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Article Cite This: ACS Omega 2019, 4, 10965−10974

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An Atmospheric Cluster Database Consisting of Sulfuric Acid, Bases, Organics, and Water Jonas Elm*

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Department of Chemistry and iClimate, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark ABSTRACT: We have collected, recomputed, and compiled a database consisting of 633 unique atmospherically relevant molecular clusters containing sulfuric acid, bases, oxidized organic compounds, and water. The database is composed of strongly hydrogen-bonded molecular clusters and spans neutral, negatively charged, and positively charged clusters of atmospheric relevance. All the cluster structures and vibrational frequencies have been re-evaluated at the ωB97X-D/6-31++G(d,p) level of theory, and the single point energies have been refined using a high-level DLPNOCCSD(T)/aug-cc-pVTZ calculation. The database unifies published atmospheric molecular clusters under a single common methodology and serves as an efficient look-up table for molecular cluster structures and thermochemical parameters. Utilizing the database, the performance of four semi-empirical methodologies (PM6, PM7, B97-3c, and PBEh-3c) in calculating the binding energies of atmospheric molecular clusters is assessed. It is identified that the B97-3c and PBEh-3c empirically corrected density functional theory methods yield low errors in the binding energies compared to DLPNO-CCSD(T)/aug-cc-pVTZ reference results and that a simple linear model can be utilized for estimating accurate binding energies based on ωB97X-D/6-31++G(d,p) results.

1. INTRODUCTION Aerosol particles are ubiquitous constituents in the ambient atmosphere and present indisputable effects on the global climate1 and human health.2 The formation and growth of aerosol particles into cloud condensation nuclei (CCN) remain the largest uncertainty in the prediction of current and future climate changes.1 Modeling studies indicate that up to half of the number of CCN originates from the new particle formation.3 However, a holistic understanding of new particle formation remains elusive, as the exact molecular constituents and fundamental mechanisms are largely unknown. The formation of new particles is believed to be initiated by strongly hydrogen-bonded molecular clusters.4 Sulfuric acid and water5 are considered to be essential components in the initial cluster formation over continental regions, but other participating compounds are required to stabilize the clusters.6 Atmospheric bases such as ammonia,7 monoamines,8−10 and diamines11 can efficiently stabilize sulfuric acid clusters via acid−base hydrogen transfer reactions. Organic compounds have also been shown to enhance the sulfuric acid-induced new particle formation.12−14 Especially, highly oxygenated organic molecules (HOMs) are believed to be able to stabilize the initial cluster embryo15−17 and can even form new particles by themselves via ion-induced nucleation in the absence of sulfuric acid.18−20 HOMs are formed from intermolecular hydrogen shift reactions of atmospheric volatile organic compounds initiated by either ozone21 or hydroxyl radicals.22 This mechanism leads to a plethora of different oxygenated organic species being present in the atmosphere. © 2019 American Chemical Society

Techniques such as the chemical ionization atmospheric pressure interface mass spectrometer (CI-APi-TOF)23 can yield information about the chemical composition of the clusters involved in new particle formation. However, these techniques rely on charging the clusters and might change the cluster composition upon detection because of fragmentation.24 Different CI reagent ions (such as nitrate,21,25,26 acetate,27−29 and iodine30,31) are sensitive toward different compounds,32 and not all clusters may be efficiently detected by one particular technique. Mass spectrometer techniques coupled with quantum chemical calculations can also be used to provide insight into the growth mechanism of the clusters.33−37 Another promising technique for studying cluster formation is Fourier-transform infrared (FT-IR) spectroscopy coupled with quantum chemical calculations. Hydrogenbonded interactions are assigned via a red shift in the vibrational frequency compared to the isolated gas-phase monomers. The FT-IR technique has been applied to study a broad range of hydrogen-bonded interactions such as O−H···X and N−H···X, with X being either oxygen atoms,38−46 nitrogen atoms,47−52 sulfur atoms,38−41 phosphorus atoms,53,54 or πbonds55,56 in atmospherically relevant complexes. IR techniques have also been applied to larger ionic clusters and can directly indicate molecular rearrangement in the molecular clusters consisting of sulfuric acid and bases.57 Received: March 28, 2019 Accepted: June 11, 2019 Published: June 24, 2019 10965

DOI: 10.1021/acsomega.9b00860 ACS Omega 2019, 4, 10965−10974

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CCSD(T)/aug-cc-pVTZ level of theory is the most costeffective method to achieve acceptable errors (mean absolute error of 0.3 kcal/mol and maximum error of 0.8 kcal/mol) in the binding energies of small atmospheric clusters compared to CCSD(T)/CBS estimates.70 The binding energies are not basis set superposition error corrected, as we have previously demonstrated that there is no significant gain in accuracy when using an aug-cc-pVTZ basis set.70,71,77 The empirically corrected DFT methods PBEh-3c78 and B97-3c,79 was run using ORCA 4.0.0. The PM680 and PM781 semiempirical methods were run using Gaussian 09 and Gaussian 16,82 respectively. 2.2. Thermochemical Parameters. The binding free energy of the clusters is calculated as the following

Quantum mechanical (QM) calculations are a powerful tool to obtain the molecular cluster structures. Calculated Gibbs free energies can be used to give direct insight into the stability of the clusters from calculated evaporation rates, and the calculated free-energy surface yields insight into the cluster growth mechanics. Thermochemistry based on quantum chemical calculations are important input parameters for cluster kinetics models to study new particle formation mechanisms in realistic environments. A wide variety of models have been developed, such as the Atmospheric Cluster Dynamics Code (ACDC),58 the ternary ion-mediated nucleation model by Yu et al.,59 the computational fluid dynamics model for a flow reactor by Hanson et al.,60 and the SANTIAGO model based on data from the CLOUD experiments by Kürten et al.61−63 In recent years, QM calculations on clusters potentially involved in atmospheric new particle formation have rapidly increased and a large range of different cluster compositions involving sulfuric acid has been studied. However, different computational methodologies are often used, which hampers the direct comparison between different computational studies. The different levels of theory might also in some cases lead to vastly different conclusions.64−66 This paper unifies currently published atmospheric molecular cluster structures and thermochemistry under a single common state-of-the-art methodology. The complied data represent a first-generation database, where we will continuously add newly published structures and further improve the data when possible.

ΔG bind = Gcluster −

∑ Gmonomer

(1)

The binding free energy can be divided into a contribution from the electronic energy (ΔEbind) and a contribution from the thermal energy (ΔGthermal) ΔG bind = ΔE bind + ΔGthermal

(2)

The approach used herein utilizes ωB97X-D/6-31++G(d,p) for obtaining the geometry and vibrational frequencies, that is, the ΔGthermal contribution, and uses DLPNO-CCSD(T)/augcc-pVTZ to obtain the ΔEbind-value, calculated on top of the DFT geometry. This allows for the calculation of an * approximate ΔGDLPNO‑CCSD(T) -value as follows bind DFT DLPNO ‐ CCSD(T) * DLPNO ‐ CCSD(T) ΔG bind = ΔE bind + ΔGthermal

2. METHODS 2.1. Computational Details. All 633 clusters and their consisting monomers were geometry-optimized, and vibrational frequencies were calculated using the ωB97X-D67 functional with a 6-31++G(d,p) basis set using the Gaussian 09, rev. D.01 program.68 From the calculated vibrational frequencies, it was confirmed that all of the cluster structures are in fact minimum energy structures. The ωB97X-D functional was chosen based on its good performance compared to other functionals in calculating the binding energy of atmospheric clusters. For instance, the ωB97X-D functional yielded the lowest mean absolute error compared to DF-LCCSD(T)-F12a/VDZ-F12 results for a test set of 107 atmospherically relevant clusters.69 Furthermore, the ωB97XD functional was the only functional that was able to yield maximum errors below 1 kcal/mol compared to the CCSD(T) complete basis set estimates for a test set of 11 small atmospherically relevant clusters.70 Utilizing the 6-31++G(d,p) basis set has been shown to yield mean absolute errors below 0.5 kcal/mol in the thermal contribution to the free energy compared to a large aug-cc-pV5Z basis set for a test set of 6 small atmospheric cluster reactions.71 Reducing the basis set size from 6-311++G(3df,3pd) to 6-31++G(d,p) has also been shown to have little effect on the thermal contribution for a test set of 205 atmospherically relevant clusters.72 Thus, the ωB97X-D/6-31++G(d,p) level of theory is used to obtain the geometries and vibrational frequencies as it represents a costeffective methodology that can be applied to the entire test set of all 633 clusters. The density functional theory (DFT) single point energies are refined using DLPNO-CCSD(T)73,74 with an aug-cc-pVTZ basis set and the normal PNO settings.75 The DLPNO calculations were performed with ORCA 3.0.3 and ORCA 4.0.076 and in both cases using an on-the-fly local transformation. We recently showed that the DLPNO-

(3)

In a manner similar to the Gibbs free energy, the * approximate enthalpy (ΔHDLPNO‑CCSD(T) ) can be calculated as bind DFT DLPNO ‐ CCSD(T) * DLPNO ‐ CCSD(T) ΔHbind = ΔE bind + ΔHthermal

(4)

The entropy (ΔS) does not contain any electronic contribution and is purely obtained at the ωB97X-D/6-31+ +G(d,p) level of theory.

3. RESULTS AND DISCUSSION 3.1. Database Construction. A GitHub repository has been created for storing the cluster data.83 This makes it easy for other authors to clone the database and contribute with their own published cluster structures and thermochemistry to the database. The database was constructed by extracting the lowest free-energy cluster structure from the literature where possible. Each cluster system is added in separate folders that contain the molecular structures (as sdf files), a properties.txt file that contain all the cluster thermodynamic properties of the system, and a literature.txt file that contains the main original literature where the clusters were extracted from. Both thermochemistry at the ωB97X-D/6-31++G(d,p) level of theory and single point energies at the DLPNO-CCSD(T)/ aug-cc-pVTZ level of theory are available. The primary output files are available upon request from the author if required. The advantage of using a sdf file format is that it can be viewed by most molecular visualization software and can easily be expanded to include local free-energy conformers in a single file. The current database should be considered as the firstgeneration database, and it will continuously be updated as more cluster data become available. We have focused on clusters involving sulfuric acid and have mainly considered clusters published before mid-2018. Unfortunately, many 10966


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complicates the potential free-energy surface, as the organic monomers often exist in multiple conformations making it difficult to obtain the global free-energy cluster structure. Furthermore, oxidation products of terpenes can reach quite large molecular sizes. For instance, from a computational point of view, including a single pinic acid molecule (13 heavy atoms) is more or less equivalent to include 4 dimethyl amine molecules (12 heavy atoms) in the cluster. This has severely limited the possibility to study the kinetics of clusters consisting of both multiple sulfuric acid molecules and multiple organic acid molecules derived from monoterpenes. The previously studied clusters are mainly partitioned into clusters either consisting of sulfuric acid, bases, and water or clusters containing organics species. There exists very few studies of multicomponent clusters consisting of all four components: sulfuric acid, bases, organics, and water. To the best of the author’s knowledge, the first study that included all four components was Xu et al.121 that reported the (sulfuric acid)(oxalic acid)(ammonia)(water) cluster. More recently, the study by Liu et al.133 presented the (sulfuric acid)(glyoxylic acid)(ammonia)(water)1−5 clusters, with glyoxylic acid both in its native form and in its hydrated diol form. However, both studies have focused on small organic acids, and clusters consisting of all four components (with larger organic molecules) require further attention in the future. Figure 1 presents the current distribution of the cluster sizes in the database represented by the number of nonhydrogen atoms (C, N, O, and S) the clusters contain.

published articles do not supply structural information of the studied clusters or present them in a format that cannot be extracted, and consequently, they have not been added to the database. Table 1 presents the different types of clusters that have previously been studied and the associated references for each type of system. Table 1. Different Types of Clusters in the Database cluster types

refs

Sulfuric Acid−Bases−Water neutral (282) negatively charged (121) positively charged (68) Organics neutral (162)

64,84−115 116−118 106,117,119 91,120−133

The majority of the studied clusters in the literature consist of sulfuric acid, bases, and water. These clusters have gained significant attention as there is a strong acid−base interaction between sulfuric acid and atmospheric bases, leading to highly stable clusters. Ammonia, methylamine, and dimethylamine have predominantly been investigated, with only a few clusters consisting of trimethylamine and diamines such as ethylenediamine, propanediamine, and butanediamine (putrescine). As more than 150 different amines have been identified in the atmosphere,134 more studies on the interaction between other abundant amines and sulfuric acid are warranted to obtain a comprehensive molecular understanding of the interaction between sulfuric acid and amines. This can be very important in regions that have very localized emissions of amines such as agriculture or urban areas. Table 2 presents an overview of the different bases currently included in the database, with their abbreviations and the main references they have been extracted from. Besides sulfuric acid−base−water clusters, the database also includes clusters consisting of sulfuric acid and organics. Currently, only a few first-generation α-pinene oxidation products such as pinic acid have been studied (see Table 2). Including organic compounds in the clusters severely

Figure 1. Distribution of cluster sizes in the database. The nonhydrogen heavy atoms are C, N, O, and S.

Table 2. Overview of the Compounds in the Database and the Main References They Have Been Extracted from specie

refs

It is seen that the majority of the clusters remain medium sized with only around 15 heavy atoms (C, N, O, and S) corresponding to, for example, three sulfuric acid molecules. To allow accurate modeling of cluster kinetics using, for instance, the Atmospheric Cluster Dynamics Code (ACDC),58,136 a grid size of at least 4 × 4 molecules is usually needed. Thus, there is a great need for further studies that report large cluster systems up to these sizes. 3.2. Assessment of the Binding Energies of Approximate Methods. Obtaining large cluster structures is extremely time-consuming, and thus, more approximate methods might be required to expand the database to contain more realistic multicomponent clusters and to expand up to larger cluster sizes. As simulated new particle formation rates depend exponentially on the binding Gibbs free energy of the clusters, it is crucial to obtain the calculated free energies as accurately as possible. DFT remains the most accurate level of theory applicable to obtain the cluster structures and

Bases ammonia (a) methylamine (ma) dimethylamine (dma) trimethylamine (tma) monoethanolamine (mea) putrescine (put) Organics glycine (gly) pinic acid (pa) methanesulfonic acid (msa) oxalic acid (oa) C6H8O7 (hom) glycolic acid (gca) malonic acid (moa) glyoxylic acid (goa) hydrated glyoxylic acid (goaw)

101,104 109,115 101,104 113 114 111,115 125 126,135 128 129 127,130 131 132 133 133 10967


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Figure 2. (Left): Correlation between the calculated binding energies (ΔE in kcal/mol) for PM6 and PM7 plotted against the DLPNO-CCSD(T)/ aug-cc-pVTZ results. (Right): Distribution of the signed errors in kcal/mol. The mean signed error (MSE) is shown in the parenthesis.

Figure 3. (Left): Correlation between the calculated binding energies (ΔE in kcal/mol) for B97-3c and PBEh-3c plotted against the DLPNOCCSD(T)/aug-cc-pVTZ results. (Right): Distribution of the signed errors in kcal/mol. The MSE is shown in the parenthesis.

vibrational frequencies. To test whether more approximate methods are capable of yielding acceptable binding energies of the clusters, we have assessed the semiempirical PM6 and PM7 methods and the empirically corrected PBEh-3c and B97-3c

DFT methods. The binding energies of the approximate methods have been compared to the DLPNO-CCSD(T)/augcc-pVTZ binding energies for the entire database of 633 clusters. Figure 2 shows the correlation between the binding 10968


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Figure 4. (Left): Correlation between the calculated binding energies (ΔE in kcal/mol) for ωB97X-D, ωB97X-D scaled by 0.8965, and a linear model of the ωB97X-D binding energies as given by eq 5, plotted against the DLPNO-CCSD(T)/aug-cc-pVTZ results. (Right): Distribution of the signed errors in kcal/mol. The MSE is shown in the parenthesis.

energies and the distribution of the errors in the binding energies of the semiempirical PM6 and PM7 methods. There is seen a very large spread in the binding energies of the PM6 and PM7 methods compared to DLPNO-CCSD(T)/ aug-cc-pVTZ calculations. This is also reflected in the broad distributed errors of both the PM6 and PM7 methods. The PM6 method yields a high MSE of −27.6 kcal/mol. The error distribution of PM7 is significantly more narrow compared to that of PM6, but still yield a mean signed error (MSE) value of −11.5 kcal/mol. Figure 3 shows the correlation between the binding energies and the distribution of the errors in the binding energies of the empirically corrected B97-3c and PBEh-3c DFT methods. Both empirically corrected DFT methods show a good correlation with the calculated DLPNO-CCSD(T)/aug-ccpVTZ binding energies. The distribution of errors is quite narrow, with MSEs of 0.3 and 4.6 kcal/mol for B97-3c and PBEh-3c, respectively. This indicates that these methods might be an efficient tool to narrow down the number of relevant

conformers, when screening complex potential free-energy surfaces of atmospheric molecular clusters. We recently demonstrated that the ωB97X-D/6-31++G(d,p) binding energies were systematically overestimated compared to higher level coupled cluster calculations on (H 2 SO 4 )(H 2 O) 1−15 137 and (organic)(H2O)1−10138 clusters. This deficiency could efficiently be corrected by scaling the ωB97X-D/6-31++G(d,p) binding energies by a factor of the mean ratio of the DLPNO/DFT binding energies. In a similar manner, a scaling factor can be obtained by the mean ratio of the DLPNO/DFT binding energies over the entire dataset of 633 clusters. A mean scaling factor of 0.8965 was obtained. Besides scaling by a strict mean ratio, a linear regression model can also be obtained for correlating the ωB97X-D/6-31++G(d,p) and DLPNO-CCSD(T)/aug-cc-pVTZ. Using ordinary least squares regression, the following linear model was found approx ωB97X ‐ D ΔE bind = 0.93 × ΔE bind + 2.32

10969

(5)


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Figure 4 shows the correlation between the binding energies and the distribution of the errors in the binding energies of ωB97X-D, ωB97X-D (scaled by 0.8965), and the linear model given by eq 5. It is seen that there is a good correlation between the DFT and DLPNO binding energies in all cases. The uncorrected ωB97X-D/6-31++G(d,p) results are seen to drift slightly when reaching large binding energy values. Although the scaling factor does indeed improve the results, it is clear that there remains a slight drift in the values to the opposite side when reaching large binding energies. The simple linear regression model is seen to correct this issue. The uncorrected ωB97XD/6-31++G(d,p) is found to yield substantial errors in the binding energies, with a MSE-value of 8.7 kcal/mol. The scaled ωB97X-D/6-31++G(d,p) binding energies are seen to yield a low MSE-value of −1.2 kcal/mol, with a narrow distribution around zero. In a similar manner, the linear model shows a narrow distribution in the errors with a MSE-value of 0.0 kcal/ mol. This shows that using the simple linear model given in eq 5 is a very efficient approach to obtain binding energies in good agreement with DLPNO-CCSD(T)/aug-cc-pVTZ results, at a DFT computational cost.

REFERENCES

(1) IPCC. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P. M., Eds.; Cambridge University Press: Cambridge, United Kingdom and New York, NY, USA, 2013; p 1535. (2) WHO (World Health Organization). Public Health, Environmental and Social Determinants of Health, 2014. (3) Merikanto, J.; Spracklen, D. V.; Mann, G. W.; Pickering, S. J.; Carslaw, K. S. Impact of nucleation on global CCN. Atmos. Chem. Phys. 2009, 9, 8601−8616. (4) Kulmala, M.; Kontkanen, J.; Junninen, H.; Lehtipalo, K.; Manninen, H. E.; Nieminen, T.; Petaja, T.; Sipila, M.; Schobesberger, S.; Rantala, P.; et al. Direct Observations of Atmospheric Aerosol Nucleation. Science 2013, 339, 943−946. (5) Sipila, M.; Berndt, T.; Petaja, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L.; Hyvarinen, A.-P.; Lihavainen, H.; et al. The Role of Sulfuric Acid in Atmospheric Nucleation. Science 2010, 327, 1243−1246. (6) Weber, R. J.; Marti, J. J.; McMurry, P. H.; Eisele, F. L.; Tanner, D. J.; Jefferson, A. Measured Atmospheric New Particle Formation Rates: Implications for Nucleation Mechanisms. Chem. Eng. Commun. 1996, 151, 53−64. (7) Kirkby, J.; Curtius, J.; Almeida, J.; Dunne, E.; Duplissy, J.; Ehrhart, S.; Franchin, A.; Gagné, S.; Ickes, L.; Kürten, A.; et al. Role of Sulphuric Acid, Ammonia and Galactic Cosmic Rays in Atmospheric Aerosol Nucleation. Nature 2011, 476, 429−433. (8) Almeida, J.; Schobesberger, S.; Kürten, A.; Ortega, I. K.; Kupiainen-Mäaẗ tä, O.; Praplan, A. P.; Adamov, A.; Amorim, A.; Bianchi, F.; Breitenlechner, M.; et al. Molecular Understanding of Sulphuric Acid-Amine Particle Nucleation in the Atmosphere. Nature 2013, 502, 359−363. (9) Jen, C. N.; McMurry, P. H.; Hanson, D. R. Stabilization of Sulfuric acid Dimers by Ammonia, Methylamine, Dimethylamine, and Trimethylamine. J. Geophys. Res. D Atmos. 2014, 119, 7502−7514. (10) Glasoe, W. A.; Volz, K.; Panta, B.; Freshour, N.; Bachman, R.; Hanson, D. R.; McMurry, P. H.; Jen, C. Sulfuric Acid Nucleation: An Experimental Study of the Effect of Seven Bases. J. Geophys. Res.: Atmos. 2015, 120, 1933−1950. (11) Jen, C. N.; Bachman, R.; Zhao, J.; McMurry, P. H.; Hanson, D. R. Diamine-sulfuric acid reactions are a potent source of new particle formation. Geophys. Res. Lett. 2016, 43, 867−873. (12) Zhang, R.; Suh, I.; Zhao, J.; Zhang, D.; Fortner, E. C.; Tie, X.; Molina, L. T.; Molina, M. J. Atmospheric New Particle Formation Enhanced by Organic Acids. Science 2004, 304, 1487−1490. (13) Zhang, R.; Wang, L.; Khalizov, A. F.; Zhao, J.; Zheng, J.; McGraw, R. L.; Molina, L. T. Formation of Nanoparticles of Blue Haze Enhanced by Anthropogenic Pollution. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 17650−17654. (14) Metzger, A.; Verheggen, B.; Dommen, J.; Duplissy, J.; Prevot, A. S. H.; Weingartner, E.; Riipinen, I.; Kulmala, M.; Spracklen, D. V.; Carslaw, K. S.; et al. Evidence for the Role of Organics in Aerosol Particle Formation under Atmospheric Conditions. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 6646−6651. (15) Schobesberger, S.; Junninen, H.; Bianchi, F.; Lonn, G.; Ehn, M.; Lehtipalo, K.; Dommen, J.; Ehrhart, S.; Ortega, I. K.; Franchin, A.; et al. Molecular Understanding of Atmospheric Particle Formation from Sulfuric Acid and Large Oxidized Organic Molecules. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 17223−17228. (16) Riccobono, F.; Schobesberger, S.; Scott, C. E.; Dommen, J.; Ortega, I. K.; Rondo, L.; Almeida, J.; Amorim, A.; Bianchi, F.; Breitenlechner, M.; et al. Oxidation Products of Biogenic Emissions Contribute to Nucleation of Atmospheric Particles. Science 2014, 344, 717−721. (17) Bianchi, F.; Tröstl, J.; Junninen, H.; Frege, C.; Henne, S.; Hoyle, C. R.; Molteni, U.; Herrmann, E.; Adamov, A.; Bukowiecki, N.; et al. New particle formation in the free troposphere: A question of chemistry and timing. Science 2016, 352, 1109−1112.

4. CONCLUSIONS A large database consisting of 633 atmospheric molecular clusters has been collected and recomputed to unify published clusters under a single common computational methodology: DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p). Utilizing the entire database, the performance of approximate methodologies in calculating the binding energies of atmospheric molecular clusters is assessed. In particular, it is found that the empirically corrected B97-3c and PBEh-3c DFT methods yield low errors in the binding energies compared to DLPNO-CCSD(T)/aug-cc-pVTZ. Similarly, a good estimate of the DLPNO binding energies can be obtained by either scaling the ωB97X-D/6-31++G(d,p) binding energies by a factor of 0.8965 or using a simple linear model as a function of the ωB97X-D/6-31++G(d,p) binding energies. In the future, the database will be further augmented to include new cluster systems, as well as local free-energy conformations of all of the clusters. The author encourages that future publications will be performed using the ωB97X-D/ 6-31++G(d,p) level of theory as presented in the database and are added to the GitHub repository upon publication.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +45 28938085. ORCID

Jonas Elm: 0000-0003-3736-4329 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS J.E. thanks the Villum foundation and the Swedish Research Council Formas project number 2018-01745-COBACCA for financial support, the Academy of Finland and ERC project 692891-DAMOCLES for funding. We thank the CSC-IT Center for Science in Espoo, Finland, and the Danish eInfrastructure Cooperation (DeIC) for computational resources. 10970


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