Binding Energies of Astrophysically Relevant Molecules on CO 2 Clusters: Benchmarking and the Donor-Acceptor Origin of Surface-Dependent Binding

The gist The binding energies of twelve astrophysically relevant molecules on CO2 clusters were calculated using DFT calibrated against CCSD(T)/CBS, revealing that binding strength depends on whether the adsorbate requires the surface to donate a hydrogen bond (H-bond)

Computational Methodology

The researchers calculated BE distributions for twelve adsorbates (N2, CH4, HCl, C2H2, H2S, HF, HCN, H2CO, HCOOH, HNC, CH3OH) on CO2 clusters containing two to five molecules using DFT calibrated against CCSD(T)/CBS. The binding strength depends on whether the adsorbate requires the surface to donate a hydrogen bond (H-bond).

The study employed a specific protocol for geometry sampling and refinement. This workflow proceeded in three stages: (i) binding-site sampling, where molecules were placed on the cluster surface in randomized orientations and positions and subjected to a coarse geometry relaxation; (ii) geometry refinement of the geometrically unique sampled sites at a production level of theory; and (iii) computation of the harmonic Hessian for the zero-point vibrational energy (ZPVE) correction and assembly of the ZPVE-corrected BE distribution.

For larger clusters (CD4 and CD5), BEEP sampling was complemented with additional bindingsite configurations derived from smaller clusters. This procedure involved superimposing relative adsorbate–CO2 geometries from smaller clusters onto a CO2 unit of the larger cluster, which was then subjected to the full BEEP refinement protocol.

Binding Energy Analysis

The researchers reported the full spread of BEs across sites for each species and cluster size, rather than a single mean, because both ends of the distribution matter astrophysically. This spread is quantified by σsite, which is the standard deviation of the BE across different sites on a single cluster, measuring how much binding strength varies with where the molecule sits.

The binding energy calculation involves defining ∆Eb = − (EX+ice − (EX + Eice) + ∆ZPVE), where the ZPVE correction is defined as ∆ZPVE = EZPVE, X+ice −(EZPVE, X + EZPVE, ice). The final reporting level BE is the ωB97XV/def2-TZVP, which is calibrated against a reference quality CCSD(T)/CBS dataset.

Species Behavior and Trends

The twelve adsorbates were divided into three broad groups based on their binding behavior: nondonors bound mainly by dispersion (N2 and CH4); weak donors with modest dipoles or mildly positive hydrogen atoms (HCl, C2H2, H2CO, and H2S); and strong H-bond donors (HF, HCN, HNC, HCOOH, CH3OH, and H2O).

For strong hydrogen-bond donors like HCOOH, the average BE more than doubles from the dimer to the pentamer, climbing from 1345 K to 4364 K (+27%). HCOOH binds most strongly of all twelve adsorbates at the trimer and pentamer, because it can anchor to two CO2 molecules at once.

Water (H2O) shows the largest relative rise from tetramer to pentamer (+40%), with most of its increase coming at the last step, although its tetramer mean rests on only three sites. The optimized geometries show that H2O binds through two complementary interactions: its oxygen approaches the electron-poor carbon of CO2, while one of its hydrogens usually donates an H-bond to a CO2 oxygen.

Astrophysical Implications

The BE distributions translate directly into the temperatures at which each adsorbate thermally desorbs from a CO2-rich surface using the Polanyi–Wigner equation. The peak desorption temperatures (Tpeak) span 11 K to 132 K.

The comparison with water ice shows that every species binds more weakly on CO2, but by a margin that varies substantially from species to species. This variation follows from the binding mechanism: the species most affected are those whose binding on water ice includes an H-bond donated by the surface, a contribution CO2 cannot make and that adding more CO2 cannot remedy.

The asymmetry explains why mixed H2O–CO2 ice separates into pure CO2 regions, as water binds more weakly to a CO2 surface than to water ice. Formaldehyde shows the largest effect, and its lower desorption temperature on CO2 may bear on the cold gas-phase formaldehyde seen in disks.

Conclusions

The results inform how volatiles partition wherever CO2 makes up a significant fraction of the grain-ice mantle, including the CO2-rich regions seen in pre-stellar cores, protostellar envelopes, and protoplanetary disks. The natural next step is to compare the two ices using more closely matched surfaces. The present comparison sets our five-molecule CO2 pentamer against the twelve-molecule ASW12 water-ice model.

The study concludes that the difference between the two ices differs per species, contrary to how astrochemical models treat them by applying BEs referenced to water ice to all grains. The comparison with water ice shows that the difference between the two ices differs per species <ref:

1. Bold binding energy distribution analysis: The AI system can calculate the full spread of BEs across sites, for each species and cluster size, rather than a single mean, which is stated as being astrophysically relevant because it reveals how much the binding strength varies with where the molecule sits on the cluster.

2. Predictive desorption temperature mapping: The system can use the calculated Binding Energies to determine the temperatures at which each adsorbate thermally desorbs from a CO2-rich surface, through the Polanyi–Wigner equation for first-order desorption kinetics, allowing it to predict the spectra in Figure 6 and the values in Table 2.

3. H-bond donor/acceptor mechanism discrimination: The system can classify adsorbates based on whether they require the surface to donate a hydrogen bond (H-bond), specifically noting that CO2 can accept an H-bond but cannot donate one, which is used to infer segregation into CO2-rich domains.

4. Species binding strength comparison: The AI system can compare binding strengths by observing that every species binds more weakly on CO2 than on water, but by a margin that ranges from a factor of ∼ 1.5 for formaldehyde to ∼ 1.1 for acetylene, formic acid, and methanol, which allows it to predict how the snowline shifts outward to a colder radius.

5. Cluster size dependence tracking: The AI system can track the mean BE with cluster size, identifying which species show a binding energy that has begun to level off at n = 5 and which are still rising, enabling predictions about the behavior of volatile species in larger ice models.

Carbon dioxide (CO 2) is among the most abundant interstellar ices and has been observed by JWST in water-rich mixtures and pure CO 2 environments. Astrochemical models adopt binding energies (BEs) measured on water ice because few BEs are available for CO 2 ice. We calculate BE distributions for twelve adsorbates (N 2, CH 4, HCl, C 2 H 2, H 2 S, HF, HCN, H 2 CO, HCOOH, HNC, CH 3 OH, H 2 O) on CO 2 clusters containing two to five molecules using DFT calibrated against CCSD(T)/CBS, a coupled-cluster treatment extrapolated to the complete-basis-set limit. Binding strength depends on whether the adsorbate requires the surface to donate a hydrogen bond (H-bond). CO 2 can accept an H-bond but cannot donate one, and all six species compared with water ice from Ahmad et al. (2026) bind more weakly on CO 2. The ratio of the BE on CO 2 to water ice ranges from 0.66 for H 2 CO and 0.75 for H 2 O to 0.87 for CH 3 OH, 0.89 for HCOOH and 0.92 for C 2 H 2. Formaldehyde is predicted to desorb near 57 K from CO 2-rich ice, compared with 85 K from water-rich ice, and could contribute to cold gas-phase H 2 CO. Although the mean binding energies are changing with cluster size for several species, the differences can be traced to local binding interactions likely to remain important in larger ice models. The BEs vary by more than 500 K between sites, while the desorption peaks range from 11 K for CH 4 to 132 K for HCOOH. The limited H-bonding capacity of CO 2 may favour separation of mixed H 2 O:CO 2 ice into CO 2-rich domains.