J Mol Model (2014) 20:2232 DOI 10.1007/s00894-014-2232-6

ORIGINAL PAPER

Quantum chemical study of atmospheric aggregates: HCl•HNO3•H2SO4 Marian Verdes & Miguel Paniagua

Received: 26 February 2014 / Accepted: 2 April 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract HCl, HNO3 and H2SO4 are implicated in atmospheric processes in areas such as polar stratospheric clouds in the stratosphere. Ternary complexes of HCl, HNO3 and H2SO4 were investigated by ab initio calculations at B3LYP level of theory with aug-cc-pVTZ and aug-cc-pVQZ basis sets, taking into account basis set superposition error (BSSE). The results were assessed in terms of structures (five hexagonal cyclic structures and two quasi-pentagonal cyclic structures), inter-monomeric parameters (all ternary complexes built three hydrogen bonds), energetics (seven minima obtained), infrared harmonic vibrational frequencies (red shifting of complexes from monomers), and relative stability of complexes, which were favorable when the temperature decreases under stratospheric conditions, from 298 K to 188 K, and in concrete, at 210 K, 195 K and 188 K. Keywords PSCs . HCl . HNO3 . H2SO4 . DFT . Clusters . B3LYP . Relative stability . Aug-cc-pVTZ . Aug-cc-pVQZ . Quantum chemistry . Aggregates . Stratosphere . Temperatures . Relative gibbs free energy . Infrared frequencies . Structures . Conformers

Introduction Strong acids, hydrogen chloride (HCl), nitric acid (HNO3) and sulfuric acid (H2SO4) play an important role in atmospheric processes, especially in ozone (O3) depletion. These strong This paper belongs to Topical Collection QUITEL 2013 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]

acids participate in the particles comprising polar stratospheric clouds (PSCs). PSCs promote the conversion of stable inorganic chlorine compounds (ClONO2 and HCl) into a photolytically active form (Cl2), enabling the formation of the chlorine radical that participates in catalytic ozone destruction processes [1–14]. These three strong acids interact with the ice surface of PSCs even in stratospheric aerosols [15–17]. Moreover, the solubility and diffusion of HCl in ice have been examined in the past by Molina et al. [6]. Measurements of the freezing point of aqueous HCl solutions of different concentrations demonstrated the existence of solid HCl hydrates [18–21]. On the other hand, particles in PSC type I are formed by nitric acid [22–24], where HNO3 is joined to one, two or three water molecules (NAM, NAD, NAT), respectively, in nucleation processes [25, 26]; the associated denitrification reactions have been studied by Tabazadeh et al. [27, 28]. Nucleation processes have also been studied previously for sulfuric acid n H2O molecules in the stratosphere [10, 16, 29]. For instance, the behavior of sulfuric acid tetrahydrate (SAT) on frozen aerosols [30], condensation or deliquescence [31, 32] was investigated. Binary systems for nitric and sulfuric acids hydrates—clusters from n 0 to 6 for HNO3• nH2O; (H2SO4)2 •nH2O; H2SO4 •nH2O nitric/sulfuric systems—have also been previously investigated theoretically [33–38]. The physical chemistry of the H2SO4/HNO3/H2O ternary system [10] and its implications for PSCs has been researched also to understand the heterogeneous reactions of sulfuric acid aerosols by means of chlorine activation. On the other hand, vapor pressures of H 2 O, HNO 3 , HCl and HBr over supercooled aqueous mixtures with H2SO4 have been calculated in the laboratory [39]. Interaction of the binary and ternary systems on HNO3•HCl•H2O has been studied theoretically [40–44] and experimentally [45–47], collecting results on the energetics, structures and spectroscopy of these complexes.

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The relative stability of similar complexes has been investigated previously by Gómez et al. [40] for a theoretical HNO3-HCl-H2O system. Moreover, nonadditive features for the same system were reported by Balci and Uras-Aytemiz [43], inclusive autoionization in water molecules [44]. These three strong acids in gas phase may contribute to joining of water molecules in the nucleation processes of PSCs. Experiments have shown the dependence on temperature of mixes of these strong acids at low temperatures [6, 26, 39, 40, 45–48]. The minimum temperature for the formation of ice in the stratosphere is 188 K, i.e., the temperature of formation of a type II PSC ice particle, where HCl interacts with the ice [46]. The type I PSCs that form during winter appear at 195 K. PCSs provide surfaces for oxidation of HCl, and also for the nucleation of nitric acid—their trihydrate (NAT)-is assumed—on preexisting H2SO4 aerosols [4, 14, 16]. A temperature of 210 K is a boundary temperature in PSCs, where nitric and sulfuric acids join to ice particles forming SAT (sulfuric acid tetrahydrate) or STS (supercooled ternary solution) [6, 10, 12, 39]. This paper presents theoretical results of the ternary complexes containing these three strong acids, specifically, hydrogen chloride, nitric acid and sulfuric acid. The structures, inter-monomeric parameters (hydrogen bonds built), relative stability, infrared spectra, potential energy surfaces, and inclusive relative Gibbs free energies at three stratospheric temperatures (188 K, 195 K and 210 K) were investigated for each system. In addition, the hydrogen bonding features of each ternary system were assessed, focusing on proton transfer peculiarities specific to the aggregates shown here.

Methods Electronic structure calculations were applied to the ternary complexes of HCl, HNO3 and H2SO4 by using DFT/B3LYP method with aug-cc-pVTZ basis set. Additional calculations with aug-cc-pVQZ basis set were performed to assess the effect of expanding the basis set on the geometrical parameters and their influence on the energies [49–52]. Note that, as a first theoretical systematic study of these three strong acids, one restriction was considered in all starting structures: nitric acid was placed as a moiety in the aggregates. First structures were created according to chemical intuition criterion to achieve maximum feasible inter-monomeric hydrogen bonds among monomers in the ternary structure. The initial step was to optimize these candidate structures—12 z-matrixes—at a low level of theory with the B3LYP method and 6-31G basis set. Only seven initial candidate structures were converged on this first optimization. These seven optimized z-matrixes at low level of theory were subjected to a larger optimization using the B3LYP method jointly with the aug-cc-pVTZ basis set. After these high level optimizations, seven configurations

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were obtained. Note that all geometries optimized were performed at 0 K. Subsequently, these seven structures were exposed to vibrational analysis to find out the real minimum on their potential energy surface (PES) by means of B3LYP/ aug-cc-pVTZ level of theory. Exceptionally, to achieve a reliable minimum PES in configuration (f) ,“very tight” option—as extremely tight optimization convergence criteria— was needed in the optimization procedure to attain a true optimized structure and energy for that structure. Harmonic vibrational frequencies were calculated at B3LYP/aug-ccpVTZ level of theory as geometry optimization. The frequencies shifting (Δν) was calculated by subtraction between frequency in the ternary complex (νt) and frequency in the monomer (νm). To eliminate the basis set superposition error (BSSE) introduced by this procedure, we used the counterpoise correction (CC) method of Boys and Bernardi [53]; CC was calculated over all structures optimized by the triple-ζ basis set. To compare the results achieved by means of B3LYP/aug-cc-pVTZ, all configurations optimized by triple-ζ were also subjected to B3LYP/aug-cc-pVQZ computational level using the full optimization option. Moreover, the CC procedure was taken into account on configurations fully optimized with the quadruple-ζ basis set. Thermochemistry was calculated for the final structures attained at triple-ζ level of theory at three stratospheric temperatures: 188 K, 195 K and 210 K, and also at 298,15 K by default in the program. For nucleation of monomers, the Gibbs free energy was calculated as follows: HCl þ HNO3 þ H2 SO4 →HCl⋅HNO3 ⋅H2 SO4 C þ N þ S→CNS where the relative Gibbs free energies associated with the production of HCl•HNO3•H2SO4 (CNS) were calculated as: ΔGmin ¼ ½ðE þ ZPEÞ þ H−TS Šcomplex −∑½ðE þ ZPEÞ þ H−TS Šmonomers where E is the energy at 0 K; ZPE is the zero-point energy; H is the thermal enthalpy contribution from translational, vibrational, rotational motions; and S is the entropy contributions from these motions. The relative reaction Gibbs free energies [Δ(ΔG)] associated at the global minimum aggregate obtained (ΔGmin) with respect to remaining local minima clusters was calculated as:   ΔðΔGÞnrelative ¼ Δ ΔGnð0−T Þ −ΔGmin where ΔGmin is the ternary complex (a) with global minimum relative energy among the clusters studied. The n is the different ternary systems obtained in this study: n=(b−g). (ΔG(0-T)) takes the following temperature values: 188 K, 195 K and

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210 K. Hence, the relative stability for the clusters Δ(ΔG)n Δ ðΔGÞnrelative at these temperatures was achieved. All calculations were performed with the GAUSSIAN 09 program suite [54].

Results and discussion Following a search for stable structures formed by HCl, HNO3 and H2SO4 by interactions produced among the three monomers, we found seven conformers. The production of a large number of conformers was limited because the nitric acid was constrained to the middle position in all of starting conformers. Afterwards these full optimizations and vibrational analysis, seven real minima on the PES were found. These optimizations were performed at B3LYP level of theory using aug-cc-pVTZ and aug-cc-pVQZ basis sets. Full geometry optimizations at the B3LYP level with the aug-cc-pVQZ basis set were achieved, employing the latter B3LYP/aug-cc-pVTZ optimizations. The effect of ZPE was taking into account in both levels, with triple and quadruple-ζ contributions added to electronic energy, respectively. In the same manner, the BSSE was considered at all levels of theory. The energy values found for different levels of theory with aug-cc-pVTZ and aug-ccpVQZ basis set are collected in Table 1. Notice that the stabilization of aggregates is irrelevant when BSSE is applied. Focusing on complexes (e) and (g) (Fig. 1), the difference in energy is only 0.1 kcal mol−1 for both complexes when calculated at B3LYP/aug-cc-pVTZ level taking into account BSSE. This difference is 0.18 and 0.16 kcal mol−1 in their energy, respectively, when these structures were calculated at B3LYP/aug-cc-pVQZ level considering BSSE. The BSSE

effects in the remaining configurations were negligible in all calculations. All stable aggregates fully optimized are given in Fig. 1. Note that none of three strong acids, HCl, HNO3 and H2SO4 was ionized. In addition, all three acids can donate their protons or not depending on the cluster treated. All structures could be classified into two types of families. First, structures with a hexagonal ring between nitric acid and sulfuric acid were grouped as the hexagonal family (Hf). Configuration (a) has the better relative energy. Second, two conformers whose structures made a quasi-pentagonal union among their monomers were grouped as non-hexagonal family (NHf). Structure (f) has the better relative energy in this family and the second best relative energy in this study. The Hf family is composed of five aggregates; in this family, it should be stressed that HCl is always positioned below the x-axis on the right for four structures: (a), (b), (c), (e) and one case on the left (d). This position of HCl takes into account biasing in energetic values of conformers, the most stable of them being named (a). However, the aggregate whose HCl is positioned below on the left of the x-axis has the penultimate energetic value in the Hf family series. The location of sulfuric acid protons influences cluster characteristics such as geometry and stability. For instance, protons of sulfuric acid in trans position give better stability to the aggregate [i.e., for conformers: (a), (b)] than cis protons [i.e., conformers (c), (d), (e)]. Conformer (e) has the lowest energy, owing to both protons of sulfuric acid being in cis position and the proton of nitric acid not being involved as donor. For the Hf family, the HCl always acts as proton donor to HNO3, which confers its proton on H2SO4 and finally, sulfuric acid donates its proton to nitric acid, creating a hexagonal ring between both acids. The NHf family

Table 1 Relative energies with respect to global minimum of the ternary complex HCl•HNO3•H2SO4 (CNS) (a). Values are expressed in kcal mol−1. Monomers in Eh. ΔE Relative energies CC Counterpoise correction, ZPE zero-point energy, ZPEC Zero-point energy correction

Complexes (a) (f) (b) (c) (d) (e) (g) Monomers HCl HNO3 H2SO4 a

B3LYP/aug-cc-pVTZ

B3LYP/aug-cc-pVQZ

E (a) =−1442.2906672 Eha ΔE ZPEC 0.0 46.9 0.35 47.0 0.53 46.8 1.67 46.5 2.18 46.6 4.27 46.6 8.58 46.3 B3LYP/aug-cc-pVTZ CCSD(T) Eh ZPEC −460.8442638 4.2 −281.0071073 16.4 −700.4183171 24.2

E (a) =−1442.356763 Eha CC Δ(E + CC) 0.22 0.0 0.20 0.4 0.23 0.6 0.21 1.7 0.22 2.2 0.18 4.3 0.16 8.6 B3LYP/aug-cc-pVQZ Eh ZPEC −460.8481792 4.2 −281.0282842 16.5 −700.4593122 24.4

1Eh =627.50955 kcal mol−1

Δ(E + ZPEC) 0.0 0.4 0.4 1.5 1.8 4.0 8.0 PW91

CC 0.45 0.40 0.47 0.44 0.45 0.40 0.36

−280.5449583 −699.4609749

−280.9774181 −700.3269005

Δ(E + ZPE + CC) 0.0 0.4 0.4 1.5 1.8 3.9 7.9

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Fig. 1 Optimized structures of HCl, HNO3 and H2SO4 at B3LYP/aug-cc-pVTZ level

comprises two structures: (f) and (g). In family NHf, the HCl is placed above in both conformers, which gives a quasipentagonal shape among monomers. Aggregate (f) shows the lowest relative energy because of linking the proton cis

of nitric acid. Structure (g) has the lowest relative energy for both families. Proton transfer in family NHf differs with respect to that of the Hf family. In addition, the HCl donates its proton to nitric acid, this one transfers its proton to H2SO4;

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however, sulfuric acid confers its proton to the chlorine of hydrogen chloride. This creates a non-hexagonal ring between sulfuric and nitric acids, similar to a quasi-pentagonal ring. Focusing on the aggregate with the global minimum relative energy, structure (a) (Fig. 2; geometrical parameters listed in Table 2) was submitted to analysis. Aggregate (a) proved to be in agreement with previous calculations performed by Gómez et al. [40] with respect to their structure named N1AC-4, and with Balci et al. [43], fir some of the ternary complexes shown in their Table 9. Note that Gómez et al. [40] and the present study use the B3LYP/aug-cc-pVQZ (and/or without BSSE) method and basis set, whereas the data of Balci et al. [43] were obtained at MP2/aug-cc-pVTZ level of theory. Comparing the results, note that the distance H–Cl (in the monomer isolated) was stated as 1.2812 Å [40], 1.282 Å (this paper) and 1.27 Å [43]. In the complex, the distance H–Cl was 1.289 Å [40], 1.287 Å (this study) and 1.28 Å [43]. This distance (1.28 Å) corresponds to Fig. 4b,c,d,n and o in [43] showing similar inter-monomeric bonding between hydrogen chloride and nitric acid monomers in the structures cited in the latter work as aggregate (a) here. In the same way, comparing the distance between H from the oxygen in HNO3 notes the results in the monomer as 0.97 Å [40], 0.97 Å (this paper), and 0.97 Å [43]. The distance of H from the oxygen of nitric acid in the complex yields the following results: 0.999 Å [40], 0.997 (this paper) while Balci et al. [43] reported 1.00 Å in their Fig. 4b, c and d, and 0.97 Å in Fig. 4n and o. The H–O–N angle in the nitric acid—HNO3 isolated— gave the following values: 103.20° [40], and 103.25° (this study). When the nitric acid is placed in the complex, the angle H–O–N was 105.73° [40] vs 107.51° obtained in this paper. The last couple of values were calculated at B3LYP/aug-ccpVQZ taking into account the BSSE. Note that the values reported here are mostly larger than those reported by Gómez et al. [40] because the nitric acid is interacting with sulfuric acid in our complex instead of a water molecule. Tables 7–11 and 12 in the Appendix list the ternary complexes (a) to (g)

Fig. 2 Structure (a) has the global minimum of all ternary complexes studied. B3LYP/aug-cc-pVTZ level used

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whose internal and intermolecular parameters are captured. Moreover, Figs. 4–9 shows structures of all stable aggregates studied here. These figures show explicit distances, angles and dihedral angles among monomers. Inter-monomeric parameters for all ternary complexes in this work are summarized in Table 3. Data were calculated at B3LYP level with aug-cc-pVQZ basis set taking into account the BSSE by means of the CC method. Inter-monomeric distance between the hydrogen of HCl and oxygen of HNO3 reported by Gómez et al. [40] gave 2.146 Å, in their N1AC-4 structure vs 2.188 Å in configuration (a) of this work. On the other hand, Balci et al. [43] obtained 2.10 Å for the similar distance in their Fig. 4n and o presented in their Table 9. The inter-monomeric angle formed by Cl–H–ON, Gómez et al. [40] reported 162.77° facing 175.44° in cluster (a) and 165.85° in cluster (e) of this work. Table 4 shows the harmonic vibrational frequencies analysis of ternary complexes at B3LYP/aug-cc-pVTZ level of theory and basis set. All frequency shift values of the ternary complexes (a) to (g) with respect to the isolated monomers are given. The maximum O–H bond shift was calculated as −525 cm−1 corresponding to (d) aggregate. On the other hand, the minimum bond shift was given by (g)-conformer (−253 cm−1), whose structure is a non-hexagonal ring with lower stability than the others. Nevertheless, the most stable structure (a) gave a O–H bond shift as −514 cm−1, while a similar O–H bond shift in ternary complex (4d) in a study reported by Balci et al. [43] gave −583 cm−1. The difference is due to the presence of sulfuric acid in conformer (a) replacing the water molecule in ternary 4d. Also, Gómez et al. [58] reported a O–H stretch value for their cluster N1AC-5 as −573 cm−1. Also, the H–Cl stretch values obtained were: −131 cm−1, −138 cm−1 and −65 cm−1 as reported for Balci et al. [43], Gómez et al. [58] and in Table 3, respectively. To account for sulfuric acid red shifting, the value was calculated as −325 cm−1. Figure 3 shows the spectrum of aggregate (a) where biggest intensities corresponded to three intermonomeric stretching modes. At 2,868.64 cm−1 (symmetric stretch mode) belonging to proton transfer of HCl; at 3,197.89 cm−1 (symmetric stretch mode) corresponding to proton transfer of HNO3; and at 3,422.93 cm−1 belonging to proton transfer of H2SO4, as well as the corresponding symmetrical stretch mode. Other spectra belonging to aggregates (b) to (g) that contain frequencies and vibrational stretching modes can be see in Appendix Figs. 10, 11, 12, 13, 14, 15. Three strong acids made up the ternary complexes, which donate, simultaneously, three hydrogen bonds to the system by means of proton transfer. This fact provides stability to the complex. Analysis of Gibbs free energy is likely to determine the relative stability for each aggregate. The relative stability was considered at three isolated stratospheric temperatures: 188 K (frozen ice), 195 K (NAT stability) and 210 K (SAT stability) for all of these ternary complexes. The Gibbs free

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Table 2 Parameters of ternary complex (a)—the structure with the global minimum in this study. Optimizations were calculated at the B3LYP level with aug-cc-pVTZ/QZ basis set Geometric parametersa

Complex -TZ

-TZ-CCb

Hydrogen chloride (Huber and Herzberg [55]) r (Cl13H14) 1.289 1.289 Nitric acid (Huber and Herzberg [56]) r (N1-O2) 1.198 1.198 r (N1-O3) 1.225 1.225 r (N1-O4) 1.359 1.359 r (O4-H5) 0.998 0.998 θ (N1-O4-H5) 107.40 107.38 θ (O2-N1-O3) 126.41 126.43 θ (O2-N1-O4) 115.41 115.38 θ (O3-N1-O4) 118.18 118.19 Sulfuric acid (Chackalackal and Stafford [57]) r (S7-O6) 1.451 1.451 r (S7-O10) 1.580 1.580 r (O9-H11) 0.970 0.970 θ (S7-O10-H12) 109.60 109.60 θ (O9-S7-O10) 103.33 103.33 θ (O6-S7-O8) 121.66 121.68 θ (O6-S7-O10) 108.82 108.81 θ (O9-S7-O6) 104.23 104.23 τ (H12-O10-S7-O6) −27.26 −27.287 τ (H12-O10-S7-O9) 83.08 83.054 Inter monomeric values of aggregate (a) r (O2-H14) 2.188 2.191 r (O3-H12) r (O6-H5) θ (O4-H5-O6) θ (O2-H14-Cl13) θ (O3-H12-O10) τ (N1O-4H-5O6) τ (N1-O3-H12-O10) τ (O4-H5-O6-S7) τ (N1-O2-H14-Cl13) a

1.779 1.675 174.20 175.41 174.74 177.76 6.44 179.43 −174.90

1.788 1.683 174.13 175.45 174.78 177.81 7.08 179.61 −174.84

Previous works

Monomers isolated

-QZ-CCb

QZ-cce

MP2/augcc-pVTZc

-TZ

MP2/augcc-pVTZc

-QZ

-QZe

1.287

1.289

1.28ª

1.2835

1.27

1.282

1.2812

1.275

1.197 1.224 1.357

1.195 1.212 1.388

1.28d 1.21ª 1.39ª

1.193 1.207 1.414

1.20 1.21 1.41

1.191 1.206 1.411

1.192 1.206 1.410

1.199 1.211 1.406

0.997 107.51 126.39 115.41 118.19

0.999 105.73

0.97ª

0.972 103.07 130.45 113.93 115.62

0.97

0.970 103.25 130.39 113.96 115.65

0.970 103.20

0.964 102.15 130.27 113.85 115.53

1.442 1.570 0.968 109.99 103.43 121.57 108.78 104.23 −27.18 83.25 2.188 1.785 1.681 174.41 175.44 174.52 177.64 7.42 179.54 −174.85

Counterpoise correction (CC) method was taking account

c

MP2 level with aug-cc-pVTZ basis set [44]

e

2.146

1.426 1.600 0.968 109.10 102.02 123.99 108.66 105.72 −25.99 85.37

1.422±0.01 1.574±0.01 0.97±0.01 108.5±1.5 101.3±1 123.3±1 108.6±0.5 106.4±0.5 20.8±1 −90.9±1

2.08

162.77

Distances (r) in Angstroms (Å), angles (θ) and dihedral angles (τ) in degrees

b

d

1.435 1.610 0.969 108.70 101.90 124.12 108.67 105.67 −25.82 85.44

Monom exp.

With respect to 3e dimer in [44] Reference [40]

energy analysis was performed at the same level of theory as the optimizations. Table 5 summarizes the results of relative Gibbs free energy (ΔG), and relative reaction Gibbs free energy Δ(ΔG) for all ternary complexes identified here. Ternary complex (a) stands out as having the most favorable relative stability at three temperatures, with −6.1 kcal mol−1

as lowest ΔΔG at 188 K, −5.7 kcal mol−1 at 195 K, and −4.8 kcal mol−1 at 210 K, respectively. For all temperatures (298, 210, 195, and 188) Kelvin, the ternary complexes (a), (b), (c) and (d)—belonging to family Hf—reveal favorable relative stability. Only ternary complex (e) is unstable at all temperatures. For family NHf, i.e., ternary (f) and (g), ternary

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Table 3 Inter-monomeric geometrical parameters of all ternary complexes shown in Fig. 2. All values were obtained at the B3LYP level with the aug-ccpVQZ basis set. Counterpoise correction (CC) was considered Aggregate Parametersa

(a)

(b)

(c)

(e)

(g)

(f)

Hexagonal ring Distances r (NO—HCl) (r NO—HO) r (SO—HO) r (OH—Cl) Angles θ (SO—H—ON) θ (NO—H-Cl) θ (SO—H—ON) θ (OH—Cl) Dihedral angles τ (N-O-H-O) τ (O-H-O-N) τ (O-H-O-S) τ (N-O-H-Cl) τ (S-O-H-Cl) a

(g)

Non hexagonal ring

2.188 1.785 1.681

2.300 1.784 1.680

2.198 1.777 1.676

2.309 1.773 1.674

2.275 2.336 2.142

1.956 – 1.762 2.204

2.056 – 1.871 2.306

174.415 175.442 174.519

174.448 168.718 174.459

175.356 175.506 177.374

175.319 165.854 177.998

146.979 172.188 162.951

169.265 171.396

141.750 165.919

177.240

170.572

165.212 – 90.845 151.457 9.815

131.148 – −25.636 49.262 173.847

177.644 7.416 179.538 −174.852

176.529 12.284 179.668 170.725

−139.627 −6.823 172.371 −150.576

144.578 7.068 −175.991 −141.713

−43.821 −34.534 31.201 −104.796

Distances (r) in Angstroms (Å), angles (θ) and dihedral angles (τ) in degrees

(f) reveals clearly better relative stability, with Δ(ΔG) of −4.8 kcal mol−1 at 188 K and 1.7 kcal mol−1 at 298 K. Nevertheless, ternary complex (g) revealed a deep instability

among all temperatures and complexes. Its strong instability was revealed by values of Δ(ΔG) of 10.5 kcal mol−1, 9.7 kcal mol−1 and 9.3 kcal mol−1 at 210 K, 195 K and

Table 4 Vibrational harmonic frequencies of HCl•HNO3•H2SO4 (CNS) ternary complexes Systems

Frequenciesa ν(Cl-H)

Monomers HCl (C) HNO3 (N) H2SO4 (S) Complexes CNS (a) CNS (b) CNS (c) CNS (d) cis CNS (e) cis CNS (f) CNS (g) a

νmonomer 2,934

νtrimer 2,869 2,899 2,873 2,897 2,892 2,710 2,732

ν(NO-H) Experimentalb 2,991

Δν −65 −35 −61 −37 −42 −224 −202

ν(SO-H1)

νmonomer

Experimentalc

3,712

3,550

νtrimer 3,198 3,195 3,189 3,187

Δν −514 −517 −523 −525

3,392 3,459

−320 −253

ν(SO-H2)

νmonomer

Experimentald

νmonomer

Experimentald

3,748 νtrimer 3,423 3,419 3,414 3,404 3,716 3,421 3,481

3,609 Δν −325 −329 −334 −344 −32 −327 −267

3,752 νtrimer

3,609 Δν

3,678

−74

All frequencies were calculated at the B3LYP level with aug-cc-pVTZ basis set. Harmonic frequency values (ν, Δν) in cm−1

b

[54]

c

[55]

d

[56]

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Fig. 3 Infrared spectrum of CNS-a ternary complex obtained at B3LYP/aug-cc-pVTZ level. Frequencies and vibrational modes for hydrogen bonds among monomers are included

188 K, and 14.8 kcal mol−1 at 298 K. For this temperature range, higher relative stability was seen with ternary (a) at 188 K with a value of Δ(ΔG) of −6.1 kcal mol−1, and the lowest relative stability was seen in ternary (d) with a Δ(ΔG) of −1.6 kcal mol−1 at 210 K.

Conclusions This theo retical study on ternary comp lexes of HCl•HNO3•H2SO4 in relation to relative energy, structures, inter-monomeric parameters, harmonic vibrational modes, and relative stability, gave the following results: (1) Seven minima were found on the PES. The global minimum falls on structure (a), the remaining structures (b– g) have local minima. In all structures, the HNO3 was moiety placed.

Table 5 Variation in relative reaction Gibbs free energies at three stratospheric temperatures. ΔGa (0–298)K = −1,810,037.5 kcal mol−1; Δ[ΔGa (0–298)K]= −5.7 kcal mol−1. Temperature in Kelvin

Ternary complex

(2) Inter-monomeric parameters revealed that all structures contain three hydrogen bonds in their structures. In five structures HNO3 and H2SO4 interchange proton transfer (a–e) and HCl transfers its proton to HNO3 (hexagonal ring). In two structures HCl, HNO3 and H2SO4 make a proton transfer from one to other (non hexagonal cyclic). In all cases HCl acts as a proton donor. (3) HCl, HNO3 and H2SO4 were never found ionically dissociated. (4) Harmonic vibrational modes such as O–H and H–Cl stretching modes on ternary complexes are red shifted relative to from modes in isolated monomers. (5) The structures with proton interchange between HNO3 and H2SO4 (trans) joining to HCl below the x-axis on the right, are more favorable energetically than other structures with cis protons in H2SO4. Aggregates (a–e). (6) Cluster (f), with HCl placed above in ternary, is joining by proton transfer between each of the three acids: HCl is linked to HNO3 (cis), which links to H2SO4, which is

Reaction: HCl + HNO3 + H2SO4 → HCl • HNO3 • H2SO4 Temperature

a b c d e f g

188 Δ[ΔG(0–188)K]

195 Δ[ΔG(0–195)K]

210 Δ[ΔG(0–210)K]

298 Δ[ΔG(0–298)K]

Shape

−6.1 −5.4 −3.2 −2.8 2.5 −4.8 9.3

−5.7 −5.0 −2.8 −2.4 2.9 −4.3 9.7

−4.8 −4.2 −2.0 −1.6 3.8 −3.4 10.5

0.0 0.6 2.7 2.9 9.0 1.7 14.8

Hexagonal ring

Non hexagonal ring

J Mol Model (2014) 20:2232

Page 9 of 19, 2232

linked to HCl. Cluster (f) has the second best relative energy. On the other hand, structure (g) had the lowest relative energy in the study owing to the trans position of H with respect to the oxygen proton acceptor in HNO3. (7) The relative stability is favorable for six ternary complexes when the temperature decreases from 298 K to 188 K. Structure (a) has higher relative stability at all temperatures. The Δ(ΔG) for ternary (a) at 188 K was −6.1 kcal mol−1. Only structure (g) is really unstable. (8) Further theoretical studies of HCl, HNO3 and H2SO4 are needed in the future, in particular addition of water molecules to give a more realistic stratospheric conditions in these small systems under study. Moreover, a systematic study with sulfuric acid in moiety of aggregates is foreseen as a continuation of this work (ongoing), including the addition of water molecules. Acknowledgment This work has been supported by Comunidad Autónoma de Madrid under grant S-2009/MAT-1467.

Appendix

Table 6 Results for CNS-a ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. Counterpoise correction (CC) was calculated

Table 6 (continued) Electronic energy (Eh)a

−1,442.2906672 −1,442.2899413 −1,442.3564136 Eh Eh Eh

θ(N1O4H5) θ(S7H12O10) θ(O8S7O9) θ(S7O9H11) θ(O6S7O9) θ(O4H5O6)b θ(O2H14Cl13)b θ(O3H12O10)b

107.399 109.601 109.601 109.255 104.229 174.203b 175.407b 174.739b

107.379 109.598 109.610 109.268 104.230 174.132b 175.455b 174.781b

107.506 109.989 109.594 109.725 104.286 174.415b 175.442b 174.519b

τ(N1O2H14Cl13) τ(O2N1O4H5) τ(O3N1O4H5) τ(H12O10S7O6) τ(O8S7O9H11) τ(O12O10S7O8) τ(H12O10S7O9) τ(O6S7O9H11) τ(N1O4H5O6)b τ(N1O3H12O10)b τ(O4H5O6S7)b τ(N1O2H14Cl13)b

−174.903 178.741 −1.109 −27.264 −30.116 −160.972 83.078 −161.802 177.764b 6.441b 179.433b −174.903b

−174.837 178.561 −1.317 −27.287 −30.034 −160.998 83.054 −161.760 177.814b 7.085b 179.611b −174.837b

−174.852 178.653 −1.125 −27.183 −30.128 −160.753 83.254 −161.745 177.644b 7.416b 179.538b −174.852b

a

1 Eh =627.50955 kcal mol−1

b

Intermonomeric parameters

−1,442.2906672 −1,442.2899413 −1,442.3564136 Eh Eh Eh

Table 7 Results for CNS-b ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. CC was calculated

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

Electronic energy (Eh)a

1.198 1.225 1.359 0.998 1.451 1.430 1.603 1.580 0.970 0.986 1.289

1.198 1.225 1.359 0.998 1.451 1.431 1.603 1.580 0.970 0.986 1.289

1.197 1.224 1.357 0.997 1.442 1.422 1.593 1.570 0.968 0.985 1.287

Distances (r), angles (θ), dihedral angles (τ) r(N1O2)

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

1.191

1.191

1.190

r(N1O3)

1.226

1.226

1.225

r(N1O4)

1.373

1.373

1.370

r(O4H5)

0.998

0.998

0.996

r(S7O6)

1.452

1.452

1.442

r(S7O8)

1.430

1.431

1.422

r(S7O9)

1.603

1.603

1.593

r(O9H11)

0.970

1.603

0.968

2.191b 1.788b 1.683b 27.102

2.188b 1.785b 1.681b 27.124

r(O10H12)

0.986

0.986

0.985

r(O3H12)b r(O6H5)b θ(N1O2O3)

2.188b 1.779b 1.675b 27.116

r(Cl13H14)

1.287

1.287

1.285

r(O3H12)b

1.776b

1.785b

1.784b

r(O6H5)b

1.673b

1.681b

1.680b

θ(N1O3O4))

118.181

32.691

32.667

b

b

2.300b

Electronic energy (Eh)a Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2) r(N1O3) r(N1O4) r(O4H5) r(S7O6) r(S7O8) r(S7O9) r(S7O10) r(O9H11) r(O10H12) r(Cl13H14) r(O2H14)b

−1,442.2898283 −1,442.2890777 −1,442.3555095 Eh Eh Eh

Parameters:

b

r(O4H13)

2.289

2.300

2232, Page 10 of 19

J Mol Model (2014) 20:2232

Table 7 (continued)

Table 8 (continued)

Electronic energy (Eh)a

−1,442.2898283 −1,442.2890777 −1,442.3555095 Eh Eh Eh

Electronic energy (Eh)a

−1,442.2880107 −1,442.2873054 −1,442.3537568 Eh Eh Eh

θ(N1O2O3)

26.715

r(H5O8)b

1.669b

1.677b

1.676b

b

b

1.777b

θ(N1O3O4))

26.708

26.715

26.722

26.708

b

33.252

r(H12O2)

1.770

1.779

θ(N1O4H5)

107.548

107.497

107.625

θ(N1O2O3)

26.429

26.415

26.440

θ(H12O10S7)

109.555

109.561

110.000

θ(N1O3O4))

34.551

34.572

34.538

θ(O8S7O9)

109.625

109.613

109.596

θ(N1O4H5)

107.179

107.138

107.283 110.467

θ(S7O9H11)

109.269

109.269

109.707

θ(H12O11S7))

110.006

109.997

θ(O6S7O9)

104.201

104.218

104.261

θ(O8S7O9)

107.556

107.566

107.651

θ(O4H13Cl14)b

168.826b

168.770b

168.718b

θ(S7O9H10)

110.343

110.324

110.841

θ(H13O4H5)b

130.906b

130.785b

130.678b

θ(O6S7O9)

106.054

106.060

106.046

b

173.990

b

173.989

174.448b

θ(O3H14Cl13)b

175.465b

175.504b

175.506b

136.656b

136.670b

136.784b

θ(O4H5O8)b

175.113b

175.079b

175.356b

b

b

b

174.459

θ(N1O2H12)

b

133.423

b

133.400

133.461b

θ(O4H5O6)

b

θ(N1O3H12)b b

θ(O3H12O10)

174.835

174.903

τ(O2N1O4H5)

178.552

178.669

178.651

τ(O3N1O4H5)

177.097

177.011

177.100

τ(O3N1O4H5)

−1.299

−1.197

−1.189

τ(O2N1O4H5)

−2.754

−2.897

−2.746

b

τ(H12O10S7O6)

−27.843

−27.622

−27.270

τ(H12O11S7O8)

−5.659

−5.643

−5.566

τ(O8S7O9H11)

−30.221

−30.116

−30.227

τ(O8S7O9H10)

33.142

33.007

33.435

164.659

164.568

164.860

τ(O12O10S7O8)

−161.533

−161.318

−160.847

τ(O6S7O9H10)

τ(H12O10S7O9)

82.479

82.713

83.151

τ(N1O3H14Cl13)b −151.213b

−150.839b

−150.576b

τ(O6S7O9H11)

−161.874

−161.818

−161.817

τ(O11H12O2N1)

−14.039

−13.187

−6.823b

b

b

b

−141.151

−141.424

−139.627b

b

b

b

b

τ(Cl14H13O4N1)

171.303

171.228

170.725

τ(O8H5O4N1)

τ(Cl14H13O4H5)

−2.361

−2.317

−2.812

τ(O4N1O3H14)

−4.194

−4.276

−4.411b

τ(O4H5O6S7)b

179.808b

179.715b

179.668b

τ(S7O11H12O2)b

47.549b

46.736b

39.920b

b b

a b

b

b

b

b

b

b

b

1 Eh =627.50955 kcal mol−1

a

1 Eh =627.50955 kcal mol−1

Intermonomeric parameters

b

Intermonomeric parameters

Table 8 Results for CNS-c ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. CC was calculated Electronic energy (Eh)a

−1,442.2880107 −1,442.2873054 −1,442.3537568 Eh Eh Eh

Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2)

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

1.226

1.226

1.225

r(N1O3)

1.198

1.198

1.197

r(N1O4)

1.360

1.360

1.357

r(O4H5)

0.999

0.998

0.997

r(S7O6)

1.424

1.424

1.416

r(S7O8)

1.462

1.462

1.453

r(S7O9)

1.597

1.597

1.453

r(O9H10)

0.969

0.969

0.968

r(O11H12)

0.986

0.986

0.984

r(Cl13H14)

1.288

1.288

1.287

r(O3H14)b

2.197b

2.202b

2.198b

b

Table 9 Results for CNS-d ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. CC was calculated Electronic energy (Eh)a Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2) r(N1O3) r(N1O4) r(O4H5) r(S7O6) r(S7O8) r(S7O9) r(O9H10) r(O11H12) r(Cl13H14) r(O6H5)b

−1,442.287191 −1,442.2864784 −1,442.3529065 Eh Eh Eh

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

1.227 1.191 1.373 0.999 1.462 1.425 1.597 0.969 0.987 1.287

1.227 1.191 1.374 0.998 1.462 1.425 1.597 0.969 0.986 1.287

1.225 1.190 1.371 0.997 1.452 1.416 1.587 0.968 0.985 1.285

1.667b

1.674b

1.674b

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Page 11 of 19, 2232

Table 9 (continued) Electronic energy (Eh)a

−1,442.287191 −1,442.2864784 −1,442.3529065 Eh Eh Eh

r(H12O2)b r(O4H14)b θ(N1O2O3) θ(N1O3O4)) θ(N1O4H5) θ(H12O11S7)) θ(O8S7O9) θ(S7O9H10)

1.762b 2.296b 25.869 34.936 107.336 109.840 106.007 110.385

1.773b 2.309b 25.853 34.955 107.242 109.970 106.006 110.378

1.773b 2.309b 25.882 34.910 107.376 110.437 106.010 110.852

θ(O6S7O9) θ(O4H14Cl13) θ(O4H5O6) θ(N1O2H12) θ(O2H12O11) τ(H12O11S7O8) τ(O8S7O9H10) τ(O6S7O9H10) τ(O2N1O4H5) τ(O3N1O4H5) τ(N1O2H12O11) τ(Cl14H13O4N1) τ(Cl14H13O4H5) τ(O4H5O6S7) τ(N1O4H14Cl13)

107.668 165.887 174.910 134.150 178.817 −136.753 −165.622 −34.189 2.778 −177.089 36.106b −142.104b 16.181b −178.026b −142.104b

107.683 165.848b 174.917b 134.354b 178.492b 136.783 −165.615 −34.143 2.861 −176.999 19.980b −141.656b 16.278b −178.180b −141.656b

107.758 165.854b 175.319b 134.539b 177.998b 136.473 −166.143 −34.795 2.723 −177.133 7.068b −141.713b 16.297b −175.991b −141.713b

a

1 Eh =627.50955 kcal mol−1

b

Intermonomeric parameters

Table 10 Results for CNS-e ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized Geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. CC was calculated Electronic energy (Eh)a

−1,442.277001 −1,442.2832231 −1,442.3427054 Eh Eh Eh

Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2)

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

1.195

1.195

1.194

r(N1O3) r(N1O4) r(O4H5) r(S7O6) r(S7O8) r(S7O9) r(S7O10) r(O9H11) r(O10H12) r(Cl14H13) r(O3H13)b r(H11O4)b r(H12O2)b θ(N1O2O3) θ(N1O3O4)) θ(N1O4H5) θ(H12O10S7) θ(O8S7O9)

1.202 1.413 0.973 1.427 1.447 1.606 1.604 0.972 0.971 1.287 2.267b 2.143b 2.342b 24.800 35.030 103.891 109.310 107.870

1.202 1.413 0.973 1.427 1.447 1.447 1.604 0.972 0.971 1.287 2.279b 2.148b 2.355b 24.808 24.808 103.888 109.272 107.861

1.201 1.410 0.972 1.418 1.438 1.596 1.594 0.971 0.969 1.285 2.275b 2.142b 2.336b 24.839 34.968 104.032 109.787 107.887

θ(S7O9H11) θ(O6S7O9) θ(O3H13Cl14)b θ(N1O2H12)b θ(O4H11O9)b τ(O2N1O4H5) τ(O3N1O4H5) τ(H12O10S7O6) τ(O8S7O9H11) τ(H12O10S7O9) τ(O6S7O9H11) τ(N1O4H11O9))b τ(N1O2H12O10)b τ(N1O3H13Cl14)b

108.792 106.721 172.139b 125.013b 163.242b −174.804 6.041 165.361 −24.080 −82.861 −158.379 −34.038b −44.621b −105.261b

108.751 106.724 172.155b 125.219b 163.681b −174.981 5.837 165.395 −24.149 −82.830 −158.464 −33.768b −44.746b −104.550b

109.220 106.724 172.188b 125.397b 162.951b −174.764 6.042 165.742 −24.452 −82.433 −158.593 −34.534b −43.821b −104.796b

a

1 Eh =627.50955 kcal mol−1

b

Intermonomeric parameters

2232, Page 12 of 19 Table 11 Results CNS-f ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-ccpVQZ level. CC was calculated

a

1 Eh =627.50955 kcal mol−1

b

Intermonomeric parameters

J Mol Model (2014) 20:2232

−1,442.2901128 Eh

−1,442.28945600 Eh

−1,442.3558064 Eh

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

r(O3H13)b r(H12Cl14)b

1.194 1.223 1.375 0.988 1.447 1.431 1.606 1.581 0.970 0.986 1.302 1.753b 1.912b 2.201b

1.194 1.223 1.375 0.988 1.447 1.432 1.606 1.582 0.970 0.986 1.301 1.762b 1.919b 2.207b

1.193 1.220 1.373 0.986 1.438 1.423 1.596 1.571 0.968 0.984 1.298 1.762b 1.956b 2.204b

θ(N1O2O3) θ(N1O3O4)) θ(N1O4H5) θ(H12O10S7) θ(O8S7O9) θ(S7O9H11) θ(O6S7O9) θ(O3H13Cl14)b θ(O13Cl14O12)b θ(O10H12Cl14)b θ(O4H5O6)b τ(H12O10S7O6) τ(O8S7O9H11) τ(O12O10S7O8) τ(H12O10S7O9) τ(O6S7O9H11) τ(O2N1O4H5) τ(O3N1O4H5)

26.424 117.128 106.652 110.700 109.603 109.226 104.417 174.798b 95.089b 178.456b 170.495b −32.247 −29.974 −166.064 78.312 −162.373 −177.858 1.827

26.417 117.121 106.615 110.688 109.604 109.223 104.420 174.886b 95.172b 178.462b 170.388b −32.167 −29.969 −165.994 79.491 −162.392 −177.925 1.769

26.439 33.421 106.818 110.990 109.565 109.696 104.442 171.396b 94.364b 177.240b 169.265b −31.097 −30.061 −164.855 79.491 −162.438 −179.411 0.613

τ(H13Cl14H12O10)b τ(O3H13Cl14H12)b τ(O4H5O6S7)b τ(N1O3H13Cl14)b

35.416b −178.669b 71.918b 121.191b

35.179b −178.520b 71.728b 121.233b

−0.773b −152.276b 90.845b 151.457b

Electronic energy (Eh)a Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2) r(N1O3) r(N1O4) r(O4H5) r(S7O6) r(S7O8) r(S7O9) r(S7O10) r(O9H11) r(O10H12) r(Cl13H14) r(O6H5)b

J Mol Model (2014) 20:2232

Page 13 of 19, 2232

Table 12 Results CNS-g ternary complex. Distances (r) in Å, angles (θ) and dihedral angles (τ) in degrees. Optimized geometry of aggregate: HCl•HNO3•H2SO4 (CNS) by B3LYP/aug-cc-pVTZ fopt freq and B3LYP/aug-cc-pVQZ level. CC was calculated −1,442.283857 −1,442.2832231 −1,442.3495041 Eh Eh Eh

Electronic energy (Eh)a Parameters: Distances (r), angles (θ), dihedral angles (τ) r(N1O2)

aug-cc-pVTZ

aug-cc-pVTZ (CC)

aug-cc-pVQZ (CC)

1.210

1.210

1.209

r(N1O3)

1.200

1.200

1.199

r(N1O4)

1.389

1.389

1.386

r(O4H5)

0.985

0.985

0.984

r(S7O6)

1.432

1.432

1.422

r(S7O8)

1.456

1.456

1.446

r(S7O9)

1.592

1.592

1.582

r(S7O10)

1.592

1.592

1.582

r(O9H11)

0.969

0.969

0.968

r(O10H12)

0.983

0.983

0.982

r(Cl13H14)

1.300

1.300

1.298

r(O2H13)b

2.051b

2.052b

2.056b

1.864b

1.870b

1.871b

b

b

2.306b

b

r(H5O8)b b

r(H12Cl14)

2.301

b

2.305

b

r(O4H13)

2.608

2.611

2.613b

θ(N1O2O3)

25.308

25.305

25.329

θ(N1O3O4))

33.688

33.684

33.661

θ(N1O4H5)

106.971

106.977

107.097

θ(H12O10S7)

111.184

111.197

111.594

θ(O8S7O9)

107.547

107.558

107.633

θ(S7O9H11)

109.388

109.385

109.856

θ(O6S7O9)

108.399

108.376

108.327

θ(O2H13Cl14)b

166.023b

165.977b

165.919b

142.257b

142.183b

141.750b

b

b

170.572b

θ(O4H5O8)b θ(Cl14H12O10)

b

170.438

170.485

τ(H12O10S7O6)

46.467

46.609

46.786

τ(O8S7O9H11)

−22.464

−22.412

−23.079

τ(O12O10S7O8)

−88.196

−88.085

−87.768

τ(H12O10S7O9)

159.815

159.925

160.101

−154.183

−154.139

−154.720

τ(O6S7O9H11) τ(N1O2H13Cl14)

b

b

b

49.710

49.262b

49.790

τ(H13Cl14H12O10) −117.575

−117.451

−116.814b

τ(O4H5O8S7)

−25.598

−25.636b

b

b

b

−25.598

a

1 Eh =627.50955 kcal mol−1

b

Intermonomeric parameters

b

Fig. 4 Structural parameters of aggregate CNS-b. Distances in (Å), angles in degrees

b

b

Fig. 5 Structural parameters of aggregate CNS-c. Distances in (Å), angles in degrees

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Fig. 6 Structural parameters of aggregate CNS-d. Distances in (Å), angles in degrees Fig. 8 Structural parameters of aggregate CNS-f. Distances in (Å), angles in degrees

Fig. 7 Structural parameters of aggregate CNS-e. Distances in (Å), angles in degrees

Fig. 9 Structural parameters of aggregate CNS-g. Distances in (Å), angles in degrees

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Fig. 10 IR spectrum of CNS-b

Fig. 11 IR spectrum of CNS-c

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Fig. 12 IR spectrum of CNS-d

Fig. 13 IR spectrum of CNS-e

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Fig. 14 IR spectrum of CNS-f

Fig. 15 IR spectrum of CNS-g

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