Possible dimers of hypochlorous acid (HOCl) arising from hydrogen- and halogen-bond interactions

Computational and Theoretical Chemistry 999 (2012) 48–54

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Possible dimers of hypochlorous acid (HOCl) arising from hydrogen- and halogen-bond interactions Zhifei Zhang a,⇑,1, Jian Shen a,1, Nengzhi Jin b, Liuping Chen c, Zhaoyong Yang d,⇑ a

College of Pharmacy & Kailuan Hospital, Hebei United University, Tangshan 063000, China The Super Computing Center of Gansu Province, Lanzhou 730000, China c KLGHEI of Environment and Energy Chemistry, School of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, China d Key Laboratory of Biotechnology of Antibiotics, Ministry of Health, Institute of Medicinal Biotechnology, Chinese Academy of Medical Sciences (CAMS) & Peking Union Medical College (PUMC), Beijing 100050, China b

a r t i c l e

i n f o

Article history: Received 15 June 2012 Received in revised form 6 August 2012 Accepted 6 August 2012 Available online 16 August 2012 Keywords: Hydrogen bond Halogen bond Hypochlorous acid Atoms in molecules Natural bond orbital

a b s t r a c t The possible hypochlorous acid dimers with six different configurations were found which were investigated by means of ab initio method at the MP2/aug-cc-pVTZ computational level. They were identified to be local minima, corresponding to two dimers with one O–H  O hydrogen bond, one dimer with one O–Cl  O halogen bond, one cyclic dimer with one O–H  Cl hydrogen bond and one O–Cl  Cl halogen bond, one cyclic dimer with two O–H  Cl hydrogen bonds, and one dimer with one O–Cl  Cl halogen bond. Their optimized geometries, stretching vibrational frequencies and interaction energies have been obtained and analyzed. The results show that the dimers with one O–H  O hydrogen bond and the cyclic one with two O–H  Cl hydrogen bonds are much stronger than the dimer with one O–Cl  O halogen bond, while the dimer with one O–Cl  Cl halogen bond is even weaker. AIM analysis was performed to examine the topological property of the hydrogen bond or halogen bond in the complex. The important roles of the intermolecular donor–acceptor orbital interactions as well as the charge transfer in these complexes were demonstrated by NBO analysis. Energy decomposition analyses indicate that the electrostatic, orbital and dispersion terms are the attractive interactions contributing to the stability of the complex, whereas the Pauli term is the repulsive interaction. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Hydrogen-bonded (HB) and halogen-bonded (XB) interactions have been well-established as two of the most important intermolecular interactions because of their great significance in chemistry and biology [1–22]. The similarities in both cases are that there exist an electron donor and an electron acceptor [15,23]. Electron donors in HB and XB might be the electronegative (or electronwithdrawing) atoms or groups, but electron acceptors are noticeably different. In HB, the electron acceptor is a positively charged hydrogen atom, whereas in XB the electron acceptor is often a negatively charged halogen atom which seems to be counterintuitive [24]. The origin of XB has been rationalized by Politzer and co-workers [25–34], that is, its formation arises from the r-hole (i.e., a patch of the positive electrostatic potential appeared on the

⇑ Corresponding authors. Tel.: +86 15373568533. E-mail addresses: [email protected] (Z. Zhang), [email protected] (Z. Yang). These authors contributed equally to the work and should be regarded as co-first authors. 1

2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.08.013

outermost region of the halogen atom’s negative electrostatic potential surface) which can accept electrons from an electron donor. In general, XB has the strength spanning over a wide range from 5 to 180 kJ mol1 [15], which is comparable to HB. Additionally, they have pronounced directionalities. As a result, there would be a competition for the electron acceptor between the hydrogen atom in HB and the halogen atom in XB when they coexist. Indeed, these phenomena were investigated both experimentally and theoretically [1,7,32,35–38]. Hypochlorous acid (HOCl), as a simple compound, is of great importance, not only in ozone layer depletion which it has a considerable influence [39–42], but in the biological relevant processes which it is closely associated with protein science [43–45], diseases [46–50], etc. Interestingly, the special structure containing OH group and Cl atom renders it an important entity in the HB and XB interactions [31,35,37,51–59], because which one (i.e., the OH group, O or Cl atom) of the HOCl molecule acts as the binding site when interacting with the ozone or protein is crucial to the understanding of the above chemical and biological processes. Solimannejad et al. have investigated the interaction between HOCl and ozone theoretically, and they found many different binding

Z. Zhang et al. / Computational and Theoretical Chemistry 999 (2012) 48–54

forms stabilized by HB or XB interactions [55]. This indicates that the intermolecular interactions involving the HOCl molecule could be very complicated. Subsequently, the firstly theoretical study of the possible dimers of HOCl was reported by them [56], and three minima (S1dCl, S2dCl and S3dCl) of HOCl dimers are observed, in which S1dCl and S2dCl are stabilized by an O–H  O HB interaction, and S3dCl is stabilized by a pair of O–H  Cl HB interactions. The S1dCl and S3dCl dimers were also investigated by Panek and Berski [53] based on the symmetry-adapted perturbation theory (SAPT) [60]. Roohi et al. further studied the gas phase hydrogenbonded dimers of HOCl [54]. They found five isomers, in which two are unstable with one low imaginary frequency and three have the same structures as those studied by Solimannejad and coworkers [56]. The results shows that O–H  O HB is stronger than that of O–H  Cl HB, but both are electrostatic in nature. However, it is noted that the O atom in the HOCl molecule is also electronegative. Accordingly, it can also be able to donate electrons to not only the H–O group but the Cl atom, forming the so-called HB and XB. Therefore, in the present work, the possible dimers of HOCl were thoroughly explored, and their structures and properties were discussed. We aim at providing a comprehensive understanding of the dimerization of HOCl molecule with such a simple and special structure.

2. Methods The optimized geometries of monomer and complexes were obtained by using the second-order Møller-Plesset perturbation theory (MP2) [61] with the aug-cc-pVTZ [62] basis set. This level of theory can provide reasonable results for weakly intermolecular interactions. Harmonic vibrational frequency analyses at the same level of theory were used to identify the local minima structures on the potential energy surface. The interaction energy (DE) was calculated as the difference between the total energy of the complex and the sum of total energies of the monomers. The basis set superposition error (BSSE) approach was calculated via the counterpoise (CP) method proposed by Boys and Bernardi [63], which was also incorporated into the geometry optimization. Because MP2 may overestimate the interaction energy [64] and describe electron correlation in a limited way [65] relative to a more refined method CCSD(T) [66], single point calculations at the CCSD(T)/aug-cc-pVQZ level were performed in order to have a better understanding of this problem. Natural bond orbital (NBO) [67–69] analysis was carried out at the B3LYP/aug-cc-pVTZ level of theory, which provides the charge transfer interaction in the complexes. These calculations were performed using the Gaussian 09 package [70]. The topological properties of the monomer and complexes were analyzed within atoms in molecules (AIM) theory [71] using AIMAll (Version 10.05.04) program [72] based on the single point calculation files at the CCSD(T)/aug-cc-pVQZ level. In addition, energy decomposition analysis (EDA) proposed by Morokuma [73] and further developed by Ziegler and Rauk [74] was performed at the BLYPD3(BJ-damping [75,76])/TZ2P level using the ADF (2012.01) software package [77]. The dispersion corrected BLYP functional [78,79] (i.e., BLYP-D3) was used because it is very accurate, while the common and popular functional B3LYP [80,81] existing in many programs after correction may be not optimal for noncovalent interactions [75,76]. In this EDA [82], the total interaction energy, DEint, can be expressed as the sum of the classical electrostatic (Eelst), orbital (Eorb), dispersion (Edisp) and Pauli repulsion (EPauli) interactions: DEint ¼ Eelst þ Eorb þ Edisp þ EPauli ; where Eelst is the electrostatic interaction energy between the fragments of the complex, Eorb is the stabilization energy as a result of the overlap between atomic orbitals, Edisp is the dispersion energy, and EPauli is the repulsive interaction between the fragments due to the electron spin.

49

3. Results and discussion 3.1. The HOCl monomer The comparisons between the parameters obtained by the experiment as well as other theoretical calculations in the literatures with the present results are made, as outlined in Table 1. It can be seen that the calculated O–H (0.968 Å) and O–Cl (1.697 Å) bond lengths at the MP2/aug-cc-pVTZ level reproduce the previous data at the same level [35,37,54], which are in good agreement with the experimental values [83,84]. In addition, the values at the MP2/aug-cc-pVDZ and MP2/6-311++G(2d,2p) levels are also consistent with the experiment, but the results obtained by other methods (i.e., CCSD/aug-cc-pVDZ, MP2/6-311++G(d,p) and B3LYP/ 6-311++G(d,p)) deviate from the experimental values to different extents. The stretching vibrational frequencies of O–H and O–Cl bonds at the different levels are basically in agreement with the experimental ones [86,87]. It should be addressed here that the method (MP2/aug-cc-pVTZ) and the harmonic frequencies adopted cannot simulate the actual experimental conditions, so their slight differences are understandable. Thus, the geometries obtained at the MP2/aug-cc-pVTZ level of theory are reliable and thus are applied in the following analyses. Molecular electrostatic potential (MEP) is considered to be an effective tool in analyzing and predicting intermolecular interactions [88]. The MEP of HOCl molecule has been reported by many groups [35,37,52,59]. The results show that the minima of MEP in the O region are deeper than those in the Cl region, as depicted in Fig. 1. Two types of maxima are also observed, one is around the H atom and another is at the outermost part of the halogen’s surface in the end of the O–Cl axis, the so-called r-hole. This suggests that the O atom in HOCl molecule can act as the HB or XB acceptor, while the Cl atom can act as the HB or XB acceptor, or XB donor.

3.2. The complexes The geometries of the complexes are shown in Fig. 2. They are denoted as D1–D6, representing the six different configurations. It is noted that D1–D4 have their mirror images, which are not shown here because of the same properties (see the mirror images of D1–D4 in Fig. S1 of Supplementary Materials for details). Solimannejad et al. [56] and Roohi et al. [54] have investigated some of these complexes (D1, D2 and D5). Each complex corresponds to the true local minimum because there is no imaginary frequency found. In these structures, D1 and D2 are formed through an O– H  O HB, D3 is stabilized by an O–Cl  O XB, D4 is a cyclic structure with an O–H  Cl HB and an O–Cl  Cl XB, while the cyclic D5 is stabilized by two O–H  Cl HBs, and D6 is stabilized by an O–Cl  Cl XB. As expected, the formed complexes confirm the above analyses based on MEP. The structural parameters, stretching vibrational frequencies, and interaction energies of the complexes D1–D6 determined without (non-CP) and with CP optimizations are summarized in Table 2. Their interaction energies via single point calculations at the CCSD(T)/aug-cc-pVQZ level are also listed in Table 2 for comparison, because the interaction energies obtained at this level of theory are highly accurate which are usually used as the benchmark data [89,90]. As can be seen from Table 2, all the O–H bond lengths in D1, D2, D4 and D5 with non-CP and CP optimizations are elongated relative to that in the monomer (Table 1), and their stretching vibrational frequencies decrease, indicating the formations of red-shifted HBs in these complexes. For D3 and D6, their lengthened O–Cl bonds are accompanied by the decreased stretching vibrational frequencies. This suggests that the red-shifted XBs are formed in these complexes. The surprising result is observed

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Z. Zhang et al. / Computational and Theoretical Chemistry 999 (2012) 48–54

Table 1 Bond lengths (R in Å) and stretching vibrational frequencies (v in cm1) in the HOCl monomer calculated at the different levels (in the references and this work) and measured by experiment.a Method

RO–H

MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ

0.969 0.968 0.968 0.969 0.966 0.966 0.970 0.988 0.968 0.964

MP2/6-311++G(2d,2p) CCSD/aug-cc-pVDZ MP2/6-311++G(d,p) [85] B3LYP/6-311++G(d,p) [85] Experiment a

RO–Cl [54] [37] [35,54] [35] [54] [54]

[83,84]

1.697 1.697 1.697 1.697 1.719 1.718 1.733 1.732 1.732 1.689

[54] [37] [35,54] [35] [54] [54]

[83,84]

vO–H

vO–Cl

– 3775.4 3776.0 3776.0 3803.5 3803.5 – 3834.6 3776.2 3794.1

– 765.5 765.0 765.0 729.7 729.7 – 726.2 700.1 739.3

[37] [37] [51] [51]

[86,87]

[37] [37] [51] [51]

[86,87]

The different calculation levels in the references [35,37,51,54,85], and the experimental data [83,84,86,87].

Fig. 1. Molecular electrostatic potential (MEP) of the HOCl molecule obtained at the MP2/aug-cc-pVTZ level, mapped on the surface of molecular electron density (0.002 a.u.). The values of the MEP are in the range from 0.050 to +0.050 a.u.

CP method can provide reasonable results, and they are then used in the following sections. Note that the complexes D1 and D2 with one O–H  O HB are much stronger than D3 with one O–Cl  O XB. For the cyclic D4, its Cl2 atom simultaneously acts as the HB acceptor and XB donor, and it has the medium strengths (13.13 kJ mol1). The cyclic D5 containing two equivalent O–H  Cl HBs is very strong (19.72 kJ mol1). Therefore, for one O–H  Cl HB in D5, it has the similar strength to that of one halogen-bonded complex like D3, confirming that HB and XB are comparable [15]. D6 is very weak, whose interaction energy (3.12 kJ mol1) is smaller than 5.0 kJ mol1, falling out of the range of XB [15]. ZPE corrected energies are relatively large, ranging from 1 to 7 kJ mol1. The result indicates that ZPE correction is important to accurately describe the stability of the complex. The positive Gibbs free energies are observed for these complexes, suggesting that the dimerization of HOCl is not spontaneous at room temperature in the gas phase. The binding distances of HO and HCl HBs, and ClO and ClCl XBs in the corresponding complexes are outlined in Table 3. It can be seen that these distances are shorter than the sums of the van der Waals radii of the atoms involved. Here, the following van der Waals radii are used: 1.20, 1.40, and 1.80 Å for H, O and Cl, respectively [91]. These geometrical characteristics imply that the H  O and H  Cl interactions belong to HBs, and Cl  O and Cl  Cl interactions belong to XBs, though the Cl1  Cl2 interaction in D6 is very weak (<5.0 kJ mol1). 3.3. Topological property

Fig. 2. Six different configurations (D1–D6) of HOCl dimers.

for D4, in which its O–Cl bond is slightly contracted but the stretching vibrational frequency decreases. The CP optimization method slightly influences the geometry and stretching vibrational frequency values compared with those without (non-CP) CP optimizations. Compared to the interaction energies of D1–D6 without CP optimizations, those obtained with CP optimizations are closer to those at the CCSD(T)/aug-cc-pVQZ level. This indicates that the optimized geometries at the MP2/aug-cc-pVTZ level of theory with

The HB or XB interactions in these complexes can be evidenced by AIM analysis. The electron density (q) and its Laplacian (r2q) are used to analyze the topological characteristics at the bond critical point (BCP). Table 3 lists the results of above quantities for D1– D6. It is observed that the q values of H  O, Cl  O, H  Cl and Cl  Cl interactions fall in the generally accepted range (0.002–0.035 a.u.) for a HB [92–94], and their corresponding Laplacian r2q values also fall in the proposed range (0.024–0.139 a.u.) for a HB [92–94]. This indicates that the XB is indeed comparable to the HB in strength, suggesting these interactions have something in common in nature. Additionally, the q values of H  O, Cl  O, H  Cl and Cl  Cl interactions have the following order: q(H  O) > q(H  Cl) > q(Cl  O) > q(Cl  Cl). It is evident that the q values of Cl1  Cl2 interactions (in D4 and D6) are smaller than those of H  O, Cl  O and H  Cl interactions, suggesting that they are weaker. It may be related to the directionality of this type of interaction which is dependent on its electrostatic potential distribution [29]. The positive r2q values mean that they are noncovalent interactions. The existence of one ring critical point (RCP) in D4 or D5 is indicative of the formation of a four-membered ring (in D4) or a six-membered ring (in D5).

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Z. Zhang et al. / Computational and Theoretical Chemistry 999 (2012) 48–54

Table 2 Bond lengths (R in Å) and stretching vibrational frequencies (v in cm1) for the subsystems of the complexes D1–D6 and their interaction energies (DE in kJ mol1), the zero-point energies (DZPE in kJ mol1) and Gibbs free energies (DG in kJ mol1) determined without (non-CP) and with CP optimizations at the MP2/aug-cc-pVTZ level, and the single point calculations of their interaction energies (DECCSD(T) in kJ mol1) at the CCSD(T)/aug-cc-pVQZ level. Method

Complex

Bond

R

v

DE

DE + DZPE

DG

DECCSD(T)

Non-CPa

D1 D2 D3 D4

O1–H1 O1–H1 O1–Cl1 O1–H1 O2–Cl2 O1–H1 O2–H2 O1–Cl1 O2–Cl2

0.976 0.978 1.702 0.973 1.697 0.975 0.975 1.698 1.698

3620.7 3600.8 753.3 3686.1 761.2 3641.5 3641.5 763.3 763.3

22.85 25.48 11.53 15.66

16.76 19.10 8.52 11.64

14.18 12.24 19.64 19.17

20.95 23.95 9.73 13.92

23.77

17.66

18.25

21.86

4.27

2.42

21.14

3.01

O1–H1 O1–H1 O1–Cl1 O1–H1 O2–Cl2 O1–H1 O2–H2 O1–Cl1 O2–Cl2

0.975 0.977 1.702 0.973 1.697 0.974 0.974 1.698 1.698

3636.3 3617.4 753.6 3695.6 761.2 3656.7 3656.7 763.4 763.4

19.54 22.05 9.80 13.13

(3.31) (3.43) (1.73) (2.53)

13.74 15.82 6.92 9.32

16.40 14.80 20.42 20.86

20.97 23.95 9.79 13.95

19.72 (4.05)

13.87

21.26

21.89

3.12 (1.15)

1.51

19.69

3.06

D5 D6 CPb

D1 D2 D3 D4 D5 D6

a DECCSD(T) was obtained by the single point calculation at the CCSD(T)/aug-cc-pVQZ level which is based on the optimized geometry at the MP2/aug-cc-pVTZ level without CP method. b The values in the parentheses are the BSSE energy, and DECCSD(T) was obtained by the single point calculation at the CCSD(T)/aug-cc-pVQZ level which is based on the optimized geometry at the MP2/aug-cc-pVTZ level with CP method.

Table 3 Geometrical and topological characteristics at the intermolecular bond critical points (BCPs) of the complexes D1–D6. Complex

Interaction

da

Dd b

qc

r2qc

D1 D2 D3 D4

H1  O2 H1  O2 Cl1  O2 H1  Cl2 Cl1  Cl2 H1  Cl2 H2  Cl1 Cl1  Cl2

1.910 1.947 2.826 2.464 3.306 2.417 2.417 3.599

0.690 0.653 0.374 0.536 0.294 0.583 0.583 0.001

0.025 0.024 0.013 0.014 0.010 0.015 0.015 0.005

0.092 0.087 0.061 0.046 0.036 0.047 0.047 0.021

D5 D6 a

The binding distances (d in Å) of H  O and H  Cl HBs, and Cl  O and Cl  Cl XBs in the corresponding complexes at the MP2/aug-cc-pVTZ level with CP method. b The difference (Dd in Å) between the sum of the van der Waals radii involved and the binding distance in the complex at the MP2/aug-cc-pVTZ level with CP method. c The topological parameters of the complexes at the BCPs (using the single point calculation files at the CCSD(T)/aug-cc-pVQZ level which are based on the optimized geometries at the MP2/aug-cc-pVTZ level with CP method). All units are in a.u.

Furthermore, the electron density q of a bond is used to describe its strength. Generally speaking, the larger the q value, the stronger the bond is. Change of the electron density q at the BCP

Table 4 The electron density (q) and its Laplacian (r2q) for the bond of the monomer and those involved in the HB or XB interaction of the complex (D1–D6).

HOCl D1 D2 D3 D4 D5 D6

2

Bond

qBCP

r q

O–H O–Cl O1–H1 O1–H1 O1–Cl1 O1–H1 O2–Cl2 O1–H1 O2–H2 O1–Cl1 O2–Cl2

0.376 0.222 0.365 0.364 0.220 0.370 0.223 0.367 0.367 0.221 0.221

3.148 0.303 3.249 3.227 0.296 3.164 0.306 3.179 3.179 0.301 0.301

also correlates well with the bond length change [95]. As can be seen from Table 4, the q(O–H) values in D1, D2, D4 and D5 are smaller than that in the HOCl molecule, suggesting that the O–H bond in these complexes become weaker after the HB formations, thus they are elongated. The q(O–Cl) values in D3 and D6 decrease relatively, which are in accordance with the lengthened O–Cl bonds. For D4, its q(O–Cl) value becomes larger, indicating the O–Cl bond is strengthened after the XB formation, which is consistent with the contracted bond length. 3.4. NBO analysis Table 5 shows the stabilization energies of the intermolecular donor–acceptor (D ? A) orbital interactions as well as the amount of Table 5 The donor–acceptor (D ? A) natural bond orbital interactions and their second-order perturbation stabilization energies (E(2), in kJ mol1) along the H  O, ClO, H  Cl and Cl  Cl interactions in the complexes D1–D6, together with the amount of charge transfer (CT, in electrons) between the subsystems of the complex at the B3LYP/augcc-pVTZ level based on the optimized geometries at the MP2/aug-cc-pVTZ level with CP method.a Complex

Interaction

D1

H1  O2

D2

H1  O2

D3

Cl1  O2

D4

H1  Cl2 Cl1  Cl2

BCP

D5

H1  Cl2

H2  Cl1

D6

Cl1  Cl2

D?A 

LP(1)O2 ? BD (1)O1–H1 LP(2)O2 ? BD(1)O1–H1 LP(1)O2 ? BD(1)O1–H1 LP(2)O2 ? BD(1)O1–H1 LP(1)O2 ? BD(1)O1–Cl1 LP(2)O2 ? BD(1)O1–Cl1 LP(1)Cl2 ? BD(1)O1–H1 LP(3)Cl2 ? BD(1)O1–H1 LP(1)Cl1 ? BD(1)O2–Cl2 LP(3)Cl1 ? BD(1)O2–Cl2 LP(1)Cl2 ? BD(1)O1–H1 LP(2)Cl2 ? BD(1)O1–H1 LP(3)Cl2 ? BD(1)O1–H1 LP(1)Cl1 ? BD(1)O2–H2 LP(2)Cl1 ? BD(1)O2–H2 LP(3)Cl1 ? BD(1)O2–H2 LP(3)Cl1 ? BD(1)O2–Cl2 LP(3)Cl2 ? BD(1)O1–Cl1

E(2)

CT

2.01 29.41 2.01 29.25 1.46 10.25 0.29 14.14 0.33 6.07 0.46 0.42 19.79 0.46 0.42 19.79 0.29 0.29

0.014 0.014 0.013 0.003

0

0

a LP denotes the occupied lone pair. BD denotes the formally empty antibonding orbital.

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Z. Zhang et al. / Computational and Theoretical Chemistry 999 (2012) 48–54

Table 6 The total interaction energy DEint and its components (in kJ mol1) for each of the complexes D1–D6 at the BLYP-D3/TZ2P level based on the optimized geometries at the MP2/ aug-cc-pVTZ level with CP method. Complex

DEinta

Eelst (Eelst/Esum)b

D1 D2 D3 D4 D5 D6

20.88 24.22 10.29 16.29 24.05 1.73

25.70 32.20 15.03 17.46 24.25 3.19

(49.0%) (51.4%) (46.8%) (40.5%) (38.3%) (26.7%)

Eorb (Eorb/Esum)b 18.73 21.31 10.37 16.97 27.03 1.92

(35.7%) (34.0%) (32.2%) (39.4%) (42.7%) (16.1%)

Edisp (Edisp/Esum)b 8.04 9.17 6.76 8.65 12.02 6.82

(15.3%) (14.6%) (21.0%) (20.1%) (19.0%) (57.2%)

EPauli 31.59 38.46 21.87 26.79 39.25 10.20

a

DEint ¼ Eelst þ Eorb þ Edisp þ EPauli . Esum is the sum of Eelst, Eorb and Edisp terms, and the value in the parenthesis is the percentage of each term relative to the Esum, representing the respective contribution to the stability of the complex. b

charge transfer between the subsystems of the dimer. The donor– acceptor stabilization energy in the complex is indicative of the strength of the orbital interaction. It is observed that the O–H  O interaction has the largest stabilization energy, followed by the O– H  Cl, O–Cl  O and O–Cl  Cl interactions. It is consistent with the order of the above q values. In D1 and D2, the very large LP(2)O2 ? BD(1)O1–H1 orbital interactions are observed, while the LP(1)O2 ? BD(1)O1–H1 orbital interactions are much weaker. For D3, the LP(2)O2 ? BD(1)O1–Cl1 with the medium strength and the very weak LP(1)O2 ? BD(1)O1–Cl1 orbital interactions contribute to the O–Cl  O XB interaction. The strong LP(3)Cl2 ? BD(1)O1–H1 interaction in D4 is an important factor contributing to its stability, on the other hand, there is also contribution coming from the LP(3)Cl1 ? BD(1)O2–Cl2 along the O–Cl  Cl XB. While the two pairs of LP(3)Cl ? BD(1)O–H interactions along the symmetric O–H  Cl HBs play important roles in stabilizing D5. Surprisingly, there are two even weaker donor–acceptor interactions (<0.5 kJ mol1) in D6, indicating the less important role of the orbital interaction. Moreover, the above results suggest that O atom can donate electrons to either HB (H–O) or XB (Cl–O) donor, while Cl atom can act as either the HB (H–O) or XB (Cl–O) acceptor and donate its lone pair electrons. The charge transfer between the subsystems of the dimer plays an important role in the complex formation. Its amount is associated with the structure of the dimer. The dimer with one HB (e.g., D1 and D2) or one XB (e.g., D3) has the larger CT value, because the charge transfer is in one direction. In contrast, for the dimers like D4–D6, the charge transfer in the complex occurs bidirectionally and counteracts, the CT amount is smaller or even zero (D5, D6).

3.5. Energy decomposition analyses Energy decomposition analysis for D1–D6 are carried out to further understand the nature of the HB and XB interactions in these complexes, as summarized in Table 6. Obviously, the total interaction energy DEint are approximate to those obtained at the MP2/ aug-cc-pVTZ level with CP method (DE in Table 2) as well as those at the CCSD(T)/aug-cc-pVQZ level (DECCSD(T) in Table 2). For D6, because it is very weak, its DEint value seems to be somewhat underestimated compared to the DE with CP method and DECCSD(T) (Table 2). In these complexes, all the Eelst, Eorb and Edisp terms are negative, indicating these three terms are the factors contributing to the stability of the complex, whereas the positive EPauli term represents that it is the repulsive interaction. The electrostatic term Eelst is the most important attractive interaction in D1–D3, which takes up in the range from 46% to 52%. The secondary important factor is the orbital interaction Eorb which includes charge transfer (i.e., donor–acceptor interaction between the occupied orbital of one moiety and the unoccupied orbital of the other), polarization and hybridization (i.e., the change of an orbital of one moiety due to the presence of the interacting one), it accounts for

32–36%. The dispersion interaction Edisp is less important in these complexes, which ranges from 14% to 21%. For D4, the electrostatic Eelst and orbital interaction Eorb terms have the similar contributions (ca. 40%), which are more than twice of the dispersion contribution. For D5, the orbital interaction Eorb term is the most significant contribution, followed by the electrostatic Eelst term, the dispersion contribution is the weakest one. For D6, the most important contribution comes from the dispersion interaction (57.2%), followed by the electrostatic Eelst and orbital interaction Eorb terms, so it is predominated by the dispersion interaction. The smaller Eorb term is consistent with the aforementioned NBO analysis of donor–acceptor interaction.

4. Conclusions A theoretical investigation of the dimerization of hypochlorous acid has been carried out at the MP2/aug-cc-pVTZ level of theory. Six different dimers were found, in which two dimers with one hydrogen bond (D1 and D2), two dimers with one halogen bond (D3 and D6), and one cyclic dimer with one hydrogen bond and one halogen bond (D4), and one cyclic dimer with two hydrogen bonds (D5). The dimer with either one or two hydrogen bonds (D1, D2 and D5) is much stronger, followed by the cyclic dimer with one hydrogen bond and one halogen bond (D4), the dimer D3 with one halogen bond has the medium strength, while D6 is even weaker (less than 5 kJ mol1). Geometrically, the intermolecular interaction in the complex is classified as either hydrogen bond or halogen bond because the binding distance in the complex is smaller than the sum of atomic van der Waals radii involved. AIM analysis reconfirms the existence of hydrogen bond or halogen bond in the complex. NBO analysis shows that the intermolecular donor–acceptor orbital interaction as well as the charge transfer between the subsystems of the dimer play important roles in the complex formation. EDA analyses indicate that the electrostatic, orbital and dispersion terms are the attractive interactions contributing to the stability of the complex, whereas the Pauli term is the repulsive interaction, and they have different contributions.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 81172965). The technical support from the Super Computing Center of Gansu Province is acknowledged.

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.comptc.2012.08.013.

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