The global atmospheric lifetime (τatm) is defined as follows: 1τatm=1τOH+1τO(1D)+1τhν, where τOH, τO(1D), and τhν are the global lifetimes with respect to OH and O(1D) reactive loss and UV photolysis, respectively. Other reactive and deposition loss processes for HCFCs are expected to be negligible and not considered in this study. τatm is also often defined in terms of its loss within the troposphere (τTrop), stratosphere (τStrat), and mesosphere (τMeso) as 1τatm=1τTrop+1τStrat+1τMeso, where for example, 1τStrat=1τStratOH+1τStratO(1D)+1τStrathν For the HCFCs considered in this study, mesospheric loss processes are negligible and not considered further. The atmospheric loss processes for the HCFCs considered in this study have not been determined experimentally, while τTrop is predominately determined by the HCFC reactivity with the OH radical. In this work, τTropOH was estimated using the CH3CCl3 (MCF) relative method (WMO, 2014) where τTropOH=τOHHCFC=kMCF(272K)kHCFC(272K)τOHMCF, with the MCF recommended rate coefficient, kMCF(272 K) = 6.14 × 10-15 cm3 molecule-1 s-1 (Burkholder et al., 2015), and tropospheric lifetime, 6.1 years (WMO, 2014).

In the absence of experimental OH reaction rate coefficients, a structure activity relationship (SAR) was used to estimate OH reaction rate coefficients. The SAR of Kwok and Atkinson (1995) and DeMore (1996) were compared with the rate coefficients for the 15 HCFCs (training dataset) for which experimental kinetic measurements are available (Burkholder et al., 2015). The DeMore SAR clearly performed better for these halocarbons and was used in this study. Figure 1 shows the agreement between the experimental 298 K rate coefficient data and the SAR predicted values. For the determination of kHCFC(272 K) an E/R value of 1400 K was used in the Arrhenius expression, k(T) = Aexp(-1400 / T), which is a representative value for the HCFC reactions included in Burkholder et al. (2015). On the basis of the training dataset calculations, we estimate the uncertainty in the SAR 298 K rate coefficients to be ∼ 30 % on average. The uncertainty at 272 K will, in some cases, be greater due to our assumption that E/R = 1400 K for the unknown reaction rate coefficients. A ∼ 50 % uncertainty spread encompasses nearly all the training dataset values at 272 K, see Fig. 1. Therefore, we estimate a 50 % uncertainty in k(272 K) for the HCFCs with unknown rate coefficients.

τStrat for the HCFCs is determined by a combination of OH and O(1D) reactive loss, and UV photolysis. Presently, there is no simple means to determine stratospheric lifetimes without the use of atmospheric models. Here, we have estimated stratospheric OH loss lifetimes, τStratOH, following a methodology similar to that used in the WMO (2014) ozone assessment, where results from 2-D atmospheric model calculations are used to establish a correlation between tropospheric and stratospheric lifetimes. We used the lifetimes taken from the SPARC (Ko et al., 2013) lifetime report for three HCFCs and eight HFCs to establish a lifetime correlation, which is shown in Fig. S1 in the Supplement. The stratospheric loss via the OH reaction accounts for ∼ ≤ 5 % of the total OH loss process for > 95 % of the HCFCs. Therefore, this method of accounting for stratospheric loss leads to only a minor uncertainty in the calculated global lifetime.

In most cases, O(1D) reaction and UV photolysis are minor contributors to the global loss of a HCFC. In the absence of experimental data, O(1D) rate coefficients were estimated using the reactivity trends reported in Baasandorj et al. (2013). τO(1D) for the HCFCs were based on a comparison with similarly reactive compounds included in the SPARC (Ko et al., 2013) lifetime report. As shown later, the O(1D) reaction is a minor loss process, < 1 %, for nearly all the HCFCs included in this study and, therefore, the estimation method used is not critical as this loss process is a minor contributor to the global lifetime. τhν was estimated based on the molecular Cl-atom content and its distribution within the molecule as follows: each isolated Cl-atom (450 years), each CCl2 group (80 years), each CCl3 group (50 years), with a minimum photolysis lifetime of 50 years (Ko et al., 2013). UV photolysis is a minor loss process, with the exception of a few long-lived highly chlorinated HCFC isomers where photolysis accounts for 15 % of the global loss at most.

A minimum stratospheric lifetime of 20 years was applied to approximately account for transport limited stratospheric lifetimes.

Semi-empirical ODPs were calculated using the following formula: ODPHCFC=nCl3fHCFCfCFC-11MCFC-11MHCFCτHCFCτCFC-11, where nCl is the number of Cl-atoms in the HCFC; M is the molecular weight; f is the molecules fractional release factor (FRF), which denotes the fraction of the halocarbon injected into the stratosphere that has been dissociated (Solomon and Albritton, 1992); and τ is the global atmospheric lifetime. The fractional release factor and global lifetime for CFC-11 were taken from the WMO (2014) ozone assessment report to be 0.47 and 52 years, respectively. Note that a new method to calculate FRF has been suggested by Ostermöller et al. (2017a, b), which has been applied by Leedham Elvdige et al. (2018) and Engel et al. (2018). Overall, there is good agreement between the new method and the empirical parameterization applied in this work. The fractional release factors for the majority of the HCFCs included in this study have not been reported. The WMO report included 3 year age of air FRFs derived from model studies and field observations for 20 ozone depleting substances (WMO, 2014). In the absence of recommended FRF values, we derived an empirical FRF vs. stratospheric lifetime relationship, shown in Fig. 2, for the compounds with reported FRFs and the 2-D model stratospheric lifetimes reported in the SPARC (Ko et al., 2013) lifetime report. Table S1 provides the values presented in Fig. 2. A fit to the data yielded FRF = 0.06 + 0.875 × exp(-0.0144 × τStrat), which was used in our calculations.

Information about molecular vibrational frequencies, central to the interpretation of infrared spectra, thermodynamics, and many other aspects of chemistry, became amenable to computational determination in the early 1980s. It was recognized that computed harmonic frequencies derived via the second derivative of energy as a function of atomic position were systematically higher than observed fundamentals and scale factors were introduced (Hout et al., 1982; Pople et al., 1981). For Hartree–Fock frequencies these were typically ∼ 0.9 and accounted both for the influence of anharmonicity and deficiencies in the underlying quantum calculations. Frequencies based on methods incorporating electron correlation such as CCSD, CCSD(T), or certain functionals within density functional theory (DFT) often perform well for harmonic frequencies and are scaled by ∼ 0.95 to match fundamental vibrational modes. Such scaling has been updated as more methods appear (Alecu et al., 2010; Scott and Radom, 1996). Rather less information is available concerning the evaluation of absorption intensities for fundamental modes. Within the same harmonic approximation, implemented in popular quantum codes, the intensity is proportional to the square of the derivative of the dipole moment with respect to position. Halls and Schlegel (1998) evaluated QCISD results against experimental results that indicated deviations of up to approximately ±20 %; they then used QCISD as a benchmark to evaluate a range of functionals. For B3LYP, they found differences from QCISD of around 10 %. More recently, tests of the B3LYP functional found good performance for frequency and intensity (Jiménez-Hoyos et al., 2008; Katsyuba et al., 2013). Some prior work where similar methods have been applied to the infrared absorption for molecules of atmospheric interest include studies of fluoromethanes (Blowers and Hollingshead, 2009), unsaturated hydrofluorocarbons (Papadimitriou and Burkholder, 2016; Papadimitriou et al., 2008b), perfluorocarbons (Bravo et al., 2010), chloromethanes (Wallington et al., 2016), SO2F2 (Papadimitriou et al., 2008a), permethylsiloxanes (Bernard et al., 2017), and large survey studies such as by Kazakov et al. (2012) and Betowski et al. (2015) to name a few.

Halls and Schlegel noted that real spectra may exhibit the influences of resonances, intensity sharing, and large-amplitude anharmonic modes. These can be partially accounted for in an analysis based on higher derivatives of the energy and the dipole moment, performed for instance within the framework of second-order vibrational perturbation theory (Barone, 2005). Advantages include treatment of resonances among vibrational levels and incorporation of overtones and combination bands. Examples of applications to molecules containing C–H and C–F bonds indicate excellent accord with experiments for band position and intensity, (Carnimeo et al., 2013) but for CH2ClF the intensity in the region involving C–Cl stretching nevertheless exhibits intensity errors of ∼ 10 % (Charmet et al., 2013).

The large number of molecules considered in this work and the associated geometry optimizations, ∼ 1500 optimizations, required that a cost-effective methodology with reasonable accuracy such as DFT methods be used. Geometry optimization and vibrational frequencies for all C1–C3 HCFCs were carried at the B3LYP/6-31G(2df,p) level using the Gaussian 09 software suite (Frisch et al., 2016). Similar approaches have been used in earlier studies for other classes of molecules with good results, see Hodnebrog et al. (2013) and references cited within. The calculations presented in this work included only the 35Cl isotope because the large number of possible isotopic substitution permutations made the calculation of all combinations prohibitive. In principle, substitution of 35Cl by 37Cl in a heavy molecule would lower the frequency of the C–Cl stretch by ∼ 3 %. The level of theory was evaluated based on comparison with available experimental HCFC infrared spectra, see Table 1. Note that our calculations and data available in the NIST quantum chemistry database (2016) obtained using a more costly triple-ζ basis set (aug-cc-pVTZ) showed only minor differences in the calculated frequencies, < 1 %, and band strengths, < 10 %, for the molecules in the training dataset.

The majority of the HCFCs have multiple low-energy conformers that have unique infrared absorption spectra. Although only the most stable conformer has been used in most previous theoretical studies, including the individual conformers provides a more realistic representation of the HCFCs infrared spectrum and is expected to improve the accuracy of the calculated radiative efficiency as discussed below. We are not aware of prior studies of infrared spectra of HCFC conformers, but there have been prior theoretical studies of the conformers of other classes of molecule, such as for validation of observed infrared spectra used to deduce relative energies of carbonyl conformations (Lindenmaier et al., 2017) and comparison with measured infrared intensities for linear alkanes (Williams et al., 2013). The different errors and their trends for the intensities of C–H stretching and HCH bending modes indicate that a simple scaling approach, so successful for frequencies, will not work for intensities. In this work, we have included all conformers within 2 kcal mol-1 of the lowest energy conformer. This limit accounts for > 98 % of the population distribution at 298 K, in most cases. For each HCFC, a relaxed scan was performed to detect all possible conformations. For the C2 compounds, three staggered conformations were examined by rotating the C–C torsional angle by 120∘. For the C3 compounds, nine possible conformations were calculated by rotating the two torsional angles by 120∘. Each stable conformer was then fully optimized at the B3LYP/6-31G(2df,p) level followed by a frequency calculation. Conformer populations were calculated for a 298 K Boltzmann's distribution using the relative energies (including a zero-point correction) from the calculations. Including stable conformers resulted in overlapping vibrational bands and, therefore, more congested spectra which is consistent with the observed spectra for HCFCs. A number of the HCFCs have stereoisomers. Although the stereoisomers have identical infrared absorption spectra, they were accounted for in the population distribution. Note that for a molecule with a single asymmetrical carbon (a molecule containing a carbon with four different groups attached), e.g., HCFC-121a (CHClFCCl3), a pair of stereoisomers exist for each conformation and, therefore, the contribution of stereoisomers to the total population factors out. The entire dataset contains 126 molecules with a single asymmetric carbon and 32 molecules containing 2 asymmetric carbons.

A comparison of the experimental and calculated infrared spectrum of HCFC-124a (CHF2CClF2) shown in Fig. 3 demonstrates the importance of including conformers in the spectrum calculation. A comparison of experimental and theoretical spectra for all molecules with experimental data is provided in the Supplement. The calculations found that HCFC-124a has three stable conformers at 298 K with the lowest energy conformer having ∼ 50 % of the population. The experimental spectrum is characterized by strong absorption features between 1100 and 1500 cm-1, which are mostly associated with C–F bond vibrations, and C–Cl vibrational modes below 1000 cm-1. The comparison with the experimental spectrum shows that the prominent absorption features at ∼ 825, 1000, and 1250 cm-1 originate from the higher energy conformers. The calculated spectrum is in good agreement with the experimentally measured spectrum with band positions and total integrated band strengths agreeing to within ∼ 2 %. Note that conformer contributions to an infrared absorption spectrum will be different for different molecules. The impact of including conformers in the radiative efficiency calculations is presented later.

Overall, the agreement between experimental and calculated frequencies was good. Figure S2 shows a comparison of experimental vibrational frequencies with the calculated values. There was a systematic overestimation of the calculated vibrational frequencies above 1000 cm-1 and an underestimation below 1000 cm-1. An empirical frequency correction, which accounts, in part, for anharmonicity and other approximations used in the level of theory employed, was derived from this correlation and applied to all the calculated spectra: νcorrected = 53.609 + 0.94429 × νcalculated. Using this correction, frequencies around ∼ 1200 cm-1 (C–F bond vibrations) and around 800 cm-1 (C–Cl bond vibrations) are shifted by only ∼ 1 %. The uncertainty associated with the calculated band positions is estimated to be ∼ 1 %. The frequency-corrected spectra were used to derive the metrics reported here.

Figure 4 shows a comparison of calculated and experimental band strengths (integrated between 500 and 2000 cm-1) for the training dataset. Overall, the agreement is good for the majority of HCFCs with the calculated band strengths being within 20 %, or better, of the experimental values. The calculated band strengths are, however, systematically biased high by ∼ 20 %, for band strengths < ∼ 1.1 × 10-16 cm2 molecule-1 cm-1. A comparison of the training dataset experimental and calculated infrared spectra reveals that the bias originates from a band strength overestimation of bands below 1000 cm-1 that are primarily associated with C–Cl bonds. The bias is greatest for molecules containing more than one Cl atom on the same carbon, e.g., CHFCl2 (HCFC-21), CH3CCl2F (HCFC-141b), and CH2FCCl2F (HCFC-132c). In fact the intensities of C–Cl stretches are a long-known problem for calculation (Halls and Schlegel, 1998). Scaling the overall spectrum strength to account for such biases has been applied to decrease the deviation between experimental and theoretical values in an earlier theoretical study by Betowski et al. (2015). However, since the bias is primarily for the bands associated with C–Cl bonds, a scaling of the entire band strength would not be appropriate nor an accurate representation of the experimental spectrum. The spectra reported here do not include a band strength correction, as the prediction of which bands are overestimated is too uncertain without knowledge of the experimental spectrum. Although it is difficult to estimate the uncertainty for the theoretical calculations, an estimated ∼ 20 % band strength uncertainty includes nearly all the training dataset values and encompasses the possible systematic bias observed for certain vibrational bands.

Radiative efficiencies (REs) were calculated using the 298 K infrared absorption spectra calculated theoretically in this work and the Earth's irradiance parameterization given in Hodnebrog et al. (2013). The calculated spectra were broadened using a Gaussian broadening function with a FWHM (full width at half maximum) of 20 cm-1, which reproduces the training dataset spectra reasonably well and provides a more realistic representation of the spectrum and overlap with Earth's irradiance profile. Note that the Gaussian broadening function may not necessarily be an accurate representation of the actual vibrational band shape. Previous theoretical studies of greenhouse gases have applied band broadening as part of their analysis (see Hodnebrog et al., 2013 and references within), although the necessity of broadening has generally not been treated quantitatively. In our work, the calculated bands were broadened to obtain better agreement with available experimental HCFC spectra, which are assumed to be representative of the spectra of the unknown HCFCs, and, in principle, more reliable radiative efficiencies. Figure 5 shows the difference in retrieved REs with and without band broadening. The differences are molecule dependent, but are less than 10 % for nearly all the HCFCs. Although the differences are relatively small the use of a realistic broadening function reduces the uncertainty in the RE calculation and should be applied. A comparison of the experimentally derived REs and the calculated values for the training dataset is given in Fig. S3.

As illustrated earlier for HCFC-124a, Fig. 3, stable HCFC conformers can make a significant contribution to its infrared absorption spectrum. Figure 5 shows the impact of including the conformer population on the calculated RE for each of the HCFCs included in this study. Overall, including conformers increases or decreases the calculated RE by 10 %, or less, in most cases. However, there are some HCFCs where a difference of 20 %, or more, is observed, e.g., HCFC-124a, HCFC-151, and HCFC-232ba. In conclusion, including the contribution from populated conformers improves the accuracy of the calculated RE values and decreases potential systematic errors in the theoretically predicted RE values.

The strongest HCFC vibrational bands are due to C–F stretches, 1000–1200 cm-1, which strongly overlap the ”atmospheric window” region. The molecular geometry of the HCFC determines the exact vibrational band frequencies, i.e., HCFCs and their isomers have unique infrared absorption spectra and REs. Note that the calculated infrared spectra in this work include vibrational bands below 500 cm-1, which is usually the lower limit for experimental infrared absorption spectra measurements. The contribution of vibrational bands in this region to the RE is quantified in our calculations and is usually minor, i.e., < 1 %. The Earth's irradiance profile, HCFC infrared absorption spectra, and HCFC radiative efficiency spectra for each HCFC included in this study are included in the Supplement.

Lifetime-adjusted REs were calculated using the CFC-11 emission scenario ”S” shaped parameterization given in Hodnebrog et al. (2013), which is intended to account for non-uniform mixing of the HCFC in the atmosphere. The adjustment is greatest for short-lived molecules. A +10 % correction was applied to all molecules to account for the stratospheric temperature correction (see IPCC, 2013; Supplement Sect. 8.SM.13.4 for the origin of this factor). Well-mixed and lifetime-adjusted RE values are included in the Supplement.

Global warming potentials on the 20- and 100-year time horizons (T) were calculated relative to CO2 using the formulation given in IPCC (2013): GWPT=REτ1-exp(-T/τ)MHCFCIntRFCO2(T), where IntRFCO2(T) is the integrated radiative forcing of CO2 and MHCFC is the HCFC molecular weight. The RE used in the calculation was lifetime-adjusted with a stratospheric temperature correction applied. The global lifetimes were estimated as described in Sect. 2.1. The CO2 denominator is consistent with the GWP values reported in the WMO (2014) and IPCC (2013) assessments corresponding to a CO2 abundance of 391 ppm. Therefore, the values reported in this work can be compared directly to values reported in the WMO and IPCC assessments. A comparison of our training dataset values is given in Fig. 6, where the majority of the GWPs agree to within 15 %. HCFCs-21, -22, -122, and -123 have larger differences, due primarily to discrepancies between the estimated OH rate coefficients and those from the literature. Our GWP results can be scaled to the 2016 CO2 abundance of 403 ppm (NOAA, 2017) by multiplying by 1.03, which accounts for a decrease in the CO2 radiative efficiency (see Myhre et al., 1998; Joos et al., 2013).

Global temperature change potentials were calculated for the 20-, 50-, and 100-year time horizons using the parameterizations given in the IPCC (2013) Supplement Sect. 8.SM.11.2.

The training calculations have been used to estimate the uncertainties in our atmospheric lifetime estimates and infrared absorption spectra and how these uncertainties propagate through to the key ODP, RE, GWP, and GTP metrics. It is not possible to assign a single uncertainty for all HCFCs for each metric due to their dependence on the individual properties of the HCFCs. To provide a general perspective for the reliability of the metrics reported in this study, we limit our discussion to the average behavior.

The predominant atmospheric loss process for HCFCs was shown to be reaction with the OH radical, while UV photolysis in the stratosphere was found to be a non-negligible loss process for HCFCs with long lifetimes and significant Cl content. The DeMore (1996) SAR predicts the training dataset OH rate coefficients at 298 K to within 25 % on average, which directly translates to a 25 % uncertainty in the HCFC tropospheric lifetime. A conservative uncertainty estimate in the predicted OH rate coefficients at 272 K would be ∼ 50 %, see Fig. 1. Including an estimated ∼ 40 % uncertainty for the stratospheric UV photolysis and O(1D) reactive loss processes increases the global lifetime uncertainty by only ∼ 2 %.

The semi-empirical ODP uncertainty is directly proportional to the global lifetime uncertainty with an additional factor to account for the uncertainty in the fractional release factor (FRF). For HCFCs with total lifetimes less than 2 years, the total ODP uncertainty is estimated to be 35 %, for a 25 % uncertainty in the global lifetime. For longer lived HCFCs, the ODP uncertainty is greater, 50 % or more.

The theoretically calculated REs for the training dataset agreed to within 10 % with the values derived using the experimentally measured spectra, even though our estimated band strength uncertainty is 20 %. This method of RE determination is, therefore, expected to provide good estimates of REs in the absence of experimentally based determinations. The accuracy of the lifetime-adjusted RE values depends primarily on the uncertainty in the lifetime, calculated infrared band strengths, and to a lesser degree on the calculated band positions. We estimated the uncertainty in the calculated band strengths to be < 20 %, although not all vibrational bands are expected to have the same level of uncertainty. The uncertainty in the calculated vibrational band centers primarily impacts the RE through changes in the overlap with the irradiance profile. This sensitivity was estimated by artificially shifting the calculated spectrum in the RE calculation of several representative HCFCs by the estimated band center uncertainty of 1 %. The band center uncertainty was found to make less than a 5 % contribution to the total RE uncertainty. Note that molecules with strong absorption features near the large CO2 and O3 dips in the Earth's irradiance profile would have a greater sensitivity to shifts in the spectrum. In such cases, direct laboratory studies would be invaluable in the determination of the molecules radiative properties. The lifetime correction to the RE introduces an additional uncertainty that is dependent on the lifetime of the HCFC and its uncertainty. For compounds with a lifetime of 0.2 to 1 year, i.e., on the steep portion of the lifetime correction profile given in Hodnebrog et al. (2013), an additional ∼ 25 % uncertainty is introduced, while for longer-lived HCFCs the lifetime-adjustment uncertainty is smaller. A lifetime-adjusted RE uncertainty of ∼ 30 % is estimated for the majority of the HCFCs included in this study assuming a 25 % uncertainty in the global lifetime.

The overall uncertainty in the GWP and GTP metrics depends on the lifetime and RE uncertainties, with a different dependence on different time horizons. Compounds with lifetimes of less than 1 year have propagated uncertainties of ∼ 55 % on average. As the lifetime increases the uncertainty decreases to ∼ 30 % on average, or less. The greater uncertainty values for the shorter lived HCFCs is primarily associated with the uncertainty introduced by the lifetime-adjusted RE.

As mentioned earlier, there have been a number of previous studies that have applied methods similar to those used in the present study. The most relevant of these studies is that of Betowski et al. (2015) who reported radiative efficiencies for a large number of the C1–C3 HCFCs included in this study. Although they report REs for 178 of the 274 HCFCs included in our work there are significant differences between their REs and those reported here. Figure S4 shows a comparison of the RE values calculated here with those reported in Betowski et al. (2015) for the HCFCs common to both studies. The RE values from Betowski et al. (2015) are systematically lower than the ones reported here by ∼ 29 % on average. A similar systematic underestimation is observed when the Betowski et al. (2015) RE values are compared with the available HCFC experimental data used in our training dataset. Betowski et al. (2015) used B3LYP/6-31G(d) to calculate the HCFC infrared spectra and applied a band strength correction in their RE calculation. Note that a band strength correction was not applied in the present study as discussed earlier. In addition, Betowski et al. (2015) did not use broadened infrared spectra in their RE calculation and included only the lowest energy conformer. These differences can account for some of the scatter in the correlation shown in Fig. S4. The average difference between the reported RE values can only partially be explained by the different methods used here, B3LYP/6-31G(2df,p), and in Betowski et al. (2015), B3LYP/6-31G(d), as they produce very similar HCFC infrared spectra, i.e., the band strengths obtained with these methods agree to within ∼ 10 %.

Betwoski et al. (2015) used the available HCFC experimental data and data for a large number of compounds from other chemical classes in their training dataset, e.g., perhalocarbons, haloaldehydes, haloketones, and haloalcohols. On the basis of their analysis, a band strength scaling factor of 0.699, for the B3LYP/6-31G(d) method, was derived. However, for the HCFCs this scale factor introduces a systematic error in the band strength analysis. In Fig. 4 we showed that the DFT theoretical methods, without scaling, agree with the available experimental HCFC data to within 20 %, or better. Although the HCFC training dataset is relatively small, the band strength scaling factor based on results for other chemical compound classes is most likely not appropriate and introduces a systematic bias for the calculated RE values. Therefore, the infrared spectra reported in the present work and used to derive REs and GWPs were not scaled.