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A First-Principles Study of Molecular Clusters Formed by Nitric Acid and Ammonia Jinfei Ling, Xun-Lei Ding, Zhenyu Li, and Jinlong Yang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09185 • Publication Date (Web): 01 Jan 2017 Downloaded from http://pubs.acs.org on January 6, 2017

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The Journal of Physical Chemistry

A First-Principles Study of Molecular Clusters Formed by Nitric Acid and Ammonia Jinfei Ling,a Xunlei Ding,b* Zhenyu Li,a* and Jinlong Yanga a

Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China b

Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, P. R. China

ABSTRACT: Molecular clusters formed by m nitric acid molecules and n ammonia molecules are studied with density functional theory. For smaller clusters with m, n ≤ 4, all possible combinations of m and n are considered, while for larger clusters in the 5 ≤ m, n ≤ 8 range we only consider the possibilities with |m - n| ≤ 1. Hydrogen bond network formation is an important stabilization mechanism in these clusters. At the same time, proton transfer is generally preferred except in the smallest clusters. Nitric acid and ammonia evaporation rates of these clusters are calculated with both collision activation barriers and reaction thermodynamics explicitly considered. However, unlike in the case of cluster growth from sulfuric acid and ammonia, activation barriers do not play an important role here. If m and n are unequal, evaporation of the abundant species is always preferred. For clusters with m = n > 2, ammonia evaporation is faster than nitric acid. Stabilities of all clusters can be quantitatively evaluated by the evaporation rate of the preferred species. Larger clusters are generally more stable. However, exceptions can occur at structure motif transition point. Deviation from the stoichiometry of m = n significantly lowers the cluster stability. For a cluster pair formed by the same number of molecules, the nitric acid abundant one is more stable, which determines the growth pathway of these clusters.

INTRODUCTION Suspended particles in the atmosphere have important impacts on both climate and weather by modulating radiative forcing and hydrological fluxes.1 Origins of these particles include both primary emissions and new particle formation from gaseous precursors.2 The latter process is very complicated,3 and an intense research effort has been devoted to investigate the nucleation and growth of atmospheric particulate matter.4 While molecules participating in particle nucleation and growth can vary with climatic conditions and geographic locations,5 it is well known that sulfuric acid is a main precursor species.6, 7 At the same time, participation of ammonia can significantly enhance the nucleation of sulfuric acid molecules.8 Ammonia molecules are widely existed in the atmosphere due to agricultural fertilizer, livestock production, biomass burning emissions, and etc.9-11 Besides sulfuric acid, ammonia can also react with nitric acid, the final product of the NO oxidation processes involved in photochemical smog formation.12 The generated ammonium nitrate is an important component of PM 2.5 particle.13 It is believed that ammonium nitrate makes a significant contribution to radiative forcing and global climate consequently by directly changing aerosols optical properties14, 15 and indirectly changing cloud properties and lifetime.16-18 Ammonium nitrate can effectively neutralize acidic aerosol and in return affect the rates of some pivotal chemical reactions.19, 20 Reaction between nitric acid and ammonia is also an important part of the atmospheric nitrogen cycle.21 At the same time, reaction between nitric acid and ammonia and its reverse reaction are also an important topic in high-energy material and public security. Ammonium nitrate has been widely used as fertilizers and explosives, and it is also a promising rocket propellant oxidizer. Solid state

ammonium nitrate has several phases and phase transition can be observed at different pressure and temperature.22, 23 It can thermally decompose and generate gas phase products including ammonia and nitric acid.24 Confinement or contamination can significantly change its explosive sensitivity23, 25, 26 and many ammonium nitrate accidents have occurred over the years. Therefore, it is important to study the vaporization and decomposition of NH4NO3.27 As an important topic, the interaction/reaction of nitric acid and ammonia has also been studied theoretically. Studies of the interaction between single HNO3 and NH3 date back to 1980,28 in the context of strong hydrogen bond.29 Then, it is pointed out that water29-32 or electric field33, 34 can facilitate proton transfer between single nitric acid and ammonia. For clusters with two or more nitric acid and ammonia pairs, proton transfer does stabilize the system.33-35 Properties of different phases of ammonium nitrate solid have also been studied.36, 37 Different phases can be stabilized by changing the temperature and pressure.36, 38-40 At the same time, decomposition channels of ammonium nitrate at high temperature are explored with either quantum chemistry24 or reactive force field.37, 41 To obtain new insights in their growth and evaporation mechanisms, a systematic study of properties of molecular clusters formed by nitric acid and ammonia is very desirable. In this article, we investigate clusters formed by m nitric acid molecules and n ammonia molecules (m, n ≤ 4 or 5 ≤ m, n ≤ 8 with |m-n| ≤ 1) using quantum chemistry method. With Gibbs free energies of formation (ΔG) obtained, an evaluation of molecular uptake coefficient by calculating the collision activation barrier (ΔG‡) leads to an estimation of the nitric acid and ammonia evaporation rates of these clusters, which reflect their stabilities. These results provide useful

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insights to understand the growth pathway of molecular clusters formed by nitric acid and ammonia.

THEORETICAL METHODS

3

6𝑘𝑇

4𝜋

𝑚𝑖

+

6𝑘𝑇 1/2 ) ([𝑉𝑖 ]1/3 𝑚𝑗

where mi and mj are the masses of i and j, Vi and Vj are their respective volumes. An estimation of the uptake coefficient α can be obtained from the activation barrier ΔG‡: −∆𝐺≠

Quantum chemical calculations. Density functional theory (DFT) implemented in the Gaussian 09 package42 was used in geometry optimization and electronic structure calculations. To properly describe intra- and inter- molecular interactions arising from non-overlapping electron densities,43 a dispersion energy correction was added to the hybrid B3LYP exchange correlation functional via the DFT-D3 model.44 The 6-311++G(d,p) basis set was used to express molecular orbitals, and the associated basis set superposition error (BSSE) is expected to be small.30 Previous studies indicate that smaller basis sets, such as 6-31+G(d), overestimates the magnitude of the columbic interactions which leads to artificial proton transfer.35 Test calculations at the MP2/augcc-pVDZ level of theory give similar results as we obtained in this study using the current method (Figure S1 in Supporting Information). Transition-state (TS) optimizations were performed by using the Berny algorithm.45 Vibrational frequencies were calculated to make sure that each reaction intermediates has zero imaginary frequency while each TS has one and only one imaginary frequency. Intrinsic reaction coordinate (IRC) calculations46 were used to confirm that each TS connects two appropriate local minima in the reaction pathways. Activation barriers were then computed as the difference in Gibbs free energy between the reactant cluster and the optimized TS structure. Gibbs free energies were calculated at 298.15 K and 101.3 kPa. Formation energy ∆E and Gibbs free energy of formation ∆G are defined as the energy/free energy of clusters referring to the energy/free energy of individual nitric acid and ammonia molecules which form the clusters. Structure searching. In geometry optimization, the final structure obtained can be very sensitive to the structure of the initial guess. In order to find the ground state structure of each cluster, we randomly generated as many as possible initial structures. Redundant similar structures were discarded before being used for geometry optimizations at the semi-empirical PM647 level of theory. Optimized structures with the lowest PM6 energies were saved for more accurate DFT-D3 geometry optimization. A typical run generates 1,000 conﬁgurations and saves 10. Several runs were conducted until no new low energy structure can be found. Such a kind of random structure searching method has been widely used in studies of structures of solids, surfaces, and clusters,48 especially in molecular clusters49-51. Reliable ground state structures are expected to be obtained for small clusters based on structure searching method described above. For larger clusters (5 ≤ m, n ≤ 8), the artificial bee colony algorithm52, 53 was used to speed up global optimization. Evaporation rate calculation. Evaporation rates of nitric acid or ammonia from molecular clusters were calculated by considering the detailed balance in the i + j reactions,54 where i or j can be either single molecules or molecular clusters. In equilibrium, evaporation rate is equal to the cluster formation rate: 𝛾𝐶𝑖+𝑗 = 𝛼𝛽𝑖𝑗 𝐶𝑖 𝐶𝑗 (1) where γ is the evaporation rate of i or j from i+j, βij is the collision rate of i with j, and α is the corresponding uptake coefficient which gives the probability that the collision finally results in an i + j reaction. The collision rate βij can be determined from kinetic gas theory as:55 𝛽𝑖𝑗 = ( )1/6 (

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1/3 2

+ [𝑉𝑗 ]

)

(2)

𝛼 = 𝑒 𝑘𝑇 (3) Concentrations Ci+j, Ci, and Cj are related by the equilibrium constant: 𝐾=

𝐶𝑖+𝑗 𝐶𝑖 𝐶𝑗

=

𝑘𝐵 𝑇 𝑃𝑟𝑒𝑓

𝑒𝑥𝑝⁡(

−∆𝐺𝑟𝑒𝑎 𝑘𝐵 𝑇

)

(4)

where Pref is the reference pressure and ∆Grea is the Gibbs free energy of the i + j reaction. Combining equations above, we can get an expression for the evaporation rate of i or j from the cluster i+j: ⁡𝛾 = ⁡𝛼𝛽𝑖𝑗

𝑃𝑟𝑒𝑓 𝑘𝐵 𝑇

𝑒𝑥𝑝⁡(

∆𝐺𝑖+𝑗 −∆𝐺𝑖 −∆𝐺𝑗 𝑘𝐵 𝑇

)

(5)

where ∆Gi+j, ∆Gi and ∆Gj are the Gibbs free energies of formation of clusters i+j, i, and j at the reference pressure of 101.3 kPa. In this study, either i or j is monomer and the corresponding ∆Gi or ∆Gj then equals to zero.

RESULTS AND DISCUSSION 1. Geometry structures and energetics Stable structures with the lowest Gibbs free energy of formation are identified for all clusters. We use m-n to represent the cluster formed by m nitric acid molecules and n ammonia molecules to avoid explicitly specifying the proton transfer status. Ring structures are generally preferred for homogeneous clusters (Figure 1). From dimer (0-2) to tetramer (0-4), ammonia clusters are all bound by N-H...N hydrogen bonds. A closed ring is formed with two hydrogen bonds in nitric acid cluster 2-0. Both 3-0 and 4-0 form hydrogen bond connected ring as well. The 3-0 ring is twisty while the 2-0 and 4-0 ring have a quasi-planar structure.

Figure 1. Optimized stable structures of single-species clusters. Red, blue, and white spheres represent oxygen, nitrogen, and hydrogen atoms, respectively. Dashed lines indicate formation of hydrogen bonds. In the smallest heterogeneous cluster with one nitric acid molecule and one ammonia molecule (1-1), the system is stabilized by hydrogen bond and there is no proton transfer, agreeing well with previous results.31, 34, 35 When the cluster size increases, proton transfer becomes favorable. For example, in the 2-2 cluster, protons in both nitric acid molecules transfer to ammonia molecules, forming a cluster with C2h point group symmetry (Figure 2).34, 35 As shown in Tables 1 and 2, both formation energy and Gibbs free energy of formation of 2-2 are significantly larger than double of their 1-1 values. From the proton transfer point of view, 1-2 and 2-1 clusters are the intermediate cases. No proton transfer is found in the 1-2 cluster.35 Consistently, when scanning the O-H bond length, we find that proton transfer is unfavorable (Figure 3). The calculated free energy of the proton transferred structure is also higher than the structure without proton transfer. In the case of 2-1, after conquering a negligible energy barrier,


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proton transfer lowers the energy by about 5 kJ/mol. As a result, the proton-transferred structure has been reported as the ground state of 2-1.35 However, if we compare the free energy, we find that the structure without proton transfer is more stable at a finite temperature. Therefore, proton transfer does not occur in 2-1. In these two intermediate cases, we have observed an elongated O-H bond (rO-H = 0.972 Å in free nitric acid monomer, 1.026 Å in 1-1, 1.068 Å in 1-2 and 1.098 Å in 2-1). We also notice that, although the formation energy of 1-2 is much lower than that of 1-1 (Table 1), the Gibbs free energy of formation of 1-1 is lower than 1-2 at the room temperature (Table 2). Therefore, to reliably describe the relative stabilities of these molecular clusters, it is important to calculate the free energy in addition to the internal energy.

that the strength of hydrogen bonds in these clusters can be very different. The 3-3 cluster also has complete proton transfer. To form a better hydrogen bond network, a three dimensional structure is formed. Three ammonium groups and two nitrate groups form a cage, and the last nitrate group is anchored to the cage by one of its oxygen atoms forming two hydrogen bonds with two adjacent ammonium groups. Compared to the quasi-planar structure reported previously,33 the structure found by us is more compact and its Gibbs free energy of formation is 1.34 kJ/mol lower. The structure of 3-4 is based on 3-3, with an ammonia molecule added and three additional hydrogen bonds formed. The ground state structure of 4-3 is very different from 3-3. The 4-4 cluster, with a cage structure, is also completely proton transferred. One oxygen atom in a nitrate group is pointing to the center of the cluster. Such a compact structure with the same number of hydrogen bonds as in a previous result33 has a larger Gibbs free energy of formation (-223.46 versus -218.12 kJ/mol). If the D3 dispersion correction is discarded, the present structure becomes 4.02 kJ/mol less stable than the previous structure. Therefore, a proper description of weak interactions is important in studies of such molecular clusters. Table 1. Formation energies ∆E (kJ/mol) of different clusters (m, n ≤ 4). Row and column indices indicate m (nitric acid) and n (ammonia), respectively. ∆E

Figure 2. Optimized stable structures of heterogeneous molecular clusters (1 ≤ m, n ≤ 4). Red, blue, and white spheres represent oxygen, nitrogen, and hydrogen atoms, respectively. Dashed lines indicate formation of hydrogen bonds.

0

1

2

3

4

0 1 2

-0.00 -45.94

0.00 -66.77 -114.11

-17.17 -106.68 -217.50

-55.52 -154.97 -285.29

-88.04 -208.23 -352.21

3 4

-78.32 -125.24

-188.10 -256.65

-290.34 -361.00

-386.37 -477.19

-453.48 -611.14

Table 2. Gibbs free energies of formation ∆G (kJ/mol) of different clusters (m, n ≤ 4) at temperature of 298.15 K and pressure of 101.3 kPa. Row and column indices indicate m (nitric acid) and n (ammonia), respectively. ΔG 0 1 2 3 4

Figure 3. Relative energy of the 1-2 and 2-1 clusters with the structure optimized at a fixed O-H bond length rO-H. Energy of the first scan point is set to zero. The ground state structure of 2-3 is based on 2-2, with an additional ammonia molecule binding to the two nitrate groups via hydrogen bonds. Similarly, the structure of 3-2 can be obtained by adding a nitric acid molecule to 2-2. In 2-3 and 3-2 clusters, with three and two additional hydrogen bonds formed respectively, the change of formation energy compared to 2-2 is comparable to the formation energy of 11, where only one hydrogen bond exist. This result indicates

0

1

2

3

4

0.00 -0.64 16.68 11.71

0.00 -21.79 -25.30 -38.55 -54.99

14.51 -19.38 -59.90 -83.06 -103.06

29.99 -13.48 -77.35 -121.57 -149.67

33.45 -15.11 -92.90 -137.58 -223.46

When the number of nitric acid molecules is much larger than the number of ammonia molecules, branched structure can be formed. In the 3-1 cluster, aside of the central ammonium nitrate which formed via proton transfer there are two nitric acid molecules. This structure can be formed by appending an acid molecule to the 2-1 cluster, which induces a proton transfer there. If an additional nitric acid molecules is added on top of the central ammonium nitrate, we obtain the 4-1 cluster with a three-branch structure. The 4-2 cluster can be obtained by substituting one nitric acid molecule in the 4-1 cluster by an ammonium nitrate ion pair. The structure of 1-3 and 1-4 clusters can be considered as a hydrogen-bonded ammonia chain surrounding a nitric acid molecule, with a proton transfer from the nitric acid to one of the ammonia molecules. Structure of the 2-4 cluster is very different from the 1-4 cluster. It can be considered as two



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ammonia molecules added to the 2-2 cluster, which enclose the bilayer cage. We also consider larger clusters 5-5, 6-6, 7-7, and 8-8. Their formation energies and Gibbs free energies of formation are listed in Table 3. In all these four clusters, complete proton transfer from nitric acid to ammonia is observed, forming NH4+ and NO3- ions. As shown in Figure 4, the 5-5 cluster looks like a bowl supporting a slanting NO3- ion, which forms five hydrogen bonds with five NH4+ ions. In 6-6, a NO3- is encapsulated in a cage formed by other ions. The encapsulated NO3- is not exactly in the center of the cage. Actually, one of its O atom forms two hydrogen bonds with two neighboring NH4+ ions, while the other two O atoms are dangling inside the cage. Cluster 7-7 also has a NO3-encapsulated cage structure. The central NO3- is surrounded by four other NO3- ions at the equator, on top and at the bottom of which are two caps. The top cap is formed by one NO3- ion on top of three NH4+ ions, while the bottom cap is formed by one NO3- ion below four NH4+ ions. The 8-8 cluster also has a closed-shell structure with one NO3- trapped inside. The three O atoms in the encapsulated NO3- form 2, 1, and 0 hydrogen bonds with the cage, respectively. We have also studied some clusters with m = n ± 1. Their structures and energetics can be found in Supporting Information. Table 3. Formation energies ∆E (kJ/mol) and Gibbs free energies of formation ∆G (kJ/mol) of larger clusters (5-5, 6-6, 7-7, and 88). kJ/mol

5-5

6-6

7-7

8-8

△E

-770.77

-998.16

-1201.01

-1356.67

△G

-273.18

-376.58

-468.17

-519.37

Figure 4. Optimized stable structures of clusters 5-5, 6-6, 7-7, and 8-8. Red, blue, and white spheres represent oxygen, nitrogen, and hydrogen atoms, respectively. Dashed lines indicate formation of hydrogen bonds.

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2. Nitric acid and ammonia uptake by molecular clusters In the growth of aerosol particle, uptake of gas-phase molecules by clusters or small particles are usually considered to be determined by the collision rate from the kinetic gas theory assuming a sticking factor of unity.56 However, both recent theoretical57 and experimental58 studies suggest that activation barriers may exist in the incorporation of ammonia into small sulfuric acid based clusters. To take this effect into consideration, we investigate the combination pathways for single ammonia or nitric acid molecule adding to a preexisting cluster. For the combination of single ammonia and nitric acid molecules, since no bond breaking is involved, no activation barrier is expected. A barrierless uptake process is also observed in ammonia or nitric acid addition to 1-1 to form 12 or 2-1, respectively. In more complicated processes, activation barriers do exist (Table 4). For example, there is a barrier of 4.59 kJ/mol in the reaction pathway of adding an ammonia molecule to the 4-3 cluster to form 4-4 (Figure 5). As an NH3 molecule approaching to the 4-3 cluster, it spontaneously reaches a potential well to form a reactant complex (RC),59 accompanying with a proton transfer from the cluster to ammonia. In RC, the formed ammonium ion begins to interact with two oxygen atoms in 4-3. However, in the final 4-4 structure, three additional hydrogen bonds will formed. Therefore, a rotation of this ammonium ion is required to form the final 4-4 cluster, which brings an activation barrier. Structure rearrangement is a common reason to produce an activation free energy barrier during cluster formation. In some cases, the structure rearrangement can be very complicated and more than one barriers are involved in the reaction pathway. One of such examples is the addition of a nitric acid molecule to the 1-4 cluster (Figure 6). As HNO3 attaching to 1-4, structural optimization leads to nitric acid deprotonation in RC. Transition state TS1 corresponds to the fracture of one hydrogen bond and formation of new hydrogen bond associated with a 3.95 kJ/mol activation barrier. After that, an intermediate state (IS) is formed. Then, an ammonium group and an ammonia molecule in IS make a proton exchange by passing through transition state TS2 and conquer a 3.05 kJ/mol activation barrier. Therefore, a barrier may also be encountered in proton transfer. With activation barriers calculated, uptake coefficient can be calculated using equation (3). However, in all cases when they exist, activation barriers come from structure rearrangement and proton transfer after RC is formed. Formation of the pre-association RC always has a large free energy gain without an activation barrier. Therefore, the effective activation barrier of the whole uptake process is still zero,59 and the corresponding uptake coefficient is one. Based on results for small clusters listed in Table 4, we set the uptake coefficient for larger clusters also to be one.

Table 4. Activation Free energy barrier ∆G≠(kJ/mol) in the formation of m-n (1 ≤ m, n ≤ 4 ) clusters by adding a nitric acid molecule or an ammonia molecule from a corresponding smaller cluster. Row and column indices indicate m (nitric acid) and n (ammonia), respectively. ΔG 1 2 3 4

1 HNO3 0 0 0 0

2 NH3 0 0 0 11.36

HNO3 0 0 0 0

3 NH3 0 0 6.79 5.44

HNO3 0 0 0 9.71


4 NH3 0 0 5.51 10.14

HNO3 0 3.95 0 0

NH3 0 0 0 4.59

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The Journal of Physical Chemistry (Figure 7) represents the stabilities of the cluster. According to our results, molecular clusters formed by nitric acid and ammonia molecules are generally less stable than those from sulfuric acid and ammonia54 due to their weaker ability to form hydrogen bond and higher uptake capacity to nucleate and grow to larger size. From 1-1 to 4-4, the evaporation rate decreases monotonously from ~106 to ~10-3. However, it jumps to ~103 at 5-5. Then, it start to decrease monotonously to ~10-5 for 88. The general trend is that larger clusters are more stable. To understand the exceptional jump at 5-5, we should check the structure evolution in these clusters. For smaller clusters, a shell structure is developed from 1-1 to 4-4. Larger clusters (66, 7-7, and 8-8) have an encapsulated shell structure. 5-5 is the transition point, where the central NO3- ion already exist while other ions cannot form a complete cage, which finally leads to a NO3--in-a-bowl structure. Such a structure motif transition induces a sudden change of stabilities which is reflected by the jump of the evaporation rate. We expect similar jumps will be observed if even larger clusters are studied, at, for example, the transition point form one- to twoion encapsulation. In all m = n clusters studied here, evaporation of ammonia is easier than nitric acid. Cluster with m = n is more stable than other clusters with similar sizes. For example, 2-1 (1-2) have an evaporation rate at the orders of 109 (1010), which is 3 (4) orders of magnitude larger than 1-1. Therefore, 1-1 is more stable than 1-2 and 2-1. Notice that this is not the case for molecular clusters formed by sulfuric acid and ammonia, where, for example, cluster with 2 sulfuric acid and 1 ammonia molecules is even more stable than cluster with 1 sulfuric acid and 1 ammonia molecules.54 For small clusters with m>n, evaporation of nitric acid is easier than ammonia (red in Figure 7). For those with mn) is one or two orders of magnitude smaller than n-m. For 3-1 and 1-3, the difference is even on the order of 104. Such an exceptionally big difference is originated from the fact that 1-3 cluster is relatively unstable. In fact, as listed in Table 2, the Gibbs free energy of formation of 1-3 is higher than its neighbors 1-2 and 1-4. The atomistic mechanism may be that two O…H-N bonds share an O atom in 1-3.

Figure 5. Reaction pathway of NH3 addition to the 4-3 cluster.

Figure 6. Reaction pathway of HNO3 addition to the 1-4 cluster.

3. Evaporation rate and overall stability With the Gibbs free energies of m-n cluster calculated, the free energy change for reactions (HNO3)m(NH3)n-1+NH3 → (HNO3)m(NH3)n and (HNO3)m-1(NH3)n+HNO3 → (HNO3)m(NH3)n can be easily obtained. Then, monomer evaporation rates for each m-n clusters is calculated according to equation (5), as listed in Table 5. Evaporation of nitric acid and/or ammonia monomer is expected to be the main decay channel of molecular clusters studied here. Therefore, the larger one of the nitric acid and ammonia evaporation rates

Table 5. Evaporation rates γ (s−1) for different clusters. Row and column indices indicate m (nitric acid) and n (ammonia), respectively.

1

γ(m,n) HNO3

2 NH3

6

3

HNO3 6

NH3 4

HNO3 10

NH3 2

1

1.86× 10

1.86× 10

1.33× 10

2

2.95× 109

7.41× 105

9.73× 102

3

7

6.40× 10

3.81

6

1.20× 10

2.99× 10

2.51× 10

4

1.94× 107

4.22× 10-2

4.66× 106

78.94

1.83× 105

3

-5

5-5 γ(m,n)

3

2.09× 10

3.51× 10

1.14× 10

11

HNO3

NH3

36.60

7.77× 109

2.80× 10

1.54× 10

1.41× 104

8.13× 10-2

1.49× 107

3.05× 10-4

3.36× 107

2

2

3

3.50× 10

2

2.13× 10

3.17× 107

1.50× 102

1.39× 10-5

2.61× 10-3

-4

-5

6-6 3.21× 10

4

7-7 3.28× 10

-4

1.51× 10

-5


8-8 2.17× 10

1.17× 10

6.46× 10-5


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REFERENCES

Figure 7. Evaporation rate of different molecular clusters (1 ≤ m, n ≤ 4). Blue and red indicates faster ammonia and nitric acid evaporation rate, respectively.

CONCLUSIONS Electronic structure calculations have been performed at the B3LYP-D3/6-311++G(d,p) level of theory to determine the Gibbs free energy and activation barriers in the growth of molecular clusters formed by nitric acid and ammonia. In the ground state structure of these clusters, there are typically hydrogen bond formation and/or proton transfer. Reaction pathways in stepwise cluster growth by adding different monomers have been explored. It turns out that collision between an incoming molecule and reactant cluster always results in cluster growth. Evaporation rate can finally be calculated, which measures the stabilities of different clusters. Cluster with m = n has a high stability compared to other clusters. Generally, larger clusters are more stable. The exception that 5-5 is less stable than 4-4 can be understood by the structure motif transition from shell to encapsulated shell. In all m = n clusters studied here, evaporation of ammonia is easier than nitric acid. At the same time, the stability of nitric acid abundant m-n (m>n) is higher than n-m. These two facts indicate that the bonding ability of nitric acid is stronger than ammonia. Results revealed here will shed new lights in growth mechanisms of particulate matter in the atmosphere and also security of ammonium nitride.

ASSOCIATED CONTENT Supporting Information. Test calculation results, free energy of reactions, definition of hydrogen bond, reaction pathways, and structure data. This material is available free of charge via the Internet at http://pubs.acs.org

AUTHOR INFORMATION Corresponding Author *Corresponding Author. Tel: +86-551-63600934 [email protected](Z. L.), [email protected](X. D.)

Email:

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is partially supported by NSFC (21573201, 21421063 and 91545122), by the Fundamental Research Funds for the Central Universities (JB2015RCY03), by CAS (XDB01020300), and by USTCSCC, SCCAS, Tianjin, and Shanghai Supercomputer Centers.

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