We employed the Reading NBM for radiative transfer calculations. This model, which divides the spectrum into 300 bands with a resolution of 10 cm⁻¹ across the wavenumber range 0–3000 cm⁻¹, was used to calculate Earth's irradiances (W m⁻² cm). We sourced spectral line parameters from the HITRAN 2016 and 2020 databases, and used the MT_CKD continuum model versions 3.2 , 4.2 and 4.3 . To determine the instantaneous RF (IRF) for a global and annual mean (GAM) atmosphere, following , we introduced a weak absorber with a constant absorption cross-section of 1.0 × 10⁻¹⁸ cm² molec.⁻¹ at all wavenumbers into the NBM. This weak absorber was assumed to have a mole fraction of 1 ppb and to be uniformly mixed throughout the atmosphere. To evaluate the spectral variation of the IRF of the GAM with respect to the different HITRAN and MT_CKD versions, we ran the radiative code twice: with the weak absorber (perturbed) and once without it (unperturbed). This approach was possible because for the IRF the weak absorber only affects the forcing in the specific wavenumber bands where it absorbs.

We also applied stratospheric temperature adjustment (STA), since RF values that include STA have been shown to be a more reliable predictor of surface temperature response than IRF alone . STA operates on relatively short timescales (months), in contrast to the decadal response of the surface–troposphere system. Although this has been superseded by the Effective Radiative Forcing (ERF), as the preferred definition of RF in recent Intergovernmental Panel on Climate Change (IPCC) assessments , the calculation of ERF requires the use of complex Earth System Models which employ radiative transfer schemes with low spectral resolution and include few halogenated gases, and so would be unsuitable for the current assessment. The inclusion of STA makes the calculation of spectral variations in RF considerably more complex . A perturbation by a halocarbon in one spectral region influences stratospheric emissions by other gases – most notably CO₂, O₃, and H₂O – at other wavenumbers. As a result, the forcing signal for a perturbation in absorption cross-section in one wavenumber band extends across the entire IR spectrum rather than being confined to that wavenumber band. In practice, RF (with STA) is calculated with the weak absorber confined to a single wavenumber band, but STA must be performed across all bands, requiring the procedure to be repeated for all 300 bands in the NBM.

Here, we first used the IRF using the single GAM atmosphere to illustrate the effect of updates to HITRAN and MT_CKD (Sect. 3.1), because of the much lower computational expense. To calculate the final updated version of the Pinnock Curve (Sect. 3.2), including STA, we performed separate calculations for tropical and extratropical profiles, following the methodology of but incorporating the most recent updates in the HITRAN and MT_CKD. In each latitude regime the standard fixed dynamical heating approximation was used; dynamical and solar heating were assumed to balance the unperturbed longwave heating. When the weak absorber was introduced, dynamical and solar heating was held constant, and an iterative procedure was applied to determine the temperature adjustments required to restore balance. This approach has been shown to reproduce global mean forcing values from high spatial resolution calculations to within ∼ 1 % . By contrast, reported errors exceeding 7 % when using a single GAM atmosphere. The updated Pinnock Curve was then used to refine the Oslo line-by-line IRF calculations reported in .

HITRAN2024 was released after most of the work reported here had been completed. We show in Sect. 3.1 that its impact on IRF is modest compared to changes due to HITRAN2020 and therefore do not include its impact on RF calculations incorporating STA.

The set of molecules considered in this study includes chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrofluorocarbons (HFCs), hydrofluoroolefins (HFOs), hydrofluoroethers (HFE), halons and bromomethanes. For these, IR absorption spectra were either taken from the literature or obtained through new QC calculations performed here. The latter were carried out for Halon-1202 (CBr₂F₂), HFC-161 (C₂H₅F), HFC-236ea (C₃H₂F₆), HFO-1234yf (C₃H₂F₄), HFO-1234ze(E) (E-C₃H₂F₄), HFO-1234ze(Z) (Z-C₃H₂F₄), and tribromomethane (CHBr₃), following the same DFT computational framework as introduced by . Briefly, the double-hybrid density functional DSDPBEP86 was applied in conjunction with the jun-cc-pV(T+d)Z basis set for C, H and F atoms, while bromine was described by using the energy-consistent pseudopotential basis set aug-cc-pVTZ-PP downloaded from the Basis Set Exchange library . In passing, it should be noted that the use of differently augmented basis sets for C, H, F and Br atoms has only a mild influence on the vibrational frequencies and intensities of vibrations involving the first-row atoms. Some tests were carried out for methylene bromide and tribromethane by describing all the atoms through the aug-cc-pVTZ basis, obtaining REs that agreed within 10⁻⁴ W m⁻² ppb⁻¹ with respect to the combination of jun-cc-pVTZ (C,H) and aug-cc-pVTZ (Br). Dispersion corrections were consistently included through Grimme's DFT-D3 scheme with Becke-Johnson damping . Equilibrium geometries were optimized first, and harmonic vibrational frequencies and IR intensities were then evaluated. Anharmonic contributions were incorporated using second-order vibrational perturbation theory (VPT2) , with cubic- and semi-diagonal-quartic force constants and second- and third-order dipole moment derivatives computed numerically from geometries displaced along normal modes. The resulting anharmonic wavenumbers and intensities were refined within the generalized VPT2 (GVPT2) framework , which properly accounts for resonance effects. All computations were carried out with Gaussian 16 .

For HFO-1234ze(Z), two conformers, both having C_S point group symmetry, were considered to reproduce the overall spectral bandshape, whereas for HFO-1234ze(E), although both C₁ and C_S conformations exist, only the C_S form was retained because the C₁ conformer is negligibly populated under the relevant thermal conditions (the conformer distribution was evaluated at 298 K).

In addition to the above molecules, the molecular set was completed by incorporating computed spectral data reported in previous publications. Specifically, IR absorption cross section spectra were taken from and for the following halocarbons: CFC-113 (CF₂ClCCl₂F), CFC-115 (CClF₂CF₃), CFC-12 (CCl₂F₂), CFC-13 (CClF₃), Halon-1201 (CHBrF₂), Halon-2301 (CH₂BrCF₃), Halon-1211 (CBrClF₂), HCFO-1122 (ClHC=CF₂ ), HCFC-132b (C₂H₂Cl₂F₂), HCFC-141b (Cl₂CFCH₃), HCFC-142b (CF₂ClCH₃), HCFC-22 (CF₂ClH), HFC-125 (CF₃CHF₂), HFC-134a (CF₃CFH₂), HFC-152a (CHF₂CH₃), HFC-32 (CH₂F₂), HFE-143a (CH₃OCF₃), HFO-1123 (C₂F₃H), and methylene bromide (CH₂Br₂). These spectra were obtained with the same computational protocol described above, which has been shown to reproduce the RE of different halocarbon families with mean deviations of ∼ 5 % and up to ∼ 10 % for ethers. Furthermore, QC IR spectra of HFC-236fa (C₃H₂F₆), HFC-245fa (C₃H₃F₅), and HFC-43‑10mee (C₅F₁₀H₂) were taken from giving a total of 30 halocarbons. For HFC-236fa and HFC-245fa, IR absoprtion cross section spectra were similarly simulated at the DSDPBEP86-D3/jun‑cc‑pVTZ level of theory, while for HFC-43‑10mee a hybrid force‑field approach was used, in which DSDPBEP86-D3/jun‑cc‑pVTZ harmonic frequencies and IR intensities were mixed with anharmonic contributions derived using the PW6B95-D3 functional in conjunction with the jul‑cc‑pVTZ basis set. In particular, third- and semidiagonal fourth-order derivatives of the potential energy surface, and second- and third-derivatives of the dipole moment surface, were evaluated at the PW6B95-D3/jul-cc-pVTZ level by displacing the atoms along the DSDPBEP86-D3 vibrational displacement vectors to maximize the overlap between the two sets of normal modes. This methodological choice, which also stems from the accuracy of the two individual methods , offered a practical compromise between accuracy and computational efficiency in climate‑related predictions .

The stick spectra resulting from the QC calculations are provided in the Supplement. Based on previous investigations () for the RE calculations these transitions were convoluted with a Lorentzian line-shape function having a half-width at half-maximum (HWHM) of 5 or 30 cm⁻¹ (mainly depending on the molecule's molecular weight): the reader is referred to the cited literature for halocarbons that appeared in previous works, while for those newly considered here the HWHM was set to 30 cm⁻¹ for HFO-1234yf, HFO-1234zeE, HFO-1234zeZ and HFC-161, and to 5 cm⁻¹ for Halon-1202 and HFC-236ea.

REs of the targeted molecules were computed by feeding the Pinnock Curve derived in this work as described in Sect.  into the in silico QC workflow to climate metrics together with their IR absorption cross section spectra computed according to the methodology outlined in Sect. . The calculation was carried out according to the formalism of , as given in Eq. (1): 1RE=∑i=1NFσi∫ν̃i,1ν̃i,2σi(ν̃)dν̃ where, Fσi represents the global mean RF per unit cross section for a weak absorber within the spectral interval i, ranging in wavenumber from ν̃i,1 to ν̃i,2, while σi denotes the IR absorption cross section integrated over the same range. In the calculations, we employed RF including STA in bins of 10 cm⁻¹ across the spectral range from 0 to 3000 cm⁻¹ (resulting in N=300). In the following sections, contributions from wavenumbers below 500 cm⁻¹ are reported as a percentage of the total RE values.

In order to account for non-uniform vertical and horizontal gas distributions, updated REs over the 0–3000 cm⁻¹ range were obtained by applying an adjustment depending on the molecule's atmospheric lifetime (τ). Following the procedure proposed by , REs were scaled according to 2f(τ)=2.962τ0.93121+2.994τ0.9322 and 3f(τ)=1-0.1826τ-0.3339 depending on whether the main removal pathway is either photolysis in the stratosphere (typically for fully halogenated species) or degradation by hydroxyl radicals (for H-containing halocarbons). Atmospheric lifetimes were taken from .

Uncertainties in RE stem from several independent sources: as noted by , typical contributions are approximately ∼5% from the radiation scheme and clouds, 3 % from water vapor and temperature profiles, 5 % from the tropopause height, and 1 % from temporal and spatial averaging. Based on the assessment carried out with respect to experimental data , QC IR absorption cross sections, computed according to the adopted computational approach, contribute with an average uncertainty of about 5 %. Finally, tropospheric adjustments (not accounted here) which are needed to calculate ERF contribute a further estimated uncertainty of 13 % .

Spectroscopic parameters catalogued in the HITRAN database and the opacity linked to the water vapor continuum are fundamental elements in radiative transfer models. As a result, updates to these quantities are regularly introduced and thoroughly assessed . The discussion here considers spectroscopic updates since those that were discussed by .

In the first part of this work, we examine how revisions to HITRAN and MT_CKD affect the spectral IRF using the GAM atmosphere. First, to illustrate the overall role of the continuum, Fig.  shows the impact of including and excluding the MT_CKD_4.3 water vapor continuum on the Pinnock Curve. Although absorption due to the water vapor continuum is less significant within water vapor bands, it plays a larger role in the window regions, where it frequently dominates over absorption from water vapor spectral lines. Hence, in those spectral regions, the continuum becomes the dominant factor in wavenumber-averaged absorption, especially in clear-skies . As can be noted in Fig. , the largest effects of including the absorption due to water vapor continuum in the NBM radiative transfer model are found in the 200–600 cm⁻¹ region and around 720–1200 cm⁻¹, where it leads to a reduction of the IRF by about 6 % and 4 %, respectively.

reported calculations up to and including MT_CKD 3.2. Since then, there have been several updates affecting both the self and the foreign continuum and its temperature dependence in the 0–3000 cm⁻¹ region. The most recent version available on the HITRAN website is MT_CKD_4.3. This is used here but we note that the changes between versions 4.2 (discussed in ) and 4.3 do not affect the spectral region of interest here. In particular, the version 4.2 revisions corrected an overestimation of self continuum coefficients, particularly in the 70–700 cm⁻¹ range of version 3.2 , which had previously resulted in higher downwelling long-wave flux at the surface and reduced outgoing long-wave radiation. As illustrated in Fig. , MT_CKD_ 4.3 generally leads to a reduction in water vapor continuum absorption and increased atmospheric transparency, as also pointed out in previous studies , resulting in an increase in RF when a weak absorber is introduced, with changes that are not uniform across the entire spectrum. However, the absolute increase is small, peaking at about 1 % near 500 cm⁻¹.

Next, we assessed the effects that updates in spectroscopic parameters, as implemented in the 2020 and 2024 releases of the HITRAN database , have on the Pinnock Curve. HITRAN2020 introduced significant updates in transition frequencies, intensities and broadening parameters of H₂O and its isotopologues. It also adjusted the CO₂ line list in the 580–750 cm⁻¹ range and it employed a combination of data from new laboratory and theoretical works to obtain consistent intensities of O₃ bands and increase the quality of the spectroscopic parameters for individual spectral lines. By comparing the IRF function obtained by using HITRAN2020 and HITRAN2016 (see Fig. , bottom panel), it is seen that these updates generally lead to a more opaque atmospheric profile, thus reducing the IRF in, for example, the O₃ band around 1000 cm⁻¹ and in the tail of the water vapor rotational band in the 500 cm⁻¹ region. Again, the absolute impact on the IRF small, and is generally 2 % or less. Changes due to HITRAN2024 (see Fig. , bottom panel) are much smaller than those resulting from HITRAN2020; they are concentrated around 550 and 1200 cm⁻¹, due to updates to N₂O spectral data and near 425 cm⁻¹ due to small changes in H₂O spectral data. As explained in Sect. 2.1, the impacts of these small changes due to HITRAN2024 are not included in the remainder of the paper.

Interestingly, the differences reported in the bottom panel of Fig.  suggest that the combined effect of changes in both the HITRAN spectroscopic parameters and in the water vapor continuum formulation to some extent compensate each other.

In this section, we present an updated version of the Pinnock Curve, obtained by using the HITRAN2020 spectroscopic dataset together with the MT_CKD_4.3 continuum model, adjusted for STA as shown in Fig. , and are provided in the Supplement. As explained in Sect. 2.1, NBM calculations described above were repeated using three representative atmospheres: one for the tropics and one each for the northern and southern extratropics. Shine and Myhre () showed the impact of using multiple profiles rather than a single GAM atmosphere on the Pinnock Curve (see their Fig. 5).

To obtain the final updated Pinnock Curve, derived by using HITRAN2020 and MT_CKD_4.3 and accounting for STA, we adapt the method described in Shine and Myhre (). We first multiply the Oslo line-by-line (LBL) IRF results by the ratio of the new and old NBM IRF results, to account for HITRAN and MT_CKD changes and then multiply by the ratio of RF (including STA) and IRF from the new NBM results, to account for the impact of STA. The spectrally resolved RF estimates introduced by are more accurate than NBM results and provide higher spectral resolution. Nonetheless, as noted earlier, it is not computationally feasible to incorporate STA directly into LBL calculations for calculations of the Pinnock Curve.

The updated Pinnock Curve was employed to evaluate the effects of updates to HITRAN and MT_CKD on REs of halocarbons. According to Eq. (), to estimate the RE of a molecule using the method developed by , two key quantities are required: (i) the Pinnock Curve including STA and (ii) the absorption cross section of the molecule.

In this subsection, we first illustrate the impact of the updated Pinnock Curve on RE using our QC-determined cross-sections over the entire 0–3000 cm⁻¹ spectral region. We then isolate the RE contribution from the low-wavenumber (0–500 cm⁻¹) spectral region, as this is the region where experimentally-determined values are generally not available, and compare this with the previously presented QC calculations over the same spectral range from . Finally, we use our new low-wavenumber QC calculations to update the 0–3000 cm⁻¹ values of RE presented in WMO ().

For the first step, to test the impact of the updated Pinnock Curve, the integrated absorption cross-sections obtained by integrating QC-simulated IR absorption spectra of the seven additional halocarbons introduced in the molecular dataset in the present work (see Sect. 2.2) are listed in Table  together with the corresponding experimentally derived values taken from the literature. For consistency, the same integration ranges (also specified in Table ) as in the experimental investigations were adopted. The comparison between QC and experimental band strengths demonstrates that the QC predictions closely reproduce experimental measurements also for the additional molecules. The largest deviation is observed for HFC-161 for which the experimental value is overestimated by 14 %. This apparently large (but still acceptable) percentage error is due to the relatively small integrated band intensity of this molecule (2.7×10-17 cm molec.⁻¹): indeed, when considering absolute deviations, the difference between QC predictions and experiment amounts to only 0.3×10-17 cm molec.⁻¹. A similar situation is noted for tribromomethane, for which the percentage deviation is 11 % that actually corresponds to only 0.4×10-17 cm molec.⁻¹ in absolute terms.

On average, the mean deviation over the full set of 30 molecules considered is 7 %, consistent with previous QC estimates , performed by adopting the in silico protocol to calculate climate metrics recently developed by . This agreement further supports earlier findings that the use of the DSDPBEP86/jun-cc-pV(T+d)Z method and the non-empirical inclusion of both mechanical and electrical anharmonicity enhances the accuracy of calculated transition frequencies and intensities, for both fundamental- and for two-quanta-transitions , which is then transferred to REs and GWPs. In passing, it has to be noted that the latter ones also depend on atmospheric lifetimes that, when not available experimentally, can be reliably computed by adopting suitable QC protocols relying on composite schemes and some form of variational transition state theory .

Figure  illustrates the total REs of all species included in the set of halocarbons, comprising contributions from both the medium-IR (namely 500–3000 cm⁻¹) and low-wavenumber (<500 cm⁻¹) regions. The figure compares two sets of REs: (i) those estimated using the Pinnock Curve from , shown in purple, and (ii) those obtained with the updated curve presented in Sect. 3.2, in light blue. Lifetime adjustment was not incorporated into these RE values in order to separately assess the impact of the Pinnock Curve update. Overall, a slight increase in the REs can be seen for all halocarbons analyzed, with an average increase of about 0.3 %. Focusing on the low-wavenumber region, a small increase of similar magnitude can be reported on average amounting to 1.0×10-5 W m⁻² ppb⁻¹ or about 0.3 %. The increase in the REs was expected, as recent adjustments to the water vapor self-continuum reduced atmospheric opacity within the 8–12 µm atmospheric window. Our results are consistent with those reported by when comparing RF functions obtained by using HITRAN2016 and MT_CKD_3.2 with the respective previous versions. Although the latest HITRAN and MT_CKD releases introduced significant updates, the changes tend to offset one another, producing compensatory effects as pointed out earlier (see Fig. ). As a result, they only lead to a marginal modification of the Pinnock Curve and, consequently, to REs.

In the next step, for the target set of halogenated hydrocarbons, we estimated the portion of the RE stemming from the IR absorption cross sections below 500 cm⁻¹. RE values due to the low-wavenumber region and their relative contribution to the total RE are presented in Table , where available literature results, obtained from harmonic QC calculations at the ωB97X-D/def2-TZVPPD level of theory are also reported. As can be seen by inspecting Table , the low-wavenumber contributions are usually small, below 1 % for most molecules and, focusing on the present results, only for HFC-152a and HFC-161 do they exceed 2 %. By comparing our results with those of (penultimate column of Table 2), a higher low-wavenumber contribution to the REs can be seen, with the exception of HFC-236fa and HFC-245fa. The most important differences are noted for HFC-152a, HFC-236fa and HFC-245fa for which the RE due to the spectral region below 500 cm⁻¹ are determined in the present work to be 3.0 %, 0.3 % and 1.8 %, respectively, whereas according to they amount to 0.06 %, 4.8 % and 2.8 %.

At this point one may wonder whether these differences are due to the different Pinnock Curve's adopted in the two works, or whether they can be attributed to the different QC protocols. As demonstrated in the previous section, the updated Pinnock Curve does not introduce significant changes in the REs, compared to the previous RF curve , even when the low-wavenumber region is considered separately. Moreover, the consistency between QC estimates of REs using different RF functions with experimental measurements also suggests that variations in RE are more affected by the underlying IR absorption cross sections than modifications to the Pinnock Curve. Therefore, the origin of the differences is very likely due to the different approaches used in the QC estimation of the IR absorption cross section spectra.

While RE estimates based on experimentally acquired IR spectra are usually carried out in the 500–3000 cm⁻¹, because low-wavenumber experimental data are very scarce, for four molecules, i.e. HCFC-132b, HFC-236fa, HFC-245fa,and HFC-43-10mee IR absorption cross sections have been measured down to about 150 cm⁻¹, and used to estimate the corresponding RE contribution . According to these analyses, the experimentally determined proportion of the total RE due to the vibrational absorption in the region below 500 cm⁻¹ is 0.3 %, 0.3 %, 1.9 % and 0.8 % for HCFC-132b, HFC-236fa, HFC-245fa and HFC-43-10mee, respectively. The correspondimg values for the QC calculations (Table ) are 0.9 %, 0.3 %, 1.8 % and 0.8 % respectively. Hence, for HCFC-132b the low-wavenumber contribution appears slightly overestimated by QC calculations, but an excellent agreement is found for the three HFCs. Interestingly, while the lowest lying fundamental band of HFC-32, due to the ν4 normal mode, is centered at 528.3 cm⁻¹ , a low-wavenumber contribution of 7×10-4 W m⁻² ppb⁻¹ (ca. 0.5 %) is predicted from the present QC simulations. By inspecting the experimental IR cross-section spectrum , it is indeed seen that the tail of the ν4 band extends down to about 430 cm⁻¹, and the experimental REs measured over the 400–500 cm⁻¹ amounts to 2.4×10-4 W m⁻² ppb⁻¹ (ca. 0.2 %). The capability to correctly predict this very small contribution stemming from the tail of a vibrational band gives further confidence in the accuracy of QC computations reported here. The close agreement between anharmonic QC simulations and laboratory experiments highlights the importance of including anharmonic contributions in the simulations in a non-empirical way for both transition frequencies and intensities, since purely harmonic treatments may give apparently accurate results, while masking the lack of important physical effects.

Finally, the last column of Table  reports the updated total 0–3000 cm⁻¹ radiative efficiency values, obtained by adding the low-wavenumber contribution (in absolute terms) determined here to the RE determined using experimentally-measured cross-sections in the 500–3000 cm⁻¹ range taken from the literature, and by applying the lifetime correction described in Sect. . Tropospheric adjustments, which were added to CFC-11 and CFC-12 in WMO , are not included.