Hydration of Atmospheric Molecular Clusters: Systematic

Subscriber access provided by Université de Strasbourg - Service Commun de la Documentation

A: New Tools and Methods in Experiment and Theory

Hydration of Atmospheric Molecular Clusters: Systematic Configurational Sampling Jens Kildgaard, Kurt V. Mikkelsen, Merete Bilde, and Jonas Elm J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02758 • Publication Date (Web): 09 May 2018 Downloaded from http://pubs.acs.org on May 9, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Hydration of Atmospheric Molecular Clusters: Systematic Configurational Sampling Jens Vive Kildgaard,† Kurt V. Mikkelsen,∗,† Merete Bilde,‡ and Jonas Elm∗,‡ Department of Chemistry, University of Copenhagen, Denmark, and Department of Chemistry and iClimate, Aarhus University, Denmark E-mail: [email protected]; [email protected]

To whom correspondence should be addressed University of Copenhagen ‡ Aarhus University

∗

†

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We present a new systematic configurational sampling algorithm for investigating the potential energy surface of hydrated atmospheric molecular clusters. The algorithm is based on creating a Fibonacci sphere around each atom in the cluster and adding water molecules to each point in 9 different orientations. To allow the sampling of water molecules to existing hydrogen bonds, the cluster is displaced along the hydrogen bond and a water molecule is placed in between in three different orientations. Generated redundant structures are eliminated based on minimizing the root mean square distance (RMSD) of different conformers. Initially, the clusters are sampled using the semiempirical PM6 method and subsequently using density functional theory (M06-2X and ωB97X-D) with the 6-31++G(d,p) basis set. Applying the developed algorithm we study the hydration of sulfuric acid with up to 15 water molecules. We find that the additions of the first four water molecules ”saturate” the sulfuric acid molecule and are more thermodynamically favourable than the addition of water molecule 5-15. Using the large generated set of conformers, we assess the performance of approximate methods (ωB97X-D, M06-2X, PW91 and PW6B95-D3) in calculating the binding energies and assigning the global minimum conformation compared to high level CCSD(T)-F12a/VDZ-F12 reference calculations. The tested DFT functionals systematically overestimates the binding energies compared to coupled cluster calculations, and we find that this deficiency can be corrected by a simple scaling factor.

2


Page 2 of 36

Page 3 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Introduction

Water molecules are ubiquitous in the lower atmosphere of Earth where they exist in solid, liquid and gaseous states. Water molecules possess a distinct ability to form hydrogen bonds candidating them as ideal mediators of atmospheric transitions from gas phase to clusters to aerosol particles. The initial steps of cluster formation and the transition of an atmospheric cluster to an aerosol particle are also referred to as nucleation and growth processes. They remain poorly understood processes although they have important consequences for the global climate and air quality. Particles formed in nucleation events can grow to sizes of 50 nm or larger in polluted 1 as well as pristine 2 environments and act as cloud condensation nuclei (CCN) affecting cloud optical properties, lifetime and thus radiative balance. 3 Global modelling studies indicate that in general a significant fraction and as much as half the number concentrations of CCN in the marine boundary layer originate from particles formed via nucleation and growth. 4 With respect to air quality, aerosol particles in outdoor air pollution have a documented negative impact on human health 5,6 with ultrafine particles having enhanced negative effects. 7 Formation of new particles in the atmosphere via nucleation and growth has been observed to happen on local as well as regional scales 8 and nucleation can contribute significantly to the number concentration of ultrafine particles in polluted areas. 9 Evidence exists that sulfuric acid is an important chemical compound in the new particle formation process. 10 Other compounds such as bases, 11–13 highly oxidized multifunctional organic compounds (HOMs), 14–16 and ions 17,18 might also be crucial in the initial steps. Sulfuric acid is one of the most hygroscopic substances known and its identified participation in new particle formation has led to several quantum chemical studies targeting the stabilizing effects of water on gas-phase sulfuric acid clusters. 19–23 Generally, it has been found that sulfuric acid is primarily hydrated in the gas-phase, but no studies have targeted sulfuric acid hydrated by ten or more water molecules. 24,25 Although such hydration could represent important steps towards transition to a liquid phase particle. The stabilizing effect of water on sulfuric acid - base clusters have also been studied using computational methods. 26–28 3



The effect of hydration on cluster formation has been identified to depend on the basicity of the base. 29,30 Clusters consisting of sulfuric acid and strongly basic compounds such dimethylamine and trimethylamine show little stabilizing effect by hydration. However, formation rates of clusters consisting of sulfuric acid and weaker bases such as methylamine and ammonia can be enhanced by approximately one order of magnitude by hydration. Obtaining the global free energy minimum cluster structure is a persisting challenge as each additional molecule in the cluster significantly complicates the configurational space. For this reason water has been neglected in many atmospheric cluster studies or only a few water molecules have been included. Various different methods have been used for sampling atmospheric cluster configurations such as: manual sampling using chemical intuition, 31–33 molecular dynamics, 27,34,35 Monte-Carlo, 36 basin hopping 37–39 and Random Sampling. 40–42 In this paper we develop a new sampling technique that can systematically sample hydrated atmospheric cluster structures. As a proof-of-concept, we utilize the method to investigate the hydration of a single sulfuric acid molecule with up to 15 water molecules. The identified (H2 SO4 )1 (H2 O)1−15 clusters present an ideal test set for assessing approximate methods and adds a new dimension, as it allows for the analysis of both the global free energy minimum structures as well as the relative energies.

2 2.1

Methods Systematic Hydrate Configurational Sampling

Identifying the lowest free energy conformations of molecular clusters is a challenging task. A new method was developed for adding water molecules to existing unhydrated clusters in a systematic manner. The water molecules are evenly distributed, around the cluster, using Fibonacci spheres. 43 Applying these spheres around the cluster and excluding the points too close to other atoms (≤ 0.5 ˚ A), one is left with a collection of points shaped as the cluster. An example of a unit Fibonacci sphere with 50 points and a collection of points surrounding 4


Page 4 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a sulfuric acid molecule can se seen in Figure 1.

1.5 1.0 0.5 0.0 1.0 0.5 1.0 x 1.5 1.5

1.5 1.0 0.5 0.0 z 0.5 1.0 1.5 1.5 1.0 0.5 0.0 0.5 y

4 3 2 1 0 1 2 3 4

z[ ]

Page 5 of 36

4

2

x [ 0]

2

4

4

3

2 1 0 1 y[ ] 2

3

4

Figure 1: (Left) illustration of a Fibonacci sphere with 50 points and (Right) a distribution of points around a sulfuric acid molecule (red points are the atoms). Next step is to place a water molecule at each point on the Fibonacci sphere in different orientations. This can be performed by using a rotation matrix, that rotates around the x,y and z axes by an angle of φ, θ and ψ, respectively, in a right-handed coordinates system. Here the task is to sample different orientations of the water molecule and the angles will be evenly spaced between 0 and 2π. We chose to split each angle into 3 for each axis, yielding a total of 9 different orientations of the water molecule. As water belongs to the point group C2v , the complete 2π rotation along all axes could result in similar orientations. The rotation of the molecule is applied when it has been displaced to its centroid, afterwards the centroid of the water molecule is placed at the points of the Fibonacci sphere around the cluster. Before accepting the placement it is checked whether any atoms of the water molecule are less than 0.5 ˚ A from any of the atoms in the cluster. The clusters are held together by hydrogen bonds and as water is able to form two donor and two acceptor hydrogen bonds, it is likely that hydrating water molecules will also make their way and bind inside the original cluster. To create structures with water placed in between already present hydrogen bonds in the cluster we locate the existing hydrogen bond

5



Page 6 of 36

pairs as oxygen and hydrogen atoms with an interatomic distance of 1.1-2.0 ˚ A. To allow space for the water molecule, the cluster is perturbed by moving all atoms radially away from the midpoint of the hydrogen bond (rM ) according to a Gaussian function with the variable being the distance from rM to the atom ri : ri′ = ri + αˆ riM exp (−

∣rM − ri ∣2 ), σ2

rîM =

ri − rM ∣ri − rM ∣

(1)

Here σ describes how far into the cluster the perturbation should be and α is how much space is created. The water molecule is aligned, such that one of the OH bonds is aligned reversely in the now stretched hydrogen bond, i.e. water will be bridging the former hydrogen bond creating two new hydrogen bonds. The water molecule is placed with the oxygen atom at the original hydrogen bond midpoint. The water molecule is aligned by rotating around the OH vector in the water molecule and the cluster. Finally, the aligned water molecule is rotated around the former hydrogen bond to have the water orientated in three different orientations (if possible by the distance requirement), otherwise it will be lowered to 2 or 1 if required. All the conformers are written to a single text file, which afterwards can be cut and given as input for an optimization. The strength of the developed approach is that it is significantly more systematic than previously applied methods such as sampling using molecular dynamics or random sampling. This allows for a more systematic identification of low lying conformations. Furthermore, the developed code can easily be extended to other atmospherically relevant nucleation precursors, such as ammonia, sulfuric acid, ect. The complete python script for performing the configurational sampling is freely available at Github. 44 The initial creation of a large set of molecular structures and optimization of these requires a sorting technique to eliminate redundant structures. An efficient parameter is the root

6


Page 7 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mean square distance (RMSD), which given two sets of coordinates A and B is: ¿ Á1 N À ∑ ∣rA − rB ∣2 RMSD = Á i N i=1 i

(2)

where N is the number of atoms in the molecules, and ri is the spacial coordinates of the i’th atom. The RMSD can be minimized by translating and rotating one set of coordinates (the other is held fixed), since the molecules are invariant under these operations. This will lead to the two molecules being superimposed, but can lead to a false RMSD value if the atoms are not ordered identically. To get around this issue we used a newly published RMSD method by Temelso et al. 45 that permutes the indices using the Kuhn-Munkers algorithm. 46,47 The developed algorithm for systematic and automated placement of water molecules can be used as a step-by-step method for adding one water molecule to an existing cluster. In each step the RMSD method can be used to locate and exclude redundant structures. Using this procedure it is possible to generate a large set of cluster conformations.

2.2

Computational Details

All geometry optimizations and vibrational frequency calculations were performed using the Gaussian09 48 program package. PM6 49 and DFT single point energies were calculated using both the Gaussian09 and Gaussian16 50 program packages. For all calculations the Gaussian09 default values were used to ensure comparability between the results. We have chosen to utilize the M06-2X, 51 PW91, 52 ωB97X-D 53 and PW6B95-D3 54 functionals as these exhibit the lowest errors compared to higher level CCSD(T) calculations for the binding energies of atmospheric relevant cluster systems. 55–57 Explicitly correlated Coupled Cluster single point energies – CCSD(T)-F12a 58–60 /VDZ-F12 61 – were calculated using MOLPRO version 2012.1. 62 The DLPNO-CCSD(T) 63,64 single point energies were calculated with ORCA version 4.0.0. 65 In the DLPNO calculations we used the same auxiliary (/C) basis sets as the orbital basis set. In the Hartree-Fock part of the DLPNO calculations, we employed Coulomb

7



Page 8 of 36

and exchange fitting with the same auxiliary (/JK) basis sets as the orbital basis set (except for aug-cc-pVDZ, where an aug-cc-pVTZ/JK was used). The cluster binding energies and cluster binding free energies were calculated as follows: ∆Ebinding = Ecluster − ∑ Emonomer,i

(3)

∆Gbinding = Gcluster − ∑ Gmonomer,i

(4)

i

i

We define the thermal contribution to the binding free energy as: ∆Gthermal,corr = ∆Gbinding − ∆Ebinding

(5)

Thermochemical parameters, were calculated using both the harmonic and quasi-harmonic approximations 66 (cutoff value of 200 cm−1 ) and unless otherwise noted were calculated at 298.15 K and 1 atm. The quasi-harmonic calculations were performed with the ”GoodVibes” python script. 67 The sampling technique outlined in section 2.1 generates a large amount of initial conformers (roughly 1000-2000) for each cluster. To narrow these further down, the structures were optimized and vibrational frequencies were calculated using the semi-empirical PM6 method. It was found that calculating the force constants for all steps in the optimization (opt=calcall), drastically reduced the chance that the calculation would terminate with an error. After the PM6 optimization a Boltzmann sorting is performed with the Gibbs free energies from PM6, where any conformer less present than 1% compared to the ground state conformer at 298.15 K and 1 atm were excluded. The remaining structures were checked in pairs if any redundancies are present, excluding structures with a RMSD < 0.718 bohr (0.38 ˚ A). This threshold was arbitrarily chosen from visual inspection of multiple structures and their RMSD. The Boltzmann and similarity sorted structures are then geometry optimized using DFT with the functional M06-2X and the basis set 6-31++G(d,p). After DFT optimization new redundancies are excluded and the obtained cluster structures were finally 8


Page 9 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


optimized and vibrational frequencies calculated at the ωB97X-D/6-31++G(d,p) level of theory. The combination of the ωB97X-D with the 6-31++G(d,p) basis set has been shown to be a sufficient level of theory for obtaining the thermal contribution of atmospherically relevant clusters. 68,69

2.3

Method Testing

To ensure that our newly developed method is efficiently able to locate global minimum cluster structures we tested the algorithm on the (H2 O)n cluster system, with n ≤ 10. The most studied systems are (H2 O)n clusters, with n ≤ 6, as the water hexamer corresponds to the smallest water cluster with a three-dimensional hydrogen-bonding network. 70–73 Using our sampling algorithm we identified 3, 3, 3, 7, 18, 65, 17, 13 and 37 conformations of the (H2 O)2−10 clusters, respectively. The obtained cluster structures at the sampling M062X/6-31++G(d,p) level of theory, were compared to the global minimum cluster structures reported by Temelso et al. 74 as depicted in Table 1. These (H2 O)2−10 cluster structures have recently been confirmed to be the lowest in binding energy using higher level explicitly correlated coupled cluster methods. 75 In addition to identifying numerous low lying free Table 1: Global minimum (H2 O)n cluster structures from the literature. 74,75 #confs corresponds to the number of conformations we obtain using our sampling method. n global min 74,75 2 2Cs 3 3UUD 4 4S4 5 5CYC 6 6PR 7 7PR1 8 8D2d 9 9D2dd 10 10PP1 17 Sphere

#confs correct global 3 ✓ 3 ✓ 3 ✓ 7 ✓ 18 ✓ 65 ✓ 17 ✓ 13 ✓ 37 ✓ 39 ×

9



energy conformers, our sampling method is also able to correctly identify the global minimum cluster conformations for all the (H2 O)n clusters, with n ≤ 10. The global minimum structure of the (H2 O)17 cluster has also received significant attention as it corresponds to the first transition from a cluster that has all the atoms at the surface to one that has a fully coordinated water molecule solvated inside the cluster. This is a very difficult sampling case, as the transition from the (H2 O)16 to the (H2 O)17 cluster is accompanied by a large molecular rearrangement of the cluster structure. Using the newly reported global minimum (Boatb) structure of the (H2 O)16 cluster by Yoo et al. 76 we ran our sampling algorithm in an attempt to capture the (H2 O)17 global minimum structure. Unfortunately, we were unable to obtain the reported global minimum structure, but was able to identify a local minimum cluster with binding free energy within 2.8 kcal/mol of the global minimum (at the M06-2X/6-31++G(d,p) level of theory). For the purpose of our current study, this deficiency does not present any issues, as we build up the (H2 SO4 )1 (H2 O)1−15 clusters in a sequential manner, and thus has explicit knowledge about several of the previous cluster structures when adding another water molecule. However, for sampling highly flexible clusters where there is a large rearrangement in the cluster structure from one minimum to another, more than a single initial guess structure will be necessary.

3 3.1

Results and Discussion (H2 SO4 )1 (H2 O)1−15 Cluster Structures

A total of 243 cluster conformations were identified for the (H2 SO4 )1 (H2 O)1−15 cluster systems at the ωB97X-D/6-31++G(d,p) level of theory. Figure 2 presents the lowest free energy cluster structures.

10


Page 10 of 36

Page 11 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(sa)1(w)1

(sa)1(w)2

(sa)1(w)3

(sa)1(w)4

(sa)1(w)5

(sa)1(w)6

(sa)1(w)7

(sa)1(w)8

(sa)1(w)9

(sa)1(w)10

(sa)1(w)11

(sa)1(w)12

(sa)1(w)13

(sa)1(w)14

(sa)1(w)15

Figure 2: Lowest free energy (H2 SO4 )1 (H2 O)1−15 cluster structures, calculated at the ωB97XD/6-31++G(d,p) level of theory. Yellow = sulfur, red = oxygen and white = hydrogen. Formed H3 O+ ions are shown with a green circle. For most of the clusters we obtain quite similar (H2 SO4 )1 (H2 O)1−6 structures as those reported previously. 19–23,77 For the different studies there are minor variations in which minima is identified as the lowest in free energy. This is to be expected as the different studies have used different methods such as PW91/6-311++G(3df,3pd), MP2/aug-cc-pVDZ

11



and in our case ωB97X-D/6-31++G(d,p). For the (H2 SO4 )1 (H2 O)1−5 clusters we do not observe a proton transfer from sulfuric acid to a water molecule in any of the global minimum structures. In all the clusters with six or more water molecules a proton transfer is observed, as indicated by the green circle in Figure 2. This observation is consistent with the study (H2 SO4 )1 (H2 O)1−6 clusters by Temelso et al., 22 where a proton transfer was only identified in the global free energy structure of the (H2 SO4 )1 (H2 O)6 cluster. As the potential energy surfaces can be very complicated, very few studies have addressed sulfuric acid - water clusters with more than six water molecules. Ding and Laasonen studied (H2 SO4 )1 (H2 O)6−9 water clusters where it was found that the fully de-protonated sulfate ion (SO2− 4 ) existed as a local free energy minimum for the clusters with 8 or 9 water molecules, but in no cases were a fully de-protonated sulfuric acid found in the lowest free energy structure. We extended the number of hydrating water molecules from 9 to 15 water molecules and in none of the global minimum clusters do we observe the SO2− 4 ion. We see the first evidence of a sulfate ion being formed as a local minumum in the (H2 SO4 )1 (H2 O)14 cluster, but the conformation is 3.9 kcal/mol higher in free energy than the identified lowest free energy conformation. In the (H2 SO4 )1 (H2 O)15 cluster a sulfate ion is formed as a local minumum, but the conformation is found to be 2.5 kcal/mol higher in free energy than the global free energy conformation.

3.2

Free Energies of the (H2 SO4 )1 (H2 O)1−15 Clusters

Figure 3 shows the calculated binding free energies of the (H2 SO4 )1 (H2 O)1−15 clusters at the ωB97X-D/6-31++G(d,p) level of theory, with the harmonic and quasi harmonic approximations (200 cm−1 cut-off). Using the larger aug-cc-pVTZ basis set it was not possible to converge all the conformers of the (H2 SO4 )1 (H2 O)14−15 clusters, hence the data have been excluded in Figure 3. Taking higher energy conformers into consideration might be an important contribution to the free energy. However, very few studies do this as identifying low lying conformers is rather difficult, due to the complicated potential energy surfaces of 12


Page 12 of 36

Page 13 of 36

hydrogen bonded molecular clusters. As our developed sampling technique generates a large set of conformers it is easy to investigate how they influence the binding free energies. The multi-conformer binding free energy (∆Gmulti-conf ) is given by: 78 −∆Gn )) RT n −∆Grel,n )) = −∆G0 − RT ln (∑ exp ( RT n

∆Gmulti-conf = −RT ln (∑ exp (

(6) (7)

Where ∆G0 is the binding free energy of the lowest free energy conformer, ∆Gn is the binding free energy of the n’th conformer and ∆Grel,n is the binding free energy of the n’th conformer relative to the lowest free energy conformer. The calculations are performed at 298.15 K and 1 atm. 0 Binding Free Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-5 -10 -15 -20 -25 -30 -35 -40 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

# water molecules Harmonic Quasi-Harmonic

multi-confs avtz

Figure 3: Calculated binding free energies of the (H2 SO4 )1 (H2 O)1−15 clusters using the harmonic approximation (⋯ ● ⋯), quasi-harmonic approximation (⋯ ● ⋯) and accounting for multiple conformers (⋯ ● ⋯) at the ωB97X-D/6-31++G(d,p) level of theory. The calculated free energies of the (H2 SO4 )1 (H2 O)1−13 clusters using the harmonic approximation (⋯ ● ⋯) at the ωB97X-D/aug-cc-pVTZ level of theory. All calculations were performed at 298.15 K and 1 atm. At the ωB97X-D/6-31++G(d,p) level of theory, the binding free energy is seen to be more 13



or less monotonically lowered as a function of the number of water molecules. Employing the quasi harmonic approximation, consistently yield higher free energies compared to the harmonic case. Using the quasi-harmonic approximation the free energy is increased by up to 4.9 kcal/mol for the largest (H2 SO4 )1 (H2 O)15 cluster. The increase in free energy due to the quasi-harmonic approximation is directly dependent on the number of water molecules, and is only found to vary from 0.3 to 0.6 kcal/mol per water molecule in the clusters. Accounting for higher energy conformers slightly lower the free energy of the clusters. The effect is found to be a lowering of the free energy by -1.2 kcal/mol or less. We have not studied the effect of anharmonicity as simple scale factors at the ωB97X-D/6-31++G(d,p) level of theory are not available. Temelso and co-workers have studied the effect of anharmonicity for pure water (H2 O)1−10 clusters 74 and (H2 SO4 )1 (H2 O)1−2 clusters. 22 In both cases, the effect of anharmonicity was found to be a lowering in the free energy by ∼0.4 kcal/mol per water molecule. The binding free energy does not yield much information by itself. A much more useful measure is the step-wise reaction free energies for adding the n′ th water molecule: ∆Gwater,add = ∆Gn − ∆Gn−1

The reaction free energies (∆Gwater,add ) are not very dependent on which of the three methods (harmonic, quasi-harmonic or accounting for multiple conformers) is used to obtain the free energy. We find reaction free energies in the range -0.6 to -3.7 kcal/mol (harmonic), -0.5 to -3.9 kcal/mol (accounting for conformers) and -0.4 to -3.9 kcal/mol (quasi-harmonic). In all cases we find that the first 1-4 water additions are the most thermodynamically favourable and the addition of water molecule 5 and 12 is found to be the least favourable. Using the larger aug-cc-pVTZ basis set yield a completely different picture of the calculated binding free energies. The first four additions of water molecules are still seen to be thermodynamically favourable, while the remaining free energies are seen to level more out.

14


Page 14 of 36

Page 15 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The slope of the free energy for the (H2 SO4 )1 (H2 O)1−4 clusters is found to be -1.5 kcal/mol with an R2 = 0.99, and slope of the free energy for the (H2 SO4 )1 (H2 O)5−13 clusters is found to be -0.5 kcal/mol with R2 = 0.81. This clearly illustrates that the first four water molecules show a much stronger interaction with sulfuric acid than the remaining water molecules. This effect can easily be understood from the structures shown in Figure 2. The first four water molecules are able to directly interact with the S-OH hydrogen bond donor and the S=O hydrogen bond acceptor groups in sulfuric acid. After the first four water molecules the sulfuric acid molecule is ”saturated” and the remaining interactions will primarily be between other water molecules. The fact that the addition of water molecule number 5 is found to be least favourable can be understood from the combination of sulfuric acid already being saturated by the first four water molecules and the fact that an H3 O+ ion is not formed as in the case of the (H2 SO4 )1 (H2 O)6−13 clusters.

3.3

Effect of Temperature on the Free Energies

At lower temperature the free energies will become more negative. Figure 4 presents the calculated binding free energies of the (H2 SO4 )1 (H2 O)1−15 clusters at 298.15 K, 278.15 K, 258.15 K, 238.15 K and 218.15 K. These temperatures represent a large range of altitudes from the atmospheric boundary layer all the way up to the tropopause. All calculations were performed at the ωB97X-D/6-31++G(d,p) level of theory using the harmonic-approximation.

15



0 Binding Free Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 36

298.15K 278.15K 258.15K 238.15K 218.15K

-10 -20 -30 -40 -50 -60 -70 -80 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

# water molecules

Figure 4: Calculated binding free energies of the (H2 SO4 )1 (H2 O)1−15 clusters using the harmonic approximation at the ωB97X-D/6-31++G(d,p) level of theory and temperatures between 218.15K and 298.15K. At 298.15 K the reaction free energy for adding the first water molecule to sulfuric acid is found to be -3.3 kcal/mol. This is lowered to -5.7 kcal/mol at 218.15 K. Lowering the temperature by 10 K leads to a ∼10 kcal/mol lowering in the binding free energy of the largest (H2 SO4 )1 (H2 O)15 cluster. The ordering of the conformations are also found to be slightly influenced by the temperature. At temperatures of 278.15 K or below the two lowest conformations switch place for the (H2 SO4 )1 (H2 O)5 , (H2 SO4 )1 (H2 O)7 , (H2 SO4 )1 (H2 O)8 and (H2 SO4 )1 (H2 O)10 clusters.

3.4

Relative Conformer Energies of the (H2 SO4 )1 (H2 O)1−9 Clusters

Compared to the thermal contribution to the free energy, the electronic binding energy is a larger source of errors when calculating cluster free energies using DFT. 56,68 Our generated set of conformers represents a good test set to assess how well approximate methods repro16


Page 17 of 36

duce the binding energies (∆Ebind ) as well as the conformer relative energies (∆Erel ). Using the ωB97X-D/6-31++G(d,p) optimized geometries we were able to calculate CCSD(T)F12a/VDZ-F12 single point energies on the (H2 SO4 )1 (H2 O)1−9 clusters. This gives a subset of a total of 139 clusters. On this test set we calculated the single point energies using the DLPNO-CCSD(T) method with the aug-cc-pVDZ (avdz) and aug-cc-pVTZ (avtz) basis sets. We also tested both the LoosePNO, NormalPNO and TightPNO settings. 79 Figure 5 shows the correlation between the calculated relative energies for the different DLPNO-CCSD(T)

4

2

0

-2

-4 -4

-2

0

2

∆Erel DLPNO (kcal/mol)


4

2

0

-2

-4

4

-4

-2

0

2

4

2

0

-2

-4

4

-4

-2

0

2

4

∆Erel F12 (kcal/mol)


Loose/avdz (R2 = 0.88)

Normal/avdz (R2 = 0.89)

Tight/avdz (R2 = 0.90)



4

2

0

-2

-4 -4

-2

0

2

4



methods plotted against the CCSD(T)-F12a/VDZ-F12 results.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

2

0

-2

-4 -4

-2

0

2

4

4

2

0

-2

-4 -4

-2

0

2

4




Loose/avtz (R2 = 0.93)

Normal/avtz (R2 = 0.99)

Tight/avtz (R2 = 0.99)

Figure 5: Correlation between the calculated relative energies (∆Erel in kcal/mol) for DLPNO-CCSD(T) using the Loose, Normal and Tight PNO settings and with the augcc-pVDZ and aug-cc-pVTZ basis sets, plotted against the CCSD(T)-F12a/VDZ-F12 results. It is seen that using an aug-cc-pVDZ basis set increasing the PNO threshold does not improve the correlation with the CCSD(T)-F12a/VDZ-F12 results. We observe a much better improvement by increasing the basis set size to aug-cc-pVTZ. For the aug-cc-pVTZ results all three PNO settings yield a good correlation with the CCSD(T)-F12a/VDZ-F12 results, but there is an especially good correlation when NormalPNO or TightPNO is used. Figure 6 shows the correlation between the calculated relative energies for the differ-

17



ent DFT methods (PW91, ωB97X-D and PW6B95-D3) plotted against the CCSD(T)F12a/VDZ-F12 results. The result using the M06-2X functional and for may-cc-pVnZ and

4

2

0

-2

-4 -4

-2

0

2



4

2

0

-2

-4

4

-4

-2

0

2

4

2

0

-2

-4

4

-4

-2

0

2

4



PW91 (R2 = 0.57)

ωB97X-D (R2 = 0.88)

PW6B95-D3 (R2 = 0.93)



4

2

0

-2

-4 -4

-2

0

2



aug-cc-pVnZ, with n = D,T are shown in the Supporting Information.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 36

4

2

0

-2

-4

4

-4

-2

0

2

4

4

2

0

-2

-4 -4

-2

0

2

4




PW91 (R2 = 0.64)

ωB97X-D (R2 = 0.95)

PW6B95-D3 (R2 = 0.97)

Figure 6: Correlation between the calculated relative energies (∆Erel in kcal/mol) for PW91, ωB97X-D, M06-2X and PW6B95-D3, plotted against the CCSD(T)-F12a/VDZ-F12 results. Top row is calculated with the 6-31++G(d,p) basis set and bottom row is calculated with the 6-311++G(3df,3pd) basis sets. In all cases there is seen a slight improvement in the correlation, when increasing the basis set size from double-zeta to triple-zeta. However, there is little difference in which type of basis set is used (i.e pople, may-cc-pVnZ or aug-cc-pVnZ). The relative energies depend much more on the choice of DFT functional than the basis set utilized. This is a very encouraging result, as it implies that sampling can safely be performed using a smaller basis set as long as an appropriate method is chosen. In general the DFT functionals perform in the following order: PW91 < M06-2X < ωB97X-D < PW6B95-D3. However, each of the four functionals is suitable to calculate the relative energies, as long as an adequate (∼3 kcal/mol) cutoff value is chosen. Comparing Figure 5 and Figure 6, it is seen that ωB97X-D and PW6B95-D3 with a triple-zeta basis set yield results similar to or better than DLPNO/avdz and LoosePNO/avtz. 18


Page 19 of 36

It should be noted that only the DLPNO-CCSD(T)/aug-cc-pVTZ level of theory using a NormalPNO setting is capable of locating all the correct CCSD(T)-F12a/VDZ-F12 global energy conformations for the (H2 SO4 )1 (H2 O)1−9 clusters. When using an aug-cc-pVTZ basis set with a LoosePNO or a TightPNO setting, a single conformation was not correctly found as the global energy minimum and the identified local minima, was found to be 0.2 and 0.1 kcal/mol higher in energy, respectively.

3.5

Binding Energies

Besides the ability to correctly assign the relative conformer energies (∆Erel ), the applicability of an approximate method is very dependent on how accurate the binding energies are. Figure 7 shows the mean absolute error (MAE) and maximum error (MaxE) in the calculated DLPNO-CCSD(T) and DFT binding energies of the (H2 SO4 )1 (H2 O)1−9 clusters relative to the CCSD(T)-F12a/VDZ-F12 calculations. 30

MAE MaxE

25

20

15

10

5

0 DLPNO(Loose)/avdz DLPNO(Loose)/avtz DLPNO(Normal)/avdz DLPNO(Normal)/avtz DLPNO(Tight)/avdz DLPNO(Tight)/avtz PW91/(d,p) PW91/mvdz PW91/avdz PW91/(3df,3pd) PW91/mvtz PW91/avtz M06-2X/(d,p) M06-2X/mvdz M06-2X/avdz M06-2X/(3df,3pd) M06-2X/mvtz M06-2X/avtz wB97X-D/(d,p) wB97X-D/mvdz wB97X-D/avdz wB97X-D/(3df,3pd) wB97X-D/mvtz wB97X-D/avtz PW6B95-D3/(d,p) PW6B95-D3/mvdz PW6B95-D3/avdz PW6B95-D3/(3df,3pd) PW6B95-D3/mvtz PW6B95-D3/avtz

Errors (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


19



Figure 7: Mean absolute errors (MAE) and maximum errors (MaxE) in the DLPNOCCSD(T) and DFT binding energies relative to CCSD(T)-F12a/VDZ-F12 results. The basis sets are abbreviated as: avnz = aug-cc-pVnZ, mvnz = may-cc-pVnZ, (d,p) = 6-31++G(d,p) and (3df,3pd) = 6-311++G(3df,3pd). The DLPNO-CCSD(T) results based on the LoosePNO setting consistently underestimate the binding energies, and yield relatively large MAEs of up to 4.2 kcal/mol. This is significantly improved using the NormalPNO setting, where a MAE as low as 0.3 kcal/mol is achieved using an aug-cc-pVTZ basis set. Interestingly, tightening the PNO criteria further deteriorates the results, increasing the MAE up to 1.6 kcal/mol. These findings are consistent with previous results 57 and indicate that DLPNO-CCSD(T)/aug-cc-pVTZ results using a NormalPNO setting yield excellent agreement with CCSD(T)-F12a/VDZ-F12 results, due to systematic cancellation of errors. It is noted that the errors at the DFT/6-31++G(d,p) level of theory are strikingly large, with a MAE ranging from 11.2 to 19.0 kcal/mol and a MaxE up to 27.1 kcal/mol. The errors originate from a consistent overestimation of the cluster binding energies compared to the CCSD(T)-F12a/VDZ-F12 results. These large errors are simply a consequence of the error being calculated over the entire test set of 139 clusters and the errors are directly proportional to cluster size. Normalizing the errors within each set of conformers by the number of water molecules yield significantly lower MAEs of 1.8-3.4 kcal/mol per water molecule. The normalized errors for all the tested levels of theory in Figure 7 are shown in the Supporting Information. For the PW91, M06-2X and ωB97X-D functionals the MAEs follow the following pattern for the basis sets: pople-n > may-cc-pVnZ > aug-cc-pVnZ, with n either being a doubleor triple-zeta basis set. The results from the PW6B95-D3 functional follow an opposite pattern for the triple zeta basis sets. The PW6B95-D3/6-311++G(3df,3pd) level of theory exhibits a low MAE of 0.2 kcal/mol compared to the CCSD(T)-F12a/VDZ-F12 reference results. These values are very similar to the values obtained at DLPNO(Normal)/avtz level of theory, where a MAE of 0.3 kcal/mol is found. However, as the errors for the PW6B95-D3 20


Page 20 of 36

Page 21 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


functional increase as the basis set size is increased to either may- or aug-cc-pVTZ, this effect can be attributed to a lucky cancellation of errors. The MAEs identified here using DFT and a 6-311++G(3df,3pd) basis set are significantly larger than the errors previously identified for a test set of 107 atmospheric molecular clusters consisting of sulfuric acid, water and bases. 56 Against a DF-LCCSD(T)-F12/VDZ-F12 reference, MAE of 2.1, 3.3 and 3.5 kcal/mol was found for the ωB97X-D, PW91 and M06-2X functionals, respectively. For the (H2 SO4 )1 (H2 O)1−9 clusters we here find MAEs of 4.0, 7.3 and 6.9 kcal/mol for the ωB97X-D, PW91 and M06-2X functionals, respectively, relative to the CCSD(T)-F12a/VDZ-F12 reference. This drastic difference most likely originates from the fact that the studied sulfuric acid - water clusters are more affected by dispersion interactions compared to sulfuric acid - base clusters that are dominated by electrostatic interactions (due to the occurrence of several proton transfers). However, as shown by the MAEs normalized to the number of water molecules (see Supporting Information), this is directly related to the size of the cluster and is thus a systematic overestimation of the binding energies. To illustrate this point, we have calculated the errors by scaling the DFT binding energies by the ratio between the DFT and CCSD(T)-F12a/VDZ-F12 results (see Figure 8).

21



2.5

MAE MaxE

2

Errors (kcal/mol)

1.5

1

0.5

PW6B95-D3/avtz

PW6B95-D3/mvtz

PW6B95-D3/(3df,3pd)

PW6B95-D3/avdz

PW6B95-D3/mvdz

PW6B95-D3/(d,p)

wB97X-D/avtz

wB97X-D/mvtz

wB97X-D/(3df,3pd)

wB97X-D/avdz

wB97X-D/mvdz

wB97X-D/(d,p)

M06-2X/avtz

M06-2X/mvtz

M06-2X/avdz

M06-2X/(3df,3pd)

M06-2X/mvdz

M06-2X/(d,p)

PW91/avtz

PW91/mvtz

PW91/(3df,3pd)

PW91/avdz

PW91/(d,p)

0 PW91/mvdz

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 36

Figure 8: Mean absolute errors (MAE) and maximum errors (MaxE) in the scaled DFT binding energies relative to CCSD(T)-F12a/VDZ-F12 results. The basis sets are abbreviated as: aug-cc-pVnZ = avnz, may-cc-pVnZ = mvnz, 6-31++G(d,p) = (d,p) and 6-311++G(3df,3pd) = (3df,3pd). The obtained scaling factors range from 0.81-1.04, depending on DFT functional and basis set utilized (see Supporting Information for the individual scaling factors). It is seen that scaling the DFT binding energies allows the MAE to be reduced to 0.7 kcal/mol or less, depending on the DFT functional and basis set. This is an encouraging result as cheap DFT methods can easily be applied to very large clusters. It should be noted that this good agreement is of course due to the scaling factor being applied to the same set of clusters as it is derived from. To investigate whether this factor can be used as a global scaling factor for sulfuric - acid water clusters, we calculated the scaled binding energies on the full set of (H2 SO4 )1 (H2 O)1−15 clusters, where CCSD(T)-F12a/VDZ-F12 results are not available for clusters with ten or more water molecules. Figure 9 shows the calculated 22


Page 23 of 36

binding energies using ωB97X-D/6-31++G(d,p) (DFT), DLPNO-CCSD(T)/aug-cc-pVTZ (DLPNO) and CCSD(T)-F12a/VDZ-F12 (F12) and the ωB97X-D/6-31++G(d,p) energies have been scaled by a factor of 0.85 (scaled DFT).

0

Binding Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


DFT DLPNO scaled DFT F12

-50

-100

-150

-200 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

# water molecules Figure 9: Calculated electronic binding energies (kcal/mol) of the lowest free energy (H2 SO4 )1 (H2 O)1−15 cluster structures using ωB97X-D/6-31++G(d,p) (DFT), DLPNOCCSD(T)/aug-cc-pVTZ (DLPNO) and CCSD(T)-F12a/VDZ-F12 (F12). Scaled DFT refers to ωB97X-D/6-31++G(d,p) binding energies that has been scaled by a factor of 0.85. Note that the F12, DLPNO and scaled DFT results are coinciding. As also indicated in Figure 7, the pure DFT binding energies are clearly overestimating the binding energies compared to F12 results. It is seen that the F12, DLPNO and scaled DFT results all agree very well for the binding energies of (H2 SO4 )1 (H2 O)1−9 clusters. For the clusters consisting of ten or more water molecules the DLPNO and scaled DFT results yield more or less identical binding energies. This suggests that both DLPNO-CCSD(T)/aug-ccpVTZ and ωB97X-D/6-31++G(d,p) scaled by a factor of 0.85 yield results in good agreement with CCSD(T)-F12a/VDZ-F12 and can safely be used to predict accurate binding energies 23



of (H2 SO4 )1 (H2 O)n clusters. This finding might be very specific to the studied system at hand and whether the derived scaling factors can be applied for other systems is unknown. However, previous results indicate that one should be careful about applying scaling factors to unknown systems. 80

4 - Conclusions We have developed a new systematic configurational sampling technique to sample hydrate cluster structures. Using the new algorithm we study sulfuric acid - water clusters with up to 15 water molecules. We find that the addition of the first four water molecules are more thermodynamically favourable than the remaining 5-15. This is caused by the fact that the sulfuric acid hydrogen bond donor and acceptor groups are ”saturated” by interactions with four water molecules. We use the generated test set of conformers to assess the performance of approximate methods (PW91, M06-2X, ωB97X-D and PW6B95-D3) in calculating the binding energies (∆Ebind ) and correctly assigning the relative energies (∆Erel ) compared to a high level CCSD(T)-F12a/VDZ-F12 reference. We find that DFT results with a double-zeta basis set exhibit good correlation with the CCSD(T)-F12a/VDZ-F12 results for the relative conformer energies. For all DFT methods we find huge errors in binding energies even when an aug-cc-pVTZ basis set is employed. These findings indicate that DFT with a small 6-31++G(d,p) basis set is suitable for initial screening purposes to narrowing down the amount of conformers and should not exclude any important low lying energy conformations as long as a suitable cutoff value is chosen. For the system studied here a cutoff value of ∼3 kcal/mol should capture all conformations. For the single point energies DLPNO-CCSD(T)/aug-cc-pVTZ appears to be the best choice for accurate binding energies in good agreement with CCSD(T)-F12a/VDZF12 results.

24


Page 24 of 36

Page 25 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


We intend to expand the newly developed algorithm such that other small molecules can be added to an existing cluster and thereby we will be able to add small inorganic and organic bases to the cluster along with pollutants such as NOx . The generated clusters will form the starting structures for investigating chemical reactions within and on the outside of the cluster.

Acknowledgement J.E thanks the Villum foundation for financial support and K.V.M. thanks University of Copenhagen for financial support. We thank the Danish e-Infrastructure Cooperation (DeiC) for computational resources.

Supporting Information Available The following is available as supporting information: • xyz-files of the (H2 SO4 )1 (H2 O)n cluster structures at the ωB97X-D/6-31++G(d,p) level of theory and the (H2 O)n clusters at the M06-2X/6-31++G(d,p) level of theory. • Correlation between relative energies of the PW91, M06-2X, ωB97X-D and PW6B95D3 functionals plotted against CCSD(T)-F12a/VDZ-F12 results. • Errors normalized to the number of water molecules. • Derived scaling factors. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Laaksonen, A.; Hamed, A.; Joutsensaari, J.; Hiltunen, L.; Cavalli, F.; Junkermann, W.; Asmi, A.; Fuzzi, S.; Facchini, M. C. Cloud Condensation Nucleus Production from

25



Nucleation Events at a Highly Polluted Region. Geophys. Res. Lett 2005, 32, DOI: 10.1029/2004GL022092. (2) Willis, M. D.; Burkart, J.; Thomas, J. L.; Kllner, F.; Schneider, J.; Bozem, H.; Hoor, P. M.; Aliabadi, A. A.; Schulz, H.; Herber, A. B. et al. Growth of Nucleation Mode Particles in the Summertime Arctic: A Case Study. Atmos. Chem. Phys. 2016, 16, 7663–7679. (3) IPCC, 2013: 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., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 1535 pp. (4) Merikanto, J. D.; 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. (5) Davidson, C. I. .; Phalen, R. F.; Solomon, P. A. Airborne Particulate Matter and Human Health: A Review. Aerosol Sci. Technol. 2005, 39, 737–749. (6) Lelieveld, J. .; Evans, J. S.; Fnais, M.; Giannadaki, D.; Pozzer, A. The Contribution of Outdoor Air Pollution Sources to Premature Mortality on a Global Scale. Nature 2015, 525, 367–371. (7) Valavanidis, A.; Fiotakis, K.; Vlachogianni, T. Airborne Particulate Matter and Human Health: Toxicological Assessment and Importance of Size and Composition of Particles for Oxidative Damage and Carcinogenic Mechanisms. J. Environ. Sci. Health C 2008, 26, 339–362. (8) Stanier, C. O.; Khlystov, A. Y.; Pandis, S. N. Nucleation Events During the Pittsburgh Air Quality Study: Description and Relation to Key Meteorological, Gas Phase, and Aerosol Parameters. Aerosol Sci. Technol. 2004, 38, 253–264. 26


Page 26 of 36

Page 27 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(9) Heal, M. R.; Kumar, P.; Harrison, R. M. Particles, Air Quality, Policy and Health. Chem. Soc. Rev. 2012, 41, 6606–6630. (10) Sipilä, M.; Berndt, T.; Petäjä, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L.; Hyvrinen, A.-P.; Lihavainen, H. et al. The Role of Sulfuric Acid in Atmospheric Nucleation. Science 2010, 327, 1243–1246. (11) Kurtén, T.; Loukonen, V.; Vehkamäki, H.; Kulmala, M. Amines are Likely to Enhance Neutral and Ion-induced Sulfuric Acid-water Nucleation in the Atmosphere More Effectively than Ammonia. Atmos. Chem. Phys. 2008, 8, 4095–4103. (12) Almeida, J.; Schobesberger, S.; K¨ urten, A.; Ortega, I. K.; Kupiainen-Määttä, 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. (13) K¨ urten, A.; Jokinen, T.; Simon, M.; Sipilä, M.; Sarnela, N.; Junninen, H.; Adamov, A.; Almeida, J.; Amorim, A.; Bianchi, F. et al. Neutral Molecular Cluster Formation of Sulfuric Acid-Dimethylamine Observed in Real Time under Atmospheric Conditions. Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 15019–15024. (14) Schobesberger, S.; Junninen, H.; Bianchi, F.; Lönn, 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. (15) 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.

27



(16) Ehn, M.; Thornton, J. A.; Kleist, E.; Sipilä, M.; Junninen, H.; Pullinen, I.; Springer, M.; Rubach, F.; Tillmann, R.; Lee, B. et al. A Large Source of Low-Volatility Secondary Organic Aerosol. Nature 2014, 506, 476–479. (17) Kirkby, J.; Curtius, J.; Almeida, J.; Dunne, E.; Duplissy, J.; Ehrhart, S.; Franchin, A.; Gagne, S.; Ickes, L.; Krten, A. et al. Role of Sulphuric Acid, Ammonia and Galactic Cosmic Rays in Atmospheric Aerosol Nucleation. Nature 2011, 476, 429 – 433. (18) Kirkby, J.; Duplissy, J.; Sengupta, K.; Frege, C.; Gordon, H.; Williamson, C.; Heinritzi, M.; Simon, M.; Yan, C.; Almeida, J. et al. Ion-Induced Nucleation of Pure Biogenic Particles. Nature 2016, 533, 521–526. (19) Bandy, A. R.; Ianni, J. C. Study of the Hydrates of H2 SO4 using Density Functional Theory. J. Phys. Chem. A 1998, 102, 6533–6539. (20) Re, S.; Osamura, Y.; Morokuma, K. Coexistence of Neutral and Ion-Pair Clusters of Hydrated Sulfuric Acid H2 SO4 (H2 O)n (n = 1 − 5) - A Molecular Orbital Study. J. Phys. Chem. A 1999, 103, 3535–3547. (21) Ianni, J. C.; Bandy, A. R. A Theoretical Study of the Hydrates of (H2 SO4 )2 and its Implications for the Formation of New Atmospheric Particles. J. Mol. Struc-THEOCHEM 2000, 497, 19–37. (22) Temelso, B.; Morrell, T. E.; Shields, R. M.; Allodi, M. A.; Wood, E. K.; Kirschner, K. N.; Castonguay, T. C.; Archer, K. A.; Shields, G. C. Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications. J. Phys. Chem. A. 2012, 116, 2209–2224. (23) Temelso, B.; Phan, T. N.; Shields, G. C. Computational Study of the Hydration of Sulfuric Acid Dimers: Implications for Acid Dissociation and Aerosol Formation. J. Phys. Chem. A. 2012, 116, 9745–9758.

28


Page 28 of 36

Page 29 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(24) Ding, G.; Laasonen, K.; Laaksonen, A. Two Sulfuric Acids in Small Water Clusters. J. Phys. Chem. A 2003, 107, 8648–8658. (25) Ding, G.; Laasonen, K. Partially and Fully Deprotonated Sulfuric Acid in H2 SO4 (H2 O)n (n = 6 − 8) Clusters. Chem. Phys. Lett. 2004, 390, 307–313. (26) Bustos, D. J.; Temelso, B.; Shields, G. C. Hydration of the Sulfuric Acid-Methylamine Complex and Implications for Aerosol Formation. J. Phys. Chem. A 2014, 118, 7430– 7441. (27) Loukonen, V.; Kurtén, T.; Ortega, I. K.; Vehkamäki, H.; Pádua, A. A. H.; Sellegri, K.; Kulmala, M. Enhancing Effect of Dimethylamine in Sulfuric Acid Nucleation in the Presence of Water - A Computational Study. Atmos. Chem. Phys. 2010, 10, 4961– 4974. (28) Nadykto, A. B.; Herb, J.; Yu, F.; Xu, Y.; Nazarenko, E. S. Estimating the Lower Limit of the Impact of Amines on Nucleation in the Earth’s Atmosphere. Entropy 2015, 17, 2764–2780. (29) Henschel, H.; Kurtén, T.; Vehkamäki, H. Computational Study on the Effect of Hydration on New Particle Formation in the Sulfuric Acid/Ammonia and Sulfuric Acid/ Dimethylamine Systems. J. Phys. Chem. A. 2016, 120, 1886–1896. (30) Olenius, T.; Halonen, R.; Kurtén, T.; Henschel, H.; Kupiainen-Mäa¨ttä, O.; Ortega, I. K.; Jen, C. N.; Vehkamäki, H.; Riipinen, I. New Particle Formation From Sulfuric Acid and Amines: Comparison of Mono-, Di-, and Trimethylamines. J. Geophys. Res. Atmos 2017, 122, doi:10.1002/2017JD026501. (31) Herb, J.; Nadykto, A. B.; Yu, F. Large Ternary Hydrogen-bonded Pre-nucleation Clusters in the Earth’s Atmosphere. Chem. Phys. Lett. 2011, 518, 7–14.

29



(32) Nadykto, A. B.; Yu, F.; Jakovleva, M. V.; Herb, J.; Xu, Y. Amines in the Earth’s Atmosphere: A Density Functional Theory Study of the Thermochemistry of PreNucleation Clusters. Entropy 2011, 13, 554–569. (33) Nadykto, A. B.; Herb, J.; Yu, F.; Xu, Y. Enhancement in the Production of Nucleating Clusters due to Dimethylamine and Large Uncertainties in the Thermochemistry of Amine-Enhanced Nucleation. Chem. Phys. Lett. 2014, 609, 42–49. (34) Shields, R. M.; Temelso, B.; Archer, K. A.; Morrell, T. E.; Shields, G. C. Accurate Predictions of Water Cluster Formation, (H2O)n=2-10. J. Phys. Chem. A. 2010, 114, 11725–11737. (35) Husar, D. E.; Temelso, B.; Ashworth, A. L.; Shields, G. C. Hydration of the Bisulfate Ion: Atmospheric Implications. J. Phys. Chem. A. 2012, 116, 5151–5163. (36) Jiang, S.; Liu, Y.-R.; Huang, T.; Wen, H.; Xu, K.-M.; Zhao, W.-X.; Zhang, W.-J.; Huang, W. Study of Cl-(H2O)n(n= 1-4) using Basin-hopping Method Coupled with Density Functional Theory. J. Comp. Chem. 2013, 35, 159–165. (37) Peng, X.-Q.; Liu, Y.-R.; Huang, T.; Jiang, S.; Huang, W. Interaction of Gas Phase Oxalic Acid with Ammonia and its Atmospheric Implications. Phys. Chem. Chem. Phys. 2015, 17, 9552–9563. (38) Miao, S.-K.; Jiang, S.; Chen, J.; Ma, Y.; Zhu, Y.-P.; Wen, Y.; Zhang, M.-M.; Huang, W. Hydration of a Sulfuric Acid-oxalic Acid Complex: Acid Dissociation and its Atmospheric Implication. RSC Adv. 2015, 5, 48638–48646. (39) Chen, J.; Jiang, S.; Liu, Y.-R.; Huang, T.; Wang, C.-Y.; Miao, S.-K.; Wang, Z.-Q.; Zhang, Y.; Huang, W. Interaction of Oxalic Acid with Dimethylamine and its Atmospheric Implications. RSC Adv. 2017, 7, 6374–6388.

30


Page 30 of 36

Page 31 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(40) Elm, J.; Bilde, M.; Mikkelsen, K. V. Influence of Nucleation Precursors on the Reaction Kinetics of Methanol with the OH Radical. J. Phys. Chem. A 2013, 117, 6695–6701. (41) Elm, J.; Fard, M.; Bilde, M.; Mikkelsen, K. V. Interaction of Glycine with Common Atmospheric Nucleation Precursors. J. Phys. Chem. A 2013, 117, 12990–12997. (42) Elm, J.; Kurtén, T.; Bilde, M.; Mikkelsen, K. V. Molecular Interaction of Pinic Acid with Sulfuric Acid - Exploring the Thermodynamic Landscape of Cluster Growth. J. Phys. Chem. A 2014, 118, 7892–7900. ´ Measurement of Areas on a Sphere Using Fibonacci and Lati(43) González, A. tude–Longitude Lattices. Mathematical Geosciences 2009, 42, 49–64. (44) GitHub: https://github.com/JensVK/molecule adding. (45) Temelso, B.; Mabey, J. M.; Kubota, T.; Appiah-Padi, N.; Shields, G. C. ArbAlign: A Tool for Optimal Alignment of Arbitrarily Ordered Isomers Using the Kuhn–Munkres Algorithm. J. Chem. Inf. Model. 2017, 57, 1045–1054. (46) Kuhn, H. W. The Hungarian Method for the Assignment Problem. Naval Research Logistics Quarterly 1955, 2, 83–97. (47) Munkres, J. Algorithms for the Assignment and Transportation Problems. Journal of the Society for Industrial and Applied Mathematics 1957, 5, 32–38. (48) Gaussian 09, Revision E.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, et al., Gaussian, Inc., Wallingford CT, 2013. (49) Stewart, J. J. P. Optimization of Parameters for Semiempirical Methods. V. Modification of NDDO Approximations and Application to 70 Elements. J. Molec. Modeling 2007, 13, 1173–1213.

31



(50) Gaussian 16, Revision A.03, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, et al., Gaussian, Inc., Wallingford CT, 2016. (51) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 other Functionals. Theor. Chem. Account. 2008, 120, 215–241. (52) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules, Solids and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B. 1992, 46, 6671–6687. (53) Chai, J.-D.; Head-Gordon, M. Long-range Corrected Hybrid Density Functionals with Damped Atom-atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615– 6620. (54) Zhao, Y.; Truhlar, D. G. Design of Density Functionals That Are Broadly Accurate for Thermochemistry, Thermochemical Kinetics, and Nonbonded Interactions. J. Phys. Chem. A 2005, 109, 5656–5667. (55) Leverentz, H. R.; Siepmann, J. I.; Truhlar, D. G.; Loukonen, V.; Vehkamäki, H. Energetics of Atmospherically Implicated Clusters Made of Sulfuric Acid, Ammonia, and Dimethyl Amine. J. Phys. Chem. A 2013, 117, 3819–3825. (56) Elm, J.; Bilde, M.; Mikkelsen, K. V. Assessment of Binding Energies of Atmopsheric Clusters. Phys. Chem. Chem. Phys 2013, 15, 16442–16445. (57) Elm, J.; Kristensen, K. Basis Set Convergence of the Binding Energies of Strongly Hydrogen-Bonded Atmospheric Clusters. Phys. Chem. Chem. Phys 2017, 19, 1122– 1133. 32


Page 32 of 36

Page 33 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(58) Werner, H.; Adler, T. B.; Manby, F. R. General Orbital Invariant MP2-F12 Theory. J. Chem. Phys. 2007, 126, 164102. (59) Adler, T. B.; Knizia, G.; Werner, H. A Simple and Efficient CCSD(T)-F12 Approximation. J. Chem. Phys. 2007, 127, 221106. (60) Knizia, G.; Adler, T. B.; Werner, H. Simplified CCSD(T)-F12 Methods: Theory and Benchmarks. J. Chem. Phys. 2009, 130, 054104. (61) Peterson, K. A.; Adler, T. B.; Werner, H. Systematically Convergent Basis Sets for Explicitly Correlated Wavefunctions: The Atoms H, He, B-Ne, and Al-Ar. J. Chem. Phys. 2008, 128, 084102. (62) MOLPRO, version 2012.1, a package of ab initio programs, Werner H.-J. , Knowles P. J., Knizia G., Manby F. R., Sch¨ utz M., Celani P., Korona T., Lindh R., Mitrushenkov A., Rauhut G. et al. , see http://www.molpro.net. (63) Riplinger, C.; Neese, F. An Efficient and Near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138, 034106. (64) Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. Natural Triple Excitations in Local Coupled Cluster Calculations with Pair Natural Orbitals. J. Chem. Phys. 2013, 139, 134101. (65) Neese F., WIREs Comput Mol Sci 2012, 2: 73-78 doi: 10.1002/wcms.81. (66) Grimme, S. Supramolecular Binding Thermodynamics by Dispersion-corrected Density Functional Theory. Chem. Eur. J. 2012, 18, 9955–9964. (67) I.

Funes-Ardois,

R.

Paton,

GoodVibes:

GoodVibes

v1.0.1,

2016,

doi:http://dx.doi.org/10.5281/zenodo.60811. (68) Elm, J.; Mikkelsen, K. V. Computational Approaches for Efficiently Modelling of Small Atmospheric Clusters. Chem. Phys. Lett. 2014, 615, 26–29. 33



(69) Myllys, N.; Elm, J.; Kurtén, T. Density Functional Theory Basis Set Convergence of Sulfuric Acid-Containing Molecular Clusters. Comp. Theor. Chem. 2016, 1098, 1–12. (70) Pérez, C.; Muckle, M. T.; Zaleski, D. P.; Seifert, N. A.; Temelso, B.; Shields, G. C.; Kisiel, Z.; Pate, B. H. Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy. Science 2012, 336, 897–901. (71) Xantheas, S. S.; Dunning, T. H. AbInitio Studies of Cyclic Water Clusters (H2 O)n, n = 1-6. I. Optimal Structures and Vibrational Spectra. J. Chem. Phys. 1993, 99, 8774–8792. (72) Xantheas, S. S. AbInitio Studies of Cyclic Water Clusters (H2 O)n, n = 1-6. II. Analysis of Many-body Interactions. J. Chem. Phys. 1994, 100, 7523–7534. (73) Xantheas, S. S. AbInitio Studies of Cyclic Water Clusters (H2 O)n, n = 1-6. III. Comparison of Density Functional with MP2 Results. J. Chem. Phys. 1995, 102, 4505–4517. (74) Temelso, B.; Archer, K. A.; Shields, G. C. Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections. J. Phys. Chem. A. 2011, 115, 12034–12046. (75) Manna, D.; Kesharwani, M. K.; Sylvetsky, N.; Martin, J. M. L. Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets. J. Chem. Theory Comput. 2017, 13, 3136–3152. (76) S.Yoo,; Aprá, E.; Zeng, X. C.; ; Xantheas, S. S. High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H2 O)16 and (H2 O)17 : A New Global Minimum for (H2 O)16 . J. Phys. Chem. Lett. 2010, 1, 3122–3127. (77) Arrouvel, C.; Viossat, V.; Minot, C. Theoretical Study of Hydrated Sulfuric Acid: Clusters and Periodic Modeling. J. Mol. Struct.: THEOCHEM 2005, 718, 71–76.

34


Page 34 of 36

Page 35 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(78) Partanen, L.; Vehkamäki, H.; K. Hansen, H. H., J. Elm; Kurtén, T.; Halonen, R.; Zapadinsky, E. Effect of Conformers on Free Energies of Atmospheric Complexes. J. Phys. Chem. A 2016, 120, 8613–8624. (79) Liakos, D. G.; Sparta, M.; Kesharwani, M. K.; Martin, J. M. L.; Neese, F. Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory. J. Chem. Theory. Comput. 2015, 11, 1525–1539. (80) Myllys, N.; Elm, J.; Halonen, R.; Kurtén, T.; Vehkamäki, H. Coupled Cluster Evaluation of the Stability of Atmospheric Acid-Base Clusters with up to 10 Molecules. J. Phys. Chem. A 2016, 120, 621–630.

35



Graphical TOC Entry + sulfuric acid

15 water

36


Page 36 of 36

Hydration of Atmospheric Molecular Clusters: Systematic

Recommend Documents