J Mol Model (2015) 21: 78 DOI 10.1007/s00894-015-2611-7

ORIGINAL PAPER

Relative stabilities of HCl•H2SO4•HNO3 aggregates in polar stratospheric clouds Marian Verdes & M. Paniagua

Received: 27 October 2014 / Accepted: 8 February 2015 / Published online: 11 March 2015 # Springer-Verlag Berlin Heidelberg 2015

Abstract Strong acids such as HCl (C), HNO3 (N) and H2SO4 (S) acquire relevance in Polar Stratospheric Clouds (PSCs) and aerosols in which nucleation processes occur. Ab initio quantum chemical studies of aggregates were performed for these strong acids. Structures were calculated using DFT methods with the B3LYP hybrid functional and aug-ccpVTZ basis set. As an initial constraint, an H2SO4 moiety was placed in all candidate structures. A total of 11 optimized structures was found: a global minimum (CSN-a) plus ten local minima on the Potential Energy Surface (PES). The global minimum aggregate gave four hydrogen bonds, yielding a hexagonal ring in its structure. HNO3 acts as proton donor in all clusters; nevertheless, using trans-H2SO4 as the proton donor yielded the most stable structures, whereas HCl acts mainly as a proton donor/acceptor. Real harmonic frequencies, IR spectra, and inter-monomeric parameters were obtained. CSN-a symmetric stretching modes were shifted to 2805.56 cm−1 and 3520.00 cm−1 for H–Cl modes, while O–H modes shifted to 3256.87 cm−1 and 3362.47 cm−1. On the other hand, relative stabilities improved for 5 of the 11 aggregates when the temperature decreased from 298 K to 210 K, 195 K and 188 K. The aggregate CSN-f remained unstable only at 210 K. Moreover, the relative Gibbs free energy, ΔG(0–298K) was−9.26 kcalmol−1 with respect to CSN-a; relative reaction Gibbs free energy [Δ(ΔG)] values ranged from 0.0 at 298 K, to −6.9 kcalmol−1 at 188 K. It seems that CSN aggregates remain slightly more stable than CNS aggregates with a HNO3 moiety when the temperature decreases from 298 to 188 K. Five structures remained relatively stable under both study conditions. M. Verdes (*) : M. Paniagua Departamento de Química Física Aplicada, Facultad de Ciencias, C-14, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain e-mail: [email protected]

Keywords DFT . PSC . Ab initio . Sulfuric acid . Nitric acid . Hydrogen chloride . Relative stability . Gibbs free energy . Atmospheric temperatures . Atmospheric aggregates . Atmospheric clusters . Atmospheric chemistry . Thermochemistry . IR frequencies

Introduction Polar Stratospheric Clouds (PSCs) [1] play a critical role in stratospheric ozone depletion [2, 3]. The three strong acids HCl, H2SO4 and HNO3 play an active role in PSCs, which are formed by crystalline compounds of water and nitric acid trihydrate (NAT), or HNO3•3H2O [2, 4, 5]. The nucleation of NAT was investigated in heterogeneous formation of PSCs [6], whereas their denitrification [7–12] in the Arctic stratosphere has been shown to be responsible for the vertical redistribution of NOy. Similarly, H2SO4 participates in PSCs [13], interacting with H2O and HNO3 to generate particles known as SAT (sulfuric acid tetrahydrated) [14] and STS (supercooled ternary solution), respectively [4, 15, 16]. Water ice, HNO3 and STS (H2SO4/HNO3/H2O system) promote heterogeneous chlorine activation [17–21] at different temperatures, concentrations and pressures. Chemical studies of stratospheric ozone assess the ozone values in PSCs when chlorine deactivation occurs [22]. Computational models for the parameterization of PSC has been developed in which STS and NAT have been simulated by EMAC (ECHAM5/MESSy Atmospheric Chemistry model) [23]. Molecular dynamic (MD) simulation of HCl on ice in the stratosphere [24] has been used to model ionization processes in Antarctic PSCs. Nowadays, methods to study physical and chemical processes in global simulation of Arctic ozone depletion have also been developed [25], wherein a deep analysis of heterogeneous nucleation aerosols and PSCs, including NAT/ice and chlorine activation, was carried out. Theoretical studies on

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HCl-ice have been developed previously [26, 27] for systems with ClH–OH2 bonds. Similarly, theoretical systems in which implied HCl•HNO3•H2SO4 complexes have been studied [28] take into account global minimum and local minima structures, their hydrogen bonds and their relative stability when the stratospheric temperature decreases to 210 K, 195 K and 188 K. A similar experimental and theoretical study on HCl•6H2O was performed [29], in which the temperature range was 170– 205 K; moreover, kinetic and thermodynamic properties, including infrared (IR) spectroscopy, have been assessed. As known from earlier research, particular attention must be paid to temperature in stratospheric processes, especially in reactions that occur in PSCs [24, 28–34]; for example, the relative stability and thermodynamic behavior of HCl•HNO3•H2SO4 aggregates [28], and the stability of HNO3•nH2O [35], have been researched. This work presents a systematic ab initio study of aggregates created by HCl, HNO3 and H2SO4 as monomers, towards a better understanding of PSCs from a theoretical viewpoint. The findings might contribute to PSCs knowledge by providing stable optimized geometries, global and local minima optimized structures and their corresponding physicochemical properties. The evolution of relative stability for all aggregates studied here is presented, at three significant stratospheric temperatures: 188 K (freezing ice), 195 K (NAT formation) and 210 K (SAT/STS evolution). All structures present here comprise a proton (A or B) and/or an electron pair (blue dot pairs) transfer to a sulfuric acid monomer (moiety placed in clusters) as shown in Fig. 1.

Methods Computational details Ab initio structures were calculated by means of the Density Functional Theory (DFT) method using the B3LYP/aug-ccpVTZ basis set within the Gaussian09 program package [36, 37]. Geometrical optimizations were performed taking into

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account the large size of the clusters (560 basis functions), their 36 degrees of freedom, and C1 symmetry. One initial constraint was considered: a sulfuric acid moiety was placed in every initial aggregate, whereas previous work had used a nitric acid moiety [28]. Twelve initial candidates structures were constructed, taking into account the maximum feasible intermonomeric hydrogen bonds among monomers (HCl, H2SO4 and HNO3) in the ternary systems. These 12 structures were optimized initially at low level of theory using the B3LYP/631G method and basis set; 11 z-matrices converged on this first optimization. Subsequently, a second optimization was performed at a high level of theory using the same method B3LYP with aug-cc-pVTZ basis set, as mentioned above. After this optimization, 11 structures (all z-matrices calculated) gave real minima on the Potential Energy Surface (PES). It should be noted that all geometries optimized were performed at 0 K. Electronic energies of aggregates were calculated taking into account the zero point energy correction (ZPEC) and Counterpoise Correction (CC) methods [38]. Nomenclature of aggregates The aggregates were described as follows: C represents HCl, S H2SO4, and N HNO3. The acronym CSN-n means that a sulfuric acid moiety is always placed in the aggregate. The n represents the 11 optimized structures, taking the following names: n=a, b, c, d, e, f, g, h, I, j and k. Thermochemistry Real harmonic vibrational modes in IR were achieved by means of B3LYP/aug-cc-pVTZ level of theory for each optimized structure. Thermochemistry was calculated at aug-cc-pv-triple-ζ and B3LYP levels of theory over final optimized structures at three significant stratospheric temperatures: 188 K, 195 K and 210 K, and at 298.15 K. Relative stability calculation The first step was to calculate the relative Gibbs free energy (ΔG) for nucleation of monomers with the following reaction:





HCl þ H2 SO4 þ HNO3 →HCl H2 SO4 HNO3 C þ S þ N→CSN

ΔG for each aggregate was calculated by means of rgw following equation: Fig. 1 Structure of H2SO4 monomer. Blue ellipses (A, B) Protons undergoing transfer; blue dot pairs transfer positions of electron pairs for future aggregates

ΔGmin ¼ ½ðE þ ZPEÞ þ H−T S complex X − ½ðE þ ZPE Þ þ H−T S monomers

ð1Þ

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ΔG is associated with the formation of the aggregate HCl•H2SO4•HNO3 (CSN), where E is the energy at 0 K; ZPE the zero-point energy; H is the thermal enthalpy contribution from translational, vibrational and rotational motions, and S is the entropy contributions from these motions. The second step was to achieve the relative reaction Gibbs free energy Δ[ΔG(0–T)K] for all complexes. This Δ[ΔG(0– T)K] is associated with the global minimum aggregate CSNa, which has ΔGmin =−9.26 kcal mol−1, with respect to remaining local minima structures by means of the following equation:   ΔðΔGÞn−relative ¼ Δ Gnð0−T Þ −ΔGmin ð2Þ

Δ(ΔG)n-relative for each structure could be determined. The Δ[ΔG(0–298)K] of CSN-a is taken as a reference.

Results Energy and structures The 11 optimized geometries were classified into three families as shown in Fig. 2. The first family comprises aggregates with a hexagonal ring in their structure: CSN-a, CSN-b, CSNc, CSN-d and CSN-e. The hexagonal ring family was characterized by minimum electronic energy values. The global minimum electronic energy value, Eh =−1442.2954394 Hartree, belonged to the CSN-a aggregate (ΔE=0.0 kcal mol−1). The remaining aggregates (CSN-b to CSN-e) had ΔE values ranging from 0.0 to 7.3 kcal mol−1. The second family was made

Where n represents the different aggregates obtained, n = (b–k) and ΔGn(0–T) takes the temperatures values: T = 188 K, 195 K, 210 K. Hence, the relative stability Fig. 2 Eleven optimized geometries of CSN-n aggregates classified into three families: hexagonal ring, non-hexagonal ring and two rings. CSN-a was the most stable structure, with Δ[ΔG]=0.0 kcal mol−1

Optimized structures at B3LYP/aug-cc-pVTZ level Atoms: Hydrogen

Hexagonal ring

Nitrogen

Oxygen

CSN- a

CSN- b

0.0

1.25

CSN- c 2.41

Sulfur

CSN- d

CSN- e

4.72

9.02

Non Hexagonal ring

CSN- f

CSN- g

5.52

6.97

CSN- h 7.63

Two Rings

CSN- i

CSN- j

8.41

11.76

CSN- k 12.16

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Fig. 3 Infrared (IR) spectrum of the global minimum structure, CSN-a. A hydrogen bond is formed (NO–H⋯OS) as a proton is transferred from HNO3 to H2SO4, creating a shift at 3256.87 cm−1. The first proton transfer (SO–H⋯ON) of H2SO4 to HNO3 gave a strong peak shift at 3362.47 cm−1; the second proton transfer of H2SO4 to HCl shifted at 3520.00 cm−1. Proton transfer from HCl to the oxygen atom of H2SO4 shifted at 2805.56 cm−1 giving a weak peak. The four harmonic vibrational frequencies correspond to symmetric stretching modes

Intensity (atomic units)

up of aggregates with a non-hexagonal ring: CSN-f, CSN-g and CSN-h. Their electronic energy increases from 5.6 to 7.6 kcal mol−1. The geometries of structures CSN-f and CSN-g are similar to those in a previous study [28] in which the complexes were named CNS-f and CNS-g. Comparing the inter-monomeric distances, a minor change from 1.92 Å to 1.91 Å was found for the SO–H⋯Cl distance in CSN-f compared to that of CNS-f. Angles also changed slightly; for instance, the angle formed by SO–H⋯Cl is 175°27’ for CSN-f but 178°27’ for CNS-f. Small variations in relative energy were observed, with 0.4 kcal mol−1 for CNS-f as opposed to 3.14 kcal mol−1 for CSN-f. On the other hand, comparing CSN-g and CNS-g, the relative energy variation was significant, with values of 3.89 kcal mol−1 and 7.9 kcal mol−1 for CSN-g and CNS-g, respectively. This result is owing to the major variation in inter-monomeric distances, especially openness angles, i.e., the angle created by SO–H–N is 173°50’ in CSN-g and 142°15’ in the CNS-g complex. Finally, the third family—the two-ring family—is formed by aggregates having two rings: CSN-i, CSN-j and CSN-k. The two-ring family, being less favorable energetically, takes ΔE values from 8.3 to 10.7 kcal mol−1. The most stable aggregates studied here belong to the first family, which contains hexagonal rings. Focusing on CSN-a as the global minimum aggregate, Fig. 3 shows the hexagonal ring structure among H2SO4 and HNO3 while HCl is bonded to a proton of H2SO4 by a hydrogen bond. The structure is created by four hydrogen bonds between monomers of HCl, H2SO4 and HNO3. The powerful

hydrogen bond is formed between the O–H of H2SO4 and the oxygen of HNO 3 , which corresponds to a symmetric stretching mode at a frequency of 3,362.47 cm−1 belonging to the proton transfer of H2SO4 to HNO3. The second proton transfer of H 2 SO 4 was shifted to a wavenumber of 3, 520.00 cm−1, which corresponds to proton transfer to HCl. The frequency shift at 3,256.67 cm−1 belongs to proton transfer of HNO3 towards the oxygen of H2SO4. Harmonic frequencies for all aggregates are predicted in the IR spectra. Table 1 lists the electronic energies, Zero-Point Energy Correction (ZPEC), Counterpoise Correction (CC), Gibbs free energies (ΔG), and the relative Gibbs free energies [Δ(ΔG)] in the range of 0–298 K for the 11 CSN-n complexes calculated, again showing CSN-a as the global minimum reference in this study. Note that the energetic difference among hexagonal-ring ternary complexes family is 7.2 10−3 kcal mol−1. Complexes CSN-c and CSN-d have relative energies of 4.0 10−3 kcal mol−1 and 4.1 10−3 kcal mol−1, respectively, nevertheless their relative Gibbs free energy changes considerably, taking values of −6.85 kcal mol−1 and −4.54 kcal mol−1. The energy of the non-hexagonal ring family fluctuates between 5.1 kcal mol−1 and 6.9 kcal mol−1, whereas that of the tworings family oscillates between 7.6 kcal mol −1 and 10.3 kcal mol−1. Structures belonging to the hexagonal ring family yield better relative electronic energy, including better relative Gibbs free energy. Internal parameters of CSN-a are detailed in Table 2 with its optimized structure as global minimum. The bond distances in monomers of the aggregates studied here are

7000

CSN-a

6000

5000

O3-H7 O13 Symmetric streching mode 3362.47cm-1

4000

3000 O12-H10 O4 Symmetric streching Cl-H O5 mode Symmetric 3256.87 cm-1 streching mode 2805.56 cm-1

2000

1000

O2-H6 Cl 8 Symmetric streching mode 3520.00 cm-1

0 0

1000

2000

3000

4000 -1

wavenumber (cm )

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Table 1 Relative energies of CSN-n complexes relative to CSN-a as global minimum aggregate. Relative energies (ΔE), Zero-Point Energy Correction (ZPEC), Counterpoise Correction (CC), and relative Gibbs free energy (Δ[ΔG(0–298)K] ) values are expressed in kcal mol−1. Monomers in Eh B3LYP/aug-cc-pVTZ E(a) =−1442.2954394 Eha Complexes (CSN-n)

*ΔE

ZPEC

*Δ(E+ZPEC)

CC

Δ(E+ZPE+CC)

ΔG(0–298)K

Δ[ΔG(0–298)K]

Shape

a b c

0.0 3.0 4.8

47.30 46.89 46.81

0.0 2.3 4.0

0.49 0.46 0.47

0.00 1.41 2.50

−9.26 −8.01 −6.85

0.00 1.25 2.41

Hexagonal ring

d e f g h i j k Monomers

4.6 47.01 7.3 47.23 5.6 47.01 7.3 46.68 7.6 46.86 8.3 46.86 10.7 47.02 9.7 47.23 B3LYP/aug-cc-pVTZ Eh ZPEC −460.8442638 4.2 −281.0071073 16.4 −700.4183171 24.2

4.1 7.2 5.1 6.3 6.9 7.6 10.3 9.5

0.47 0.46 0.42 0.45 0.39 0.34 0.36 0.45

2.58 4.50 3.14 3.89 4.21 4.61 6.32 5.95

−4.54 −0.24 −3.74 −2.29 −1.63 −0.85 2.50 2.90

4.72 9.02 5.52 6.97 7.63 8.41 11.76 12.16

HCl HNO3 H2SO4 a

Non-hexagonal ring

Two rings

1Eh =627.50955 kcal mol−1 . *10−3 kcal mol−1

compared to experimental values of monomers isolated in other previous works. The H–Cl distance of 1.289 Å found in this work using B3LYP/aug-cc-pVTZ level of theory is in agreement with the experimental value 1.275 Å; previous work gave a value of 1.28 Å for the same distance using the MP2/aug-cc-pVDZ method and basis set. The distance of the O–H bond in HNO3 was found to

be 0.99 Å in this work, compared with experimental values of 0.964 Å and 0.97 Å determined in a in previous study. The two O–H bonds in H2SO4 gave values of 0.98 Å and 0.99 Å in this study; these are in agreement with the 0.97 Å, 0.99 Å values found in earlier works and both experimental values (0.97±0.01 Å).

Table 2 Internal parameters of CSN-(a) aggregate as global minimum optimized geometry. Results were obtained with the B3LYP/aug-cc-pVTZ level of theory with/without taking into account the Counterpoise method. Distances (r) are in Angstroms (Å) and angles (θ) in degrees Geometric parameter

Complex

Hydrogen chloride r(Cl8–H9) Nitric acid r (N11-O12) r (N11-O13) r (N11-O14) r (O12-H10)

-TZ 1.289

-TZ-CC 1.289

1.37 1.23 1.19 0.99

1.37 1.23 1.19 0.99

θ (N11-O12-H10) Sulfuric acid r (S1-O2) r (S1-O3) r (O2-H6) r (O3-H7) θ (S1-O2-H6) θ (S1-O3-H7)

107.27 [28] 1.59 1.58 0.98 0.99 110.10 109.56

107.18 1.59 1.58 0.98 0.99 110.10 109.61

Monomers (isolated)

Monomers (experimental)

Previous works [39] 1.28

-TZ 1.283

Previous works [39] 1.27

1.39 1.28 1.21 0.97

1.414 1.207 1.193 0.972

1.41 1.21 1.20 0.97

[40] 1.275 [41] 1.406 1.211 1.199 0.964

103.07 1.60 1.58 0.97 0.99 109.25 109.60

1.61 1.61 0.97 0.97 108.70

102.15 [42] 1.574±0.01 1.574±0.01 0.97±0.01 0.97±0.01 108.5±1 108.5±1

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Distances between the nitrogen and oxygen atoms in the nitric acid monomer were calculated as 1.414 Å, 1.207 Å and 1.193 Å with B3LYP/aug-cc-pVTZ level of theory, compared to values of 1.42 Å, 1.22 Å and 1.21 Å obtained with the MP2/ aug-cc-pVDZ method. The N–O–H angle in HNO3 creates an opening of 5° 7’ 12^ with respect to the experimental value of isolated HNO3. The opening of protons of H2SO4 gave values of 1° 3’ 36^ for S–O–H (proton transfer to HNO3) and 1° 36’ for S–O–H (proton transfer to HCl) for both angles compared to the respective experimental value of isolated H2SO4. Inter-monomeric parameters: rings The five most stable aggregates are displayed in Fig. 4. Four of them have a hexagonal ring in their respective structures: CSN-a, CSN-b, CSN-c and CSN-d. Only the CSN-f structure belongs to the non-hexagonal ring family. Although the 11 structures were calculated at three stratospheric temperatures—188 K, 195 K and 210 K—only 5 structures remain stable at 210 K except CSN-f structure, which becomes unstable. HCl acts as a proton donor/acceptor in the CSN-f aggregate. The two most stable structures (CSN-a and CSN-b) Fig. 4 Five relatively stable geometries of CSN: CSNa–CSNd belong to the hexagonal ring family, and CSN-f to the nonhexagonal ring family (unstable at 210 K) at stratospheric temperatures: 188 K, 195 K, and 210 K. These five structures each have four/three internal hydrogen bonds. Grelative is expressed in kcal mol−1

have their HCl below the x-axis. Nevertheless, the remaining aggregates have HCl above the x-axis in their structures. Table 3 shows inter-monomeric parameters of the five most stable aggregates that allow appraisal of the characteristics of stability among aggregates. Note that in CSN-f aggregate, which belongs to the non-hexagonal ring family, the bond distance between chlorine and hydrogen of H2SO4 (SOH– Cl) is shorter, at 2.20 Å, while its angle (S–OH⋯Cl) is 175° 27’ 36^ degrees, with a dihedral angle (S–O–H–Cl) of 90° 48’ degrees, making a right angle. The remaining structures with their internal parameters explicit in their optimized geometries can be seen in the Appendix: Figs. 6–15. Proton transfer analysis The hexagonal ring family comprises aggregates with three or four hydrogen bonds (HB). The structure of CSN-a has four HB as shown in Fig. 3. Two of these HB originate from H2SO4 protons, both acting as donor protons: one hydrogen attacks a chlorine atom, the other the acidic oxygen atom of HNO3. The HB of HNO3 is created by its hydrogen acting as a

Relative Stable Structures at Stratospheric Temperatures: 188K, 195K and 210K

CSN- b 1.25

CSN- a 0.0

CSN- d 4.72

CSN- c 2.41

Atoms: Hydrogen Nitrogen

Oxygen

Sulfur

Non relative stable at 210K

CSN- f 5.52

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Table 3 Inter-monomeric parameters for five relatively stable CSN-n aggregates at temperatures of 188 K, 195 K and 210 K. Results were calculated at B3LYP/aug-cc-pVTZ level with Counterpoise method. Distances (r) in Angstroms (Å), angles and dihedral angles (θ, τ) in degrees

Aggregate Parameters r (SOH---Cl) r (SOH---ON) r (SO---HON) r (ClH---ON) θ (O-H--Cl) θ (O-H--ON) θ (O-H--OS) θ (ClH--ON) τ (SOH-Cl) τ (SOH-O) τ (SO-HO) τ (ClH--ON)

a

b

c

d

f

Hexagonal ring 2.33 1.74 1.70 -160.04 176.10 173.58 -28.43 44.54 -176.34 --

2.32 1.76 1.68 -100.10 176.04 173.37 -172.07 23.41 -176.34 --

donor proton to the oxygen atom of H2SO4. The fourth HB results when the hydrogen of HCl also donates a proton to the oxygen atom of H2SO4. The four protons are transferred to neighboring atoms oxygen and chlorine, which behave as proton acceptors. On the other hand, structures CSN-b, CSN-c, CSN-d, CSN-e, CSN-f, CSN-g and CSN-h are formed by three HB resulting from three proton transfers, with the proton of HCl remaining outside to generate proton transfers to neighboring monomers. The structures of the non-hexagonal ring family, CSN-f, CSN-g and CSN-h, were formed by three HB as a consequence of proton transfers of hydrogens belong to HCl, HNO3 and only one proton of H2SO4. These structures were of intermediate energy. Note that the two-ring family structures CSN-i, CSN-j and CSN-k were generated by four HB in their geometry. Despite these four HB, their energy is lower than that of structures in the other families except for CSN-e structure, due to the larger distances and smaller angles in their structures relative to the global minimum stable structure CSN-a. For instance, the distances (r) between HNO3 and H2SO4 are 1.70 Å and 1,74 Å for the CSN-a aggregate, and 2.03 Å and 1.97 Å, respectively, for aggregate CSN-i. The monomer angles reveal that CSN-i is more closed than CSN-a. For example, the angle (SO⋯H– ON) takes the value 128° 16’ for CSN-i, compared with 173° 34’ in CSN-a. Similarly, the angle (SO–H⋯ON) is 152° 21’ in CSN-i and 176° 50’ in the CSN-a aggregate. These smaller angles imply instability owing to the proximity of electronic pairs reflected in their electronic energy. Shifting harmonic frequencies of inter-monomeric parameters in IR spectra with respect to these five favorable structures are collected in Table 4. It seems that structures CSN-b and CSN-c have lower energy as a result of inter-monomeric

Non Hexg. ring

2.32 1.74 1.68 -168.03 179.97 173.18 -83.13 19.33 -173.26 --

2.33 1.77 1.72 -158.54 175.36 172.51 -50.62 10.13 -177.93 --

2.20 -1.76 1.92 175.46 -171.10 176.98 90.80 --69.61 -109.17

hydrogen bond distances, whereas structure CSN-f is less stable with only one shared hydrogen bond as reflected in the Δ[ΔG(0–298)K] values.

Spectra Real harmonic vibrational frequencies in IR spectra were calculated for the 11 optimized structures. Figure 3 shows the vibrational modes (symmetric stretching modes) yielded by the inter-monomeric HB in the CSN-a aggregate. Donation of a proton from HCl to the oxygen (O5) of H2SO4 leads to a shift at 2805.56 cm−1; acceptance of a proton by HCl shifts at 3520.00 cm−1, while HNO3 and H2SO4 shift their proton donors at 3256.87 cm−1 and 3362.47 cm−1, respectively. These four wavenumbers correspond to four HB among the three monomers. The remaining structures of the hexagonal and non-hexagonal ring families show three wavenumbers. These shifts can be seen in the spectra of the Table 4 Shifting of three inter-monomeric hydrogen bonds (HB) of CSN-n with respect to the global minimum structure, CSN-a CSN-n

Shift Δν(NO-H—OS)*

Δν(NO—H-OS)**

Δν(Cl-H—O-S)***

a

0.00

0.00

0.00

b c d f

−39.54 −45.37 9.92 171.27

28.27 2.75 52.19 —

39.72 38.17 −308.75 —

* 3256.87 cm−1 , ** 3362.47 cm−1 , *** 3520.00 cm−1 (values for CSN-a)

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following complexes: CSN-b, CSN-c, CSN-d, CSN-e, CSN-f, CSN-g, and CSN-h (see Appendix, Figs. 16–22). Spectra of the two-ring family have three wavenumbers in their geometries as seen in their respective spectra: CSN-i, CSN-j and CSN-k (see Appendix, Figs. 23–25) The wavenumbers corresponding to the simultaneous symmetric stretching mode of protons belonging to HNO3 and H2SO4 are missing in these spectra. The simultaneous symmetric stretching mode in structure CSN-i for both protons (H7 of H2SO4 and H10 of HNO3) shifts at 3553.04 cm−1 with weak intensity. For structure CSN-j, simultaneous symmetric stretching mode for both protons (H6 of H2SO4 and H10 of HNO3) shifted at 3540.23 cm−1, leading to free electronic pairs of acidic oxygen atoms. Finally, for aggregate CSN-k, simultaneous symmetric stretching mode for both protons (H7 of H2SO4 and H10 of HNO3), shifted at 3400.01 cm−1, yielding a weak intensity peak. Relative stability analysis Table 5 lists the relative reaction Gibbs free energies for the 11 relative stable geometries optimized previously. As mentioned in Methods, the Gibbs free energy was calculated by means of Eq. (1) at a temperature of 298 K. Afterwards, the relative reaction Gibbs free energy, Δ(ΔG)n-relative was calculated using Eq. (2). Global minimum aggregate results for CSN-a gave ΔGmin =−9.26 kcal mol−1. This Δ[ΔG(0-T)K] is associated with the global minimum aggregate CSN-a, where the temperature takes the values 188 K, 195 K and 210 K rather than the 298 K considered previously.

Table 5

Therefore, the values in going from Δ[ΔG(0–298)K] to Δ[ΔG(0–188)K] range from 0.0 to −6.9 kcal mol−1. The relatively stable aggregates belonging to the hexagonal ring family take values from 1.3 to −4.9 kcal mol−1 (CSN-b); from 2.4 to −2.3 kcal mol−1 (CSN-c); and from 4.7 to −1.9 kcal mol−1 (CSN-d). In contrast, the values for CSN-f, which belongs to the non-hexagonal ring family, range from 5.5 to −0.9 kcal mol−1. The remaining aggregates—two-ring family—remain unstable at these three stratospheric temperatures. Relative Gibbs free energies (ΔG) of nucleation reactions for the 11 aggregates were obtained at 298 K. The relative reaction Gibbs free energies [Δ(ΔG)] were also calculated relative to the global minimum aggregate CSN-a. The aggregates were arranged by Δ[ΔG(0–298)K] using CSN-a as a reference. The Δ[ΔG(0–298)K] value ranges from 0.0 kcal mol−1 for CSN-a to 12.16 kcal mol−1 for the CSN-k aggregate, with ΔE values ranging from 0.0 kcal mol −1 for CSN-a to 10.710−3 kcal mol−1 for CSN-j. A graph of relative stability evolution for the current HCl•H2SO4•HNO3 (CSN) aggregates is displayed in Fig. 5a on the scale of relevant stratospheric temperatures. When the temperature decreases from 298 to 188 K, only five structures maintain relative stability. Hydrogen bonds form hexagonal ring among strong acids, while monomers provide greater stability to structures. Aggregates CSN-a, CSN-b, CSN-c and CSN-d stay stable, with only aggregate CSN-e changing its relative stability due to its higher relative energy in spite of the three HBs in its structure. Nevertheless, only the CSN-f aggregate from the non-hexagonal family with three HB remains relatively stable. CSN-f has lower energy than the CSN-e structure because, in CSN-f, HCl acts as a proton

Relative reaction Gibbs free energies of CSN-n complexes at stratospheric temperatures Reaction: HCl+H2SO4 +HNO3 →HCl • H2SO4 • HNO3 Temperature

Ternary complex (CSN-n)

a b c d e f g h i j k *ΔG(0–298)K =−9.26 kcal mol−1

298 K*

210 K

195 K

188 K

Δ[ΔG(0–298)K ]

Δ[ΔG(0–210)K ]

Δ[ΔG(0–195)K ]

Δ[ΔG(0–188)K ]

Shape

0.0 1.3 2.4 4.7 9.0 5.5 7.0 7.6 8.4 11.8 12.2

−5.5 −3.6 −0.9 −0.6 3.6 0.4 1.9 2.5 3.4 6.7 6.7

−6.4 −4.4 −1.9 −1.5 2.7 −0.5 1.0 1.7 2.5 5.8 5.7

−6.9 −4.9 −2.3 −1.9 2.2 −0.9 0.6 1.2 2.0 5.4 5.2

Hexagonal ring (3 or 4 HB)

Non hexagonal ring

Two rings

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Fig. 5 Graphs of relative stability evolution in a HCl•H2SO4•HNO3 (CSN) aggregates, and b HCl•HNO3•H2SO4 (CNS) aggregates [28] at stratospheric temperatures

A

-1

Relative Gibbs free energy(Kcalmol )

14 12 10 8

Temperatures: 298K 210K 195K 188K

6 4 2 0 -2 -4 -6 -8 a

b

c

d

e

f

g

h

i

j

k

-1

Relative Gibbs free energy(Kcalmol )

Aggregates (CSN-n)

16 14 12 10

Temperatures: 298K 210K 195K 188K

B

8 6 4 2 0 -2 -4 -6 -8

a

b

c

d

e

f

g

Aggregates (CNS-n)

donor/acceptor in its complex. The remaining structures, which have two rings, stay unstable considering that their Δ[ΔG] range changes from 8.4 to 12.2 kcal mol−1 taking CSN-a as the global minimum energy reference. Five relatively stable aggregates of the CNS family (Fig. 5b), with a HNO3 moiety, have been evaluated previously [28]. The relative stability evolution graph for these aggregates shows another five relatively stable structures in the same temperature range. Four structures remain stable, i.e., those that also have a hexagonal ring in their structure, while only structure CNS-f stays

relatively stable in the CNS non-hexagonal ring family. Note that the CNS aggregate set seems more efficient than the CSN group of complexes. Out of 7 optimized CNS-structures with a HNO3 moiety, 5 remain stable when the temperature decreases to 188 K compared to 5 of 11 optimized CSN-aggregates with a H2SO4 moiety, with CSN-f remaining unstable at 210 K. These results seem in agreement with theoretical work [24] on HCl, in which the Gibbs free energy calculated changes from −5.8 to −6.7 kcal mol−1 at 190 K, while current CSNvalues for relative stability from a 188–210 K temperature

78 Page 10 of 22

range changes from −5.5 kcalmol−1 to −6.9 kcal mol−1. With respect to experimental work [35] looking at the thermodynamic stability and phase transitions in PSC, their results are in the crystalline phase at 195–215 K while our results are in the gas phase at similar temperatures; both sets of results are in agreement with relative stability over a similar temperature range. Moreover, MD simulations [24] were used to study the acid ionization of HCl at the basal plane surface of ice at 190 K. The free energy changes calculated therein for the ionization mechanism ranged from −5.8 to −6.7 kcal mol−1. This range of values is in agreement with the results of this work where we found relative free energy values for the CSN family ranging from −5.5 to −6.9 kcal mol−1, and for CNS aggregates [28] relative free energy values ranging from −4.8 to −6.1 kcal mol−1. It seems that CSN aggregates—in which H2SO4 is the moiety present within the complexes—remain slightly more stable when the temperature decreases from 298 to 188 K relative to CNS aggregates [28]—with a HNO3 moiety—at the same temperature range in which the five structures remain relatively stable in both cases. These results seem to be in agreement with the behavior of PSCs at stratospheric temperatures [3, 4, 6, 34], wherein a relationship can be discerned between denitrification and chlorine activation in PSCs and stratospheric temperatures that affect ozone loss in the winter. Although these results have been obtained for small systems, this relatively stable evolution seems feasible for bigger systems that occur in PSCs, which HCl, HNO3 and H2SO4 also take part in.

Conclusions The present theoretical analysis of ternary aggregates of HCl•H2SO4•HNO3 (CSN), continuing on from a previous study on HCl•HNO3•H2SO4 (CNS), yielded the following results: (1) Eleven minima were found on the PES. Structure CSN-a was the global minimum; the remaining structures (CSN-b–CSN-k) obtained a local minima on their PES. Note that H2SO4 was the moiety placed in all initial aggregates. (2) CSN-a aggregate complexes have four HB among three monomers, and are the most energetically stable relative to the other aggregates. The remaining aggregates, CSNb, CSN-c, CSN-d and CSN-e, possess three HBs. These five clusters are classified in the hexagonal family. All these structures generate a hexagonal ring among H2SO4 and HNO 3 . This family is the most favorable energetically.

J Mol Model (2015) 21: 78

(3) Aggregates with a ring in their geometry were designated as the non-hexagonal ring family. These aggregates are CSN-f, CSN-g and CSN-h. These three clusters have three HBs in their structure. The HCl is placed above the x-axis in these structures. This makes them less favorable energetically. (4) The two-rings family is formed by CSN-i, CSN-j and CSN-k aggregates, which have two rings in their geometry constructed by four HB. The presence of two rings in the structure gives higher energy to the clusters. These complexes have shorter HB and smaller angles in their geometries. This family possesses the highest energy. (5) Strong acids: HCl, H2SO4 and HNO3, were never found ionically dissociated. (6) HNO3 acts as proton donor in all cases. (7) H2SO4 transfers both trans-protons in the following structures: CSN-a, CSN-b, CSN-e, CSN-i, CSN-j and CSN-k. It acts as a single trans-proton donor in aggregates CSN-f, CSN-g and CSN-h. Only in geometries CSN-c and CSN-d, does H2SO4 transfer its cis-protons. (8) HCl acts as the main proton donor/acceptor in the CSN structures. Only in the CSN-b, CSN-c, CSN-d and CSN-e aggregates does HCl act as a proton acceptor. (9) Eleven IR spectra were obtained. Real harmonic vibrational modes such as symmetric stretching modes correspond to H–Cl and O–H that are explicit in the spectra. The CSN-a symmetric stretching modes shift at 2805.56 cm−1 and 3520.00 cm−1 for H-Cl modes, and the O-H modes shift at 3256.87 cm−1 and 3362.47 cm−1. Others shifts are specific to each spectrum. (10) Relative stability is favorable for five aggregates when the temperature decreases from 298 to 210 K, 195 K and 188 K. These ternary complexes are: CSN-n, where n=a, b, c, and f. Only CSN-f remains unstable when the temperature decreases to 210 K. The remaining aggregates turn out to be unstable at these three stratospheric temperatures. (11) A graph of relative stability evolution in CSN complexes shows that 5 out of 11 structures remain stable when the temperature decreases, whereas for CNS clusters [28] 5 of 7 aggregates remain stable in these conditions. (12) The relative Gibbs free energy value for CSN-a global minimum is ΔG(0–298)K =−9.26 kcal mol−1. (13) CSN aggregate results are slightly more stable than those of CNS [28] in terms of relative reaction Gibbs free energy [Δ(ΔG)] where CSN has a value of −6.9 kcal mol−1 compared to −6.1 kcal mol−1 for CNS. (14) Further theoretical analysis is required, e.g., adding water molecules to both systems (CSN and CNS) at the same temperatures.

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Appendix Tables of CSN-n ternary complexes with their internal parameters are available upon request. Fig. 6 CSN-b structure with its inter-molecular parameters explicit

CSN-b

Fig. 7 CSN-c structure with its inter-molecular parameters explicit

CSN-c

O12-H10-O4 173° 10’

1.68

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Fig. 8 CSN-d structure with its inter-molecular parameters explicit

Fig. 9 CSN-e structure with its inter-molecular parameters explicit

2.33

Cl8-H6-O2 158° 32’

CSN-d

CSN-e

J Mol Model (2015) 21: 78 Fig. 10 CSN-f structure with its inter-molecular parameters explicit

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CSN-f

Fig. 11 CSN-g structure with its inter-molecular parameters explicit

CSN-g

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Fig. 12 CSN-h structure with its inter-molecular parameters explicit

CSN-h

Fig. 13 CSN-i structure with its inter-molecular parameters explicit

CSN-i

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Fig. 14 CSN-j structure with its inter-molecular parameters explicit

CSN-j

O2-H6-O13 134° 55’ 1.96

Fig. 15 CSN-k structure with its inter-molecular parameters explicit

CSN-k

O4-H9-Cl8 140° 34’

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J Mol Model (2015) 21: 78

(Intensity-atomic units)

Fig. 16 IR spectrum of CSN-b aggregate with vibration modes of HB explicit therein

H6—O13-N Symmetric streching mode 3390.74 cm-1

4000

CSN-b

3000

H7--Cl Symmetric streching mode 3559.72 cm-1

2000

N-H10—O5-S Symmetric streching mode 3217.33 cm-1

1000

0 0

1000

2000

3000

4000 -1

wavenumber (cm )

Fig. 17 IR spectrum of CSN-c aggregate with vibration modes of HB explicit therein

CSN-c

(Intensity -atomic units)

3000

2500

H6—013-N Symmetric streching mode

2000

3365.22 cm-1

H7—Cl Symmetric streching mode

1500

3558.17 cm-1

H10—O4-S Symmetric streching mode

1000

3211.5 cm-1

500

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

wavenumber (cm )

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Fig. 18 IR spectrum of CSN-d aggregate with vibration modes of HB explicit therein

(Intensity- atomic units)

CSN-d 5000 H7—O14-N Symmetric streching mode 3414.66 cm-1

4000

3000

2000

O2-H6—Cl Symmetric streching mode 3211.25 cm-1

H10—O5-S Symmetric streching mode 3266.79 cm-1

1000

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

wavenumber (cm )

Fig. 19 IR spectrum of CSN-e aggregate with vibration modes of HB explicit therein

(Intensity - atomic units)

CSN-e 3000

H6—Cl Symmetric streching mode 3498.21 cm-1

2500

H7—O13-N Symmetric streching mode 3533.31 cm-1

2000

H10—O2-S Symmetric streching mode 3464.23 cm-1

1500

1000

500

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

wavenumber (cm )

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(Intensity-atomic units)

Fig. 20 IR spectrum of CSN-f aggregate with vibration modes of HB explicit therein

CSN-f

3000

O-H6—Cl Symmetric streching mode 3403.78 cm-1

2500

2000

1500

N-H14—O5 Symmetric streching mode 3428.14 cm-1

Cl-H9—O12-N Symmetric streching mode 2715.10 cm-1

1000

500

0 0

1000

2000

3000

4000 -1

wavenumber (cm )

Fig. 21 IR spectrum of CSN-g aggregate with vibration modes of HB explicit therein

(Intensity- atomic units)

CSN-g 3500

3000 H1O—O5-S Symmetric streching mode 3314.18 cm-1

2500

2000

1500

H7—Cl Symmetric Streching mode 3467.76 cm-1

Cl-H9—O14 Symmetric streching mode 2800.17 cm-1

1000

500

0 0

1000

2000

3000

4000 -1

wavenumber (cm )

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(Intensity -atomic units)

Fig. 22 IR spectrum of CSN-h aggregate with vibration modes of HB explicit therein

CSN-h

5000

4000 H7—Cl Symmetric streching mode 3468.05 cm-1

3000

2000 Cl-H9—O12-N Symmetric streching mode 2715.85 cm-1

1000

H10—O4-S Symmetric streching mode 3437.14 cm-1

0 0

1000

2000

3000

4000 -1

wavenumber (cm )

(Intensity -atomic units)

Fig. 23 IR spectrum of CSN-i aggregate with vibration modes of HB explicit therein

CSN-i

3000

2500

O2-H6—Cl Symmetric streching mode 3523.88 cm-1

2000

1500 H10—O4-S Symmetric streching mode 3590.52 cm-1

H9—O5-S Symmetric streching mode 2793.96 cm-1

1000

500

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

wavenumber (cm )

Fig. 24 IR spectrum of CSN-j aggregate with vibration modes of HB explicit therein

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(Intensity -atomic units)

78 Page 20 of 22

CSN-j

3000

2500

O3-H7– Cl Symmetric Streching mode 3523.19 cm-1

2000

H6 & H10 Asymmetric Streching mode 3583.69 cm-1

1500

Cl-H9—O4-S Symmetric streching mode 2787.66 cm-1

1000

500

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

Fig. 25 IR spectrum of CSN-k aggregate with vibration modes of HB explicit therein

(Intensity -atomic units)

wavenumber (cm )

CSN-k

3500 H7-H10-H6 Asymmetric Streching Mode 3447.14 cm-1

3000

2500

H6—Cl Symmetric Streching Mode 3511.71 cm-1

2000

1500 Cl-H9—O4 Symmetric streching mode 2788.98 cm-1

1000

500

0 0

500

1000

1500

2000

2500

3000

3500

4000 -1

wavenumber (cm )

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Relative stabilities of HCl•H2SO4•HNO3 aggregates in polar stratospheric clouds.

Strong acids such as HCl (C), HNO3 (N) and H2SO4 (S) acquire relevance in Polar Stratospheric Clouds (PSCs) and aerosols in which nucleation processes...
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