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Article Cite This: J. Phys. Chem. A 2017, 121, 8288-8295

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Elucidating the Limiting Steps in Sulfuric Acid−Base New Particle Formation Jonas Elm* Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark

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S Supporting Information *

ABSTRACT: The molecular interactions between sulfuric acid (sa) and methylamine (ma) are investigated using computational methods. The molecular structures and vibrational frequencies of (sa)a(ma)b clusters, with a, b ≤ 4, were obtained with the ωB97X-D functional using a 6-31++G(d,p) basis set. The single-point energies were corrected using the domain-based local pair natural orbital coupled cluster methodDLPNO−CCSD(T) with an aug-cc-pVTZ basis set. The calculated Gibbs free energies (ΔG) of the clusters are used to calculate the evaporation rates of the (sa)a(ma)b cluster system and compare them to the corresponding ammonia clusters. With the atmospheric cluster dynamics code (ACDC), the new particle formation rates of the (sa)a(ma)b clusters were simulated and compared to the (sa)a(dma)b cluster system. It is found that methylamine is not capable of explaining observed new particle formation event in the ambient atmosphere. Looking into the calculated Gibbs free energy profiles it is found that the limiting steps in forming stable (sa)3−4(base)3−4 clusters depend strongly on the formation of the (sa)1(base)1 and (sa)2(base)2 clusters. These findings further support that compounds with high basicity are required to form the very initial cluster nucleus, which serves as the basis for forming new particles in the atmosphere.

1. INTRODUCTION Atmospheric ultrafine aerosol particles present a threat to human health. Inhalation of ultrafine particles can lead to an increased risk for lung cancer and cardiovascular diseases and is currently responsible for ∼7 million premature deaths around the world, annually.1 Aerosols also influence the global climate, by either absorbing or scattering incoming radiation.2 The largest source of new aerosol particles in the atmosphere is from gas to particle transformation, but the participating vapors remain highly uncertain. Sulfuric acid concentrations can be linked directly to new particle formation events,3 but another stabilizing constituent is needed to explain observed production rates in the ambient atmosphere.4−6 Atmospheric bases represent one of the most important species for forming strong clusters with sulfuric acid through proton transfer reactions. Albeit being the most abundant base, ammonia does not form stable clusters with sulfuric acid and cannot explain observed new particle formation rates.5 Highly basic amines are more likely candidates for efficiently stabilizing sulfuric acid clusters. Using computational methods, Kurtén et al. demonstrated that the enhanced stability of sulfuric acid− dimethylamine (dma) clusters compared to sulfuric acid− ammonia clusters was large enough to overcome the typical difference in atmospheric concentrations of ammonia and amines.7 On the contrary the computational study of Nadykto et al. found the opposite conclusion.8 The different conclusions between the two studies can be attributed to the applied computational level of theory for computing the binding © 2017 American Chemical Society

energies (RI-CC2/aug-cc-pVTZ vs PW91/6-311++G(3df,3pd)).9 The computational study by Depalma et al. on large clusters with up to eight sulfuric acid molecules and eight bases also found that substituting ammonia with dimethylamine in sulfuric acid clusters was energetically favorable. 10 Furthermore, Depalma and co-workers showed that water had a minor effect on the cluster energetics, with a lowering of ∼10% depending on the cluster size and number of water molecules.11 Experiments simulating realistic atmospheric conditions at the CLOUD chamber12 has definitively proven that 3 pptv of dimethylamine enhance new particle formation rates up to 1000-fold compared to 250 pptv of ammonia. Kürten et al. showed that neutral sulfuric acid−dimethylamine clustering either proceeds at or close to the kinetic limit.13 The experiments revealed the formation of clusters containing up to 14 sulfuric acid and 16 dimethylamine molecules, corresponding to ∼2 nm in mobility diameter. These findings illustrate that, in the context of forming new particles, the basicity of the base can be more important than its atmospheric abundance. Recent flow reactor experiments also indicate that the potential to form new particles follows the base strength with NH3 < methylamine (ma) < dimethylamine (dma) ≤ Received: September 8, 2017 Revised: October 11, 2017 Published: October 11, 2017 8288

DOI: 10.1021/acs.jpca.7b08962 J. Phys. Chem. A 2017, 121, 8288−8295

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The Journal of Physical Chemistry A

Figure 1. Lowest Gibbs free-energy structures of the (sa)1−4(ma)1−4 clusters. The cluster structures were obtained at the ωB97X-D/6-31++G(d,p) level of theory. Green = carbon, blue = nitrogen, yellow = sulfur, red = oxygen, and white = hydrogen.

trimethylamine (tma).14,15 In a similar manner diamines are more basic than their corresponding monoamines and diamines, such as putrescine, has been shown to enhance new particle formation rates significantly compared to, for instance, dma and ma.16−18 A recent study by Nadykto et al. compared the potential of ammonia and ma in enhancing sulfuric acid-induced new particle formation,19 and they found that ma new particle formation begins to dominate over ammonia when [ma]/[NH3] > ∼1 × 10−3. A recent computational study by Olenius et al. showed that ma behaves significantly different from dma and tma with respect to cluster growth mechanisms and hygroscopicity.20 Although methylamine is one of the most abundant amines in the atmosphere,21 it has been studied to a much lesser extent than ammonia and dma. This paper investigates the molecular interactions between sulfuric acid and methylamine using computational methods. The currently available thermochemical data are extended by one more cluster both along the methylamine and sulfuric acid coordinate, leading to (sa)a(ma)b clusters, with a, b ≤ 4. Employing the Atmospheric Cluster Dynamics Code (ACDC) cluster growth rates are presented, and the results are compared to the sulfuric acid−dimethylamine cluster system. The comparison allows for the determination of the limiting steps in sulfuric acid−base new particle formation.

2. METHODS 2.1. Compuational Details. The Gaussian 09 program, revision D.01,22 was used for all geometry optimizations and vibrational frequency calculations. As the studied cluster structures consist of acid and bases, some degree of proton transfer can be assumed. This implies that standard force field methods are not applicable for these systems; hence, density functional theory (DFT) was the method of choice for obtaining the structures and vibrational frequencies. On the basis of benchmark results on binding energies of atmospheric clusters,23,24 the ωB97X-D25 functional was utilized. For all the DFT calculations the 6-31++G(d,p) basis set was used, as it is a good compromise between accuracy and efficiency and does not yield significant errors in the thermal contribution to the free energy compared to much larger basis sets such as 6-311+ +G(3df,3pd)26 or aug-cc-pV5Z.27 Domain-based local pair natural orbital coupled cluster calculationsDLPNO−CCSD(T)28,29were calculated using the ORCA 3.0.3 program30 with an aug-cc-pVTZ basis set, using an on-the-fly local transformation (LT3). Invoking LT3 has been shown not to be any source of errors in DLPNO−CCSD(T) calculations on atmospheric clusters.31 Low-lying vibrational frequencies can be a large source of errors when calculating thermochemical parameters. The quasi8289


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Figure 2. Gibbs free-energy surface (in kcal/mol) of the (sa)1−4(NH3)1−4 clusters (left) and (sa)1−4(ma)1−4 clusters (right), calculated at the DLPNO−CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. Calculations were performed at 278.15 K, with [H2SO4] = 1 × 106 molecules cm−3 and 10 ppt of methylamine and 100 pptv of ammonia.

simulated new particle formation rate is the flux of clusters that leave the system. An additional loss term due to coagulation with larger particles was used in the simulations. On the basis of typical values observed in boreal forest environments,40,41 a constant coagulation sink with a value of 2.6 × 10−3 s−1 was chosen.

harmonic approximation was employed32 using the freely available “Goodvibes” python script by Funes-Ardois and Paton.33 In the quasi-harmonic approximation the contribution from low vibrational frequencies to the entropy is replaced by a corresponding rotational entropy. Larger clusters will have more vibrational modes below the chosen cutoff value, and hence more vibrational modes will be replaced by rotational entropies. The effect of the chosen cutoff value will thus depend on the size of the clusters. On the basis of test calculations (see Supporting Information) and recent results,18 a vibrational frequency cutoff value of 200 cm−1 was chosen. 2.2. Obtaining the Cluster Geometries. The molecular cluster structures consisting of sulfuric acid (sa) and methylamine (ma) are studied. Clusters up to (sa)1−3(ma)1−3 have previously been reported in the literature,19,20,34 and here the cluster structures are extended to (sa)1−4(ma)1−4. The cluster structures were re-evaluated by including an additional new round of conformational sampling at the ωB97X-D/6-31++G(d,p) level of theory. On the basis of inspecting the favorable binding patterns of the existing (sa)1−3(ma)1−3, (sa)1−4(ammonia)1−434 and (sa)1−4(dma)1−418 cluster structures, 10 or more new cluster structures were constructed for each cluster configuration using chemical intuition. The main part of the clusters was constructed by either adding a methyl group to ammonia or by deleting one methyl group from dimethylamine in all possible permutations. This new round of configurational sampling led to the identification of several new lower-lying free energy minima than previously reported, as well as extending the existing data by one more cluster both along the methylamine and sulfuric acid coordinate. 2.3. ACDC Simulations. The new particle formation rates were simulated using the ACDC.35−37 In ambient measurements the formation rate of clusters with 1.7 nm mobility diameter is used as a measure for new particle formation.12,38,39 The clusters considered in our simulation includes up to four sulfuric acid molecules and four base molecules, and the largest cluster studied measures roughly 1.5 nm in mobility diameter. A new particle is defined as a cluster that has a low-enough evaporation rate to assume that it will not re-evaporate, and the

3. RESULTS AND DISCUSSION 3.1. Cluster Structures. Figure 1 presents the lowest Gibbs free energy (sa)1−4(ma)1−4 cluster structures, obtained at the ωB97X-D/6-31++G(d,p) level of theory. The (ma)2−4 clusters are shown in the Supporting Information. One very important feature in sulfuric acid−base clusters is proton transfers. The transfer of a proton from sulfuric acid to the base changes the intermolecular interactions from hydrogen-bonding interactions to electrostatic interactions. This will inevitably strengthen the intermolecular interactions in the cluster, increasing its stability. There is observed a proton transfer from sulfuric acid to a methylamine in most of the cluster structures. Only in a single cluster(sa)3(ma)4is the formation of a sulfate ion (SO42−) observed. This is very similar to the case of (sa)a(NH3)b clusters, where a sulfate ion is only formed in the (sa)3(NH3)4 and (sa)4(NH3)5 clusters. We previously observed the formation of a single sulfate ion in the (sa)1(dma)4, (sa)2(dma)3−4, and (sa)3(dma)4 cluster structures.18 On the basis of simple acid−base principles the formation of sulfate ions in the cluster is highly dependent on the basicity of the base. This is well-demonstrated by the fact that very basic diamines (putrescine, put) readily form several sulfate ions in (sa)a(put)b clusters.18 3.2. Cluster Free Energy Surfaces and Evaporation Rates. From the law of mass action, the concentrationdependent Gibbs free energies of the clusters at given vapor concentrations Ci can be obtained as n ⎛ C ⎞ ΔGactual(C1 , C2 , ..., Cn) = ΔGref − kBT ∑ Ni ln⎜ i ⎟ ⎝ Cref ⎠ i=1

(1) 8290


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Figure 3. Total evaporation rates ∑γ (in s−1) of the (sa)1−4(NH3)1−4 clusters (left) and (sa)1−4(ma)1−4 clusters (right) calculated at the DLPNO− CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. Calculations were performed at 278.15 K.

Here the sum is over all compounds i in the cluster, Ni is the number of molecules of type i in the cluster, ΔGref is the standard Gibbs free energy calculated at the reference pressure pref, kB is Boltzmann’s constant, and T is the temperature. The reference concentration Cref is given by Cref = pref/(kBT). The calculated formation free energy surfaces of the (sa)1−4(NH3)1−4 and (sa)1−4(ma)1−4 clusters are presented in Figure 2. The concentration of sulfuric acid was set to [H2SO4] = 1 × 106 molecules cm−3 and with a mixing ratio of 10 pptv of ma and 100 pptv of NH3. All calculations were performed at the DLPNO−CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory, at 278.15 K. There is seen a large free-energy barrier in all directions in the sulfuric acid−ammonia system. This is in good agreement with previous results obtained by Olenius et al.37 On the contrary, the sulfuric acid−methylamine system show a low free-energy barrier along the diagonal on the acid−base grid. However, in all cases the (sa)1−4(ma)1−4 clusters have higher formation free energies compared to the (sa)1−4(dma)1−4 clusters at similar conditions and same level theory.18 This indicates that the free energy surface of ma and dma follow the basicity of the two amines, albeit having very similar trends in the free energy surfaces. Previous results based on RI-CC2/augcc-pVTZ//B3LYP/CBSB7 calculations have suggested that the free energies are lowest along the diagonal on the acid−base grid, indicating that the most stable clusters are when there is a 1:1 ratio between sulfuric acid and the amines. The experiments performed at the CLOUD chamber on sulfuric acid−ammonia5 and sulfuric acid−dimethylamine13 corroborates that the clusters grow along the diagonal of the system. This is further indicated by electrospray ionization mass spectrometry experiments of ammonium sulfate solutions both in positive and negative mode.42 The updated quantum chemical free energies calculated here for (sa)1−4(NH3)1−4 and (sa)1−4(ma)1−4 and previously for (sa)1−4(dma)1−4 clusters18 show a slightly different picture. Indeed the free energy along the diagonal is rather low, but low free energies are also observed for the off-diagonal (sa)n+1(base)n clusters for n up to 2. To stimulate pure growth along the diagonal of the system, the formation of the (sa)1(base)1 cluster needs to be rather favorable. Depending on

the basicity of the base, the formation of the sulfuric acid dimer (sa)2 is in competition with the formation of the initial (sa)1(base)1 cluster. This is, for instance, the case for NH3 and ma but not the case for dma or more basic compounds such as diamines.18 A better way to estimate the stability is to look at the evaporation rates of the clusters. From the free energies calculated using quantum chemical methods (ΔG), the total evaporation rates (∑γ) were calculated as a sum over all the individual contributions:36 γ(i , j) → i , j = βi , j

⎛ ΔGi + j − ΔGi − ΔGj ⎞ Pref exp⎜ ⎟ kBT kBT ⎝ ⎠

(2)

Here βi,j is the collision coefficient between molecule/cluster i and j, kB is the Boltzmann constant, T is the temperature, and ΔG is the quantum mechanically calculated free energy at the reference pressure Pref. Figure 3 shows the calculated evaporation rates of the (sa)1−4(NH3)1−4 and (sa)1−4(ma)1−4 cluster systems at 278.15 K. The diagonal (sa)n(base)n clusters for n up to 2 have high evaporation rates for both ammonia and methylamine, with values in the range from 2 × 102 to 6 × 105 s−1. In contrast for the (sa)1(dma)1 and (sa)2(dma)2 clusters, low evaporation rates of 5 and 2 × 10−1 s−1 have been reported, respectively.18 Thus, the evaporation rates of the (sa)1(base)1 and (sa)2(base)2 clusters follow the basicity of the base molecules. The (sa)2(ma)1, (sa)3(ma)2, (sa)3(ma)3, and (sa)4(ma)4 clusters show similar magnitude in the evaporation rates as the corresponding dma containing clusters.18 In accordance with previously studied sulfuric acid−monoamine systems, we begin to see a general trend in the evaporation rates of the clusters. The (sa)2(base)1, (sa)3(base)2, (sa)3(base)3, and (sa)4(base)4 clusters all have the lowest evaporation rates in the system. This suggests that the (sa)3(base)3 and (sa)4(base)4 clusters are relatively stable against evaporation for both ma and dma clusters and should be capable of growing into larger particle when formed. Thus, the flux toward these clusters is the limiting step in sulfuric acid−base new particle formation. The basicity of the base will highly influence the formation of the initial (sa)n(base)n clusters for n up to 2, which in turn will govern the potential of the base to form new particles. For 8291


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Figure 4. Simulated new particle formation rates (cm−3 s−1) as a function of sulfuric acid concentration with ma mixing ratios of 100 pptv (red), ma with a mixing ratio of 100 pptv, scaled by a factor of 10 (green) and ma with a mixing ratio of 100 pptv while lowering the free energy of the (sa)1(ma)1 and (sa)2(ma)2 clusters by −4.5 kcal/mol (blue). The dashed black line corresponds to dma with a mixing ratio of 10 pptv (---) (data taken from ref 18). The gray dots correspond to atmospheric observations.

Figure 5. Enhancement in new particle formation rate by lowering the free energy of the (sa)1(ma)1 cluster (left), the (sa)2(ma)2 cluster (middle), and both the (sa)1(ma)1 and (sa)2(ma)2 cluster (right). Simulations were performed at 278.15 K, with [H2SO4] set to 1 × 107 molecules cm−3, and with a mixing ratio of 100pptv methylamine.

ambient observations for mixing ratios of 100 pptv. This can be attributed to the weak formation of the (sa)1(ma)1 and (sa)2(ma)2 clusters and the general weaker stability of the clusters compared to the (sa)1−4(dma)1−4 cluster system. The formation free energy profile will determine the intersection with the x-axis, and to describe new particle formation rates at low sulfuric acid concentrations, a stronger base than ma is required. It is seen that the slopes of the new particle formation rates do not fit the entire range of observed new particle formation rates. In a multicomponent system with different monomer concentrations and competition between different pathways the effect on the slope is not straightforward. Factors such as coagulation, cluster−cluster collisions and monomer depletion all contribute.46 The atmospheric observations are the collective contribution of many different compounds and mechanisms, thus it is unlikely that a single component, coupled with sulfuric acid, should capture all the possible rates. It is much more likely that a large range of compounds is capable of explaining various regions of the observed new particle formation events. To look further into how the formation free energy of the (sa)1(ma)1 and (sa)2(ma)2 clusters affect the new particle formation rates, the cluster free energies were artificially strengthened. Figure 5 shows the enhancement in new particle

bases with low basicity the formation of the (sa)n(base)n clusters, for n up to 2, will be a stochastic process, which involves consecutive cluster formation and re-evaporation events. For bases with high basicity, the process is barrierless, and new particle formation will be at the kinetic limit. 3.3. New Particle Formation Rates. The new particle formation rates of the (sa)1−4(ma)1−4 cluster system were simulated, and the results were compared with the previously reported (sa)1−4(dma)1−4 cluster system. The new particle formation rates for the (sa)1−4(NH3)1−4 system were also calculated, but at realistic atmospheric conditions no particles were formed. As the free energy surface of the (sa)1−4(ma)1−4 cluster system has very similar characteristics to the (sa)1−4(dma)1−4 cluster system, the same criteria for when a given cluster can be allowed to grow out of the system was chosen. Hence the (sa)5(ma)4 and (sa)5(ma)5 clusters are considered stable against evaporation and considered a newly formed particle. The sulfuric acid concentration was varied between 1 × 105 and 1 × 108 molecules cm−3 and at a 100 pptv mixing ratio of ma. The simulations were performed at 278.15 K. Figure 4 shows the new particle formation rates compared to 10 pptv of dma (black dotted line, data taken from ref 18) and atmospheric observations43−45 (gray dots). The simulated new particle formation rates for the (sa)1−4(ma)1−4 cluster system is seen to fall outside the 8292


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These findings indicate that it is mainly the basicity of the base that governs its ability to form new particles with sulfuric acid. While the base is still required to be present in sufficient concentrations, such that sulfuric acid−base collisions will occur, the exponential dependence on the binding free energy significantly outweighs the linear dependence on base concentration. The formation of the (sa)1(base)1 cluster is the most important step for the formation of new particles from sulfuric acid and bases. This further suggests that highly basic amines are indeed key species in the very initial formation of stable atmospheric prenucleation clusters. These findings are supported by a recent synopsis by Bzdek et al., which also indicated that amines are effective at assisting the initial formation of clusters but are less important as the cluster size increases.42 After a stable sulfuric acid−base nucleus is formed, the subsequent growth of the cluster is most likely driven by condensation of highly oxidized multifunctional compounds (HOMs).49

formation rates by lowering the free energy of the (sa)1(ma)1 cluster, the (sa)2(ma)2 cluster, or both (sa)1(ma)1 and (sa)2(ma)2 clusters. Lowering the free energy of the (sa)1(ma)1 cluster by −4.5 kcal/mol yields a 120-fold increase in the new particle formation rate. The enhancement is less profound for the (sa)2(ma)2 cluster, where a lowering of the free energy by −3 kcal/mol only yields an eightfold increase in the new particle formation rate. This is caused by the fact that the formation of the (sa)2(ma)2 cluster remains hindered by the weak formation of the (sa)1(ma)1 cluster. By simultaneously lowering the free energy of the (sa)1(ma)1 and (sa)2(ma)2 clusters by −4.5 kcal/ mol, a 1700-fold increase in the new particle formation rate is found. Lowering the formation free energy of both clusters leads to a higher flux toward the stable (sa)3(ma)3 cluster and thus significantly higher new particle formation rates. As depicted in Figure 4 (blue solid line), lowering the free energy of the (sa)1(ma)1 and (sa)2(ma)2 clusters by −4.5 kcal/mol yields new particle formation rates even higher than the sulfuric acid−dimethylamine system. These findings clearly illustrate that it is in fact the formation of the (sa)1(base)1 and (sa)2(base)2 clusters that hinders the formation of new particles for bases with low basicity. The temperature has a large effect on the new particle formation rates. The formation of hydrogen bonds will lead to fewer degrees of freedom in the cluster and thus a decrease in the entropy. This implies that the formation free energies will be more favorable as the temperature decreases. To quantify this effect the new particle formation rates were simulated in 10 K intervals from 258.15 to 298.15 K with [H2SO4] = 1 × 107 molecules cm−3 and 100 pptv of methylamine. Lowering the temperature from 278.15 to 268.15 K leads to a 16-fold increase in the new particle formation rate. Lowering it further to 258.15 K leads to another ninefold increase. Increasing the temperature to 288.15 K leads to a 50-fold decrease in the new particle formation rates. At 298.15 K, practically no particles are formed. The large temperature dependence on the new particle formation rates originates from the change in the initial (sa)1(ma)1 and (sa)2(ma)2 cluster formation free energies in a similar manner as shown with the artificial strengthening in Figure 5. It should be noted that hydration is neglected in the simulated new particle formation rates. Bustos and co-workers showed that the addition of 1−2 water molecules to an (sa)1(ma)1 cluster was more favorable than for sulfuric acid alone.47 This suggests that (sa)a(ma)b clusters might be hydrated in the ambient atmosphere. Recent studies have shown that the effect of hydration on new particle formation rates depends strongly on the basicity of the base.20,48 New particle formation rates involving strong bases such as dma and tma are more or less unaffected by hydration, whereas weaker bases such as NH3 and ma show a stronger dependence. For ma an increase of up to one order of magnitude was observed in the new particle formation rates at 278 K, [H2SO4] = 1 × 106 molecules cm−3 and 100 pptv of methylamine, at 100% relative humidity.20 The green line in Figure 4 represents our calculated new particle formation rate at 100 pptv mixing ratio of ma, scaled by a factor of 10 to simulate the most drastic effect of hydration. While the effect of hydration moves the simulated new particle formation rates closer in proximity to the (sa)1−4(dma)1−4 system, hydrated (sa)1−4(ma)1−4 clusters do not appear to be able to explain observed new particle formation rates in the atmosphere.

4. CONCLUSIONS The molecular interactions between sulfuric acid and methylamine have been investigated. Molecular geometries and formation free energies of (sa)1−4(ma)1−4 clusters are reported. It is found that the clustering of sulfuric acid and methylamine is not capable of explaining observed new particle formation rates in the atmosphere, even when considering hydration in an ad hoc fashion. By comparing the energetics and new particle formation rates of the (sa)1−4(ma)1−4 clusters to previously reported (sa)1−4(dma)1−4 clusters it becomes apparent that the limiting step in sulfuric acid−base new particle formation is the formation of the initial (sa)1(base)1 and (sa)2(base)2 clusters. These findings further corroborate that strong bases are important chemical species in the initial formation of new particles in the atmosphere.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08962. xyz-files of the studied molecular structures at the ωB97X-D/6-31++G(d,p) levels of theory (ZIP) All calculated Gibbs free energies (PDF)

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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 for financial support and the Danish e-Infrastructure Cooperation (DeIC) and CSC-IT Center for Science in Espoo, Finland, for computational resources.

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REFERENCES

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