Theoretical study on H2Y⋯AgX (X = F, Cl, Br, I; Y = O, S) complexes: Structures, energies and bonding

Chemical Physics Letters 614 (2014) 5–9

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Theoretical study on H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes: Structures, energies and bonding Qi Wang, Bohai Zhang, Zhengguo Huang ∗ Tianjin Key Laboratory of Structure and Performance for Functional Molecules, Key Laboratory of Inorganic–Organic Hybrid Functional Material Chemistry, Ministry of Education, College of Chemistry, Tianjin Normal University, Tianjin 300387, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 30 May 2014 In final form 3 September 2014 Available online 10 September 2014

a b s t r a c t The H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes have been investigated by ab initio methods. All complexes are non-planar with Cs symmetry, and the Ag X bond is strengthened during complexation processes. The binding energies of complexes were accurately calculated using the CCSD(T)/CBS by extrapolation method. The interaction between H2 Y and AgX is weakened as X varies from F to I. The intermolecular interactions in these complexes show partial covalent character; moreover, the intermolecular interactions in H2 S· · ·Ag X (X = F, Cl, Br, I) complexes are stronger than those in H2 O· · ·Ag X complexes. © 2014 Elsevier B.V. All rights reserved.

1. Introduction

2. Computational details

Intermolecular interaction has been an active research field of chemistry since it is very important in many chemical/biological phenomena [1–3]. Recently, some small, metalcontaining molecules of the type B· · ·M X (where B is a simple Lewis base, such as N2 , H2 O, H2 S, NH3 and C2 H4 , M is Cu or Ag, and X is halogen atom) have been synthesized in the gas phase and characterized by rotational spectra [4–8]. Two complexes, namely H2 O· · ·AgCl and H2 S· · ·AgCl, were first synthesized and characterized by rotational spectra [4]. H2 O· · ·AgF [5] and H2 S· · ·AgI [6] were subsequently synthesized and characterized by rotational spectra. These complexes are isomorphic with their hydrogen- and halogen-bonded counterparts. Moreover, they are more strongly bound than their hydrogen- and halogen-bonded analogues. Recently, the researches on the bonding characters of H2 O· · ·AgCl and H2 S· · ·AgCl show that the hyper-conjugation interaction between H2 O/H2 S and AgCl takes part in the bonding [9]. Except above complexes, no other H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes have been studied experimentally or theoretically so far. Do they exist possibly? What are the differences between H2 O· · ·Ag X and H2 S· · ·Ag X (X = F, Cl, Br, I) complexes? These questions motivated us to systematically investigate the H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes in this article.

The structural, energetic, and spectroscopic properties of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes were studied by ab initio methods using the gamess program [10]. For H, O, S, F and Cl atoms, the augmented Dunning’s correlation consistent valence n-zeta (aug-cc-pVnZ, n = D and T, abbreviated as AVnZ, the same below) basis sets were used. The aug-cc-pVnZ-PP (n = D and T, abbreviated as AVnZ-PP, the same below) small-core relativistic effective core potential (RECP) and basis sets of Peterson et al. [11,12] were used for Ag, Br and I atoms, which retain 19, 25 and 25 explicit electrons, respectively. The geometries of complexes were fully optimized without any symmetry constraints using MP2 and CCSD(T), respectively. The harmonic vibrational frequencies were calculated with analytic second derivatives at the same level to confirm that the structures are minima and zero-point vibrational energies (ZPVE) were calculated. To properly quantitatively describe the stabilities of complexes, high accuracy is required. It is well known that MP2 method usually overestimates the binding energy of complex, while CCSD(T)/CBS scheme can provide accurate binding energies within chemical accuracy (∼1 kcal·mol−1 ) for various types of non-covalent interactions and has been called the ‘golden standard’ [13]. However, CCSD(T) calculation is very time-consuming and expensive. Therefore, based on MP2/AVnZ (n = D and T) calculations, CCSD(T)/CBS limit was extrapolated in the present work. Firstly, the binding energies (E) were calculated at the MP2/AVnZ (n = D and T) level to study the effect of the basis-set size on the binding energy. Then

∗ Corresponding author. E-mail address: [email protected] (Z. Huang). http://dx.doi.org/10.1016/j.cplett.2014.09.009 0009-2614/© 2014 Elsevier B.V. All rights reserved.

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Q. Wang et al. / Chemical Physics Letters 614 (2014) 5–9

E at the MP2/AVnZ level extrapolated to the CBS limit [14,15]. The MP2 correlation energy at CBS limit is obtained as: CBS Ecorr,MP2 =

n3 n3 − (n − 1)3 −

AVnZ Ecorr,MP2

(n − 1)3 n3 − (n − 1)3

AV(n−1)Z

Ecorr,MP2 ;

n=3

Figure 1. The model of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes.

(1)

3. Results and discussion and the MP2 binding energy at CBS limit is obtained as: 3.1. Structures and frequencies CBS AVTZ CBS EMP2 = EHF + Ecorr,MP2

(2)

Finally, a reliable E at the CCSD(T)/CBS limit is thus approxiCBS ) mated by the sum of the MP2 binding energy at CBS limit (EMP2 AVDZ AVDZ ) correction term covering the difference − EMP2 and a (ECCSD(T) between MP2 and CCSD(T) binding energies [16]: CBS CBS AVDZ AVDZ ECCSD(T) = EMP2 + (ECCSD(T) − EMP2 )

(3)

AVDZ AVDZ ) term This is based on the assumption that the (ECCSD(T) − EMP2

has faster convergence than ECCSD(T) with respect to the basis set, and thus this difference can be evaluated with a small or midsized basis set. This assumption has been validated for some model intermolecular interaction complexes [16,17]. The localized molecular orbital energy decomposition analyses (LMO-EDA) [18], quantum theory of atoms in molecules (QTAIM) [19–22] and NBO analyses were used to study the nature of the interactions of complexation at the MP2/AVTZ level. In LMO-EDA, total binding energy (EMP2 ) is decomposed into five terms: EMP2 = Eele + Eex + Erep + Epol + Edisp

(4)

where Eele is the electrostatic energy describing the Coulomb interaction between the charge distributions of undistorted monomers, Eex and Erep are the exchange and repulsion energies, respectively, due to Pauli’s exclusion principle, Epol is the polarization energy that describes the Coulomb interaction between the charge distributions of the distorted monomers, and Edisp is the dispersion energy, EMP2 represents the total binding energy without considering the deformation energy of monomers, which was calculated at MP2/AVTZ level. QTAIM were investigated using the wave functions obtained at the same level by AIM2000 [23], and NBO analyses were performed by NBO5 software [24].

The model of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes is illustrated in Figure 1, and the selected structural parameters are listed in Table 1. All complexes are non-planar with Cs symmetry, and the halogens, Ag and Y are collinear. The angle ˚ is the indicated angle between the C2 symmetry axis of H2 Y and the Y· · ·Ag inter-nuclear line. As shown in Table 1, the theoretical calculation results almost agree well with the experimental results [5–8]; moreover, the CCSD results of the present work are better than previous results obtained at the MP2 level [9]. The angle ˚ (75.2–77.4◦ ) in H2 S· · ·Ag X complexes are larger than corresponding ones (about 45.4–42.0◦ ) in H2 O· · ·Ag X, and one possible explanation is that the repulsive force of sulfide is much stronger than oxidate, which will be discussed later in Section 3.3. Moreover, the angle ˚ increases from H2 S· · ·Ag F (75.2◦ ) to H2 S· · ·Ag I (77.4◦ ), whereas it shows a different trend in H2 O· · ·Ag X and decreases from 45.4◦ (H2 O· · ·Ag F) to 42.0◦ (H2 O· · ·Ag I). The Ag X bonds in H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes are strengthened during complexation processes since the Ag X bond lengths (RAg X ) are shortened significantly with respect to free AgX monomers. Since the radius of sulfur atom is larger than that of oxygen atom, the distance of Ag· · ·Y (RAg· · ·Y ) cannot be directly used to estimate the strength of interaction in H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes. So we define one bond parameter ␦RAg· · ·Y which allow us to unify interactions to estimate their strengths even if different pairs of atoms [25,26] ␦RAg···Y = RAg + RY − RAg···Y

(5)

where RAg and RY are covalent radii of Ag and Y atoms [27], respectively. The larger ␦RAg· · ·Y is, the stronger the interaction is, and vice versa. As shown in Table 1, as X varies from F to I, the ␦RAg· · ·O decreases from −0.062 A˚ to −0.119 A˚ and the ␦RAg· · ·S ˚ which indicates that the interdecreases from 0.165 A˚ to 0.078 A, molecular interaction in H2 Y· · ·Ag X is weakened as X varies

Table 1 ˚ angles in degrees) of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes calculated at the CCSD(T)/AVTZ-PP/AVTZ level.a Structural parameters (bond lengths in A, Complex H2 O· · ·AgF H2 O· · ·AgCl H2 O· · ·AgBr H2 O· · ·AgI H2 S· · ·AgF H2 S· · ·AgCl H2 S· · ·AgBr H2 S· · ·AgI AgF AgCl AgBr AgI H2 O H2 S a b c d e

RY

H

0.963 0.963 0.963 0.963 1.343 1.343 1.342 1.342

RY 0.002 0.002 0.002 0.002 0.003 0.003 0.003 0.003

H

RAg

RAg

X b

1.966 (1.985) 2.272 (2.274)c 2.391 2.551 1.963 2.279 (2.269)d 2.398 2.562 (2.542)e 1.990 2.293 2.409 2.567

X

−0.024 −0.021 −0.018 −0.016 −0.027 −0.015 −0.011 −0.006

0.962 1.339

Numbers in parentheses are those of the experimental results. Ref. [5]. Ref. [8]. Ref. [7]. Ref. [6].

␦RAg· · ·Y

RAg· · ·Y b

2.179 (2.168) 2.205 (2.198)c 2.218 2.236 2.343 2.390 (2.384)d 2.406 2.430 (2.423)e

−0.062 −0.088 −0.101 −0.119 0.165 0.118 0.102 0.078

˚ b

45.4 (41.9) 43.2 (37.4)c 42.6 42.0 75.2 76.4 (78.0)d 76.8 77.4 (78.9)e

H O H

RH

105.7 105.7 105.7 105.7 92.7 92.7 92.7 92.7

1.5 1.5 1.5 1.5 0.5 0.5 0.5 0.5

104.2 92.2

O H

X Ag Y 179.9 179.5 179.3 179.0 179.2 179.6 179.8 179.9

Q. Wang et al. / Chemical Physics Letters 614 (2014) 5–9

7

Table 2 The harmonic vibrational frequencies (in cm−1 ) of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes calculated at the CCSD(T)/AVTZ-PP/AVTZ level.a sAg

H2 O· · ·AgF H2 O· · ·AgCl H2 O· · ·AgBr H2 O· · ·AgI H2 S· · ·AgF H2 S· · ·AgCl H2 S· · ·AgBr H2 S· · ·AgI AgF AgCl AgBr AgI H2 S H2 O

528.7, 338.9 (20.9, −168.9) 368.6, 274.7 (31.4, −62.5) 314.6, 224.7 (70.0, −19.9) 297.2, 191.6 (92.7, −12.9) 525.1, 300.4 (17.3, −207.4) 358.8, 231.4 (21.5, −105.8) 283.0, 201.7 (38.3, −43.0) 255.1, 175.5 (50.6, −28.9) 507.8 337.2 244.7 204.5

X

(sAg

b X)

Complex

asH

O H

(asH

O H)

sH

O H

(sH

ωH

O H)

O H

(ωH

3887.9 (−24.2) 3888.5 (−23.6) 3889.3 (−22.8) 3889.6 (−22.4) 2704.7 (−26.4) 2706.9 (−24.2) 2707.8 (−23.3) 2709.0 (−22.1)

3789.3 (−13.5) 3789.3 (−13.6) 3789.8 (−13.1) 3789.4 (−13.4) 2692.0 (−23.8) 2693.8 (−22.0) 2694.5 (−21.3) 2695.5 (−20.3)

1649.8 (4.8) 1650.4 (5.5) 1650.1 (5.2) 1650.1 (5.2) 1204.3 (−7.3) 1203.4 (−8.2) 1203.0 (−8.6) 1202.7 (−8.9)

3912.1 2731.1

3802.9 2715.8

1644.9 1211.6

O H)

a All frequencies are in cm−1 . ‘v’ denotes the Ag X stretching vibrational mode, ‘as’ denotes the asymmetric H O H stretching vibrational mode, ‘s’ denotes the symmetric H O H stretching vibrational mode and ‘ω’ denotes the H O H bending vibrational mode. b The mixture exists between the vAg X and the vAg· · ·Y stretching vibrational modes, so two values are given.

from F to I. Moreover, the ␦RAg· · ·S of H2 S· · ·Ag X is obviously larger than the corresponding ␦RAg· · ·O of H2 O· · ·Ag X, therefore, the intermolecular interactions in H2 S· · ·Ag X are stronger than those in H2 O· · ·Ag X. In addition, the positive values of ␦RAg· · ·S in H2 S· · ·Ag X show that the RAg· · ·S is less than the sum of the covalent radii of Ag and Y atoms, hence we assume that there are some covalent character in the intermolecular interactions of H2 S· · ·Ag X complexes, which will be discussed in detail later. The harmonic vibrational frequencies of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes calculated at the CCSD(T)/AVTZ-PP/AVTZ level are listed in Table 2. The Ag X stretching vibrational mode (sAg X ) can be used to study the nature of the intermolecular interactions in complexes. Since there are mixtures between the sAg X and the Ag Y stretching vibrational mode (sAg· · ·Y ), so two values were given, and one shows red-shift character, while the other is blue-shift. As X varies from F to I, the red shift of sAg X in H2 Y· · ·Ag X complexes becomes weak along with the strengthening blue shift. It is clear that the absolute red-shift value of sAg X in H2 S· · ·Ag X complexes is larger than that of H2 O· · ·Ag X, whereas the blueshift value of sAg X in H2 S· · ·Ag X complex is less than that of H2 O· · ·Ag X. The influences of complexation on other vibrational modes are weak. For example, the symmetric (sH O H ) and asymmetric (asH O H ) stretching vibrational modes in these complexes show red-shift about tens of wavenumbers. The only little difference is that the bending vibrational mode (ωH O H ) in H2 S· · ·Ag X is red-shift, whereas it shows blue-shift in H2 O· · ·Ag X. 3.2. Energies One of the goals of the present work is to determine accurately the binding energies of these complexes. Two methods, MP2 and CCSD(T) with different basis sets (AVDZ and AVTZ), were used,

and the results are listed in Table 3. As shown in Table 3, for all H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes, the MP2 binding energies (EMP2 ) calculated at various levels (AVTZ, AVDZ and CBS) are lower than those of CCSD(T) (ECCSD(T) ). Moreover, no matter what kind of computational level, the differences (about 3.1–5.4 kcal·mol−1 ) between EMP2 and ECCSD(T) for H2 S· · ·Ag X are obviously larger than those (about 1.1–1.9 kcal·mol−1 ) of H2 O· · ·Ag X. Therefore, MP2 method overestimates the binding energies of these complexes, especially H2 S· · ·Ag X. Since CCSD(T)/CBS has been called the ‘golden standard’ in calculation of non-covalent interactions, the discussions below focus on ECCSD(T)/CBS . H2 Y· · ·Ag X are more strongly bound than their hydrogen- and halogen-bonded analogues. As shown in Table 3, H2 S· · ·Ag X show stronger intermolecular interactions since their ECCSD(T)/CBS (−26.63 to −22.14 kcal·mol−1 ) are significantly smaller than those (−19.46 to −17.35 kcal·mol−1 ) of H2 O· · ·Ag X. Moreover, as X varies from F to I, the ECCSD(T)/CBS of H2 Y· · ·Ag X is diminishing. Therefore, H2 S· · ·Ag F has the strongest interaction due to the lowest ECCSD(T)/CBS (−26.63 kcal·mol−1 ), while the weakest interaction happened in H2 O· · ·Ag I. Previous studies show that the counterpoise-corrected interaction energies (Ecp , 10.38 kcal·mol−1 ) of H2 O· · ·AgCl calculated at the MP2 level is larger than that (9.03 kcal·mol−1 ) of H2 S· · ·AgCl [9], which has some discrepancies with our results and is due to the different computational levels (method and basis sets). Moreover, only two complexes (H2 O· · ·AgCl and H2 S· · ·AgCl) were studied in Ref. [9], detailed information on the interaction energies (Ecp ) of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes was not available. From a viewpoint of energy, since some complexes (H2 O· · ·AgF, H2 O· · ·AgCl, H2 S· · ·AgCl and H2 S· · ·AgI) have been synthesized and characterized by rotational spectra [4–6], the rest complexes (H2 O· · ·AgBr, H2 O· · ·AgI, H2 S· · ·AgF and H2 S· · ·AgBr) are expected to

Table 3 The binding energies and the zero-point energies (ZPE) of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes calculated at the MP2 and CCSD(T) methods with AVnZ-PP/AVnZ (n = D and T) basis sets. All values in kcal·mol−1 .a Basis sets

Energy

H2 O· · ·AgF

H2 O· · ·AgCl

H2 O· · ·AgBr

H2 O· · ·AgI

H2 S· · ·AgF

H2 S· · ·AgCl

H2 S· · ·AgBr

H2 S· · ·AgI

AVDZ

EMP2 ECCSD(T) EZPE,CCSD(T)

−20.01 −18.91 1.79

−19.66 −18.43 1.86

−18.95 −17.74 2.02

−18.10 −16.89 1.73

−28.84 −25.49 1.79

−26.85 −23.61 1.87

−25.79 −22.59 2.04

−24.33 −21.19 1.72

AVTZ

EMP2 ECCSD(T) EZPE,CCSD(T)

−20.79 −19.35 1.85

−20.34 −18.79 1.92

−19.68 −18.18 2.07

−18.80 −17.32 1.78

−30.90 −26.59 1.76

−28.61 −24.45 1.83

−27.48 −23.42 2.01

−25.85 −21.93 1.70

CBS

EMP2 ECCSD(T)

−21.34 −19.46

−20.82 −18.92

−20.19 −18.25

−19.26 −17.35

−32.04 −26.63

−29.65 −24.65

−28.50 −23.60

−26.81 −22.14

a

All energies without BSSE correction and zero-point energy correction.

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Q. Wang et al. / Chemical Physics Letters 614 (2014) 5–9

Table 4 The LMO-EDA results of H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes calculated at the MP2/AVTZ-PP/AVTZ level. All values in kcal·mol−1 .

H2 O· · ·AgF H2 O· · ·AgCl H2 O· · ·AgBr H2 O· · ·AgI H2 S· · ·AgF H2 S· · ·AgCl H2 S· · ·AgBr H2 S· · ·AgI

Eele

Eex

Erep

Epol

Edisp

EMP2

−34.50 (32.9%) −32.36 (34.2%) −31.40 (34.6%) −30.17 (35.1%) −54.51 (28.3%) −48.05 (28.3%) −46.35 (28.3%) −44.00 (28.3%)

−44.72 (42.7%) −39.69 (42.0%) −38.17 (42.0%) −36.19 (42.1%) −84.89 (44.0%) −74.67 (43.9%) −72.25 (44.1%) −68.85 (44.3%)

84.78 75.00 71.97 68.03 163.10 142.56 137.66 130.77

−14.96 (14.3%) −13.24 (14.0%) −12.61 (13.9%) −11.85 (13.8%) −32.69 (16.9%) −28.53 (16.8%) −27.34 (16.7%) −25.74 (16.6%)

−10.60 (10.1%) −9.23 (9.8%) −8.60 (9.5%) −7.73 (9.0%) −20.81 (10.8%) −18.79 (11.1%) −18.02 (11.0%) −16.86 (10.8%)

−20.00 −19.52 −18.80 −17.93 −29.80 −27.48 −26.29 −24.69

be synthesized experimentally. In addition, the differences of binding energies between CCSD(T)/AVDZ and CCSD(T)/CBS levels are less than about 1.1 kcal·mol−1 , while ECCSD(T)/AVTZ is very close to ECCSD(T)/CBS and the differences are less than about 0.2 kcal·mol−1 . However, CCSD(T)/AVTZ is very time-consuming, therefore, considering the accuracy and efficiency, CCSD(T)/AVDZ calculation is an appropriate choice. The nature of intermolecular interactions in H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes was further investigated by LMO-EDA with MP2 method, and the results are listed in Table 4. It should be noted that the main goal of LMO-EDA is to provide energy components but not accurate total binding energies, which has been discussed above. As shown in Table 4, it is easily learned that Eele , Eex , Epol and Edisp are attractive terms which make positive contribution to the total binding energies of complexes, while Erep makes against the formation of complexes. The largest stabilizing forces are Eex , but coming with strong repulsion energies (Erep ) simultaneously, so the sum contributions of the exchange-repulsion terms are not conducive to the formations of complexes. The Eele are the second largest stabilizing forces, and the sum of electrostatic and exchange interactions are dominant stabilizing forces among all complexes, while the Epol and Edisp make minor contributions to the total binding energies of these complexes. In addition, the contributions of Eele to the total binding energies of H2 S· · ·Ag X are 28.3%, which are less than those (32.9–35.1%) of H2 O· · ·Ag X, while other terms (Eex , Epol and Edisp ) make more contributions to the total binding energies of H2 S· · ·Ag X than those of H2 O· · ·Ag X, which indicates that the intermolecular interactions of H2 S· · ·Ag X show more covalent character than those of H2 O· · ·Ag X. 3.3. NBO analyses According to NBO theory, for H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes, the delocalization interactions take place between the lone pair (LP) of the donor Y atom (nY ) and the empty anti-bond ∗ orbital (Ag ), which is estimated by second-order perturbaX tion theory [28]. Therefore, the second-perturbation energies E(2)

lowering is responsible for the orbital interaction of Ag· · ·Y bond, the larger E(2) value corresponds to stronger CT interaction occurred in the intermolecular interaction. The results of NBO analyses are listed in Table 5. As shown in Table 5, the O (S) atom involved in complexation has two branches, and one has less sp hybrid characteristics than the other one. For each of H2 Y· · ·Ag X complex, the main orbital interaction happened between LP2 and ∗ since its E(2) is significantly larger than that of LP1. MoreAg X over, the hybrid indices of the LP2 in H2 O· · ·Ag X are about 2.0, which indicates that the LP2 orbital tends to reduce the degree of non-coplanarity with the other two O H bonds since the typical sp2 hybrid is a planar structure. On the contrary, the hybrid indices of the LP2 in H2 S· · ·Ag X are about 3.8–4.0, which indicates that they are non-planar structures since the typical sp3 hybrid is a tetrahedron structure. In molecular structures this is reflected by that the angle ˚ in H2 S· · ·Ag X is larger than corresponding one in H2 O· · ·Ag X. For all H2 Y· · ·Ag X complexes, the population ∗ number of nY is diminishing, while the population number of Ag X increases, which shows that there is electron transfer from nY to ∗ Ag . The positive EDT value means that the direction of elecX tron transfer is from the donor (H2 Y) to the acceptor (Ag X) in complexes as well. Moreover, the extents of such electron transfer happened in H2 S· · ·Ag X are obviously larger than those in H2 O· · ·Ag X, therefore, stronger orbital interactions happened in H2 S· · ·Ag X complexes are expected. It is easy to find that the E(2) values of H2 S· · ·Ag X (X = F, Cl, Br, I) are remarkably larger than those of H2 O· · ·Ag X, which indicates that stronger orbital interaction happened in H2 S· · ·Ag X. Moreover, from H2 O· · ·Ag F to H2 O· · ·Ag I, the orbital interaction becomes stronger since the E(2) increases. There is similar trend for H2 S· · ·Ag X, while H2 S· · ·Ag I seems to be an exception since its E(2) is slightly less than those of H2 S· · ·Ag Cl and H2 S· · ·Ag Br, and the reason is not clear. In addition, the E(2) of H2 S(O)· · ·Ag F is obviously less than those of other H2 Y· · ·Ag X (X = Cl, Br, I) complexes, which may be due to the stronger electronegativity of F atom. The Wiberg bond index (WBI) of Ag· · ·Y (Y = O, S) bond in complexes are presented in Table 5 as well. The WBIs of H2 O· · ·Ag Cl to

Table 5 The results of the NBO analyses calculated at the MP2/AVTZ-PP/AVTZ level.a WBI

H2 O· · ·AgF H2 O· · ·AgCl H2 O· · ·AgBr H2 O· · ·AgI H2S· · ·AgF H2S· · ·AgCl H2S· · ·AgBr H2S· · ·AgI

EDT

Ag Xb

Ag· · ·Y

0.1901 (0.0587) 0.3346 (0.0575) 0.3768 (0.0425) 0.4443 (0.0197) 0.2050 (0.0736) 0.3444 (0.0673) 0.3850 (0.0507) 0.4478 (0.0232)

0.0799 0.0832 0.0807 0.0777 0.2832 0.2674 0.2585 0.2458

q ∗ Acceptor (Ag

0.03338 0.03751 0.0366 0.03565 0.10962 0.12007 0.11918 0.11789

0.03699 0.04063 0.03957 0.03838 0.12835 0.13103 0.12787 0.12375

) X

Donor LP1(Y)

Donor LP2(Y)

Donor (nY )

spn

E(2)

spn

E(2)

−0.03892 −0.04262 −0.04171 −0.04063 −0.13783 −0.14098 −0.13858 −0.13508

4.29 4.98 5.18 5.47 1.05 1.04 1.04 1.04

0.75 0.78 0.81 0.79 2.89 2.75 2.88 2.94

2.21 2.01 1.96 1.90 3.97 3.81 3.86 3.85

27.70 36.36 37.33 37.90 104.65 136.55 136.36 132.77

a LP represents lone pair electrons; BD* represents the anti-bond; the second-perturbation energies (E(2)) are in kcal·mol−1 ; q is the occupancy increases; EDT is the electron density transfer from the donor (H2 Y) to the acceptor (Ag X) in complexes. b The value in parentheses is the difference of WBI(Ag X) between complex and monomer.

Q. Wang et al. / Chemical Physics Letters 614 (2014) 5–9 Table 6 Electron density (b ), Laplacian of the electron density (2 b ) and total electron energy density (Hb ) in a.u. at BCPs of Y· · ·Ag bonds in H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes by QTAIM analyses. Complex

BCP

b

2 b

Hb

H2 O· · ·AgF H2 O· · ·AgCl H2 O· · ·AgBr H2 O· · ·AgI H2 S· · ·AgF H2 S· · ·AgCl H2 S· · ·AgBr H2 S· · ·AgI

O· · ·Ag O· · ·Ag O· · ·Ag O· · ·Ag S· · ·Ag S· · ·Ag S· · ·Ag S· · ·Ag

0.0727 0.0678 0.0656 0.0628 0.0943 0.0857 0.0829 0.0792

0.4383 0.4122 0.4001 0.3827 0.2905 0.2750 0.2698 0.2599

−0.0104 −0.0079 −0.0069 −0.0056 −0.0303 −0.0248 −0.0230 −0.0210

H2 S· · ·Ag Cl have been studied by Zhang [9], which are consistent with our results. As shown in Table 5, due to the stronger intermolecular interactions, H2 S· · ·Ag X (X = F, Cl, Br, I) complexes show covalent character to a certain extent and the WBI(Ag· · ·S) fall in the range of 0.283–0.245, which are significantly larger than those (∼0.08) of H2 O· · ·Ag X. Moreover, from H2 S· · ·Ag F to H2 S· · ·Ag I, the covalent character diminishes since the WBI(Ag· · ·S) decreases. As for H2 O· · ·Ag X, the changes of WBI(Ag· · ·O) are insignificant. It should be noted that the difference of WBI(Ag X) between complex and AgX monomer is positive, which indicates that the Ag X bond is strengthened during complexation process although the ∗ population number of Ag increases. X 3.4. QTAIM analyses According to QTAIM, both bond path and bond critical point (BCP) between different motifs of complexes are the direct and the most important evidence of intermolecular interaction. Based on the Virial theorem between energetic topological parameters and the Laplacian of electron density (2 b ) at BCP, the following criterion for the strength of intermolecular interaction was proposed: for weak or medium-strength interactions, 2 b > 0 and Hb (total electron energy density) > 0; for strong interactions, 2 b > 0 and Hb < 0; for very strong interactions, 2 b < 0 and Hb < 0. Moreover, topological criteria for existence of hydrogen bonding were proposed by Koch and Popelier [19,29], the electron density (b ) at BCP should range from 0.002 to 0.035 a.u., and the 2 b at BCP should be within 0.024–0.139 a.u. Such topological criteria also can be used to estimate the strength of other intermolecular interactions. The electronic topological properties at the Ag· · ·Y (Y = O, S) BCPs of studied complexes are listed in Table 6. As shown in Table 6, for all H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes, both b and 2 b values beyond the upper limit of the range of 0.002–0.035 a.u. for hydrogen bonds, which shows that the intermolecular interactions happened in these complexes are stronger than hydrogen-bonding interaction and are in accordance with above discussions. The positive 2 b and negative Hb show that the intermolecular interactions in complexes have partial covalent character. Moreover, the b values of H2 S· · ·Ag X complexes are larger than those of H2 O· · ·Ag X, while their 2 b values are less than those H2 O· · ·Ag X, which indicates that H2 S· · ·Ag X show more covalent character than H2 O· · ·Ag X. In addition, as X varies from F to I, the Hb value is increasing for H2 Y· · ·Ag X, which implies that the covalent character of Ag· · ·Y bond is diminishing from H2 Y· · ·Ag F to H2 Y· · ·Ag I. Therefore, it can be infer that H2 S· · ·Ag F has the most covalent character and H2 O· · ·Ag I shows the most close-shell interaction character.

9

4. Conclusions In this work, we studied the H2 Y· · ·Ag X (X = F, Cl, Br, I; Y = O, S) complexes at both MP2 and CCSD(T) levels. All complexes were predicted to be non-planar Cs symmetry structures. The Ag X bond is strengthened during complexation process due to the shortening of RAg Y . The intermolecular interactions in these complexes are stronger than hydrogen- and halogen-bonded interactions and show partial covalent character, moreover, H2 S· · ·Ag X complexes show more covalent character than H2 O· · ·Ag X. The interaction between H2 Y and AgX is weakened as X varies from F to I. The result of LMO-EDA indicates that the sum of Eele and Eex are dominant stabilizing forces among H2 Y· · ·Ag X complexes, while Epol and Edisp make minor contributions to the total binding energies of these complexes. From a viewpoint of energy, some complexes (H2 O· · ·AgBr, H2 O· · ·AgI, H2 S· · ·AgF and H2 S· · ·AgBr) are expected to be synthesized experimentally. Acknowledgements This work is supported by the Natural Science Foundation of Tianjin (No. 12JCYBJC13400) and the Program for Innovative Research Team in University of Tianjin (TD12-5038). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

[21] [22] [23] [24] [25] [26] [27] [28] [29]

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