Interaction in the Ternary Complexes of HNO3··· HCl··· H2O: A

ARTICLE pubs.acs.org/JPCA

Interaction in the Ternary Complexes of HNO3 3 3 3 HCl 3 3 3 H2O: A Theoretical Study on Energetics, Structure, and Spectroscopy F. Mine Balcı and Nevin Uras-Aytemiz* Department of Chemistry, Suleyman Demirel University, 32260 Isparta, Turkey

bS Supporting Information ABSTRACT: Ternary complexes of HNO3 3 3 3 HCl 3 3 3 H2O were investigated by ab initio calculations with aug-cc-pVDZ and aug-cc-pVTZ basis sets. The results are analyzed in terms of structures, energetics, and infrared vibrational frequencies. In all minima, neither HNO3 nor HCl becomes ionized. The contribution of the nonadditivity effect, which is significant for hydrogen-bonded clusters, is bigger for the cyclic structures in which HNO3 acts as a proton donor to HCl, although the global minimum contains HNO3 donating its proton to a H2O molecule.

1. INTRODUCTION Experimental and theoretical studies of hydrogen-bonded complexes have been reported for many research areas, including chemical, physical, and biological.1,2 The properties of hydrogen bonding of molecular complexes are directly connected to the cooperativity effect. The cooperativity effect is a factor when the molecular cluster has more than two molecules. For example, in the A
H 3 3 3 B
H 3 3 3 C arrangement of the hydrogen-bonded system, if the proton-acceptor group, B
H, accepts a proton from the proton-donating group A
H and donates its proton to C at the same time, the hydrogen bonding between the A
H 3 3 3 B and B
H 3 3 3 C becomes stronger. Therefore, the hydrogen bonding in this molecular cluster makes a positive contribution to the cooperativity; as a result, the total interaction energy becomes larger than the sum of the molecular pair interaction energies. This effect changes the dipole moment and vibrational frequencies of the hydrogen-bonded clusters. However, sometimes, the hydrogen bonding in the molecular clusters makes a negative contribution to the cooperativity, and it is called the anticooperativity effect. For example, in the hydrogen-bonded molecular cluster, such as the A
H 3 3 3 C 3 3 3 H
B arrangement, if the proton-acceptor group C accepts two protons from the two proton-donating group A
H and B
H at the same time, the total interaction energy becomes less than the sum of the molecular pair interaction energies (see ref 3 and references therein). This effect also changes the dipole moment and the vibrational frequencies of the hydrogen-bonded clusters just like the cooperativity effect, as described above. Both cooperativity and anticooperativity effects are known as nonadditivity features of the molecular clusters. Solvation and ionization of strong acids of HNO3 and HCl play a vital role in atmospheric processes, especially in ozone depletion.4
7 These strong acids are the components of the polar stratospheric clouds (PSCs), wherein both HNO3 and HCl interact with the ice surface and form their respective molecular r 2011 American Chemical Society

and ionic hydrates.8
11 The hydrogen bonding in the solvation and ionization process of HCl on/in water clusters and ice has been investigated intensively.3,12
23 The stable ionic form of HCl with water clusters was found when the number of water molecules was four.14,19,20 On the other hand, there are few studies of the HNO3 3 3 3 (H2O)n, n g 1, interaction and HNO3 3 3 3 ice interaction in the literature.8,24
31 McCurdy et al. have found that at least four water molecules were needed for ionization of HNO3.28 It will be very instructive and useful to give some literature reports of the binary systems of HNO3 3 3 3 H2O and HCl 3 3 3 H2O. HNO3 3 3 3 H2O dimer has been studied extensively, using both quantum mechanical calculations at different levels of theory and experimental techniques.25
28,30
32 The stable structure of HNO3 3 3 3 H2O dimer has cyclic and homodromic arrangements, and the strongest hydrogen bond forms between the acidic hydrogen of HNO3 and the oxygen of the water molecule.25
28,30
32 The binding energy of this dimer was calculated as
10.3 kcal/mol at the second-order Moller
Plesset perturbation (MP2) level with the aug-cc-pVDZ basis set, a value approximately twice that of the water dimer.28 The HCl 3 3 3 H2O dimer has also been subjected to much research.14,17,20 The energetically stable structure of this dimer has a strong hydrogen bond in which HCl acts as a proton-donating group with the interaction energy
5.30 kcal/mol at the MP2/aug-cc-pVDZ level.17 Besides the studies of HNO3 3 3 3 H2O and HCl 3 3 3 H2O dimers, there are very recent theoretical studies of the HNO3 3 3 3 HCl 3 3 3 H2O system in the literature; Gomez et al. Special Issue: Victoria Buch Memorial Received: October 29, 2010 Revised: February 18, 2011 Published: March 16, 2011 5943

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The Journal of Physical Chemistry A have investigated the HNO3 3 3 3 HCl 3 3 3 H2O ternary systems in terms of their structures, stabilities, and chemical properties as well as the microwave and infrared spectra by the hybrid density functional theory method (DFT/B3LYP) with the aug-cc-pVQZ basis set. They have found 15 species on the intermolecular potential energy surface (IPES) and calculated their Gibbs free energies.33,34 Furthermore, the atmospheric implications of the HNO3 3 3 3 HCl 3 3 3 H2O ternary complexes were reviewed and investigated in these studies.33,34 The results of these studies will be discussed in the Results and Discussions section. In this study, we aim to investigate the hydrogen-bonding features of the ternary complexes containing two strong acids, namely, HNO3 and HCl and one water molecule. In this respect, the nonadditivity features of the ternary complexes of HCl, HNO3, and H2O have been investigated, which was not considered in the work of Gomez et al.33,34 Furthermore, the intermolecular potential energy surfaces of the heterodimers (HCl 3 3 3 H2O, HNO3 3 3 3 H2O, and HCl 3 3 3 HNO3) were also investigated in order to understand the salient features of hydrogen bonding in these systems. The main tool for this investigation is ab initio calculations performed at the MP2 level with aug-cc-pVDZ and aug-cc-pVTZ basis sets. Moreover, the coupled clusters (CCSD(T)) calculations were done as single-point calculations. The layout of the article is as follows. First, the computational details will be given, the HCl 3 3 3 H2O, HNO3 3 3 3 H2O, and HCl 3 3 3 HNO3 heterodimers will be described, and then the nonadditivity effects within the ternary complexes investigated in line with their structural features and infrared frequencies will be discussed.

2. COMPUTATIONAL DETAILS Ab initio calculations were applied to the dimers of HNO3 3 3 3 H2O, HNO3 3 3 3 HCl, and HCl 3 3 3 H2O and the ternary complexes of HNO3, HCl, and H2O by using the DFT/ B3LYP and MP2 level calculations with aug-cc-pVDZ basis sets. However, additional calculations with the aug-cc-pVTZ basis set were also applied to estimate the effect of expanding the basis set on the resulting geometries and interaction energies.35
38 All calculations were performed at the frozen core approximation. Different starting geometries were constructed according to the chemical intuition to search several regions of the IPES with optimizations at the B3LYP/aug-cc-pVDZ level employed on these geometries. Then, the candidate dimers and the ternary complexes were fully optimized by using the MP2/aug-cc-pVDZ and aug-cc-pVTZ levels. All of the optimized configurations were also subjected to the vibrational analysis to determine correspondence with a minimum on the IPES at MP2/aug-cc-pVDZ. The interaction energies have been also computed with the CCSD(T) method by using the optimal structures obtained at MP2 level calculations. The interaction energies, ESM int (where the superscript SM represents the method used in the calculations), were calculated as the difference between the energy of the isolated subunits and that of the entire complex under the supermolecular approach. It is well-known that this procedure introduces error called basis set super position error (BSSE). To eliminate this, the counterpoise method of Boys and Bernardi was used.39 In geometry optimization, the counterpoise procedure (CP) was employed for the final structures (namely, optimized ones). It has been shown by Gomez et al. for one of the ternary complexes studied also in this article that the counterpoise-corrected surface intermolecular

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Table 1. Structural Properties of HNO3, HCl, and H2O Moleculesa structural parameters

MP2/aug-cc-pVDZ

MP2/aug-cc-pVTZ

ref 41

HNO3 r(O
H) r(N
O)

0.98 1.42

0.97 1.41

0.96 1.41

r(N
O2)

1.22

1.21

1.21

r(N
O3)

1.21

1.20

1.20

HCl r(H
Cl)

ref 42 1.29

1.27

0.97

0.96

H2O r(O
H) a(HOH) a

experiment

1.27 ref 43

104

104

0.96 105

Distances (r) are given in Angstroms and angles (a) in degrees.

Figure 1. Optimized structure of the HCl 3 3 3 H2O dimer at the CCSD(T) level with the aug-cc-pVDZ basis set.

distances are a little longer than the values evaluated by the standard gradient optimization.33 This difference was found to be 3  10
3 Å
with B3LYP/aug-cc-pVQZ. Furthermore, it was reported by Hobza et al. for the water dimer that this difference gets smaller with larger basis set.40 Table 1 contains the structural parameters of monomers, HNO3, HCl, and H2O calculated at the MP2 level with two different basis sets and compared with the experimental values. When we compare the results, the values calculated at the MP2 level with the aug-cc-pVTZ basis set correlate well with the experimental values. Therefore, for the structural parameters, we will use aug-cc-pVTZ basis set results. However, the harmonic frequencies could be calculated at only the MP2/aug-cc-pVDZ level within our computational resources. The cooperativity effect is calculated as ΔEnonadd ¼ ESM int
ΔEint, AB
ΔEint, BC
ΔEint, AC

ð1Þ

where ΔEint,AB, ΔEint,BC, and ΔEint,AC are the interaction energies of respective dimers. The monomer and dimer energies were calculated by using the full basis of the complex. All calculations were performed with the GAUSSIAN 03 program.44 5944

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Figure 2. Optimized structures of HNO3 3 3 3 H2O dimers at the CCSD(T) level with the aug-cc-pVDZ basis set; (a) global minimum and (b
f) local minima.

Figure 3. The optimized structures of HCl 3 3 3 HNO3 dimers calculated at the CCSD(T) level with the aug-cc-pVDZ basis set; (a) global minimum and (d
e) local minima.

3. RESULTS AND DISCUSSIONS Results of HCl 3 3 3 H2O, HNO3 3 3 3 H2O, and HCl 3 3 3 HNO3 Dimers. The optimized structures of the HCl 3 3 3 H 2O,

HNO3 3 3 3 H2O, and HCl 3 3 3 HNO3 dimers are shown in Figures 1
3, respectively, with the interaction energies given in Table 2. The results for these dimers will be discussed separately. 5945

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Table 2. BSSE and ΔZPEMP2 Corrected Interaction Energies for the HCl 3 3 3 H2O, HNO3 3 3 3 H2O, and HCl 3 3 3 HNO3 Dimers Obtained from the MP2/aug-cc-pVDZ and aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ Calculationsa EMP2 int (aug-cc-pVDZ)

EMP2 int (aug-cc-pVTZ)

ECCSD(T) (aug-cc-pVDZ) int

ΔZPEMP2 (aug-cc-pVDZ)


4.11


4.31


3.40

1.19


7.19
1.09


7.94
1.28


7.22
1.21

2.16 1.20


1.08


1.27


1.21

1.15


1.00


1.17


1.11

1.28


0.85


1.02


0.92

1.22


0.71


0.73


0.84

1.13

3 HNO3 Figure 3a


2.66


3.35


2.30

1.14

3 HNO3 Figure 3b 3 HNO3 Figure 3c 3 HNO3 Figure 3d


1.71


2.21


1.46

0.86


1.78
1.55


1.91
1.70


1.45
1.32

1.10 1.12


1.60


1.72


1.30

1.15

HCl 3 3 3 H2O Figure 1 HNO3 3 3 3 H2O Figure 2a HNO3 3 3 3 H2O Figure 2b HNO3 3 3 HNO3 3 3

3 H2O Figure 2c 3 H2O Figure 2d

HNO3 3 3 HNO3 3 3

3 H2O Figure 2e

HCl 3 3 HCl 3 3 HCl 3 3 HCl 3 3 a

3 H2O Figure 2f

HCl 3 3 3 HNO3 Figure 3e

The zero-point energies (ΔZPEMP2) were calculated at the MP2/aug-cc-pVDZ level. All values are in kcal/mol.

HCl 3 3 3 H2O Dimer. The HCl 3 3 3 H2O dimer has been studied theoretically at different levels of theory.14,17,20 The global minimum structure of the HCl 3 3 3 H2O dimer is given in Figure 1. HCl is more acidic than H2O; therefore, the global minimum structure for the HCl 3 3 3 H2O dimer was found with the HCl molecule acting as a proton donor to H2O. The interaction energy of this dimer is
5.30 kcal/mol (
4.11 kcal/mol when the harmonic zero-point energy (ZPE) corrections are included) at the MP2 level with the aug-cc-pVDZ basis set.17 Increasing the basis set also ups the energy by 0.20 kcal/mol at the MP2 level with aug-cc-pVTZ; on the other hand, the interaction energy at the CCSD(T) level has been calculated as
4.59 kcal/mol (
3.40 kcal/mol with ZPE corrections). The geometrical parameters of the complex will be discussed below along with the cooperativity effect of the HNO3 3 3 3 HCl 3 3 3 H2O ternary systems. HNO3 3 3 3 H2O Dimer. Six stationary points have been found on the IPES for the HNO3 3 3 3 H2O dimer and are shown with the decreasing energy order at the CCSD(T) level with the augcc-pVDZ basis set (the CCSD(T) level energies are corrected by the MP2 level with the aug-cc-pVDZ basis set) in Figure 2a
f. The global minimum structure for the HNO3 3 3 3 H2O dimer shown in Figure 2a has been reported by many researchers.25
28,30
32 The strongest hydrogen bonding between acidic hydrogen of HNO3 and oxygen of the water molecule was proposed by McCurdy and his colleagues with an interaction energy of
9.35 kcal/mol (
7.19 kcal/mol when the harmonic ZPE corrections are included) at the MP2 level with the aug-cc-pVDZ basis set.28 This energy is almost two times greater than that of the HCl 3 3 3 H2O dimer. Scott et al. used two different levels with the same basis set. They calculated the interaction energy of the HNO3 3 3 3 H2O dimer shown in Figure 2a as
10.2 kcal/mol with the ZPE correction at B3LYP/ 6-311þþG(2d,p) and
8.5 kcal/mol (with ZPE correction) at MP2/6-311þþG(2d,p).27 On the other hand, the interaction energy of this dimer increases by 0.75 kcal/mol at the MP2/augcc-pVTZ level and 0.03 kcal/mol at CCSD(T)/aug-cc-pVDZ. The acidic hydrogen of HNO3 does not contribute to the hydrogen bonding, as revealed in Figure 2b
f in contrast to the structure shown in Figure 2a. In these isomers (Figure 2b
f), the hydrogen of the water molecule interacts with one of the oxygens of HNO3 not possessing a hydrogen atom. The corrected


) between Atoms in HNO3 H2O Table 3. Distances (r, Å 333 Dimers Shown in Figure 2a
fa distance

a

2a

2b

2c

2d

2e

2f

r(O
H)

0.99

0.97

0.97

0.97

0.97

0.97

r(N
O)

1.37

1.39

1.39

1.40

1.38

1.38

r(N
O2) r(N
O3)

1.22 1.21

1.28 1.20

1.21 1.20

1.21 1.21

1.21 1.21

1.22 1.20

r(O1
H1)

0.96

0.96

0.96

0.96

0.96

0.96

r(O1
H2

0.96

0.96

0.96

0.96

0.96

0.96

r(O1 3 3 r(H1 3 3

3 H) 3 O3)

1.70










r(H1 3 3 r(H2 3 3 r(H2 3 3

3 O2)

2.34

2.17










3.20













3 O3) 3 O2)


2.22

2.92


2.16



2.14


2.15





All values were calculated at the MP2 level with the aug-cc-pVTZ basis set.

interaction energies for the structures given in Figure 2b
f are
1.21,
1.21,
1.11,
0.92, and
0.84 kcal/mol at the CCSD(T) level with the aug-cc-pVDZ basis set, respectively. In addition to the global minimum, the structure given in Figure 2b has also been explored by McCurdy et al. at the MP2/aug-cc-pVDZ level.28 Staikova et al. have investigated the HNO3 3 3 3 H2O dimers at the B3LYP/6-311þþG(3df,3dp) level, finding three true minima. Panels b and d of Figure 2 were represented as true minima, and Figure 2f was found as a saddle point,32 whereas Figure 2f was found as a minimum on the IPES in this study. To the best of our knowledge, results for the isomers of HNO3 3 3 3 H2O have not been published before. The structural parameters and the harmonic frequencies for Figure 2a
f are given in Tables 3 and 4, respectively. The O
H
at the MP2 bond of HNO3 in Figure 2a was calculated as 0.99 Å level with the aug-cc-pVTZ basis set and was elongated when compared to the O
H bond of monomeric nitric acid (0.97 Å
). Because the O
H bond of HNO3 is not involved in H-bonding for the structures shown in Figure 2b
f, the bond length of O
H of HNO3 for the respective dimers does not change upon complexation. The same trend was obtained when the O
H 5946

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Table 4. Harmonic Frequency Values (cm
1) and Infrared Intensities Given in Paranthesis (kM mol
1) of HNO3 3 3 3 H2O Dimers Shown in Figure 2a
fa frequency ν(N
O)

2b

2c

2d

2e

2f

940 (160)

901 (215)

896 (205)

898 (175)

896 (203)

900 (217)

ν(NO2)sym δ(NOH)

1334 (263) 1503 (100)

1329 (254) 1356 (107)

1328 (270) 1357 (74)

1327 (220) 1352 (67)

1325 (218) 1353 (122)

1328 (287) 1357 (82)

δ(HOH)

1615 (116)

1632 (52)

1633 (41)

1635 (52)

1632 (41)

1635 (87)

ν(NO2)asym

1830 (247)

1851 (246)

1857 (246)

1856 (302)

1849 (262)

1852 (226)

ν(O
H)

3283 (999)

3696 (106)

3696 (106)

3698 (105)

3700 (158)

3696 (104)

3769 (22)

3787 (73)

3780 (86)

3783 (81)

3781 (84)

3791 (51)

3905 (118)

3916 (115)

3918 (159)

3919 (159)

3919 (158)

3914 (80)

ν(O
H)bonded (water) ν(O
H)free (water) a

2a

All calculations performed at the MP2 level with the aug-cc-pVDZ basis set.

frequency values of these dimers were compared. The O
H frequency value for monomer HNO3 was calculated as 3704 cm
1 at the MP2 level with the aug-cc-pVDZ basis set. The calculated red shift for Figure 2a is
421 cm
1 with an enhanced intensity value (998 kM mol
1). The O
H stretch in the other minima shows a very small shift. These values for the structures shown in Figure 2b
f are
8,
8,
6,
8, and
4 cm
1, respectively. This is because the acidic oxygen atom of HNO3 is not involved in the hydrogen bonding. HCl 3 3 3 HNO3 Dimer. In liquid water, both HNO3 and HCl instantly ionize. The values of pKa for HNO3 and HCl are approximately
7 and
2, and the experimental gas-phase proton-acceptor capacities of HNO3 and HCl were found to be
179.5 and 137.5 kcal/mol, respectively.45,46 HNO3 has a large proton-acceptor capacity because of having three oxygen atoms. In this study, several possible configurations of the HNO3 and HCl dimer were subjected to the geometry optimization at the MP2 level with the aug-cc-pVDZ and aug-cc-pVTZ basis sets and at the CCSD(T) level with the aug-cc-pVDZ basis set. All of the minima are illustrated in decreasing energy order calculated at the CCSD(T) level with the aug-cc-pVDZ basis set in Figure 3a
e (the CCSD(T) level energies are corrected by the MP2/aug-cc-pVDZ level). The structures shown in Figure 3a and c have been investigated at BLYP/6-311þþG(d,p) by Mantz et al., but in their study, only geometrical parameters at the above-mentioned level have been reported.47 The remaining ones shown in Figure 3b, d, and e have not been explored before, to our best knowledge. The global minimum structure for the HCl 3 3 3 HNO3 dimer is shown in Figure 3a. The strongest hydrogen bonding is formed in the global minimum between the hydrogen of HNO3 and the Cl atom of HCl (H 3 3 3 Cl). Its interaction energy has been calculated as
2.30 kcal/mol at the CCSD(T) level with the aug-cc-pVDZ basis set. This value is also rather smaller than that of the HNO3 3 3 3 H2O and HCl 3 3 3 H2O dimers. Four local minimum structures have been found on the IPES and are shown in Figure 3b
e. The difference between Figure 3a and b is the position of the HCl molecule as the hydrogen of HCl does not contribute to hydrogen bonding as in Figure 3a. Although the latter interaction is very weak, it gives extra stability to the structure in Figure 3a by 0.84 kcal/mol at the CCSD(T) level with the aug-cc-pVDZ basis set. The structures given in Figure 3c and d have different configurations in terms of connection points, that is, the hydrogen atoms of HNO3 do not contribute to the hydrogen bonding, and HCl donates its proton to either the O2 or O3 atom of nitric acid. It is interesting


) between Atoms in HCl HNO3 Table 5. Distances (r, Å 333 Dimers Shown in Figure 3a
ea distance

a

3a

3b

3c

3d

3e

r(O
H)

0.98

0.98

0.97

0.97

0.97

r(N
O)

1.39

1.40

1.40

1.39

1.39

r(N
O2) r(N
O3)

1.22 1.20

1.21 1.20

1.21 1.21

1.22 1.20

1.21 1.28

r(H1
Cl)

1.28

1.28

1.28

r(H1 3 3 3 O3) r(H 3 3 3 Cl)







2.09




2.31

2.33







r(O2 3 3 3 H1)

2.22







1.28

2.07

1.28 2.08



All values were calculated at the MP2 level with the aug-cc-pVTZ basis set.

to note that the initial configuration of Figure 3c was constructed between the hydrogen of HCl and the acidic oxygen of nitric acid, but it converged to Figure 3c when subjected to geometry optimization. That is, HCl does not favor interaction with the acidic oxygen of nitric acid. The interaction energies of Figure 3c
e are
1.45,
1.32, and
1.30 kcal/mol at the CCSD(T) level with the aug-cc-pVDZ basis set, respectively. Table 5 shows the structural parameters of the HCl 3 3 3 HNO3 dimers. The bond length of the monomer H
Cl was calculated as 1.27 Å
at the MP2 level with the aug-cc-pVTZ basis set. The H
Cl distances in HCl 3 3 3 HNO3 dimers illustrated in
in each case. Figure 3a
e are elongated just 0.01 Å The weak H-bond between the H of HCl and O2 of HNO3 in the structure shown in Figure 3a has almost no effect on the O
H bond of HNO3 because the length for HNO3 is calculated
in both Figure 3a and b. In the remaining isomers as 0.98 Å shown in Figure 3c
e, the HNO3 proton is not involved in any interaction. Therefore, the structures given in Figure 3c
e have
calculated at the same O
H bond distance value, that is, 0.97 Å the MP2 level with the aug-cc-pVTZ basis set. The important vibrational frequencies of the structures shown in Figure 3a
e are given in Table 6. It is seen that the maximum O
H bond red shift that occurred in Figure 3a was calculated as
109 and 90 cm
1 for Figure 3b. Other structures illustrated in Figure 3c
e have small O
H bond shifts (
9,
8, and
10). HCl interacts with the oxygen of nitric acid in Figure 3a, and c
e, for which the H1
Cl bond shifts for these structures were 69, 83, 89, and 86 cm
1, respectively. On the other hand, Figure 3b has the lowest H
Cl stretch value (3003 cm
1). 5947

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Table 6. Harmonic Frequency Values (cm
1) and Infrared Intensities Given in Parentheses (kM mol
1) of HCl 3 3 3 HNO3 Dimers Shown in Figure 3a
ea frequency ν(N
O)

a

3a

3b

3c

3d

3e

909 (173)

893 (203)

896 (179)

903 (215)

903 (218)

ν(NO2)sym δ(NOH)

1326 (199) 1390 (74)

1323 (234) 1386 (86)

1324 (222) 1352 (57)

1327 (253) 1356 (126)

1330 (319) 1359 (66)

ν(NO2)asym

1839 (303)

1852 (260)

1857 (338)

1845 (267)

1852 (242)

ν(H1
Cl)

2954 (112)

3003 (60)

2940 (364)

2937 (105)

2934 (373)

ν(O
H)

3595 (409)

3614 (427)

3695 (106)

3696 (105)

3694 (108)

All calculations performed at the MP2 level with the aug-cc-pVDZ basis set.

Results for HNO3 3 3 3 HCl 3 3 3 H2O Ternary Complexes. By optimizing the different starting structures, we have identified 15 conformers as the most stable for the HNO3 3 3 3 HCl 3 3 3 H2O ternary system. All of the structures corresponded to minima on the IPES and the MP2 level of theory with aug-cc-pVDZ and augcc-pVTZ basis sets employed. Full geometry optimizations at the MP2 level with the aug-cc-pVTZ basis set were achieved using the latter MP2/aug-cc-pVDZ optimization. The geometrical parameters will be discussed at the MP2/aug-cc-pVTZ level, but the values calculated at the MP2/aug-cc-pVDZ level are given in the Supporting Information for the ternary systems. The CCSD(T)/aug-cc-pVDZ energies were obtained using singlepoint energy calculations on the MP2/aug-cc-pVTZ geometries. The MP2 level with the aug-cc-pVTZ basis set could not be used realistically with our computer resources for the harmonic frequency calculations; therefore, the vibrational analysis was conducted using the MP2/aug-cc-pVDZ methods. The CCSD(T)/aug-cc-pVDZ and MP2/aug-cc-pVTZ energies were corrected by using the ZPEs obtained from the MP2/aug-cc-pVDZ level calculations. The size of the basis set and the level of theory have no substantial effect on the ZPE (see, for example, refs 48
50). All of the minima are shown in Figure 4a
o in order of decreasing energy calculated at the CCSD(T) level with the augcc-pVDZ basis set (the ZPE-corrected energies can also be calculated at MP2/aug-cc-pVDZ, and the order included this correction). The energy values for the different levels of theory with aug-cc-pVDZ and aug-cc-pVTZ basis sets are given in Table 7. For all structures, neither HNO3 nor HCl was ionized. Both HNO3 and HCl are strong acids; therefore, both can donate their proton to water. However, when they are both present in the same cluster with water, the most stable structures have the configurations in which the HNO3 donates its proton to the H2O molecules with binding energies between
14.39 and
12.33 kcal/mol (
10.96 and
8.67 kcal/mol including the ZPE corrections) at the MP2/aug-cc-pVDZ level (i.e., Figure 4a
e and g). On the other hand, the structures shown in Figure 4f and h consist of a HNO3 molecule which donates its proton to HCl while accepting a proton from H2O with sizable energies (
13.12 and
11.16 kcal/mol without the ZPE correction and
9.73 and
7.94 kcal/mol with the correction at the MP2/aug-cc-pVDZ level, respectively) with respect to the ones examined above. This is because of the cyclic arrangement of the molecules in the ternary system, as explained below. In the remaining 7 structures (shown in Figure 4i
o) out of 15, the H2O molecule donates its proton to the HNO3 molecule at either the O2 or O3 position. Excluding the structures shown in Figure 4n and o, there are five minima on the IPES shown in Figure 4i
m that have similar configurations where HNO3 donates a proton to HCl. In Figure 4k
m, the proton of HCl

does not interact with any oxygen of HNO3. On the other hand, in the structures given in Figure 4i and j, HCl has an extra coordination to the O2 position of HNO3, and this interaction, although it is very weak, gives approximately 1 kcal/mol of extra binding energy with respect to structures shown in Figure 4k
m. The interaction energies of Figure 4i
m are
6.98,
6.98,
6.06,
5.98, and
5.68 kcal/mol, respectively. In the cases of structures given in Figure 4n and o, the proton of HNO3 is not involved in any interactions with either H2O or HCl (which donates a proton to an oxygen of the HNO3, O2 or O3). The binding energies have been calculated at MP2/aug-ccpVDZ as
4.81 kcal/mol for the structure shown in Figure 4n and
4.66 kcal/mol for those in Figure 4o. These energies are rather smaller than those for structures shown in Figure 4a
h. At this point, it is interesting to compare the interaction energy of the HNO3 3 3 3 (H2O)2 system with the conformers, as illustrated in Figure 4a and f. McCurdy and his colleagues28 have investigated the HNO3 3 3 3 (H2O)2 system at the MP2 level with the aug-cc-pVDZ basis set and found similar trimer structures as those in Figure 4a and f. Therefore, we can compare the binding energy of these trimers using the same level and basis set. One can see the energetic results for these trimers in Table 7. The interaction energy of the HNO3 3 3 3 (H2O)2 system was calculated as 16.2 kcal/mol (including the ZPE correction), lying about 1.81 kcal/mol above that for the structure shown in Figure 4a and 3.08 kcal/mol for the structure shown in Figure 4f.28 Furthermore, we can also compare the HCl 3 3 3 (H2O)2 trimer structure to Figure 4a and f. The binding energy of HCl 3 3 3 (H2O)2 was calculated as
13.27 kcal/mol at the MP2 level with the aug-cc-pVDZ basis set.17 This trimer structure value lies only ∼0.1 kcal/mol below that in Figure 4f and ∼1.1 kcal/mol above that in Figure 4a. The sequence of the energy-ordered structures changes when the larger basis set is used; that is to say, when the aug-cc-pVTZ basis at the MP2 level is applied to complexes, the structure shown in Figure 4f becomes the second most stable structure with the energy of
14.52 kcal/mol (without ZPE correction). It should be mentioned here that there were no dramatic changes in the structural parameters when applied the larger basis set was applied (see Supporting Information for the structural parameters calculated at the MP2/aug-cc-pVDZ level). When the higher level of theory, that is, CCSD(T), was used, the sequence of the energy order was changed with the sequence depending on the ZPE correction. The binding energy order for the structures shown in Figure 4e and f, i and j, k and l interchanges at the CCSD(T) level. The interaction energies decrease (become less negative) for CCSD(T) calculation in comparison with those for the MP2 values. The same trend was found in other complexes.48,49,53,54 When the interaction energies calculated 5948

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Figure 4. The optimized structures of HNO3 3 3 3 HCl 3 3 3 H2O ternary complexes at the CCSD(T) level with the aug-cc-pVDZ basis set; (a) the global minimum and (b
o) the local minima. 5949

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Table 7. BSSE and ΔZPEMP2 Corrected Interaction Energies for the HNO3 3 3 3 HCl 3 3 3 H2O Ternary Complexes Obtained from the MP2/aug-cc-pVDZ and aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ Calculationsa EMP2 int (aug-cc-pVDZ)

a

EMP2 int (aug-cc-pVTZ)

ECCSG(T) (aug-cc-pVDZ) int

ΔZPEMP2 (aug-cc-pVDZ)

4a


10.96


12.45


10.30

3.43

4b 4c


10.08
10.08


11.02
10.97


9.70
9.64

3.31 3.28

4d


10.02


10.91


9.58

3.34

4e


9.43


10.58


8.79

3.33

4f


9.73


11.13


8.35

3.39

4g


8.67


9.51


8.29

3.66

4h


7.94


8.95


6.43

3.22

4i


3.84


4.74


3.63

2.24

4j 4k


3.72
3.15


4.59
3.90


3.44
3.02

2.39 2.08

4l


3.15


3.91


3.01

2.15

4m


2.82


3.55


2.64

2.13

4n


2.50


2.79


2.34

2.31

4o


2.34


2.65


2.22

2.32

The zero-point energies (ΔZPEMP2) have been calculated at the MP2/aug-cc-pVDZ level. All values are in kcal/mol.

Table 8. Nonadditivity Energies ΔEnonadd (kcal/mol) for the Ternary Complexes of HNO3 3 3 3 HCl 3 3 3 H2O Shown in Figure 4a
oa 4a HNO3 3 3 3 H2O EMP2/aug-cc-pVDZ int HNO3 3 3 3 H2O EMP2/aug-cc-pVTZ int HNO3 3 3 3 H2O ECCSD(T)/aug-cc-pVDZ int H2O 3 3 3 HCl EMP2/aug-cc-pVDZ int H2O 3 3 3 HCl EMP2/aug-cc-pVTZ int H2O 3 3 3 HCl ECCSD(T)/aug-cc-pVDZ int HCl 3 3 3 HNO3 EMP2/aug-cc-pVDZ int HCl 3 3 3 HNO3 EMP2/aug-cc-pVTZ int HCl 3 3 3 HNO3 ECCSD(T)/aug-cc-pVDZ int EMP2/aug-cc-pVDZ nonadd )/(EMP2/aug-cc-pVDZ ) (EMP2/aug-cc-pVDZ nonadd int

4b

4c

4d

4m

4e

4f

4g

4h

4i

4j

4k

4l

4n

4o


8.94
9.25
9.09
9.57
8.36
2.04
9.10
2.42
2.34
2.09
2.27
2.34
2.10
2.40
2.30
9.84
10.43
10.28
10.36
9.11
2.31
9.75
2.65
2.53
2.30
2.49
2.55
2.29
2.57
2.47
9.04
9.62
9.49
9.55
8.32
2.05
9.16
2.39
2.45
2.18
2.41
2.46
2.18
2.52
2.40
1.37
0.07
0.20
0.18
1.81
4.76
5.29
4.92

0.25
0.14
0.10
0.08
0.02

0.40

0.10


1.57
0.05
0.19
0.17
1.94
5.09
5.39
5.24

0.24
0.10
0.10
0.08
0.03

0.40

0.09


0.90
0.05
0.19
0.17
1.66
3.51
4.75
4.00

0.24
0.10
0.09
0.08
0.02

0.39

0.09


2.04
2.88
3.00
2.93
1.24
3.34

1.07
1.91
3.87
3.85
2.61
2.61
2.60
2.89
2.71


2.29
3.06
3.17
3.08
1.54
3.96

1.02
2.37
4.55
4.53
3.13
3.14
3.12
2.99
2.84


1.63
2.56
2.60
2.54
0.88
3.02

1.02
1.45
3.53
3.50
2.33
2.33
2.32
2.60
2.48


2.02
1.18
1.05
0.67
1.33
2.97 0.98
1.89
0.12
0.01
0.23
0.26
0.21 0.08 0.25 14.07 8.85 7.89 5.02 10.46 22.70
7.98 16.98 2.12 0.23 4.50 4.92 4.43
1.70
5.36

(%) EMP2/aug-cc-pVTZ nonadd


2.16
0.77
0.60
0.63
1.31
3.14

)/(EMP2/aug-cc-pVTZ ) (EMP2/aug-cc-pVTZ nonadd int

13.65

5.41

4.25

4.47

0.96
1.90
0.13
0.03
0.25
0.28
0.23

9.42 21.64
7.29 15.65

1.95

0.51

4.18

4.61

0.06

0.25

4.17
1.24
5.05

(%) EMP2/aug-cc-pVDZ nonadd


2.14
0.76
0.63
0.65
1.24
3.15

)/(ECCSD(T)/aug-cc-pVDZ ) 15.62 (ECCSD(T)/aug-cc-pVDZ nonadd int

5.91

4.88

0.94
1.80
0.13
0.03
0.25
0.27
0.24

5.08 10.29 26.83
7.91 18.69

2.27

0.62

4.94

5.39

5.07

0.07

0.25

1.71
5.53

(%) a

All values were calculated with the MP2 level with the aug-cc-pVDZ/aug-cc-pVTZ basis sets and the CCSD(T) level with the aug-cc-pVDZ basis set.

at the CCSD(T) level are compared to ones at the MP2 level, the energy values calculated at MP2 and CCSD(T) are more similar with the same basis set (i.e., aug-cc-pVDZ). The same tendency of this basis set issue was observed for the dimers (see Table 2) as well as for other systems reported in the literature.48
54 As mentioned in the Introduction, Gomez et al. have analyzed the HNO3 3 3 3 HCl 3 3 3 H2O ternary complexes and found 15 trimer structures on the IPES by using the B3LYP level with the aug-cc-pVQZ basis set.33,34 However, because of using different a computational level (MP2 and CCST) and basis set (augcc-pVDZ and aug-cc-VTZ) with tight converging criteria in the optimization steps, we have identified four additional trimer structures (i.e., structures shown in Figure 4e, k, m, and n) that

were not obtained at the B3LYP/aug-cc-pVQZ level. However, they have also found the structure given in Figure 4a as the global minimum. On the other hand, they calculated the Gibbs freeenergy variation with temperature for some selected clusters and concluded, within the estimated errors, that all structures required very low temperatures to be formed.33 In Table 8, the results of decomposition of the interaction energy into the pair energy contributions and the nonadditivity energies of the HNO3 3 3 3 HCl 3 3 3 H2O ternary complexes, calculated at the different level of theory and with different basis sets, are presented. One can see from the table that the pair energies strongly depend on the nature of the interacting systems and on the conformation. For the HNO3 3 3 3 HCl 3 3 3 H2O 5950

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) and Angles (a, deg) between Atoms in the Ternary Complexes of HNO3 HCl H2O Shown in Table 9. Distances (r, Å 333 333 a Figure 4a
o 4a

4b

4c

4d

4e

4f

4g

4h

4i

4j

4k

4l

4m

4n

4o

r(O
H)

1.00

1.00

1.00

1.00

1.00

0.99

0.99

0.98

0.98

0.98

0.98

0.98

0.98

0.97

0.97

r(N
O) r(N
O2)

1.36 1.22

1.36 1.23

1.37 1.22

1.36 1.22

1.39 1.28

1.37 1.22

1.38 1.22

1.41 1.21

1.38 1.22

1.38 1.22

1.38 1.21

1.38 1.22

1.39 1.21

1.38 1.21

1.38 1.22

r(N
O3)

1.20

1.20

1.21

1.21

1.20

1.20

1.20

1.20

1.21

1.21

1.21

1.20

1.21

1.21

1.20

r(H3
Cl)

1.29

1.28

1.28

1.28

1.28

1.32

1.28

1.31

1.28

1.28

1.28

1.28

1.28

1.28

1.28

r(O1
H1)

0.97

0.96

0.96

0.96

0.97

0.97

0.97

0.97

0.96

0.96

0.96

0.96

0.96

0.96

0.96

r(O1
H2)

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

0.96

2.30

2.28

2.28

2.30

2.29

2.30

Distances

r(H 3 3 r(O1 3 r(O 3 3 r(O1 3

3 Cl)

2.19

3 3 H3) 3 H1) 3 3 H)

1.67

r(O2 3 3 r(O3 3 3 r(O2 3 3

1.76 2.17

1.66

1.66

r(O3 3 3 3 H3) r(O 3 3 3 H3) r(Cl 3 3 3 H1) r(O2 3 3 3 H3)

1.97

1.66

1.67

2.03

2.02

1.65

1.78 2.10

2.10 2.35 1.95

3 H1) 3 H1) 3 H2)

2.68

2.10

1.99 2.48

2.50

2.47

2.04

2.37

2.34

2.18

2.14

2.17

2.14 3.06

2.20

2.13

2.10

2.18

2.86

Angles a(O,H,Cl)

170

a(O2,H1,O1)

148

a(Cl,H3,O1) a(O,H,O1)

171 172

176

a(Cl,H3,O2)

164

169

a(O1,H1,Cl)

157

176

176

175

174

178

178

178

175 178

165

170 177

130

a(Cl,H3,O) a(Cl,H3,O3) a(O1,H1,O) a(H2,O1,H1)

168

142

148 174

176

176 132

a(O1,H1,O3)

169

177

162

178

172

171

a(N,O,H) a

All of the values were calculated at the MP2 level with the aug-cc-pVTZ basis set.

ternary systems shown in Figure 4, the nonadditivity effect leads to an increase in the total interaction energy in the order 14.07, 8.85, 7.89, 5.02, 22.70, 10.46, 16.98, 0.23, 2.12, 4.92, 4.50, 4.43% for the trimers shown in Figure 4a
f and h
m, respectively, at the MP2 level with the aug-cc-pVDZ basis set. A net binding energy gain from the effect for formation of the trimers is implied in all cases mentioned above, but this is especially significant for the trimers given in Figure 4a, f, and h. Using a larger basis set (i. e., aug-cc-pVTZ) or higher level of theory (i.e., CCSD(T)) does not change this conclusion. On the other hand, the nonadditivity effect destabilizes the trimers for the structures in Figures 4g, n, and o by ∼8, ∼2, and ∼5%, respectively. Although the structure in Figure 4a was found to be the most stable structure among all isomers shown in Figure 4, the cooperative effect component of the binding energy is largest for the structure of Figure 4f. Both structures shown in Figure 4a and f contain a cyclic structure with eight-membered rings in which the cooperativity effect becomes favorable. For example, the nonadditivity energy contributions for the structures in Figure 4a and f have been calculated to be
2.02 and
2.97

kcal/mol at MP2/aug-cc-pVDZ (
2.14 and
3.15 kcal/mol at CCSD(T)/aug-cc-pVDZ), respectively. The cooperativity effect also has a sizable stabilization contribution to structures containing the six-membered ring, as shown in Figure 4e and h. The nonadditivity contributions to these trimers were
1.33 and
1.89 kcal/mol for the structures in Figure 4e and h, respectively. In Table 9, the important geometric parameters for all minimum structures shown in Figure 4a
o have been given. The results for the trimer complexes will be compared and discussed in terms of the respective heterodimers in order to understand the cooperative effect on geometric parameters. Addition of one HCl molecule to the global minimum of the HNO3 3 3 3 H2O dimer causes the elongation of the O
H bond length of HNO3 for Figure 4a
e. The O
H bond distance was elongated just 0.01 Å at the MP2 level with the aug-cc-pVTZ basis set. In the HNO3 3 3 3 H2O dimer shown in Figure 2a, the hydrogen
, and inclusion of one bond distance has been found to be 1.70 Å HCl molecule to the HNO3 3 3 3 H2O dimer decreases the O1 3 3 3 H distances to 1.66 Å
in Figure 4a
c, 1.67 Å
in 5951

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Table 10. Harmonic Frequency Values (cm
1) and Infrared Intensities Given in Parentheses (kM mol
1) of HNO3 3 3 3 HCl 3 3 3 H2O Ternary Systems Shown in Figure 4a
oa system

frequency

νc

Ic

Δν = νc
νm Ic/Im

HNO3

ν(OH)

3704

90

HCl

ν(HCl)

3023

43

HNO3
HCl
H2O
4a

ν(HCl)

2865

433


158

ν(OH)

3195 1215


509

13.4

HNO3
HCl
H2O
4b

ν(HCl) ν(OH)

2890 542 3212 1164


133
492

12.7 12.8

HNO3
HCl
H2O
4c

ν(HCl)

2903

514


120

12.0

ν(OH)

3211 1234


493

13.6

HNO3
HCl
H2O
4d

ν(HCl)

2892


131

12.5

ν(OH)

3214 1186


583

13.1

HNO3
HCl
H2O
4e

ν(HCl)

2879

265


144

6.2

ν(OH)

3139 1110


565

12.2

HNO3
HCl
H2O
4f

ν(HCl) ν(OH)

2435 1345 3473 726


588
231

31.5 8.0

HNO3
HCl
H2O
4g

ν(HCl)

2869

536


154

12.5

ν(OH)

3402

737


302

8.1

HNO3
HCl
H2O
4h

ν(HCl)

2570

965


453

22.6

ν(OH)

3562

385


142

4.2

HNO3
HCl
H2O
4i

ν(HCl)

2976

72


47

1.6

ν(OH)

3565

303


139

3.3

ν(HCl) ν(OH)

2970 3568

81 491


53
136

1.9 5.4

HNO3
HCl
H2O
4j HNO3
HCl
H2O
4k

534

10.1

ν(HCl)

3000

65


23

1.5

ν(OH)

3588

505


116

5.5

ν(HCl)

3001

64


22

1.5

ν(OH)

3586

511


118

5.6

HNO3
HCl
H2O
4m ν(HCl)

3001

63


22

1.4

ν(OH)

3592

505


112

5.5

ν(HCl) ν(OH)

2947 3688

354 122


76
16

8.2 1.3

HNO3
HCl
H2O
4l

HNO3
HCl
H2O
4n HNO3
HCl
H2O
4o

ν(HCl)

2949

341


74

7.9

ν(OH)

3690

118


14

1.3

a

All calculations were performed at the MP2 level with the aug-cc-pVDZ basis set.


in Figure 4e due to the cooperativity effet Figure 4d, and 1.65 Å
in Figure 4g because of the anticand increases it to 1.78 Å ooperativity effect. In the clusters in which the HNO3 donates the proton to HCl and accepts a proton from water (i.e., structures shown in Figure 4f and h
m), the lengthening of the O
H bond is about 0.01 Å
for Figure 4f, and there is no elongation for Figure 4h
m. In Figure 4n and o, the hydrogen atom of HNO3 does not participate in any interaction. Hence, the O
H distances are the same as those observed in the structures given Figures 2d or 3d and e. HCl interacts with water only in Figure 4f
h; therefore, the distances will be discussed for these trimers. The H
Cl bond distance in the HCl 3 3 3 H2O dimer was found to be 1.29 Å
at the MP2 level with the aug-cc-pVTZ basis set. The HCl bond is elongated 0.03 and 0.02 Å
for the trimer structures given in Figure 4f and h, respectively, Although the HCl molecule interacts with water in the structure of Figure 4g, the HCl bond
due to the positions of the H's of distance shortens by 0.01 Å

H2O. When HCl donates a proton to HNO3, the HCl bond
(Figure 4a). The remaining structures elongation is only 0.01 Å (Figure 4b
e and i
o) have the same distance values as those in the dimers shown in Figure 3b
d. At this point, it should be pointed out that an intuition-guided process has been conducted during the search for the IPES for minima. However, it is known that there are other methodologies to explore the IPES, such as stochastic optimization and graph theoretical technique (see, for example, refs 50 and 55 and references therein). These methods are definitely superior to the intuition-guided one when the number of interacting systems is large. On the other hand, for the small clusters, like the ones considered in this work, the chemical intuition-guided construction of geometries in the search of several regions of the IPES is practical, allowing easy observation of the distinct structures. Therefore, a systematic intuition-guided process was applied to 36 initially different configurations that converged to the 15 minima shown in Figure 4. By applying this procedure, fine structures, such as the position of free hydrogens of water, were not considered. Moreover, should 3 hydrogen bonds in the ternary system and a total of 12 dimer configurations (1 for HCl 3 3 3 H2O, 6 for HNO3 3 3 3 H2O, and 5 for HNO3 3 3 3 HCl isomers) be considered, more arrangements might be found to exist on the IPES. Therefore, there might be other minima, but we believe that these fall into the conformational possibilities considered in this work. Results of Harmonic Frequency Analysis of Ternary Complexes. The harmonic frequencies of the optimized trimer complexes of Figure 4a
o were calculated at the MP2 level with the aug-cc-pVDZ basis set. The results are presented in Table 10. All frequency shifts of the trimer complexes with respect to the isolated monomer values are given with their relative intensities. First, we will discuss the O
H bond stretch of HNO3 for Figure 4a
o in which either HCl or H2O accepts a proton from HNO3. Nitric acid donates a proton to H2O in Figure 4a
e and g, for which the O
H vibrational frequency is red shifted by 509, 492, 493, 583, 565, and 302 cm
1. The red shift of the O
H stretch for Figure 4a was found to be
573 cm
1 at the B3LYP level with the aug-cc-pVQZ basis set by G
omez et al.34 McCurdy et al. reported the shift of the O
H stretch of HNO3 to be 654 cm
1 for the HNO3 3 3 3 (H2O)2 cluster.28 On the other hand, in Figure 4f and h
m, HCl accepts a proton from HNO3 with the O
H vibrational frequency of these trimers red shifted by 231, 142, 139, 136, 116, 118, and 112 cm
1, respectively. The red shift values of these trimers are rather smaller than those of the other complexes, explained above and shown in Figure 4a
e and g. The reason for this is the stronger interaction of the HNO3 3 3 3 H2O dimer than that in the HCl 3 3 3 HNO3 dimer. Hydrogen of HNO3 does not interact with any of the atoms in Figure 4n and o; therefore, the O
H frequency shifts are very small (i.e., 16 and 14 cm
1, respectively). Let us now discuss the H
Cl frequency values of the ternary complexes. In all of the trimer complexes, except Figure 4k
m, HCl acts as a proton donor to either HNO3 or H2O; therefore, the HCl stretch frequency changes from its monomer value. The red shift of the H
Cl frequency ranges between
47 and
158 cm
1 in the structures shown in Figure 4a
e, i and j, and n and o. The H
Cl stretch in Figure 4k
m shows very small shifts (∼22 cm
1) because HCl is not involved in the interaction. The largest shift (Figure 4f,
588 cm
1) is accompanied by a sizable relative intensity value (31 kM mol
1) that shows a strong 5952

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The Journal of Physical Chemistry A cooperative effect. Gomez et al. have found the biggest shift for the structure of Figure 4f of
661 cm
1 at the B3LYP level with the aug-cc-pVQZ basis set.33 Moreover, the calculated red shift for the structure of Figure 4h is
453 cm
1. H2O accepts a proton from HCl in both panels f and h of Figures 4, and we can compare these trimers when the HNO3 molecule is replaced by a second H2O molecule. The H
Cl frequency shift was reported to be 545 cm
1 with a big intensity (1212 kM mol
1) in a HCl 3 3 3 (H2O)2 cluster by Buch et al.17 It can be seen that the H
Cl frequency shift in Figure 4f and h is very similar to that of the HCl 3 3 3 (H2O)2 system.

4. CONCLUSIONS The results for the ternary complexes of HNO3 3 3 3 HCl 3 3 3 H2O in terms of structures, energetics, and harmonic vibrational modes can be summarized as follows. 1. Fifteen minima (Figure 4a
o) have been found on the IPES, with the structure of Figure 4a found as the global minimum. 2. In all ternary systems, neither HNO3 nor HCl was ionically dissociated. 3. The structural parameters (i.e., the bond distances), interaction energies, and harmonic vibrational modes (i.e., red shift of the O
H stretch of HNO3 and red shift of the H
Cl stretch of HCl) of these complexes depend on not only the nature of the monomer subunit but also the donor or acceptor role played by these monomers. 4. The structures in which HNO3 donates a proton to H2O have been found to be energetically more favorable than other structures. On the other hand, the maximum nonadditivity effect has been calculated for the structure in which HNO3 donates a proton to HCl. 5. The nonadditive effect favors the cyclic structures; for instance, the structures illustrated in Figure 4a and f consist of eight-membered rings, with this effect contributing to the total energy of the structures of Figure 4f and a by ∼22 and 14%, respectively. 6. Finally, the minima on the IPES obtained from the intuition-guided construction of geometries for the HNO3 3 3 3 HCl 3 3 3 H2O ternary complexes in this work might not be the only possible ones. However, we believe that the most representative distinct structures on the IPES were searched. ’ ASSOCIATED CONTENT

bS

Supporting Information. The structural parameters and some of the harmonic frequencies of the ternary systems shown in Figure 4a
o calculated at the MP2/aug-cc-pVDZ level. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel: þ90-246-2114114. Fax: þ90-246-2371106.

’ ACKNOWLEDGMENT We thank TUBITAK (Project No. 107T044) for financial support. We gratefully acknowledge Volkan S€onmez and Sertac-

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S. Sarıca for the computer administrative work as well as anonymous referees for interesting suggestions on the manuscript. Finally, the authors are grateful to Prof. J. Paul Devlin for editing the manuscript.

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