provided by Hudgens 100 using the CCl3 + Br2 −−→ CCl3 Br + Br reaction ◦ energy. For ∆f H298 (CCl4 ), the diet-HEAT-F12-network result, −95.47 ± 4.11 kJ/mol, sup-

ports the combustion calorimetry data of Hu and Sinke, 87 95.6±0.6 kJ/mol. However, the regression diagnostics of diet-HEAT-F12-network showed that further corroboration is needed for this value. ATcT lists −96.44 ± 0.64 kJ/mol, which is almost lower by 1 kJ/mol. This is mostly based on the same reactions and several low-level, G3X, G4, and W1, calculations. ATcT used the bromination reactions of Mendenhall et al. 101 (Br2 +CCl4 −−→ BrCl+CCl3 Br and Br2 + CHCl3 −−→ HBr + CCl3 Br), but they were not included in our network, because

20


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◦ our focus was on HFCs and related radical species. However, their value for ∆f H298 (CCl4 )

is −93.7 ± 1.7 kJ/mol, which also shows that the real value of the heat of formation for CCl4 may be higher than the currently accepted one. ◦ For ∆f H298 (CHCl2 ), the JPL adopts the value of Seetula, 102 89 ± 3 kJ/mol, which is in

line with our result of 89.33 ± 0.85 kJ/mol. To obtain the heat of formation of CHCl3 , Hu and Sinke 87 set up a bomb calorimetry experiment, and got −102.9 ± 0.8 kJ/mol. Later, this was recommended by the authors of the JPL. Our network also contains the data of Hu and Sinke, reaction 36, and it agrees reasonably well with both the diet-HEAT-F12, −102.09 ± 3.74 kJ/mol, and the diet-HEAT-F12-network result, −102.74 ± 1.30 kJ/mol. ATcT lists a similar value, −103.39 ± 0.64 kJ/mol, based on the Hu and Sinke reaction and the bromination reactions of Mendenhall, as well as on diet-HEAT, G3 and G3X calculations. The case of CH2 Cl2 is similar to that of CHCl3 . The measurements of Hu and Sinke, 87 reaction 28, led to −95.1 ± 0.8 kJ/mol for the heat of formation of CH2 Cl2 and both our diet-HEAT-F12, −95.37 ± 3.32 kJ/mol, and diet-HEAT-F12-network data, −95.09 ± 0.40 kJ/mol, agree well with this value. The ATcT value is also based on reaction 28 87 as well as on the hydrogenation reaction of Lacher, 85 reaction 22. In our TN, reaction 22 is weighted down due to the agreement between the diet-HEAT-F12 calculations and the result of Hu and Sinke. Please note that the ATcT data is also influenced by the diet-HEAT, G3, and ◦ G3X calculations. For ∆f H298 (CH3 Cl), our network provides −81.96±1.11 kJ/mol, which is

essentially the same as the value reported by Fletcher, 84 −81.9±0.6 kJ/mol utilizing reaction 21. The ATcT data is predominated by the bomb calorimetry reaction of Fletcher along with several reactions with bromine-containing species and G3, G3X, and G4 calculations. Our diet-HEAT-F12 result is −83.16 ± 2.83 kJ/mol, which is between the value of Fletcher and the excluded results of Lacher and associates. 86,103

21



Chlorofluoromethanes For the heats of formation of CHFCl and CFCl, there is no reliable experimental data available. For other chlorofluoromethanes, if not mentioned otherwise, JPL lists our previous diet-HEAT results, while the ATcT results are based on our diet-HEAT calculations ◦ combined with low-level G3 and G3X results mostly. The JPL value for ∆f H298 (CFCl3 ),

−285.3 kJ/mol, is based on the reaction CF3 Cl + 2CCl4 −−→ 3CCl3 F by Petersen and Pitzer, 89 reaction 25. Our network result, −289.32 ± 1.84 kJ/mol, is lower by almost 4 kJ/mol and supported by the diet-HEAT-F12 value of −290.02 ± 3.74 kJ/mol. Petersen and Pitzer 89 examined the reaction of 2CF3 Cl + CCl4 −−→ 3CF2 Cl2 , reaction 26, which ◦ (CF2 Cl2 )= −494.1 kJ/mol. This is in line with the result of our network, led to ∆f H298 ◦ (CF3 Cl), JPL adopts the result of Ruscic, 44 −709.2 ± 2.9 −494.90 ± 0.96 kJ/mol. For ∆f H298

kJ/mol. Our network data, −712.08 ± 1.17 kJ/mol, is slightly lower, but it is closer to the current ATcT value of −710.08 ± 0.72 kJ/mol. As discussed earlier, for these species further investigation is needed according to the regression diagnostics of our network.

Fluoroethanes ◦ (CH2 CHF), which is based JPL lists the value of Pedley, 104 −138.8 ± 1.7 kJ/mol, for ∆f H298

on the bomb calorimetry result of Kolesov, 105 reaction 18. This value is higher than ours, −142.93 ± 0.84 kJ/mol, and that of ATcT, −142.51 ± 0.47 kJ/mol, which is based on high ◦ level W4 calculations by Martin and associates. 99 For ∆f H298 (CH2 CF2 ), JPL also takes the

value from the review of Pedley. 104 However, Pedley’s data, −335 ± 4.5 kJ/mol, is higher by about 15 kJ/mol than ours, −351.07 ± 0.84 kJ/mol, or the ATcT value of −350.78 ± 0.85 kJ/mol. The ATcT value emerges from the results of Feller 106 and G3, G3X, and CBS-n calculations. The currently accepted JPL heat of formation value of CF2 CF2 is −658.9 ± 4.9 kJ/mol. This also differs by almost 15 kJ/mol from our diet-HEAT-F12-network value of −674.30±0.78 kJ/mol. ATcT gives a similar result, −674.93±0.57 kJ/mol, based on several data including our previous computations 52 and that of Feller; 106 several ionization reaction 22


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energies and low-level and G3, G3X, and G4 values are also included.

Conclusions This study provides accurate benchmark quality heat of formation values for 50 atmospherically relevant species including various chlorocarbons, CFCs, HFCs, HCFCs, and PFCs. In 28 out of the 50 cases, the diet-HEAT-F12-network presents the most reliable estimates for the heats of formation. For the other species, the results agree well with the most accurate data, ATcT or JPL, except CF3 −CF3 , CF3 , CHF3 , and CH2 F2 , where small discrepancies occur, i.e., the error bars do not overlap. The largest non-overlapping region, 0.5 kJ/mol, ◦ (CHF3 ). appears for ∆f H298

To analyze the results of the TN, well-known statistical metrics were used, namely the DFBETA and SDFBETA values, and the residual. According to these metrics a few additional species, CF4 , CH3 Cl, CHCl3 , CCl4 , CFCl3 , CF2 Cl2 , exist in the diet-HEAT-F12-network, for which further investigation is needed to collect more established heats of formation. This study also shows that conventional CCSD(T) calculations, even with the 5Z basis sets, can suffer from BSSE, while explicitly correlated methods are hardly affected by this error. Therefore, the usage of the model chemistry diet-HEAT-F12 is recommended over diet-HEAT. Furthermore, the present work highlights the importance of the quality and reliability of the data provided by the theoretical model and supplied into the TN, because, as it was observed, low-quality theoretical results undermine the benefits of the TNA. Obviously, the most vulnerable cases are those where there is no accurate experimental data available to challenge/control the influence of the inaccurate calculations.

23



Acknowledgement The authors are grateful for the financial support from the National Research, Development, and Innovation Office (NKFIH, Grant No. KKP126451). Time consuming calculations were carried out on the Hungarian HPC infrastructure (NIIF Institute, Hungary). JC acknowledges the financial support of the János Bólyai fellowship of the Hungarian Academy of Sciences.

Supporting Information Available Total energies, geometries, frequencies, anharmonicity constants, and thermochemical networks. This material is available free of charge via the Internet at http://pubs.acs.org.

24


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Table 1: Summary of the steps defined in the diet-HEAT and diet-HEAT-F12 protocols. steps geometry, ∆EZPE,harm a

diet-HEAT

diet-HEAT-F12

CCSD(T)/cc-pVQZ AE

CCSD(T)/cc-pVTZ(-f)bFC

MP2/cc-pVTZ

MP2/cc-pVDZ

HF/aug-cc-pV{T,Q,5}Z

HF+CABS/cc-pVQZ-F12

CCSD(T)/aug-cc-pV{Q,5}Z

CCSD(F12*)(T)f/cc-pV{T,Q}Z-F12

∆EZPE,anharm c ∞ d EHF ∞ e ∆ECCSD(T)

∆ECCSDT g

cc-pVTZ

∆ECCSDT(Q) h

cc-pVDZ

cc-pVDZ

CCSD(T)/cc-pCV{T,Q}Z

CCSD(T)/cc-pCV{D,T}Z

MVD2: CCSD(T)/cc-pCVTZ

X2C: CCSD(T)/cc-pVTZ-DK

∞ i ∆Ecore

∆EREL j ∆EDBOC k

cc-pVTZ(-f)b

CCSD/cc-pCVTZ

∆ESO l

experimental

HF/cc-pVTZ(-f)b experimental

a

∞ is the harmonic zero-point vibrational energy (ZPE) ∆EZPE,harm

b

cc-pVTZ(-f) denotes the cc-pVTZ basis set without f functions

c

∞ is the anharmonic contribution to the zero-point vibrational energy ∆EZPE,anharm

d

∞ is the complete basis set limit for the Hartree–Fock (HF) energy EHF

e

∞ ∆ECCSD(T) is the correlation energy extracted from CC singles and doubles with perturbative

triples [CCSD(T)] calculations and extrapolated to the basis set limit f

The explicitly correlated CCSD(F12*) method is described in ref 107

g

∆ECCSDT is the difference between the correlation energies obtained with the CC iterative single, double, and triple excitations (CCSDT) and CCSD(T) method

h

∆ECCSDT(Q) is the difference between correlation energies obtained with the CCSDT method with perturbative quadruples [CCSDT(Q)] and CCSDT method

i

∞ is the core correlation contribution defined as the difference between all-electron (AE) ∆Ecore

and frozen-core (FC) CCSD(T) energies j

∆EREL is the scalar relativistic contribution; MVD2 is the mass-velocity and 1- and 2-electron Darwin contribution and X2C is the spin-free exact two component method 108–111

k

∆EDBOC is the diagonal Born–Oppenheimer correction

l

∆ESO is the spin-orbit correction

25



Page 26 of 48

Table 2: Fixed heats of formation values in kJ/mol used in the networks Species

◦ ∆f H298

source

H

217.999 ± 0.006 NIST-JANAF 8

H2 O(l)

−285.83 ± 0.042 NIST-JANAF 8

C CO2 F

717.13 ± 0.32

ref 59

−393.522 ± 0.05 NIST-JANAF 8 79.39 ± 0.3 NIST-JANAF 8

HF · 10 H2 O

−322.03 ± 0.29

ref 91

HF · 20 H2 O

−322.18 ± 0.29

ref 91

HF · 23 H2 O

−322.20 ± 0.29

ref 91

HF · 25 H2 O

−322.21 ± 0.29

ref 91

HF · 30 H2 O

−322.24 ± 0.29

ref 91

HF · 40 H2 O

−322.27 ± 0.29

ref 91

HF · 45 H2 O

−322.29 ± 0.29

ref 91

HF · 55 H2 O

−322.31 ± 0.29

ref 91

Cl

121.302 ± 0.008 NIST-JANAF 8

HCl

−92.312 ± 0.21 NIST-JANAF 8

HCl · 600 H2 O −166.540 ± 0.10 COCl2

ref 76

−220.08 ± 3.3 NIST-JANAF 8

CH

595.8 ± 0.6

ref 112

CH2

391.2 ± 1.6

ref 112

CH3

146.7 ± 0.4

ref 112

CH4 C2 H5

−74.873 ± 0.034 NIST-JANAF 8 120.9 ± 1.7

26


JPL 7

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Table 3: The discrepancy between the diet-HEAT and diet-HEAT-F12 ∆f H0◦ results. All values are in kJ/mol, and only a representative subset of the data is shown here. Species

diet-HEAT diet-HEAT-F12

∆a ∆HF+CCSD(T) b

CH2 F−CH3

−257.0 ± 3.2

−257.1 ± 2.8 0.1

0.7

CHF2 −CH3

−488.6 ± 3.2

−490.0 ± 2.8 1.4

1.7

CH3 −CF3

−738.3 ± 3.2

−741.1 ± 2.8 2.8

2.7

anti−CH2 F−CH2 F

−429.8 ± 3.2

−431.2 ± 2.8 1.4

1.7

gauche−CH2 F−CH2 F

−433.5 ± 3.2

−434.9 ± 2.8 1.4

1.7

anti−CHF2 −CH2 F

−653.7 ± 3.2

−656.3 ± 2.8 2.6

2.7

gauche−CHF2 −CH2 F

−648.3 ± 3.2

−650.9 ± 2.8 2.6

2.6

CF3 −CH2 F

−894.6 ± 3.2

−898.5 ± 2.8 3.9

3.6

anti−CHF2 −CHF2

−867.9 ± 3.2

−871.7 ± 2.8 3.8

3.6

gauche−CHF2 −CHF2

−861.7 ± 3.2

−865.5 ± 2.8 3.8

3.6

CF3 −CF2 H

−1100.6 ± 3.2

−1105.7 ± 2.8 5.1

4.5

CF3 −CF3

−1331.3 ± 3.2

−1337.7 ± 2.8 6.4

5.5

a

Difference between diet-HEAT and diet-HEAT-F12

b

Difference between the HF and CCSD(T) contributions of diet-HEAT and diet-HEAT-F12

27


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 -1629.25

-1630.59

aug-cc-pVQZ


28 -2641.27

-2643.70

aug-cc-pVQZ

C2 F6

Counterpoise corrected results.

Sum of HF/{T,Q,5} extrapolation and CCSD(T)/{Q,5} extrapolation results.

Sum of HF+CABS/cc-pVQZ-F12 and CCSD(F12*)(T)/{T,Q} extrapolation results.

c

-2642.50

-2642.84

cc-pVQZ-F12

-2642.18

-2641.10

{T,Q,5} extrapolation

-1630.17

-1630.34

b

-2641.37

cp-diet-HEAT-F12a

HF+CABS

-2642.27

-2642.49

-1630.07

-1629.42

{T,Q,5} extrapolation

cc-pVQZ-F12

aug-cc-pV5Z

HF

HF+CABS

-1630.01

-1630.14

aug-cc-pV5Z

HF

a

-2642.30

diet-HEAT-F12

cc-pVTZ-F12

-2634.88

cp-diet-HEATa

Method

-2642.03

diet-HEAT

aug-cc-pVTZ

-1629.44

cp-diet-HEAT-F12a

Method

-1629.97

diet-HEAT-F12

cc-pVTZ-F12

-1625.32

Method

-1628.58

cp-diet-HEATa

aug-cc-pVTZ

diet-HEAT

Method

CF4

-177.60

-181.09

cc-pVTZ-F12

-153.51

-162.98

aug-cc-pVQZ

-47.31

-49.20

cc-pVTZ-F12

-32.46

-39.09

aug-cc-pVQZ

-180.46

-181.86

cc-pVQZ-F12

-182.55

-182.41

{T,Q} extrapolation

-181.87

-179.83

{Q,5} extrapolation

-49.46

-49.40

{T,Q} extrapolation

CCSD(F12*)(T)

-167.35

-171.20

aug-cc-pV5Z

CCSD(T)

-48.55

-49.31

cc-pVQZ-F12

-48.72

-47.45

{Q,5} extrapolation

CCSD(F12*)(T)

-40.39

-43.17

aug-cc-pV5Z

CCSD(T)

-2825.05

-2825.25

Pc

-2824.05

-2820.94

Pb

-1679.64

-1679.74

Pc

-1678.79

-1676.88

Pb

Table 4: Comparison of HF and CCSD(T) contributions to the heats of formation of CF4 and C2 F6 with and without counterpoise correction. All values are in kJ/mol.

The Journal of Physical Chemistry Page 28 of 48

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Table 5: Reactions discussed in the main text, for theoretical reactions the dietHEAT-F12 result is shown. The full list of reactions can be found in the SI. ◦ ∆r H298 (kJ/mol) source

Number Reaction Experimental reactions 17

C(graphite) + 2 F2 −−→ CF4

−933.20 ± 0.75 ref 77

18

CH2 CHF + 2.5O2 −−→ 2CO2 + H2 O(l) + HF · 40 H2 O

21

CH3 Cl + 32 O2 −−→ CO2 + H2 O(l) + HCl · 600 H2 O

−764.01 ± 0.50 ref 76,84

22

CH2 Cl2 + 2 H2 −−→ CH4 + 2HCl

−163.39 ± 1.26 ref 73,76,85

23

CH2 F2 + O2 −−→ CO2 + 2 HF · 23 H2 O

−585.05 ± 0.92 ref 73,97

24

C(graphite) + 2 F2 −−→ CF4

−932.49 ± 1.59 ref 73,74,79

25

CF3 Cl + 2CCl4 −−→ 3CFCl3

44.31 ± 7.66 ref 75,89

26

2CF3 Cl + CCl4 −−→ 3CF2 Cl2

31.76 ± 7.66 ref 75,89

28

CH2 Cl2 (l) + O2 −−→ CO2 + 2 HCl · 600 H2 O

−602.50 ± 0.84 ref 76,87

36

CHCl3 (l) + H2 O(l) + 12 O2 −−→ CO2 + 3 HCl · 600 H2 O

−473.21 ± 0.84 ref 76,87

43

CCl4 (l) + 2 H2 O(l) −−→ CO2 + 4 HCl · 600 H2 O

−359.91 ± 0.59 ref 76,87

48

[C2 F4 ]n + O2 + 2H2 O(l) −−→ 2 CO2 + 4 HF · 10 H2 O

−670.70 ± 3.77 ref 78,81

49

[C2 F4 ]n + O2 −−→ CF4 + CO2

−497.06 ± 2.09 ref 78,81

50

CF4 + 2 H2 O(l) −−→ CO2 + 4 HF · 20 H2 O

−173.13 ± 1.38 ref 82

52

[C2 F4 ]n + 2 F2 −−→ 2 CF4

65

2 CFCl3 −−→ CCl4 + CF2 Cl2

−1256.00 ± 1.72 ref 73,113

−1037.29 ± 0.29 ref 74,79 −10.88 ± 4.18 ref 8,88

Excluded reactionsa E1

CH3 Cl + H2 −−→ CH4 + HCl

−80.80 ± 0.40 ref 73,76,103

E2

CH3 Cl + H2 −−→ CH4 + HCl

−81.50 ± 0.40 ref 73,76,86

E3

C2 F4 −−→ C(amp) + CF4

−265.98 ± 1.67 ref 74,80

E4

C2 F4 + 2 H2 −−→ 2 C(amp) + 4 HF · 15 H2 O

−618.39 ± 4.18 ref 74,80

Continued on Next Page. . . 29



Page 30 of 48

Table 5 – Continued ◦ ∆r H298 (kJ/mol) source

Number Reaction E5

C −−→ C(amp)

7.11 ± 0.84 ref 74,80

Theoretical reactions 81

CF4 −−→ Cgas + 4F

1969.87 ± 3.00

91

CCl4 −−→ Cgas + 4Cl

1292.75 ± 5.75

127

Cgas + 2F2 −−→ CF4

−1653.32 ± 2.24

132

Cgas + H2 + F2 −−→ CH2 F2

−1168.67 ± 2.24

136

Cgas + 32 Cl2 −−→ CCl3

−645.88 ± 3.61

137

Cgas + 2Cl2 −−→ CCl4

−812.58 ± 4.12

149

Cgas + 12 H2 + 12 F2 + Cl2 −−→ CHFCl2

−1003.00 ± 3.32

151

Cgas + 21 F2 + 23 Cl2 −−→ CFCl3

−1007.15 ± 3.74

152

Cgas + F2 + Cl2 −−→ CF2 Cl2

−1213.28 ± 3.32

153

Cgas + 32 F2 + 21 Cl2 −−→ CF3 Cl

−1429.43 ± 2.83

a

During the initial solution of the TN, these reactions were considered by the iterative process, however, they were excluded from the final TN because they were both influential, according to the calculated DFBETAs, and challenged by other studies in the field (see text).

30


Page 31 of 48 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


Table 6: Highly influential reactions in the diet-HEAT-F12 network.a Species

◦ (kJ/mol) reactionsb ∆f H298

CH2 F2

−451.664 ± 0.671 (132: -0.680)

CF4

−933.477 ± 0.416 (17: -1.756), (49: -1.738), (24: -1.656)

[C2 F4 ]n

−829.675 ± 0.838 (52: -3.881), (17: -3.491), (49: -3.463), (24: -3.291)

CH3 Cl CCl3 CHCl3

−81.959 ± 0.279 (21: -1.113) 71.860 ± 1.205 (43: 1.598), (136: 0.827) −102.736 ± 0.457 (36: 1.299)

CHCl3 (l) −134.004 ± 0.456 (36: 1.300) CCl4

−95.474 ± 0.348 (43: 4.113)

CCl4 (l)

−128.012 ± 0.347 (43: 4.113)

CHFCl2

−284.757 ± 1.197 (149: 0.606)

CFCl3

−289.318 ± 0.900 (43: 1.838), (65: 0.798)

CF2 Cl2

−494.898 ± 0.958 (26: 0.699), (43: 0.629), (152: 0.603)

CF3 Cl

−712.077 ± 1.167 (153: 0.608)

a

The species listed have at least one reaction with a DFBETA value larger than 0.5 kJ/mol.

b

The format of the elements in this column, reaction number: DFBETA value, denotes the number of the reaction in the network with the corresponding DFBETA value.

31



Page 32 of 48

Table 7: Error statisticsa for the used protocols and for the corresponding networks. The diet-HEAT-F12-network is used as reference. All values are in kJ/mol. method

RMSD MAD MSD

MAX

diet-HEAT-F12

0.66

0.49

-0.45

2.71 (CF4 )

diet-HEAT

2.13

1.61

1.38

5.71 (C2 F6 )

G3

6.62

5.10

-4.68 17.51 (C2 F6 )

G4

4.08

3.23

-2.38 13.04 (CF3 −CF2 )

CBS-Q

8.29

6.27

-2.06 26.78 (CCl4 )

diet-HEAT-network

1.76

1.24

G3-network

4.36

3.15

-1.91 12.71 (C2 F6 )

G4-network

3.06

2.28

-1.05

CBS-Q-network

5.08

3.97

-0.44 14.00 (C2 F6 )

a

0.81

5.33 (C2 F6 )

8.25 (CF3 −CF2 )

RMSD: root-mean-square deviation; MAD: mean absolute deviation; MSD: mean signed deviation; MAX: maximum unsigned difference along with the corresponding species in parentheses.

32


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 −59.80 ± 2.65 −59.72 ± 2.65

−59.90 ± 2.80 −59.70 ± 2.80 −297.60 ± 2.80

CH2 F−CH2 (C1 )

CH2 F−CH2

CH3 −CF2

−754.24 ± 2.83 −444.84 ± 2.83

−751.50 ± 3.20 −443.30 ± 3.20

anti−CH2 F−CH2 F


33 −910.10 ± 2.83

246.99 ± 1.41 −194.36 ± 1.73 −469.41 ± 2.00 −936.19 ± 2.24

247.00 ± 0.80 −193.20 ± 1.20 −467.60 ± 1.60 −933.80 ± 2.00

CF

CF2

CF3

CF4

Continued on Next Page. . .

−1346.21 ± 2.83

−1110.60 ± 3.20 −1339.80 ± 3.20

CF3 −CF2 H

CF3 −CF3

−876.04 ± 2.83

−1115.62 ± 2.83

−881.37 ± 3.32

−872.20 ± 3.20 −878.40 ± 3.80

gauche−CHF2 −CHF2

−882.24 ± 2.83

−663.53 ± 2.83

CHF2 −CHF2

−906.20 ± 3.20 −878.40 ± 3.20

−666.10 ± 3.40

CHF2 −CH2 F

CF3 −CH2 F

−661.00 ± 3.20

gauche−CHF2 −CH2 F

anti−CHF2 −CHF2

−668.73 ± 3.00

−666.40 ± 3.20

anti−CHF2 −CH2 F

−669.03 ± 2.83

−448.73 ± 2.83 −448.26 ± 2.96

−447.30 ± 3.20 −446.90 ± 3.40

gauche−CH2 F−CH2 F

CH2 F−CH2 F

−504.38 ± 2.83

−503.00 ± 3.20

CH3 −CF3

−272.58 ± 2.83

−899.07 ± 2.65

CHF2 −CH3

−894.40 ± 2.80

CF3 −CF2

−699.87 ± 2.65

−272.50 ± 3.20

−695.10 ± 3.80

CF3 −CHF

−248.14 ± 2.77 −528.05 ± 2.65

CH2 F−CH3

−526.00 ± 2.80

CF3 −CH2

−238.56 ± 2.65

−238.30 ± 2.80

CH2 F−CHF(ap) −247.90 ± 2.90

CH2 F−CHF(sc)

CH2 F−CHF

−282.82 ± 2.65 −248.29 ± 2.65

−248.00 ± 2.80

CHF2 −CH2

−282.95 ± 2.65

−281.90 ± 2.80

CHF2 −CH2 (C1 )

−282.45 ± 2.65

−281.70 ± 2.80 −282.10 ± 2.80

CHF2 −CH2 (Cs )

−298.28 ± 2.65

−58.30 ± 2.65

−58.70 ± 2.80

CH2 F−CH2 (Cs )

diet-HEAT-F12 −73.96 ± 2.65

diet-HEAT −74.50 ± 2.80

CH3 −CHF

Species

−933.48 ± 1.76

a

−469.06 ± 0.52

−194.06 ± 0.41

247.08 ± 0.46

−1345.51 ± 1.00

−1114.81 ± 1.04

−880.86 ± 1.05

−909.70 ± 0.95

−668.37 ± 0.97

−447.97 ± 0.98

−753.94 ± 0.89

−504.11 ± 0.76

−272.37 ± 0.80

−898.77 ± 0.97

−699.45 ± 1.07

−527.95 ± 0.91

−247.94 ± 0.85

−282.72 ± 0.80

−298.20 ± 0.79

−59.77 ± 0.85

−74.06 ± 0.84

diet-HEAT-F12 network

−933.20 ± 0.75

−465.7 ± 2.1

−192.0 ± 3.3

244.1 ± 10

−1344.3 ± 3.4

−1110.6 ± 3.2

−872.2 ± 3.2

−878.4 ± 3.2

−906.2 ± 3.2

−661 ± 3.2

−666.4 ± 3.2

−447.3 ± 3.2

−443.4 ± 3.2

−751.5 ± 3.2

−503 ± 3.2

−272.5 ± 3.2

−891 ± 5

−690

−517.1 ± 5

−235.5

−277

−302.5 ± 8.4

−59.4 ± 8

−70.3 ± 8

JPL

−933.39 ± 0.25

−467.94 ± 0.49

−193.51 ± 0.38

246.71 ± 0.13

−1342.8 ± 1.5

−447.94 ± 0.86

−502.81 ± 0.65

−272.16 ± 0.37

ATcT

−469.0 ± 1.7 98

−194.1 ± 1.3 98

246.6 ± 0.6 25

−755.7 ± 1.0 47

−272.2 99

−892.9 ± 4.2 119

−691.1 ± 5.3 58,118

−523.1 ± 5.7 58,117

−247.3 ± 5.4 115

−280.9 ± 6.4 115

−300.2 ± 5.1 116

−56.2 ± 5.8 115

−74.1 ± 4.6 114

other source

◦ Table 8: Summary of the ∆f H298 results for the species studied. If the most reliable estimate is provided by this study it is typeset in boldface. All values are in kJ/mol.

Page 33 of 48 The Journal of Physical Chemistry


34 30.51 ± 2.45 −276.36 ± 2.65 −95.15 ± 3.16 −285.87 ± 3.32 −484.68 ± 2.83

32.00 ± 2.30 −274.40 ± 2.70 −93.30 ± 3.80 −283.10 ± 4.20 −482.20 ± 3.10

CF2 Cl

CFCl2

CHFCl2

CHF2 Cl

JPL

−674.30 ± 0.78

−351.07 ± 0.84

−142.93 ± 0.84

−712.08 ± 1.17

−494.90 ± 0.96

−289.32 ± 1.84a

−483.57 ± 0.96

−284.76 ± 1.20

−94.33 ± 1.02

−275.90 ± 0.87

31.04 ± 0.78

−264.48 ± 0.98

−67.77 ± 0.78

−81.96 ± 1.11a

−95.09 ± 0.40

116.36 ± 0.80

−102.74 ± 1.30a

89.33 ± 0.85

320.41 ± 0.76

−658.9 ± 4.9

−335 ± 4.5

−138.8 ± 1.7

−709.2 ± 2.9

−494.1

−285.3

−482.6 ± 3.2

−283.1 ± 4.2

−93.3 ± 3.8

−274.4 ± 2.7

31 ± 13

−263.9 ± 3.1

−61 ± 10

−81.9 ± 0.6

−95.1 ± 2.5

117.3 ± 3.1

−102.9 ± 2.5

89.0 ± 3.0

319.4 ± 0.8

71.1 ± 2.5 −95.6 ± 2.5

71.86 ± 1.60a

229.4 ± 0.8

433.7 ± 1.1

−238.9 ± 0.8

−452.7 ± 0.8

−32.8 ± 8

−692.9 ± 2.1

−239 ± 4

149.8 ± 2.1

−95.47 ± 4.11a

229.43 ± 1.03

434.59 ± 0.76

−235.55 ± 0.70

−451.66 ± 0.68

a

−30.39 ± 0.50

−697.45 ± 0.65

−243.45 ± 0.51

148.76 ± 0.49

diet-HEAT-F12 network

Table 8 – Continued

Uncertainty raised according to the DFBETA values (see text for details).

−674.75 ± 2.45

−671.02 ± 2.40

CF2 CF2

a

−143.19 ± 2.45 −351.33 ± 2.45

−142.23 ± 2.40 −349.54 ± 2.40

CH2 CHF

−712.29 ± 2.83

−708.60 ± 3.10

CF3 Cl

CH2 CF2

−290.02 ± 3.74 −496.15 ± 3.32

−286.00 ± 5.30 −492.10 ± 4.20

CFCl3

CF2 Cl2

CFCl

−68.46 ± 2.65 −265.33 ± 2.83

−67.80 ± 4.70 −263.90 ± 3.10

−95.37 ± 3.32 −83.16 ± 2.83

−93.70 ± 4.20 −82.60 ± 3.10

CH2 Cl2

CH3 Cl

CH2 FCl

115.71 ± 2.65

116.00 ± 2.70

CH2 Cl

CHFCl

88.67 ± 3.16 −102.09 ± 3.74

88.80 ± 5.80 −99.70 ± 5.30

CHCl2

319.99 ± 2.45

320.30 ± 2.30

CHCl

CHCl3

71.25 ± 3.61 −95.45 ± 4.12

73.10 ± 4.90 −91.00 ± 6.40

CCl3

CCl4

434.17 ± 2.24 228.79 ± 3.00

433.70 ± 1.10 230.10 ± 1.90

−451.54 ± 2.24 −235.66 ± 2.24

−450.50 ± 2.00 −236.90 ± 2.00

CH2 F2

CH3 F

CCl

−30.43 ± 2.00

−31.20 ± 1.60

CH2 F

CCl2

−243.81 ± 2.00 −698.22 ± 2.24

−243.00 ± 3.60 −694.90 ± 2.00

CHF2

148.64 ± 1.73

149.00 ± 1.20

CHF

CHF3

diet-HEAT-F12

diet-HEAT

−674.93 ± 0.57

−350.78 ± 0.85

−142.51 ± 0.47

−710.08 ± 0.72

−495.46 ± 0.97

−290.1 ± 1.2

−482.6 ± 1.2

−284.2 ± 1.2

−263.6 ± 1.3

−82.18 ± 0.25

−94.71 ± 0.59

−103.39 ± 0.64

−96.44 ± 0.64

−235.8 ± 0.23

−450.73 ± 0.36

−695.87 ± 0.43

148.54 ± 0.44

ATcT

−494.7 ± 2.6 84

−285.8 ± 1.7 84

435.1 ± 1.7 121

−236.4 ± 4.2 120

−28.0 ± 4.2 120

−697.1 ± 3.3 43

other source

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

Species

The Journal of Physical Chemistry Page 34 of 48

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Figure 5: Table of Contents image

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High Accuracy Quantum Chemical and Thermochemical Network Data

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