Competition Between H2SO4–(CH3)3N and H2SO4–H2O Interactions

Article pubs.acs.org/JPCA

Competition Between H2SO4−(CH3)3N and H2SO4−H2O Interactions: Theoretical Studies on the Clusters [(CH3)3N]·(H2SO4)·(H2O)3−7 Zhen-Zhen Xu and Hong-Jun Fan* State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning Province, P. R. China S Supporting Information *

ABSTRACT: The role of the nucleation of sulfuric acid with amines in aerosol formation and its implications for environment is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the cluster of [(CH3)3N]·(H2SO4)·(H2O)n (n = 3−7) by molecular dynamics to obtain configurational sampling combination with CAM-B3LYP/6-311G(d,p) level to locate the global and many local minima for each cluster size. According to the binding energies at the method of MP2/6-311++G(d,p), the total binding energies decrease with the increasing of the water molecules. For each global minimum, the average binding energies decrease from n = 3 to 4, then increase slowly. The protons of H2SO4 are preferred to transfer to the (CH3)3N to form ion-pair HSO4− and (CH3)3NH+, and the (CH3)3NH+ ions are coordinated at the first hydrated shell of HSO4− when n is between 3 and 5 and coordinated at the second or third hydrated shell when n is larger than 5.

1. INTRODUCTION Aerosol particle formation via the gas to particle conversion impacts the earth’s climate and environment. The atmospheric nucleation1,2 involved sulfuric acid (SA), the key atmospheric nucleation precursor, water, the dominant constituent in nucleation, and something else. Due to the large affinity for water, gaseous SA in the atmosphere existed in various hydrated forms; hence, the clusters of (H2SO4)m(H2O)n, where m = 1−3 and n = 0−9, were investigated by a large number of quantum chemists.3−9 Although all studies concluded that deprotonation of SA and formation of ions occurred only in large hydrated clusters, there was little agreement regarding the minimum number of water molecules (3−8) required to stabilize the resulting ion-pair [H3O+−HSO4−]. However, the binary nucleation cannot explain the nucleation rates,2 so ammonia,10,11 amines,11,12 and organic acid13,14 have been involved on the basis of laboratory studies, which demonstrated that the presence of these species had a clear enhancement effect over the SA−water system.15 The theoretical calculations of ternary clusters (NH3)·(H2SO4)· (H2 O)1−5 have been investigated widely.1,2,4,16−18 The ammonia can strength the binding of SA to clusters due to the proton transfer from H2SO4 to NH3 in the hydrated clusters, and their NH4+ ions had coordinated at the first hydrated layer according to their stable isomers. Then, amines (R3N, R = alkyl/H) had become increasingly important,2,18−21 which were able to form stable salts with strong inorganic acids under the atmospheric conditions. Loukonen and his co-workers18 found that the dimethylamine, (CH3)2NH, could enhance the SA to the clusters much more © 2015 American Chemical Society

efficiently than ammonia when the number of water molecules in the cluster was either zero or greater than two. Here, according to their calculations for ternary clusters [(CH3)2NH]·(H2SO4)·(H2O)0−5, (CH3)2NH2+ ions coordinated at the first hydrated shell of SA in the hydrated clusters. Loewenschuss19 et al. pointed that the proton transfer from SA to trimethylamine (TMA), (CH3)3N, a new N−H bond was formed, and the [(CH3)3NH+−HSO4−] complex was further stabilized by hydration. This (CH3)3NH+ was also at the first hydrated sphere, while the number of water is three. In these ternary clusters, the theoretical works were almost all focused on the structures where ammonium (NH4+ or R3NH+) is at the first hydrated coordinate sphere of sulfate ion. However, we know that separated ions surrounded by H2O exist in solution or hydrated metal salts cluster,22,23 and four water is enough to separate the Mg2+ and NO3−. The ions pair structure is benefited by the charge−charge interaction, while the separated ions have larger ion-induced interaction, which increases with the number of water molecules. Thus, we wonder that at certain n in [(CH3)3N]·(H2SO4)·(H2O)n cluster, ammonium ions could also not be in the first coordinate sphere of bisulfate ion. That is how many water molecules need to push the positive and negative ions. To figure out whether this hypothesis is true, and to further understand the competition between SA−ammonia (or amines) interaction and SA−water interaction, in this work Received: June 1, 2015 Revised: August 12, 2015 Published: August 12, 2015 9160

DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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The Journal of Physical Chemistry A

optimizations with the CAM-B3LYP functional30 and 6311G(d,p) basis set using Gaussian 09.31 Vibrational frequency analyses were also performed to confirm that the obtained structures corresponded to energy minima or saddle points. Then, several of the most promising clusters were chosen for single-point energy calculations using MP2 method with 6311++G(d,p) basis sets. The main lowest structures are presented in Figures 1 to 5, and the other sable structures are presented in Figures S1 to S5 in the Supporting Information (SI). All detail Cartesian coordinates are also listed in the third part of the SI. In the following discussion, the energies all refer to the MP2/6-311++G(d,p)//CAM-B3LYP/ 6-311G(d,p) with zero-point energies corrected at CAMB3LYP/6-311G(d,p); the energies of main structures, binding energies (Ebinding), and average binding energies (Eabinding) are listed in Table 2, where the binding energy and average binding energies are defined as follows:

we have investigated the structural and energetic properties for the ternary cluster, one trimethylamine together with one H2SO4 molecule and three to seven water molecules, [(CH3)3N]·(H2SO4)·(H2O)3−7.

2. COMPUTATIONAL DETAILS Here, we investigate the [(CH 3 ) 3 N]·(H 2 SO 4 )·(H 2 O) 3−7 clusters. There are four ways to transfer the proton of H2SO4. First, the proton transfers to water to form the ion pair type, including H3O+ and HSO4− ions (a type). Second, one of the H protons is favored to the TMA to form another ion pair type, (CH3)3NH+ and HSO4− (b type). Third, both protons are transferring to water and TMA simultaneously to produce a tri-ion cluster, including H3O+, SO42−, and (CH3)3NH+ (c type). Last type, there is no proton to transfer; this cluster consists of water cluster, SA, and TMA (d type). In our calculations, first, we carried out the molecular dynamics (MD) simulations to generate initial guess structures for the quantum chemistry geometry optimizations. Based on the above four different proton transfer types, a to d types, the MD simulations were performed, respectively. All MD simulations used the OPLLSA force filed of Gromacs package24−26 in vacuum condition, the system was always at the temperature 300 K in a period of 100 ps, and the time step size was 0.01 ps. The electrostatic potential charges for the Coulomb interactions were calculated at the method of MP2/ Aug-CC-pVTZ18,27,28 shown in Table 1. The van der Waals parameters were also listed in this table from the refs 27−29, and the OPLLSA parameters for bonds, bond angles, and dihedral angles used were from the ref 18. Then, on the basis of above MD simulations, 20 initial structures with minimum potentials for each proton transfer type were obtained from the trajectories files. These configurations were used as the starting structures for geometry

E binding = Ecomplex − E H 2SO4 − E(CH3)3N − nE H2O Ea binding =

molecular type

H3O+ (hdy) H2SO4 (sa)

HSO4− (hs)

SO42− (si) N(CH3)3 (tma)

[N(CH3)3H]+ (tmi)

atom type

charge

σ (nm)

ε (kcal/mol)

Ow Hw Ohyd Hhyd Ssa Osa Osah Hsa Shs Ohs Ohsh Hhs Ssi Osi Ntma Ctma Htma Ntmi Htmin Ctmi Htmi

−0.84827 0.42427 −0.41728 0.47228 1.290a −0.525a −0.560a 0.440a 1.450a −0.720a −0.670a 0.380a 1.660a −0.915a −0.750a −0.200a 0.150a 0.023a 0.315a -0.260a 0.160a

0.31727 0.00027 0.32328 0.00028 0.35529 0.30029 0.30029 0.00029 0.35529 0.30029 0.30029 0.00029 0.35529 0.30029 0.32529 0.35029 0.25029 0.32529 0.25029 0.35029 0.25029

0.65027 0.00027 0.62028 0.00028 1.04629 0.71229 0.71229 0.00029 1.04629 0.71229 0.71229 0.00029 1.04629 0.71229 0.71129 0.27629 0.12629 0.71129 0.12629 0.27629 0.12629

(2)

where, in eq 1, the Ecomplex is the energy of cluster, the energies of monomer for H2SO4, (CH3)3N, and H2O are −699.068, −173.848, and −76.253 kcal/mol, respectively, and n is the number of the water. In eq 2, the average binding energy is defined that the binding energy of cluster divided by the number of monomers in the cluster, where 2 denotes the number of TMA and SA.

3. RESULTS AND DISCUSSION 3.1. [(CH3)3N]·(H2SO4)·(H2O)3. Six stable conformers with b type proton transfer were obtained while the number of water molecules is three. Isomers b_3w1 and b_3w2 are shown in Figure 1, and the others are presented in Figure S1 of SI. The binding energy of b_3w1 is −54.853 kcal/mol as listed in Table 2, which is the lowest energy cluster. In this structure, one of the H protons in SA transfers to TMA to form the ions pair [(CH3)3NH+-HSO4−], which associated with a N−H···O hydrogen bond (1.679 Å), and each water molecule forms one hydrogen bond (1.814, 1.814, and 1.841 Å) with the rest of O atoms in HSO4−, respectively. The (CH3)3NH+ ion is coordinated at the first hydrated shell of HSO4− due to the charge−charge interaction between (CH3)3NH+ and HSO4− in this cluster. The second stable isomer is b_3w2, whose (CH3)3NH+ ion is at the second coordinated shell of HSO4− through N−H···O H-bond 1.975 Å with H2O. It is slightly higher in energy than b_3w1 (0.034 kcal/mol), which indicates that these two isomers are comparable in stability. As for other four geometries, the relative energies are from 0.034 to 3.910 kcal/mol, seen Table S1 of SI, where the (CH3)3NH+ ions of isomers b_3w3 to b_3w5 are at the first hydrated sphere and that of isomer b_3w6 is at the second sphere. 3.2. [(CH3)3N]·(H2SO4)·(H2O)4. Eight low-lying isomers with four water molecules have been found, as shown in Figure 2 and Figure S2 of SI, respectively. Isomer b_4w1 is the most stable isomer with −66.730 kcal/ mol binding energy (Table 2), the ion-pair [(CH3)3NH+− HSO4−] is produced by the proton transfer with a very short hydrogen bond (1.574 Å), where the positive ion and water are all at the first coordinate shell of sulfate ion. Here, we also think

Table 1. Force Field Parameters for Coulomb and LennardJones Potentials H2O (w)

1 E binding 2+n

(1)

a

Charge was computed using the CHelpG charge at MP2/Aug-CCpVTZ level.18 9161

DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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Figure 1. Lowest structures with three H2O for (CH3)3NH+ ions coordinated at the first and second hydrated shells, respectively, by the method of CAM-B3LYP/6-311G(d,p), where the relative energies in the brackets and the distance of H-bond are also presented; the unit is Å.

Table 2. Energies E, Binding Energies Ebinding, and Average Binding Energy Eabinding at MP2/6-311++G(d,p) Level for [(CH3)3N]·(H2SO4)·(H2O)3‑7 Clusters b_3w1 b_4w1 b_5w1 b_6w1 b_7w1

E (hartree)

Ebinding (kcal/mol)

Eabinding (kcal/mol)

−1101.763 −1178.036 −1254.304 −1330.573 −1406.843

−54.853 −66.730 −76.328 −85.657 −96.026

−10.971 −11.122 −10.904 −10.707 −10.670

b_3w2 b_4w2 b_5w5 b_6w2 b_7w2

E (hartree)

Ebinding (kcal/mol)

Eabinding (kcal/mol)

−1101.763 −1178.032 −1254.301 −1330.571 −1406.841

−54.819 −64.286 −73.901 −84.893 −94.854

−10.964 −10.714 −10.557 −10.612 −10.539

Figure 2. Lowest structures with four H2O for (CH3)3NH+ ions coordinated at the first and third hydrated shells, respectively, by the method of CAM-B3LYP/6-311G(d,p), where the relative energies in the brackets and the distance of H-bond are also presented; the unit is Å.

such structure is contributed to the charge−charge interaction between (CH3)3NH+ and HSO4−. Isomer b_4w2 is also the lowest structure with b type proton transfer, which (CH3)3NH+ ion is at the third hydrated shell of HSO4− by N−H···O H-bond (1.642 Å) with a H2O at the second shell. There is more relative energy of about 2.444 kcal/ mol for isomer b_4w1.

For the other isomers b_4w3 to a_4w8, their relative energies are from 2.857 to 6.641 kcal/mol, with respect to isomer b_4w1, seen Table S2 in SI. Most isomers occur b type proton transfer except isomers c_4w7 and a_4w8, where isomer c_4w7 is c type proton transfer, i.e., the tri-ion type structure [H3O+−SO42−−(CH3)3NH+] is generated, and an isomer with a type proton transfer is also found, a_4w8, i.e., 9162

DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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Figure 3. Lowest structures with five H2O for (CH3)3NH+ ions coordinated at the first and third hydrated shells, respectively, by the method of CAM-B3LYP/6-311G(d,p), where the relative energies in the brackets and the distance of H-bond are also presented; the unit is Å.

Figure 4. Lowest structures with six H2O for (CH3)3NH+ ions coordinated at the second and first hydrated shells, respectively, by the method of CAM-B3LYP/6-311G(d,p), where the relative energies in the brackets and the distance of H-bond are also presented; the unit is Å.

another kind of ion pair [H3O+−HSO4−] appears, but with a higher relative energy of 6.641 kcal/mol. 3.3. [(CH3)3N]·(H2SO4)·(H2O)5. The two lowest stable structure for the (CH3)3NH+ ions being at first and nonfirst hydrated shells are b_5w1 and b_5w5, as shown in Figure 3. The binding energy of isomer b_5w1 is −76.328 kcal/mol (Table 2) with b type proton transfer. The ion-pair [(CH3)3NH+−HSO4−] formation is attributed to the hydrogen bond of N−H···O (1.514 Å). Meanwhile, a five-membered water ring appears by five H-bond interactions; hence, in our view, the H-bond network between water clusters is formed preliminarily. Although the ion-induced interaction between HSO4− and H-bond network has enhanced gradually with the increased water molecules, it is not enough to separate the ion-

pair formation. Hence the (CH3)3NH+ ion and four water molecules of water cluster remain at the first hydrated layer. However, in isomer b_5w5, the interaction between HSO4− and water cluster overcomes the HSO 4 − −(CH 3 ) 3 NH + interaction so that the ion pair formation is forced to separate as shown in Figure 3. Furthermore, its binding energy is 2.427 kcal/mol higher than isomer b_5w1, which indicates that this structure is not steadier than isomer b_5w1. Then, we also find other seven stable conformers; their structures and binding energies are presented in Figure S3 and Table S3 of SI, respectively. The relative energies are from 0.664 to 7.045 kcal/mol, where isomer b_5w2 to b_5w4 and b_5w6 are b type proton transfer, isomer c_5w7 and c_5w9 are c type proton transfer, and isomer a_5w8 is a type proton transfer. 9163

DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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The Journal of Physical Chemistry A

Figure 5. Lowest structures with seven H2O for (CH3)3NH+ ions coordinated at the third and first hydrated shells, respectively, by the method of CAM-B3LYP/6-311G(d,p), where the relative energies in the brackets and the distance of H-bond are also presented; the unit is Å.

3.4. [(CH3)3N]·(H2SO4)·(H2O)6. When the number of water molecules increases to six, we have acquired nine low-lying configurations, as shown in Figure 4 and Figure S4 of SI, where there are five isomers for b type proton transfer, including b_6w1 to b_6w3, b_6w5, and b_6w10, six isomers for c type, including c_6w4, c_6w6, c_6w7, c_6w9, c_6w11, and c_6w12, and one a type proton transfer, a_6w8. Isomer b_6w1 is the most stable conformer with −85.6574 kcal/mol binding energy (Table 2). As shown in Figure 4, one proton of SA does not take part in the formation of H-bond, and the other one takes part in b type proton transfer to produce HSO4− and (CH3)3NH+. Because of the formation of H-bond network with the increasing of the water molecules, the ion-induced interaction between HSO4− and water cluster becomes stronger than the charge−charge interaction between that ion pair, so that the [(CH3)3NH+−HSO4−] is separated by water molecules. Finally, the positive ion is coordinated at the second hydrated shell of HSO4− by a N−H···O hydrogen bond with H2O (1.954 Å). Isomer b_6w2 is the second lowest structure with 0.762 kcal/mol higher binding energy than b_6w1. Nevertheless, different from isomer b_6w1 is the coordinated position of (CH3)3NH+ ion; here the positive ion is at the first hydrated sphere. In addition, the other 10 stable conformers are b_6w3 to c_6w12 with 1.470 to 6.135 kcal/mol relative energies as represented in Table S4 of SI. Here, we have found a key difference from the [(CH3)3N]· (H2SO4)·(H2O)3−5. When the water molecules increased to six, the ion-induced interaction is also enhanced increasingly, so that the water clusters can push the ammonium ion to the second coordinated sphere of bisulfate ion for the lowest isomer to make the cluster further stabilized. Therefore, the cluster of [(CH3)3N]·(H2SO4)·(H2O)7 is also investigated next. 3.5. [(CH3)3N]·(H2SO4)·(H2O)7. When the number of the water molecules is seven, we have gained 14 low-lying configurations, as shown in Figure 5 and Figure S5 of SI,

where there are eight isomers for b type proton transfer, including b_7w1, b_7w3 to b_7w5, b_7w7, b_7w9, b_7w10 and b_7w12, five c type isomers, including c_7w2, c_7w6, c_7w8, c_7w11, and c_7w13, and one a type isomer, a_7w14. The isomer b_7w1 is the most stable conformer, with −96.026 kcal/mol binding energy, in these 14 configurations. In this structure, the water cluster surrounds the HSO4−, where six water molecules locate at the first hydration layer, and one water is coordinated at the second hydrated shell. Due to the enhancement of ion-induced interaction between HSO4− ion with water cluster, the (CH3)3NH+ ion is also far away from the HSO4− through a hydrogen bond N−H···O with a H2O at the second coordinated shell (1.733 Å); hence, this positive ion coordinates at the third hydrated shell. This result is in agreed with the isomer b_6w1. The isomer c_7w2 is the second minimum with 1.173 kcal/ mol relative energy. In this structure, the two protons of SA are directly transferred to the water forming H3O+, and TMA formed (CH3)3NH+, so the tri-ion structure [H3O+-SO42−− (CH3)3NH+] is forming. Their hydrogen bonds of O−H···O and N−H···O are 1.560 and 1.513 Å. As for the other 12 structures, b_7w3 to a_7w14, the relative energies are from 3.487 to 7.630 kcal/mol as shown in Table S5 of SI. 3.6. Discussion. We also have analyzed the vibrational frequency for the lowest geometries at the level of CAMB3LYP/6-311G(d,p). As for the cluster with three water, the ν(O−H) frequency, including O−H bonds in H2O and HSO4−, are from 3485 to 3797 cm−1 (scaled by 0.97 from the manual of Gaussian09), which is close to the experimental results19 (3462−3594 cm−1), and other theoretical results19 are 3153− 3709 cm−1. We have also calculated the ν(O−H) frequency for the clusters with four to seven water, and the scopes are 3292− 3782 cm−1 for n = 4, 3242−3790 cm−1 for n = 5, 3365−3793 cm−1 for n = 6, and 0.3334−3796 cm−1 for n = 7. The ν(N− H+) frequencies are 3006, 2704, 2445, 3121, and 2892 cm−1 for n = 3−7. 9164

DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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Figure 6. Binding energies and average binding energies for the two lowest structures of (CH3)NH+ ions at the first and nonfirst hydrated shells, respectively.

The calculated ν(O−H) and ν(N−H+) frequencies do not change dramatically when the (CH3)3NH+ ions are in the first or nonfirst hydrated shell. We propose this is because no matter where the (CH3)3NH+ ions are, the hydrogen bond-type (N− H···O and H−O···H) does not change. Hence, we think that the IR spectrum may not be a good technique to distinguish the coordinated position of (CH3)3NH+. Based on the calculations for these clusters [(CH3)3N]· (H2SO4)·(H2O)n, n = 3−7, the lowest two binding energies and average binding energies for (CH3)3NH+ ions being at the first and nonfirst (second or third) hydrated shells of HSO4− ions are summarized at Figure 6. As shown in these pictures, with the increase of the number of water molecules, the total binding energies decrease gradually. As to each global minimum, the average binding energies decrease first from n = 3 to 4, and then increase slowly from n = 5 to 7. No matter whether comparing the binding energy or average binding energy, all appear to break when n = 6. When the number of water is three to five , the structures where (CH3)3NH+ is at the first hydrated sphere are more stable in combination than the structures where the positive ion is at the nonfirst hydrated spheres. When the number of water increases to six and seven, the opposite side appears due to the enhancement of ion-induced interaction.

the cluster binding. Hence, in such system, six waters are enough to separate the [(CH3)3NH+−HSO4−] formation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05200. Structures of clusters [(CH3)3N]·(H2SO4)·(H2O)3−7 from Figures S1 to S5 except the structures shown in Figures 1 to 5, the energy information for all clusters from Tables S1 to S5 except the results shown in Table 2, and the detail Cartesian coordinates for all clusters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: (86) 411-84379913. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been aided by the grants from National Nature Science Foundation of China (Nos. 21173212 and 2121004) and the Key Research Program of the Chinese Academy of Sciences.

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4. CONCLUSIONS In conclusion, we have reported comprehensive studies of the structural properties of [(CH3)3N]·(H2SO4)·(H2O)n, n = 3−7, clusters. With the increasing of water molecules, the binding energies decrease, and the average binding energies first decrease and then increase for the minimum. In general, the proton of sulfuric acid is easier to transfer to trimethylamine than to water cluster according to the binding energy, which indicated that b type proton transfer is always favored over other types. In a small hydrated cluster (n = 3−5), the (CH3)3NH+ ions at the first hydrated coordinate sphere benefit from the charge− charge interactions between (CH3)3NH+ and HSO4, while in a large hydrated cluster (n = 6−7), the enhancement of the ioninduced interactions between HSO4− and water molecules can push the (CH3)3NH+ ions to coordinate at the second (with six H2O) and third (with seven H2O) hydrated spheres to stabilize

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DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166

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DOI: 10.1021/acs.jpca.5b05200 J. Phys. Chem. A 2015, 119, 9160−9166