Theoretical studies of cooperativity effects in the ternary complexes of nitrous acid with ammonia and water

Journal of Molecular Structure 738 (2005) 193–203 www.elsevier.com/locate/molstruc

Theoretical studies of cooperativity effects in the ternary complexes of nitrous acid with ammonia and water Adriana Olbert-Majkut, Krzysztof Mierzwicki, Zofia Mielke* Faculty of Chemistry, University of Wrocław, Joliot-Curie 14, 50-383 Wrocław, Poland Received 10 August 2004; revised 8 December 2004; accepted 9 December 2004 Available online 18 January 2005

Abstract Theoretical MP2 and B3LYP studies of the structures, energetics and vibrational spectra of the ternary complexes of nitrous acid with the ammonia and water molecules are presented. Six stable structures for the 1:1:1 HONO/NH3/H2O complexes were found. The lowest energy complexes formed by the trans- and cis-HONO isomers have cyclic seven- and eight-membered structures in which the mediating water molecule is strongly bound to the OH group of trans-HONO and to the nitrogen atom of NH3. In the other eight-membered cyclic structure (formed by cis-HONO), two six-membered structures (formed by trans- and cis-HONO) and the chain structure (formed by trans-HONO) the main contribution to the complex stabilization comes form the interaction between the OH group of HONO and the nitrogen atom of ammonia, however, the other two weak bonds formed by the H2O molecule with NH3 and HONO give also nonegligible contributions. For all stable complexes the attractive three-body interaction energy terms, (DE3), are calculated. The strongest cooperativity effects, as determined by DE3 values, occur for the seven and eight-membered cyclic complexes, in the six-membered structures the cooperativity is reduced due to the strong distortion of the hydrogen bonds in the smaller rings. The analysis of the cooperative effects have been also performed for the ternary HONO/H2O/H2O complexes and the results are compared with those obtained for the HONO/H2O/H2O ones. q 2004 Elsevier B.V. All rights reserved. Keywords: Hydrogen bonding; Ab initio; DFT; Cooperativity; Nitrous acid; Ammonia; Water

1. Introduction Hydrogen bond has attracted many experimental and theoretical studies in the last few decades due to its importance in many physical, chemical and biological systems [1–3]. An important characteristic of hydrogen bonding is cooperativity, considered as the enhancement of the first hydrogen bond between a donor and an acceptor when a second hydrogen bond is formed between one of these two species and a third partner. A quantitative treatment of H-bond cooperativity was first described by Huyskens [4]. Both theoretical [5] and experimental methods [6,7] have been applied to quantify this effect. H-bond cooperativity is an important concept in the theory of hydrogen bonding fluids [8] as it enhances the formation of the additional hydrogen bond as a result of an already * Corresponding author. Tel.: C48 71 3757475; fax: C48 71 3282348. E-mail address: [email protected] (Z. Mielke). 0022-2860/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2004.12.019

formed bond and, so, leads to a strong increase of the equilibrium constant for multimer hydrogen bond formation as compared to dimers. Hydrogen bonded clusters containing water molecules are of special interest [9–15] which is due to the role the water plays as ubiquitous solvent and in atmospheric and extraterrestrial chemistry. Recently, we have investigated experimentally and theoretically binary and ternary complexes between nitrous acid and water molecules [16]. The experimental spectra showed strong red shift (from 3323.0 to 2818.2 cmK1) of the OH stretching frequency of transHONO when the second water molecule was attached to the binary complex between trans-HONO and H2O proving strong cooperativity effect in the ternary complex. In this paper we report the theoretical study of the cooperativity effects in the ternary complexes between nitrous acid and two water molecules and in the ternary nitrous acid complexes with water and ammonia molecules. The theoretical studies of the structures, energetics and

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vibrational spectra of the latter complexes have not been earlier the subject of study and are also presented. The strong binary NH3–H2O, NH3–HONO complexes have been earlier studied by help of infrared matrix isolation spectroscopy [17,18] and for the latter complex the ab initio calculations have been also performed [17]. The contributions of the two-body interactions to the total interaction energy of the ternary complexes formed between nitrous acid, ammonia, water and between nitrous acid and two water molecules have been calculated and the cooperative effects in the stable complexes of these two clusters are discussed.

2. Computational details The GAUSSIAN 98 program [19] was used for geometry optimization and harmonic vibrational calculations. Geometries have been optimized at the MP2/6-311CC G(2d,2p) and B3LYP/6-311CCG(2d,2p) levels. Vibrational frequencies and intensities were computed both for the monomers (HONO, H2O and NH3) and ternary (HONO/H2O/NH3 or HONO/H2O/H2O) complexes at B3LYP/6-311CCG(2d,2p) level. The interaction energies of the clusters have been corrected for basis set superposition error (BSSE) using the counterpoise correction method (CP) [20,21]. The interaction energy of the ternary complex has been obtained by substracting the energies of the isolated monomers from the energy of the complex. Here, the geometries of the monomers correspond to those in the complex and are deformed from their equilibrium values tot DEint Z Etrimer K ðEH2 O C ENH3 C EHONO Þ or tot Z Etrimer K ðEH2 Oð1Þ C EH2 Oð2Þ C EHONO Þ DEint 2 in the ternary The two-body interaction energy DEtot complex was evaluated as a sum of the two-body interaction terms (obtained from energies of pairs of interacting molecules with the geometries corresponding to those in the complex) and can be expressed as: 2 DEtot Z ½EHONO;H2 O K ðEH2 O C EHONO Þ

C ½EHONO;NH3 K ðENH3 C EHONO Þ C ½ENH3 ;H2 O K ðEH2 O C ENH3 Þ or 2 DEtot Z ½EHONO;H2 Oð1Þ K ðEH2 Oð1Þ C EHONO Þ

C ½EHONO;H2 Oð2Þ K ðEH2 Oð2Þ C EHONO Þ C ½EH2 Oð1Þ;H2 Oð2Þ K ðEH2 Oð1Þ C EH2 Oð2Þ Þ: tot The difference between the total interaction energy DEint 2 of trimer and the pairwise interaction energies DEtot

represents the cooperative tot 2 DE3 Z DEint K DEtot .

effect

in

trimer:

3. Results and discussion 3.1. Ternary complexes between ammonia, water and nitrous acid 3.1.1. Complex structures The geometrical parameters of the ternary complexes formed by trans- and cis-HONO isomers with NH3 and H2O, calculated at MP2 and B3LYP levels, are collected in Tables 1 and 2. The structures of all stationary points are shown in Fig. 1. The most stable complex formed by trans-HONO, denoted as 1T, shows cyclic, seven-membered structure. Three hydrogen bonds are present in the complex, O1– H1/O3 between nitrous acid and water, O3–H2/N2 between water and ammonia and N2–H4/N1 between ammonia and nitrous acid molecules. The O1–H1/O3 bond shows small deviation from linearity (Q(O1H1O3)Z 174.468 according MP2) and the weakest N2–H4/N1 bond is strongly distorted (Q(N2H4N1)Z139.138). The elongation of the O–H bond of trans-HONO in ternary ˚ at MP2 or 0.029 A ˚ at complex is equal to 0.025 A ˚ ˚ B3LYP level thus is 0.014 A (MP2), 0.011 A (B3LYP) larger as compared with OH elongation in the most stable binary complex between trans-HONO and H2O [16]. The intermolecular distance between oxygen atoms of H2O and trans-HONO molecules (O1/O3) in ternary ˚ (MP2), 2.687 A ˚ (B3LYP) as complex is equal to 2.695 A ˚ ˚ compared to 2.808 A (MP2), 2.776 A (B3LYP) for the corresponding distance in the binary complex between trans-HONO and H2O [16]. The comparison of the structural parameters of the two bonds proves that the O1–H1/O3 hydrogen bond in the ternary complex is stronger than the corresponding hydrogen bond in the binary complex between trans-HONO and H2O. Complex 2T involves formation of six-membered ring (see Fig. 1). Three hydrogen bonds are present in the complex, a very strong O1–H1/N2 bond between nitrous acid and ammonia, a weak O3–H2/O1 bond between nitrous acid and water and a very weak N2–H4/O3 bond between ammonia and water molecules. All three hydrogen bonds exhibit distinct nonlinearity (Q(O1H1N2)Z166.238, Q(O3H2O1)Z142.438 and Q(N2H4O3)Z132.778 at MP2 level). The elongation of the OH bond of the nitrous acid ˚ molecule after complex formation is equal to 0.039 A (MP2) and is almost 1.5 as large as that predicted for the binary complex of trans-HONO with ammonia (DrZ ˚ [17]). The intermolecular H1/N2 distance is 0.029 A ˚ at the MP2, calculated to be equal to 1.710, 1.720 A B3LYP levels, respectively. For comparison the H/N distance in the strong Cl–H/N bond that is present in the ˚ cyclic NH3–HCl–H2O complex is calculated to be 1.613 A

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Table 1 Calculated structural parameters of trans-HONO–NH3–H2O complexesa and their monomers MP2

r(O1H1) r(N1–O1) r(N1aO2) q(H1O1N1) q(O1N1O2) H2O r(O3H2) r(O3H3) q(H2O3H3) NH3 r(N2H4) r(N2H5) q(H5N2H4) r(H1/O3) r(H2/N2) r(H4/N1) r(H1/N2) r(H2/O1) r(H4/O3) r(O2/H2) q(O1H1O3) q(O3H2N2) q(N2H4N1) q(O1H1N2) q(O3H2O1) q(N2H4O3) q(O3H2O2) a

B3LYP

HONO

1T

2T

3T

HONO

1T

2T

3T

0.967 1.440 1.170 101.44 110.87

0.992 1.370 1.190 102.64 112.28

1.006 1.390 1.190 103.35 111.82

1.002 1.360 1.200 101.86 112.13

0.968 1.430 1.150 102.67 111.10

0.997 1.370 1.180 103.94 112.57

1.012 1.390 1.170 105.07 112.10

1.007 1.360 1.180 103.62 112.25

0.958 0.958 104.24

0.984 0.958 106.23

0.964 0.958 105.23

0.963 0.957 104.30

0.961 0.961 105.13

0.990 0.960 107.12

0.967 0.960 106.02

0.966 0.960 105.05

1.009 1.009 106.96 – – – – – – – – – – – – – –

1.013 1.010 107.04 1.703 1.830 2.506 – – – – 174.46 164.07 139.13 – – – –

1.014 1.010 107.37 – – – 1.710 2.085 2.230 – – – – 166.23 142.43 132.77 –

1.011 1.010 107.10 – – – 1.735 – – 2.060 – – – 175.01 – – 172.65

1.013 1.013 107.21 – – – – – – – – – – – – – –

1.016 1.013 107.60 1.690 1.820 2.531 – – – – 174.93 164.30 137.71 – – – –

1.010 1.010 108.10 – – – 1.720 2.130 2.250 – – – – 164.83 140.63 133.96 –

1.014 1.014 107.37 – – – 1.740 – – 2.060 – – – 178.20 – – 177.45

˚ , angles in degrees. Bond lengths are in A

˚ using at the MP2/6-311CCG(d,p) level [22] and 1.835 A CCSD(T) method [23]. The H2/O1 distance in the weak O3–H2/O1 bond formed between the OH group of water molecule acting as a proton donor and the OH group of nitrous acid acting as a proton acceptor is calculated to be ˚ at the MP2, B3LYP levels, respectively. So, 2.085, 2.13 A the MP2 method predicts this distance to be shorter by ˚ and the B3LYP method by 0.02 A ˚ with respect to 0.115 A corresponding distance in the binary complex between trans-HONO and H2O that involves the same type of hydrogen bond (structure 1IIT in Ref. [16]). The ternary complex 3T shows a chain structure with a strong hydrogen bond between the OH group of transHONO and the nitrogen atom of ammonia (O1–H1/N2) and a much weaker bond between the terminal oxygen atom of trans-HONO and the OH group of water (O2/H2–O3) (Fig. 1). The hydrogen bridge O1–H1/N2 is predicted to be ˚ long (at MP2) and is slightly shorter than the 2.737 A corresponding distance in the binary complex of trans˚ ) [17]. In turn the interHONO with ammonia (2.766 A ˚ (MP2 molecular distance O2/H2 is predicted to be 2.060 A and DFT) for 3T, while the corresponding distance predicted for the binary complex between trans-HONO and H2O is ˚ using MP2 or B3LYP calculated to be 2.156 or 2.240 A method, respectively [16].

The cis-HONO isomer forms also three stable complexes with water and ammonia. All complexes have cyclic structures, in which HONO acts both as a proton donor and a proton acceptor (Fig. 1). The 1C and 3C complexes have cyclic, eight-membered structures whereas the 2C complex has six-membered structure. In the 1C complex three hydrogen bonds are present and the strongest one is formed between the OH group of cis-HONO and the oxygen atom of the water molecule. The O–H bond of cis-HONO is ˚ upon complexation, according MP2 elongated by 0.034 A ˚ elongation of the OH calculations, as compared to 0.013 A bond in the binary complex between cis-HONO and H2O (1IC, [16]). The noticeably larger elongation of the O–H bond in the ternary complex as compared to the binary one indicates the strong H-bond cooperativity in the ternary complex. The largest elongation of the O–H bond of cisHONO isomer is predicted for the O–H/N hydrogen bond between HONO and NH3 in the 3C structure (0.046 and ˚ according MP2 and B3LYP methods), however, it 0.055 A ˚ larger than the OH elongation calculated for is only 0.005 A the binary complex between cis-HONO and ammonia. 3.1.2. Interaction energies The total interaction energies of the ternary complexes tot ðDEint Þ formed both by trans- and cis-HONO isomers are

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Table 2 Calculated structural parameters of cis-HONO–NH3–H2O complexesa and their monomers MP2

r(O1H1) r(N1–O1) r(N1aO2) q(H1O1N1) q(O1N1O2) H2 O r(O3H2) r(O3H3) q(H2O3H3) NH3 r(N2H4) r(N2H5) q(H5N2H4) r(H1/O3) r(H2/N2) r(H4/O2) r(H1/N2) r(H2/O1) r(H4/O3) r(H2/O2) q(O1H1O3) q(O3H2N2) q(N2H4O2) q(O1H1N2) q(N2H4O3) q(O3H2O1) q(O3H2O2) a

B3LYP

HONO

1C

2C

3C

HONO

1C

2C

3C

0.976 1.390 1.190 104.67 113.41

1.010 1.350 1.200 108.63 114.37

0.970 1.370 1.180 110.57 114.29

1.022 1.340 1.210 111.19 114.92

0.978 1.390 1.170 106.18 113.83

1.008 1.350 1.190 110.22 114.89

1.024 1.370 1.180 110.73 114.29

1.033 1.330 1.200 112.84 115.49

0.958 0.958 104.24

0.980 0.950 106.31

0.966 0.960 106.05

0.964 0.958 105.48

0.961 0.961 105.13

0.990 0.960 107.19

0.966 0.960 106.05

0.967 0.960 106.30

1.009 1.009 106.96 – – – – – – – – – – – – – –

1.010 1.000 107.01 1.708 1.830 2.365 – – – – 172.69 167.25 139.92 – – – –

1.017 1.013 108.32 – – – 1.740 2.120 2.260 – – – – 161.77 132.91 140.94 –

1.015 1.010 107.33 – – – 1.700 – 2.033 2.010 – – – 169.64 150.83 – 162.88

1.013 1.013

1.010 1.010 107.63 1.690 1.810 2.399 – – – – 172.47 167.12 140.08 – – – –

1.017 1.013 108.30 – – – 1.720 2.120 2.260 – – – – 161.27 132.86 141.75 –

1.019 1.014 107.81 – – – 1.680 – 2.035 2.010 – – – 170.21 150.94 – 163.61

– – – – – – – – – – – – – –

˚ , angles in degrees. Bond lengths are in A

shown in Table 3. The MP2 and DFT calculations predict the 1T complex to be the most stable one among six stable structures. The 2T, 3T complexes are 1.99, 4.06 kcal/mol less stable than the 1T one according MP2 method. Three complexes, 1C, 2C and 3C, formed by cis-HONO are 1.65, 4.58 and 1.56 kcal/mol less stable than the 1T complex; as one can note, two of them (1C and 3C) show similar stability. In order to understand the nature of the interaction in the studied complexes, the analysis of the nonadditive effects was considered. In Table 3 are compared the total interaction energies with two-body interaction energies. All energy values are corrected for BSSE. In the following discussion only the MP2 values will be presented, in most cases the DFT energy values are close to those obtained by MP2 method as one can see in Table 3. In the case of the 1T and 1C structures two hydrogen bonds, namely the hydrogen bond between trans-HONO and water and between water and ammonia give relatively large contributions to the total interaction energy of these complexes (the H2O–HONO, H2O–NH3 complexes give, respectively, contributions of K7.12, K5.94 kcal/mol in the complex 1T and K6.62, K5.67 kcal/mol in the complex 1C, see Table 3). The weaker hydrogen bonds between ammonia and nitrous acid contribute K2.68, K1.78 kcal/mol to the total interaction energies in the 1T, 1C complexes, respectively. The BSSE-corrected two-body

2 Þ is calculated to be K15.74, interaction energy ðDEtot K14.07 kcal/mol for the complexes 1T, 1C, respectively, which results in an attractive three-body interaction energy DE3 of K3.00, K3.02 kcal/mol. In the structures 2T, 2C the largest two-body interaction energy component comes from interaction between ammonia and nitrous acid molecules (K9.87, K7.58 kcal/mol for the complexes 2T 2C, respectively). The hydrogen bonds formed between H2O and trans or cis-HONO and between H2O and NH3 give comparable contributions that are equal to ca. K2.50 kcal/mol for 2T and 2C complexes (Table 3). The total two-body interaction 2 is equal to K14.95, K12.68 kcal/mol for energy DEtot the complexes 2T, 2C, respectively, which results in an attractive three-body interaction energy (DE3) of K1.80, K1.48 kcal/mol. Similarly as in the structures 2T and 2C the largest twobody interaction energy contribution in the complexes 3T and 3C comes from the interaction between ammonia and nitrous acid. The contribution is equal to K11.12, K10.31 kcal/mol for the 3T, 3C complexes, respectively. The other contributions coming from the ammonia–nitrous acid and ammonia–water interactions are relatively very small (Table 3). The three body interaction energy terms (DE3) calculated for the two complexes are equal to K1.15, K2.69 kcal/mol for the 3T, 3C complexes, respectively.

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Fig. 1. The MP2 optimized structures of ternary complexes between water, ammonia and trans- or cis-nitrous acid.

197

3.1.3. Vibrational analysis The calculated frequencies of the ternary complexes are strongly perturbed as compared to the frequencies of the H2O–HONO [16] and NH3–HONO [17] binary complexes. The harmonic frequencies, intensities and frequency shifts calculated by help of the B3LYP method for all stable trimers are presented in Tables 4 and 5. The frequencies calculated for the binary trans- and cisHONO complexes with water have been previously reported [16]. The comparison of the frequencies of the O–H/O hydrogen bonding between the OH group of nitrous acid and the oxygen atom of water in the binary 1IT (1IC) [16] and the ternary 1T (1C) complexes indicates much stronger frequency perturbation in the latter complexes, the strongest perturbation exhibits the OH stretch of nitrous acid. In the ternary 1T, 1C complexes the n(OH) stretch is calculated to be 586 and 552 cmK1 red shifted from the corresponding mode of the trans-HONO and cis-HONO monomers, respectively, while only 283 and 299 cmK1 red shifts were predicted for the binary complexes of trans- or cis-HONO with H2O. This clearly indicates the successive weakening of the O–H bond in HONO in the set of species: HONO monomer, HONO– H2O heterodimer and H2O–HONO–NH3 ternary cluster. The increase of the strength of the hydrogen bond (as determined by the n(OH) stretching frequency) is accompanied by an increase of the intensity of the OH vibration which grows 1.4, 1.7 times in the ternary trans- and cis-HONO complexes as compared to the corresponding binary ones. In turn the frequency of the OH torsion in the 1T and 1C complexes is calculated to shift 416 and 329 cmK1 toward higher frequencies with respect to the corresponding frequency of the trans- and cis-HONO monomers whereas only 287 and 230 cmK1 blue shifts were predicted for the binary

Table 3 The decomposition of the interaction energy for HONO–NH3–H2O complexes into two-body and three-body contributions 1T

DEH2 2 OKHONOt 2 DENH 3KHONOt DEH2 2 OKNH3 2 DEtot tot DEint 3 DE

2T B3LYP

MP2

B3LYP

MP2

B3LYP

K7.12 K2.68 K5.94 K15.74 K18.74 K3.00

K7.54 K2.27 K6.02 K15.83 K18.90 K3.07

K2.58 K9.87 K2.50 K14.95 K16.75 K1.80

K2.35 K10.50 K2.10 K14.95 K16.73 K1.78

K2.07 K11.12 K0.34 K13.53 K14.68 K1.15

K2.09 K11.67 K0.27 K14.03 K15.12 K1.09

2C

1C

DEH2 2 OKHONOc 2 DENH 3KHONOc DEH2 2 OKNH3 2 DEtot tot DEint 3 DE

3T

MP2

3C

MP2

B3LYP

MP2

B3LYP

MP2

B3LYP

K6.62 K1.78 K5.67 K14.07 K17.09 K3.02

K7.14 K1.57 K6.05 K14.76 K18.17 K3.41

K2.57 K7.58 K2.53 K12.68 K14.16 K1.48

K2.15 K9.58 K2.12 K13.85 K15.49 K1.64

K1.97 K10.31 K2.21 K14.49 K17.18 K2.69

K2.12 K11.23 K1.93 K15.28 K18.30 K3.02

2 Results are corrected for BSSE. Total two-body contribution energy: DEtot Z DEH2 O;HONO C DENH3 ;HONO C DEH2 O;NH3 . Total trimer interaction energy: tot tot 2 Z Etrimer K ðEH2 O C ENH3 C EHONO Þ. Three-body non-additive interaction energy DE3 Z DEint K DEtot . DEint

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Table 4 Calculated frequencies, frequency shifts (cmK1) and intensities (km/mol)a of NH3/H2O/HONO-trans complexes Monomers, n

trans-HONO 3768 (80) 1763 (178) 1306 (184) 817 (143) 615 (146) 583 (103) H2 O 3923 (62) 3821 (7) 1639 (71) NH3 3598 (4) 3600 (4) 3483 (3) 1674 (19) 1673 (19) 1037 (168) Intermolecular

2T

1T

Assignment

n

Dn

n

Dn

n

Dn

3182 (1210) 1722 (99) 1508 (211) 937 (141) 728 (25) 999 (107)

K586 K41 C202 C120 C113 C416

2935 (1858) 1727 (110) 1500 (361) 888 (322) 722 (61) 1113 (134)

K833 C36 C194 C71 C107 C530

3008 (2004) 1710 (109) 1515 (326) 963 (368) 748 (15) 1101 (86)

K760 K53 C209 C146 C133 C518

n OH n NaO d HON n N–O d ONO t OH

3879 (68) 3305 (1082) 1688 (26)

K44 K516 C49

3898 (113) 3750 (165) 1650 (65)

K25 K71 C11

3896 (126) 3754 (271) 1662 (51)

K27 K67 K17

nas OH ns OH d H2O

3596 (14) 3574 (44) 3468 (26) 1680 (31) 1661 (38) 1134 (147)

K2 C6 K15 C6 K12 C97

3601 (15) 3572 (48) 3461 (32) 1682 (13) 1668 (42) 1150 (138)

C3 K8 K22 C8 K5 C113

3592 (19) 3588 (20) 3480 (0) 1672 (18) 1668 (18) 1151 (159)

K6 K12 K3 K2 K5 C114

nas NH2 nas NH3 ns NH3 d NH3 d NH3 d HNH

909 (203) 576 (55) 368 (100) 308 (60) 270 (36) 249 (34) 220 (29) 170 (3) 131 (2) 117 (1) 72 (10) a

3T

483 (40) 425 (119) 361 (21) 307 (159) 245 (37) 157 (6) 146 (5) 137 (4) 116 (110) 115 (12) 84 (11)

456 (107) 395 (22) 345 (17) 287 (111) 248 (32) 149 (0) 121 (8) 97 (1) 62 (92) 50 (31) 39 (1)

The intensities are given in brackets.

water–nitrous acid complexes. The strong perturbation of the frequencies of water in 1T and 1C complexes is due to the formation of two strong hydrogen bonds in which H2O acts as a proton acceptor for HONO (O1–H1/O3) and as a proton donor toward NH3 (O3–H2/N2). The ns H2O stretching vibrations are predicted to be 516 cmK1 (for 1T) and 538 cmK1 (for 1C) red shifted from the corresponding H2O monomer band (Tables 4 and 5). In the ternary 2T and 2C structures the n(OH) stretching frequency of nitrous acid is calculated to shift 833 and 823 cmK1 toward lower frequencies with respect to the OH stretch of trans- and cis-HONO monomers; in both ternary complexes the predicted shift is ca. 200 cmK1 larger than in the binary complexes of trans- and cis-HONO with ammonia [17]. In similar clusters formed by HCl molecule the calculated HCl stretching frequency exhibits 627 cmK1 red shift when going from NH3–HCl heterodimer to the NH3– HCl–H2O cluster [22]. The torsional OH vibrations in the 2T, 2C complexes exhibit similar perturbations as in the binary trans- or cis-HONO complexes with ammonia (530, 490, 432, and 434 cmK1 in the ternary and binary complexes formed by trans- and cis-HONO, respectively). Similar perturbation of torsional vibrations in the binary and ternary

complexes in spite of the stronger O–H/N bond in the latter ones is probably due to strong distortion of the O–H/N bridge in the trimers with respect to the heterodimers; torsional vibration is very sensitive not only to the strength but also to the geometry of the hydrogen bridge. The OH stretching vibration of cis-HONO in the ternary 3C complex is much more perturbed than the corresponding vibration of trans-HONO in 3T (971, 760 cmK1 red shifts in 3C, 3T complexes with respect to the trans- and cis-HONO monomers) which is due to the cyclic nature of the 3C complex. The attachment of the water molecule to the binary cis-HONO complex with ammonia leads to 350 cmK1 decrease of the OH stretching frequency of cis-HONO whereas only 150 cmK1 red shift of the corresponding frequency of trans-HONO isomer is observed when the water molecule is attached to the binary complex between transHONO and ammonia. 3.2. Ternary complexes between nitrous acid and two water molecules The optimized geometries and calculated vibrational spectra of the binary complexes of nitrous acid with one

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Table 5 Calculated frequencies, frequency shifts (cmK1) and intensities (km/mol)a of NH3/H2O/HONO-cis complexes Monomers, n

cis-HONO 3597 (26) 1697 (211) 1343 (8) 875 (309) 630 (36) 689 (104) H2O 3923 (62) 3821 (7) 1639 (71) NH3 3598 (4) 3600 (4) 3483 (3) 1674 (19) 1673 (19) 1037 (168) Intermolecular

2C

1C

Assignment

n

Dn

n

Dn

n

Dn

3045 (1109) 1633 (184) 1467 (40) 1007 (338) 710 (6) 1018 (123)

K552 K64 C124 C132 C80 C329

2774 (1490) 1655 (123) 1477 (70) 955 (373) 689 (47) 1124 (194)

K823 K42 C134 C80 C59 C432

2626 (1697) 1599 (358) 1480 (85) 1042 (353) 739 (4) 1180 (89)

K971 K98 C137 C167 C109 C490

n OH n NaO d HON n N–O d ONO t OH

3879 (65) 3283 (980) 1696 (27)

K44 K538 C67

3754 (148) 3899 (116) 1643 (196)

K67 K24 C4

3739 (253) 3898 (129) 1646 (29)

K82 K25 C7

nas OH ns OH d H2 O

3579 (13) 3583 (42) 3475 (19) 1681 (19) 1659 (43) 1128 (135)

K18 K17 K8 C7 K14 C91

3600 (15) 3574 (47) 3462 (25) 1680 (11) 1673 (74) 1146 (84)

C12 K26 K21 C6 0 C109

3591 (14) 3550 (68) 3430 (103) 1688 (13) 1673 (8) 1188 (134)

K7 K50 K53 C14 0 C151

nas NH2 nas NH3 ns NH3 d NH3 d NH3 d HNH

902 (64) 583 (46) 356 (103) 292 (51) 273 (7) 243 (62) 206 (28) 181 (7) 122 (2) 103 (0) 88 (11) a

3C

476 (26) 420 (107) 360 (19) 306 (164) 252 (31) 185 (4) 142 (8) 134 (4) 105 (26) 100 (78) 87 (36)

566 (13) 465 (121) 386 (14) 316 (128) 257 (45) 192 (7) 189 (14) 157 (5) 154 (6) 142 (109) 105 (14)

The intensities are given in brackets.

water molecule and the ternary complexes of nitrous acid with two water molecules have been previously studied both experimentally and theoretically (by MP2 and DFT methods) and have been already discussed in our previous paper [16]. Those results will be addressed here when appropriate for the discussion of the interaction energies of the ternary complexes. In this chapter we discuss the interaction energies of all stable complexes between nitrous acid and two water molecules considering two- and threebody interactions and nonadditivity of interactions in ternary complexes of nitrous acid with two water molecules. 3.2.1. Interaction energies As already presented in our previous paper [16] three stationary points were found for the complexes of transHONO isomer and two stationary points for the complexes of cis-HONO isomer with two water molecules both at the MP2 and B3LYP levels; all optimized structures are shown in Fig. 2. The counterpoise corrected MP2 and DFT interaction energies of all trans- and cis-HONO ternary complexes are given in Table 6 (these values differ from the values of binding energies that are presented in Ref. [16]). In the discussion below only the MP2 values will be discussed,

the calculated DFT energies are close to those obtained at the MP2 level as can be seen in Table 6. The most stable is the IT complex for which the interaction energy is equal to K16.88 kcal/mol at the MP2 level. The interaction between the OH group of trans-HONO and the oxygen atom of H2O contributes K6.36 kcal/mol to the total interaction energy and the interaction between the two water molecules gives K4.95 kcal/mol contribution. For comparison, the interaction energy between the two water molecules in cyclic CH3OH–(H2O)2 ternary complex is equal to K3.68 kcal/mol, while the contribution of water– water interaction to the total interaction energy in water trimer is calculated to be equal to K3.71 kcal/mol [24]. The 2 BSSE-corrected two-body interaction energy ðDEtot Þ in IT complex is calculated to be K14.18 kcal/mol which results in an attractive three-body interaction energy of K2.70 kcal/mol. For water trimer the nonadditivity of energy is equal to K2.92 kcal/mol while the substitution of one water molecule by methanol increases this effect by about K0.5 kcal/mol [24]. In the other cyclic structure formed by trans-HONO (IIT) the OH group of the acid serves as a proton donor for one water molecule and as a proton acceptor for

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Fig. 2. The MP2 optimized structures of the water complexes with transand cis-nitrous acid of 2:1 stoichiometry.

the other one. The predicted interaction energy is equal to K14.49 kcal/mol, so, the complex is 2.39 kcal/mol less stable than the IT one. Similarly as in the complex IT, the largest two-body interaction energy (K5.53 kcal/mol) comes from the hydrogen bonding between the OH group of trans-HONO and an oxygen atom of H2O, however, the interaction between the two water molecules gives also relatively large contribution (K4.09 kcal/mol) that is comparable with the contribution provided by the interaction between the two water molecules in the IT complex. The third contribution from the hydrogen bond between an oxygen atom of the OH group of HONO and the water molecule is calculated to be equal to K2.86 kcal/mol. The three-body interaction energy term calculated for IIT structure is attractive by K2.01 kcal/mol. The less stable complex formed by trans-HONO isomer has a chain structure in which the OH group of the acid acts as a proton donor for one water molecule and the terminal oxygen atom of the acid as a proton acceptor for the other water molecule. Also in this complex, like in the previous two, the largest two-body interaction energy is due to the interaction between the OH group of HONO and water (K7.23 kcal/mol). The BSSE-corrected total two-body 2 interaction energy ðDEtot Þ is equal to K9.60 kcal/mol which results in an attractive three-body interaction energy of K0.68 kcal/mol. Both stable complexes formed by cis-HONO isomer with two water molecules have the cyclic structures (IC and IIC). The total interaction energy for the IC eight-membered complex is equal to K15.57 kcal/mol. Comparison of this result with the total interaction energy of the water cyclic trimer [24] indicates that the substitution of one water molecule by cis-HONO leads to an increase of

Table 6 The decomposition of the interaction energy for HONO–H2O–H2O complexes into two-body and three-body contributions IIT

IT

DEH2 2 Oð1ÞKHONOt DEH2 2 Oð2ÞKHONOt DEH2 2 Oð1ÞKH2 Oð2Þ 2 DEtot tot DEint 3 DE

B3LYP

MP2

B3LYP

MP2

B3LYP

K6.36 K2.87 K4.95 K14.18 K16.88 K2.70

K7.14 K2.77 K4.55 K14.47 K17.63 K3.16

K5.53 K2.86 K4.09 K12.48 K14.49 K2.01

K5.94 K2.52 K4.31 K12.76 K15.12 K2.36

K7.23 K1.93 K0.44 K9.60 K10.28 K0.68

K7.55 K1.81 K0.40 K9.76 K10.41 K0.65

IIC

IC

DEH2 2 Oð1ÞKHONOc DEH2 2 Oð2ÞKHONOc DEH2 2 Oð1ÞKH2 Oð2Þ 2 DEtot tot DEint 3 DE

IIIT

MP2

MP2

B3LYP

MP2

B3LYP

K6.68 K1.69 K3.93 K12.30 K15.57 K3.27

K7.33 K1.51 K4.23 K13.07 K16.77 K3.70

K4.97 K2.74 K4.10 K11.81 K13.70 K1.89

K5.35 K2.46 K4.30 K12.12 K13.78 K1.66

2 Results are corrected for BSSE. Total two-body contribution energy: DEtot Z DEH2 O;HONO C DENH3 ;HONO C DEH2 O;NH3 . Total trimer interaction energy: tot tot 2 Z Etrimer K ðEH2 O C ENH3 C EHONO Þ. Three-body non-additive interaction energy DE3 Z DEint K DEtot . DEint

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the interaction energy of the cluster by K1.7 kcal/mol. Similarly as in the trans-HONO complexes the largest twobody interaction energy in the two cis-HONO complexes is due to the interaction between the OH group of HONO acting as a proton donor and water acting as a proton acceptor; this contribution is equal to K6.68 kcal/mol in the IC complex. This value is close to that predicted for the binary complex between cis-HONO and H2O involving the same type of bond [16]. The interaction between the two water molecules gives relatively large and comparable contribution in all complexes that is equal to K3.93 kcal/mol for the IC complex. In turn, the interaction between a water molecule and terminal oxygen atom of cis-HONO gives relatively small contribution (K1.69 kcal/mol) comparable with the value of the binding energy of the binary complex between cis-HONO and H2O involving the same type of hydrogen bond (K1.41 at MP2 level) [16]. The three-body interaction energy term calculated for IC complex is equal to K3.27 kcal/mol. In the structure IIC, similarly as in the IIT, the OH group of the acid serves as a proton donor for one water molecule and as a proton acceptor for the other water molecule. The calculated interaction energy for this complex is K13.70 kcal/mol. The interaction energy between an oxygen atom of water and the OH group of cis-HONO is equal to K4.97 kcal/mol and is 0.87 kcal/mol lower than the two-body interaction energy between the two water molecules (K4.10 kcal/mol). The third bond that is formed between the water molecule acting as a proton donor toward the oxygen atom of the acid gives also meaningful contribution (K2.74 kcal/mol) to the total two-body interaction energy. The three-body interaction energy component is attractive and is equal to K1.89 kcal/mol. 3.3. Cooperativity in the ternary complexes of HONO with the NH3, H2O or H2O, H2O molecules For all ternary complexes of nitrous acid with ammonia and water the attractive three-body interactions are calculated, however, the cooperativity in the 1T, 1C and 3C complexes, as determined by DE3, is distinctly stronger than in the 2T, 3T and 2C ones (Table 3). The stronger cooperativity in the 1T, 1C complexes can be explained by the presence of two strong hydrogen bonds, O1–H1/O3, O3–H2/N2, from which the first one shows small deviation from linearity (Q(O1–H1/O3)Zca. 174, 1738 for 1T, 1C according MP2). In the 3C complex the O1–H1/N2 hydrogen bond that gives the largest contribution to the total interaction energy exhibits also a relatively small deviation from linearity (Q(O1–H1/N2)Z1708 according MP2). The reduction of the H-bond cooperativity in the 2T, 2C complexes as compared to the 1T, 1C ones is due to the distortion of the three hydrogen bonds in these sixmembered ring complexes (Q(O1–H1/N2)Zca. 162, 1668; Q(O3–H2/O1)Zca. 142, 1418 and Q(N2–H4/ O3)Z133, 1338 for the 1T, 1C complexes, respectively).

201

It has been shown earlier that in the case of complexes with distorted hydrogen bonds a reduction of the H-bond cooperativity occurs [25,26]. The weaker cooperativity effect in the 3T complex is due to its chain structure in which the strong O1–H1/N2 bond is only slightly effected by the additional interaction between the terminal oxygen atom of HONO and water molecule. For all five stable complexes of nitrous acid with two water molecules the attractive three-body interactions are calculated, the H-bond cooperativity in the ternary complexes between HONO and two water molecules shows some similarities to the cooperativity of the ternary complexes between HONO, NH3 and water. So, the strongest cooperativity (K2.70, K3.27 kcal/mol according MP2 method) exhibit the most stable IT, IC seven- and eightmembered complexes that have similar structures as the 1T, 1C complexes. In the two IIT, IIC six-membered complexes the cooperativity is reduced (K2.01, K1.89 kcal/mol, respectively, according MP2 method). Our previous results showed [16] that in the six-membered IIT, IIC complexes all three hydrogen bonds are strongly distorted and show large deviations from linearity. As expected, the weakest cooperativity is predicted for the chain IIIT complex. The three body term is representing as much as ca. 14– 21% of the total MP2 interaction energy of the 1T, 1C, 3C, IT, IC, IIT and IIC trimers; this contribution is similar to the contribution of the three-body interaction energies in the recently studied (H2O)2–HX complexes [27]. Only in the 2T, 2C structures with strongly distorted hydrogen bonds and in the chain 3T and IIIT structures the contribution of the three body term is ca. 10% or less. The FTIR matrix isolation studies of the complexes between nitrons acid and water presented in our recent paper [16] proved the presence of the IT complex in the matrix. The other four complexes of HONO were not identified. The observed IR spectra were in good agreement with the calculated spectra with the exception of the OH stretching frequency of trans-HONO. The value of the predicted red frequency shift (556 cmK1) of the OH stretch after complex formation was still considerably lower than the observed red shift of this mode (750 cmK1). This difference was attributed to the strong solvation effect of argon matrix on the very strong hydrogen bond in complex, however, the observed strong shift confirms the strong H-bond cooperativity in this complex. In the 1T, 1C ternary complexes of nitrous acid with ammonia and water, in which the OH group of HONO is bonded to the oxygen atom of H2O, the calculated perturbation of OH stretching frequency is close to the perturbation predicted for the corresponding ternary complexes of HONO with two water molecules (586, 556 cmK1 for the 1T, IT structures and 552, 533 cmK1 for the 2C, IIC ones, respectively). In all other structures in which the OH group of HONO is attached to the nitrogen atom of ammonia the OH stretch exhibits much stronger perturbation than in the ternary complexes with two water

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molecules and in the binary complexes between ammonia and nitrous acid. The calculated shift of this frequency in 2T, 2C complexes is ca. 200 cmK1 larger and in the 3T complex it is ca. 150 cmK1 larger than the shift of the corresponding frequencies in the binary complexes of trans and cis-HONO isomers with ammonia. The largest shift (350 cmK1) is calculated for the 3C complex and is in accord with the large DE3 value predicted for this complex.

4. Conclusions Theoretical calculations performed for the HONO ternary complexes indicate the stability of six complexes formed by the trans- and cis-HONO isomers with the H2O and NH3 molecules. In the seven- and eighttot membered cyclic structures, 1T and 1C (DEint ZK18:74, K17.09 kcal/mol) the water molecule forms two strong hydrogen bonds, acting as a proton acceptor for the OH group of trans- or cis-HONO and as a proton donor toward the nitrogen atom of ammonia. The two strong bonds give large and comparable contributions to the total interaction energies of the complexes. The third bond between ammonia acting as a proton donor and nitrous acid acting as a proton acceptor is weak as reflected by the relatively small value of the two-body interaction energy between NH3 and HONO. In the tot cyclic six-membered 2T, 2C complexes (DEint ZK16:75, K14.16 kcal/mol) water and ammonia are attached to the OH group of nitrous acid forming six-membered ring in which the three hydrogen bonds exhibit strong deviation tot from linearity. The 3T complex (DEint ZK14:68 kcal/mol) has a chain structure with ammonia and water bonded to the OH group and terminal oxygen atom of HONO, tot respectively. In the 3C complex (DEint ZK17:18 kcal/mol) ammonia and water are also attached to OH and terminal oxygen atom of HONO, respectively, however, the cisHONO isomer leads to the formation of a cyclic eightmembered structure. The analysis of the two-body interaction energies indicates that the main contribution to the total interaction energies of the 2T, 3T, 2C and 3C complexes comes from the interaction between the OH group of HONO and the nitrogen atom of ammonia, the other interactions between nitrous acid and water (2T, 2C, 3T, 3C complexes) and between water and ammonia (2T, 2C, 3C complexes) give much smaller contributions. The cyclic seven-membered 1T and eight-membered 1C, 3C complexes show the strongest cooperativity effects, in the 2T and 2C structures the cooperativity is reduced due to the deviation of hydrogen bonds from linearity in the six-membered rings. The still weaker cooperativity in the 3T complex is due to its chain structure and to the presence of one strong hydrogen bond only (O–H/N bond between HONO and ammonia), the second interaction between HONO and water is very weak.

When the ammonia molecule is replaced by the water molecule the total interaction energy of the cluster decreases. The largest difference in energy show the chain structures 3T and IIIT (4.40 kcal/mol), that is due to the replacement of very strong O–H/N bond between HONO and NH3 in 3T by the weaker O–H/O bond between HONO and water in IIIT. Similarly, as for the ternary complexes of nitrous acid with ammonia and water, the strongest cooperativity exhibit the seven- and eightmembered cyclic complexes IT, IC, respectively. The cooperativity is reduced in the cyclic six-membered IIT, IIC complexes in which the hydrogen bonds are distorted. It decreases even more in the chain complex IIIT that involves only one strong hydrogen bond between HONO and H2O, the additional very weak interaction between water and the terminal oxygen atom of HONO has small effect on the strong bond.

Acknowledgements We gratefully acknowledge a grant of computer time for the Wrocław Center for Networking and Supercomputing.

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