Halogen Bonding: A Study based on the Electronic Charge Density

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J. Phys. Chem. A 2010, 114, 552–562

Halogen Bonding: A Study based on the Electronic Charge Density Nancy J. Martinez Amezaga,† Silvana C. Pamies,† Ne´lida M. Peruchena,†,‡ and Gladis L. Sosa*,†,‡ Laboratorio de Quı´mica Teo´rica y Experimental-QuiTEx, Departamento de Quı´mica, Facultad Regional Resistencia, UniVersidad Tecnolo´gica Nacional, French 414 (3500) Resistencia (Chaco), Argentina, and Laboratorio de Estructura Molecular y Propiedades, A´rea de Quı´mica Fı´sica, Departamento de Quı´mica, Facultad de Ciencias Exactas y Naturales y Agrimensura, UniVersidad Nacional del Nordeste, AVda. Libertad, 5460, (3400) Corrientes, Argentina ReceiVed: August 5, 2009; ReVised Manuscript ReceiVed: October 2, 2009

Density functional theory (DFT) and atoms in molecules theory (AIM) were used to study the characteristic of the noncovalent interactions in complexes formed between Lewis bases (NH3, H2O, and H2S) and Lewis acids (ClF, BrF, IF, BrCl, ICl, and IBr). In order to compare halogen and hydrogen bonds interactions, this study included hydrogen complexes formed by some Lewis bases and HF, HCl, and HBr Lewis acids. Ab initio, wave functions were generated at B3LYP/6-311++G(d,p) level with optimized structures at the same level. Criteria based on a topological analysis of the electron density were used in order to characterize the nature of halogen interactions in Lewis complexes. The main purpose of the present work is to provide an answer to the following questions: (a) why can electronegative atoms such as halogens act as bridges between two other electronegative atoms? Can a study based on the electron charge density answer this question? Considering this, we had performed a profound study of halogen complexes in the framework of the AIM theory. A good correlation between the density at the intermolecular bond critical point and the energy interaction was found. We had also explored the concentration and depletion of the charge density, displayed by the Laplacian topology, in the interaction zone and in the X-Y halogen donor bond. From the atomic properties, it was generally observed that the two halogen atoms gain electron population in response to its own intrinsic nature. Because of this fact, both atoms are energetically stabilized. 1. Introduction The interactions of dihalogens XY with Lewis bases have been an active topic of research in the last years.1-5 Originally called charge-transfer bonds by Benesi and Hildebrand,6 and subsequently renamed as electron donor-acceptor by Mulliken,7 these interactions were attributed to the transfer of negative charge from an oxygen, nitrogen, or sulfur atom (a Lewis base) to a polarizable halogen (a Lewis acid). In a pioneer work in the solid state, Hassel and co-workers8 analyzed, by X-ray diffraction, the structural aspects of chargetransfer bonding, finding out a strong analogy to classical hydrogen bonds. In his novel lecture, Hassel9 utilized the term halogen bond to refer to these bindings. More recently, Legon10 reviewed the rotational spectroscopic studies on a series of HX and XY (where X and Y are halogens) complexes with different Lewis bases, B. These complexes were formed in gas phase by supersonic expansion and observed by Fourier transform microwave spectrometer. The B...HX and B...XY complexes were found to be isostructural in all cases. The properties of halogen bonding have also been explored in the field of molecular biology, founding evidence of the important role that these interactions play in the molecular recognition processes.11,12 Resnati and colleges have taken advantages of these halogen bonds in order to control the crystallization of organic compounds in the design of new materials, as well as in supramolecular chemistry.13-16 Conse* Corresponding author. E-mail: [email protected]. † Universidad Tecnolo´gica Nacional. ‡ Universidad Nacional del Nordeste.

quently, the halogen bonds are of great interest in organic, inorganic, and biological chemistry, and their study could contribute to our understanding of the mechanisms of reaction and chemistry reactivity. The topological description derived from the atoms in molecules theory17 has been extensively applied to study and characterize the hydrogen bonding interactions.18-23 In the present study, this theory will be systematically applied to study halogen bonds in order to obtain a deep insight into different factors defining these interactions. We are trying to see how this theory answers a central question of the halogen bond origin. Conventional hydrogen bonds are understood to function in such a manner that the hydrogen atom bears a partial positive charge and thus can attractively interact with two more electronegative atoms. In contrast, halogen atoms are generally viewed as being negatively charged. So how can we explain the fact that they can form similar bonds to those of hydrogen? In a recent work, Politzer et al.24 introduced the concept of σ-hole to explain the existence of halogen bonding. In their study, based on electrostatic potential of halogen bonding systems H3C-X, they showed that, when the X is bromine or iodine, a positive region on the outermost portion of the halogen surface (where it intersects the C-X axis) can be observed. For chlorine, this positive region appears only when another electron-withdrawing atom exists in the molecule, such as F3C-Cl. These positive outer portions on the halogen surface can interact with an electronegative atom of other molecules giving rise to halogen bonding. In order to answer the previously mentioned question, a total of 18 halogen complexes formed with water, ammonia, and

10.1021/jp907550k  2010 American Chemical Society Published on Web 11/17/2009

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Figure 1. Optimized geometries of H3N...ClF, H2O...ClF, and H2S...ClF complexes at B3LYP/6-311++G** level.

TABLE 1: Selected Geometric Parametersa and Interaction Energies Calculated at B3LYP/6-311++G** Level and Corrected by BSSE H3N...ClF H2O...ClF H2S...ClF H3N...BrF H2O...BrF H2S...BrF H3N...IF H2O...IF H2S...IF H3N...BrCl H2O...BrCl H2S...BrCl H3N...ICl H2O...ICl H2S...ICl H3N...IBr H2O...IBr H2S...IBr H3N...HF H2O...HF H2S...HF H3N...HCl H2O...HCl H2S...HCl H3N...HBr H2O...HBr H2S...HBr

d(B...X)

∆d(B...X)b

2.2778 2.4559 2.7254 2.3558 2.4874 2.7803 2.5460 2.6520 2.9995 2.4876 2.6545 2.9708 2.6359 2.7791 3.1478 2.6846 2.8324 3.2117 1.6730 1.7037 2.2730 1.7262 1.8559 2.4430 1.6851 1.9095 2.4941

1.0222 0.7941 0.8246 1.0442 0.8626 0.8697 0.9840 0.8280 0.6005 0.9124 0.6955 0.6792 0.8941 0.7009 0.4522 0.8454 0.6476 0.3883 1.0770 0.9963 0.727 1.0238 0.8441 0.557 1.0649 0.7905 0.5059

d(X-Y)c 1.7715 1.7096 1.7480 1.8886 1.8427 1.8725 2.0024 1.9706 1.9861 2.2763 2.2170 2.2480 2.4320 2.3862 2.4056 2.5796 2.5348 2.5534 0.9614 0.9416 0.9364 1.3497 1.3073 1.3036 1.5101 1.4469 1.4440

(1.6784) (1.8116) (1.9460) (2.1907) (2.3590) (2.5105) (0.9223) (1.2874) (1.4273)

∆d(X-Y)d

B...X-Y

Ecorr(kcal/mol)

0.0931 0.0312 0.0696 0.0770 0.0311 0.0609 0.0564 0.0246 0.0401 0.0856 0.0263 0.0573 0.0730 0.0272 0.0466 0.0691 0.0243 0.0429 0.0391 0.0193 0.0141 0.0623 0.0199 0.0162 0.0828 0.0196 0.0167

180.0 179.2 179.8 179.9 179.3 180.0 179.9 179.3 179.7 180.0 179.2 179.6 179.9 179.2 179.9 179.9 179.2 179.8 179.8 177.1 176.5 179.9 178.3 177.7 180.0 178.3 176.5

16.57 6.67 8.19 18.87 8.70 9.83 16.92 8.40 8.29 12.15 5.00 5.42 12.33 5.70 5.31 10.58 4.76 4.36 14.15 9.25 5.28 10.39 5.82 3.07 9.92 4.78 2.50

a

Distances in angstrom and angles in degrees. b ∆d(B...X) is the difference between the equilibrium intermolecular distances and the sum of the van der Waals radii of B and X atoms (van der Waals radii, in Å from ref 36: H, 1.20; N, 1.55; O, 1.50; S, 1.80; Cl, 1.75; Br, 1.85; and I, 1.98). c X-Y bond lengths in the isolated compounds are given in parentheses. d ∆d(X-Y) is the change of X-Y bond length upon complex formation.

hydrogen sulfide bases, and the diatomic interhalogenated molecules as Lewis acids were selected. This systematic study also included hydrogen complexes formed with the previously mention bases and the HF, HCl, and HBr acids. Additionally, in this work, an analysis of the charge distribution and chargetransfer processes using the natural bond orbital (NBO) partitioning scheme25,26 was performed. 2. Computational Details Calculations were performed using the Gaussian03 suite of programs.27 Given the importance of correlation effects to ensure reliability in the process of obtaining properties for halogen and hydrogen complexes, calculations were based on the density functional theory.28 The geometries of all complexes and the corresponding isolated compounds were fully optimized using the combined Becke’s three parameter exchange functional and the gradient corrected functional of Lee, Yang, and Parr (B3LYP functional).29,30 All calculations were performed with the 6-311++G** bases set. For iodine atoms, considering the errors caused by relativistic effects, an effective core potential (ECP) was used.31,32 The minimum energy nature of the optimized structures was verified using the vibrational frequency analysis. The interaction energies were obtained at the same level of theory

using the supermolecular approach, that is, calculated by subtracting the energies of the isolated compounds to the energy of the complex (the geometries of the isolated compounds correspond to those in the complex). The basis set superposition error (BSSE) was corrected by the counterpoise procedure of Boys and Bernardi.33 Then, the optimized geometries were used to perform NBO analysis from NBO 3.1 program34 as implemented in Gaussian03. This analysis was conducted to quantitatively evaluate the interactions of charge transfer involved in the formation of halogen and hydrogen bonds. AIM calculations were carried out using the wave functions generated from the B3LYP/6-311++G** calculations with the AIM200035 and AIMPAC36 software. 3. Results and Discussion 3.1. Geometrical Parameters and Interaction Energies. Figure 1 shows the optimized geometries for the complexes studied in this work; for simplicity, an example of each base is shown. Table 1 reports the values of the main parameters that describe the geometry of the studied systems and the interaction energies as calculated at the B3LYP/6-311++G** level and corrected for bases set superposition error by the counterpoise procedure. The geometric parameters refer to the intermolecular distances, B...X, (where B ) N, O, S, and X ) H, Cl, Br, I),

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the bond length, X-Y (where Y ) F, Cl, Br), and the equilibrium angles, R, B...X-Y. ∆d(B...X) represents the difference between the sum of B and X van der Waals radii37 and the intermolecular distances, B...X and ∆d(X-Y) represents the change in the optimized X-Y bond length that occurred in various complexes relative to the isolated pertinent molecule. From Figure 1, it can be seen that the halogen bridge approached along the direction in which it was hoped to find a lone pair of the B atom of the Lewis base, defining in this way, the angular geometry. Thus, the complexes with ammonia, H3N...X-Y, have C3V geometry, which means that the axis of the X-Y molecule lies along the axis of the nonbonding electron pair of the nitrogen atom. In the H2O...X-Y, H2S...X-Y complexes, the oxygen and sulfur atoms are pyramidal and, again, the axis of the X-Y molecule lies along the axis of one of the nonbonding electron pairs, the oxygen or the sulfur atom in each case. Also, it can be observed in Table 1 that the equilibrium angle, R, is closer to 180° in halogen than in hydrogen complexes (except in H3N...HBr, in which is exactly 180°), indicating that the first one tends to be more collinear than the second one. In all cases, B...X intermolecular distances is substantially shorter than the sum of the van der Waals radii of the B and X atoms. ∆d(B..X) can be interpreted as the distance of penetration of B and X atoms electronic densities. It reached the highest values in complexes formed with ammonia. A characteristic of conventional hydrogen bonds, also called proper hydrogen bonds, B...H-Y, is that its formation leads to a weakening of the H-Y bond. This weakening is accompanied by a bond elongation and a concomitant decrease of the H-Y stretch vibration frequency, compared with the isolated H-Y molecule. Such a shift to lower frequencies is called a red shift. In contrast, in the formation of the so-called improper hydrogen bonds, the H-Y bond shortens, and the frequency of the vibration increases; this is called a blue shift. Recently, it has been reported that the formation of halogen bonds can also lead to a lengthening (red shift) or shortening (blue shift) of the X-Y bond.38 For this reason, the effects of the formation of hydrogen and halogen complexes upon the X-Y bond involving the bridging atom were also explored in this work. In Table 1, it can be seen that all changes, ∆d(X-Y), are positive in sign; that is, the X-Y bond stretched as a result of complexation. The stretchiness of the X-Y bond length roughly correlates with the strength of the interaction. Moreover, a comparison of ∆d(X-Y) in complexes formed with different bases and a given acid showed that the elongation of the X-Y bond is always higher in complexes with ammonia. With respect to the interaction energies, as shown in Table 1, the halogens bonding energies varied in a wide range between 4.36 and 18.87 kcal/mol and, in general, are higher than those of hydrogen bonds, which ranged from 2.50 to 14.15 kcal/mol. Also, it is observed that for a particular Lewis base the strength of halogen bonds increases as the acid, in the order IBr < BrCl < ICl < ClF < IF < BrF (an exception was found for the H2S, where the H2S...BrCl bond was slightly stronger than H2S...ICl), and for a particular Lewis base, the strength of hydrogen bonds increases as the acid, in the order HBr < HCl < HF. Moreover, whatever the Lewis acid was, the stronger halogen and hydrogen bonds occurred with the ammonia base, reflecting their greater nucleophilicity compared with those of water and sulfide bases. These results are consistent with the calculated penetration distances, ∆d(B..X), and with the experimental results reported by Legon.11

Amezaga et al. One final point concerning the interaction energies is the fact that, while the halogen bonds formed with ammonia and sulfide bases are stronger than hydrogen bonds formed with these bases, the halogen bonds formed with water are weaker than hydrogen bonds formed with this base. We consider that these data can be an important fact in the study of competitive processes of molecular recognition. 3.2. Topological Analysis. In order to characterize hydrogen bonds in a rigorous manner within the AIM theory, Caroll and Bader39 and Koch and Popelier40 proposed a set of criteria indicative of these interactions. These criteria comprise a set of local topological properties of the electron density and a set of integrated atomic properties on the hydrogen atom. These properties had been determined for the different complexes studied in this work and were used to compare the AIM features in hydrogen and halogen bonds. In Figure 2, the molecular graphs of the halogen and hydrogen complexes are displayed. The local properties calculated at B...XY and X-Y bond critical points (BCPs, critical points with two negative curvatures, λ1 and λ2, and the remaining one, λ3 being positive) in the halogen and hydrogen complexes are given in Table 2a,b. The values for the X-Y isolated compounds are given in Table 2c. The properties reported in these tables are the ratio |λ1|/λ3, the electron density, F(rc), the Laplacian of the electron density, ∇2F(rc), the densities of kinetic energy, G(rc), potential energy, V(rc), total energy, H(rc) ) V(rc) + G(rc), and the |V(rc)|/G(rc) ratio. Prior to a discussion of these results, it is important to recall that the Laplacian of the electron density provides a measure of the local curvature of F(r) and indicates whether the electron density is locally concentrated,∇2F(r) < 0 or depleted ∇2F(r) > 0 at a given point in the space. Furthermore, the Laplacian is related to the local components, kinetic and potential, of the total energy via the local expression of the virial theorem (in a.u.: (1/4)∇2F(r) ) 2G(r) + V(r)). The sign of ∇2F(r) determines which of these two contributions to the total energy are in excess over their average virial ratio of 2:1. Thus, when the Laplacian is negative, the electronic charge is concentrated and the potential energy dominates both the local total electronic energy H(rc) and the local virial relationship. Additionally, when the Laplacian is positive, the electronic charge is locally depleted and the kinetic energy is in local excess. According to Bader and Esse´n,41 the first situation occurs in shared interactions, while the second situation is characteristic of closed-shell interactions. At B...X intermolecular bond critical point, as can be seen in Table 2a,b, in all systems studied here, the BCP localized between the B atom of the Lewis base and the hydrogen or halogen atom of the Lewis acid (see Figure 2) present typical properties of closed-shell interactions: the value of electron density, F(rc), is relatively low; the ratio of the perpendicular contractions of F to its parallel expansion |λ1|/λ3 was G(rc) and H(rc) is therefore negative, the interaction is indicative of being shared, but when G(rc) > |V(rc)| and H(rc) is positive, the interaction is indicative of being

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Figure 4. Correlation between the potential energy densities per unit of electronic charge, |V(rc)|/F(rc) at B...XY critical points of H3N...X-Y and H2S...X-Y complexes and the interaction energy.

Figure 3. (a) Correlation between the electron density at B...XY and B...HY critical points and the interaction energy of hydrogen and halogen complexes. (b) Idem Figure 3a considering complexes formed with different Lewis bases and the same Lewis acid.

closed-shell. Thus, they suggested that the larger the value of |V(rc)| and the more negative the value of H(rc), the more shared the bonded interaction and the greater the stabilization of the structure. On the other hand, Espinoza et al.48 in their study of XsH...F-Y systems stated that bonded interactions can be classified on the basis of the |V(rc)|/G(rc) ratio where a bonded interaction is defined as a closed-shell when the ratio |V(rc)|/ G(rc) < 1, as shared when |V(rc)|/G(rc) > 2, and as intermediate when the ratio falls between 1 and 2. In Table 2a, it can be seen, in general, that the potential energy density is only slightly larger than the kinetic energy density, although both of them are of the same order of magnitude. This leads to values of total energy, H(rc), close to zero and values of |V(rc)|/G(rc) ratio slightly larger than 1. Exceptions are halogen complexes formed with water and hydrogen complexes: H2O...HCl, H2O...HBr, H2S...HCl, and H2S...HBr, (see Table 2b) in which G(rc) is slightly larger than V(rc), H(rc) is positive, and |V(rc)|/G(rc) is slightly less than 1. It is worth stressing that, even when the most negative value of H(rc) (-0.0063 au) corresponds to an energetically stronger halogen complex (18.87 kcal/mol), H(rc) correlates poorly with the binding energy (R ) 0.87, plot not included here). In addition, we also explore the relationship between the potential energy density per unit of electronic charge, |V(rc)|/ F(rc) and the binding energy. A good correlation was found in H3N...X-Y and H2S...X-Y complexes (see Figure 4). However, the inclusion of H2O...X-Y complexes produced a significant decrease of the correlation coefficient. It was also interesting to examine in detail the structure exhibited by the Laplacian distribution of one of the halogen

complexes. Figure 5a contains a display of the zero envelope of ∇2F(r) for H3N...ClF. This surface encloses a region where the electronic charge is maximally concentrated, defining the reactive surface. The molecules are oriented so that the lumps in the valence shell charge concentration (VSCC) of the nitrogen atom of the Lewis base is aligned with the hole in the VSCC of the chlorine atom of the Lewis acid. In Figure 5b, a contour map of ∇2F(r) for the same complex is displayed. In this figure, the anisotropic charge distribution on the chlorine atom can also be clearly seen. The maximum of charge concentration in the VSCC of the chlorine atom is located above and below the internuclear axis, around which is found the previously mention hole. This anisotropy allowed us to explain the observed49 amphiphilicity of halogens, which can exhibit electrophilic character along the X-Y bond axes in the direction of the less electronegative halogen, X, and nucleophilic character along those vectors perpendicular to these bonds. Another important result was obtained to compare the contour maps of the Laplacian of H3N...ClF and H3N...BrF complexes (see Figure 5b,c). Interestingly enough, the extension of the charge depletion region in the H3N...BrF complex (localized over the X halogen atom and facing the donor atom) is greater than in the H3N...ClF complex. Probably, this is the reason of why the first complex has a higher binding energy than the second one. At X-Y bond critical point, comparison of the topological properties of the (3, -1) critical points of the X-Y and H-Y bonds, involved in halogen and hydrogen bond interactions, as well as in the isolated compounds, reveals significant differences. The H-Y bonds exhibit typical properties of shared interactions: the values of the electron density at the bond critical points are relatively large and range from 0.07 to 0.18 au. The relationship |λ1|/λ3 is >1 and the Laplacian of the charge density is negative, indicating that the electronic charge is concentrated in the internuclear region. Furthermore, the potential energy density V(rc) is of greater magnitude than the kinetic energy density. These results lead to high and negative values of total energy density H(rc) and elevated values of |V(rc)|/G(rc) ratio (much higher than in closed-shell interactions). In contrast, in the X-Y bond, although the density is relatively large, the Laplacian is positive. The potential energy density is only slightly greater than the kinetic energy density, and therefore, the value of the total energy density H(rc) is negative and low; and |V(rc)|/G(rc) > 1. In accordance to the classifications mentioned above, these bonds have features of intermediate interaction and must be considered as partially covalent and partially electrostatic.46,47,49 The differences between H-Y bond and X-Y bond can also be seen by comparing the contour maps of Laplacian for the

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Figure 5. (a) The zero values of ∇2F (zero envelope) for H3N...ClF, the molecules are oriented so that the lump in the VSCC of nitrogen is aligned with the hole in the VSCC of chlorine. (b) Contour maps of ∇2Ffor H3N...ClF in a plane containing the N, Cl and F nucleus. (c) Contour maps of ∇2Ffor H3N...BrF in a plane containing the N, Br and F nucleus. Red contours denote negative, black contours positive values of ∇2F. Starting at a zero contour, contour values change in steps of ( 2.10n, ( 4.10n, ( 8.10n with n beginning at -3 an increasing in steps of unity. The arrows indicate a charge concentration in the valence shell charge concentration (VSCC) of nitrogen atom and the charge depletion in the valence shell concentration of the chlorine or bromine atom. Note also the anisotropic distribution of, the charge concentration in the VSCC of the Cl or Br atom are located above and below the plane containing the interacting nuclei.

H3N...HF and H3N...BrF complexes displayed in Figure 6a,b, respectively. In the first complex, the HF BCP occur at a region of charge concentration (region of negative values of 32F), while in the second complex, the X-Y BCP occur at a region of charge depletion (region of positive values of 32F). In this last case, the X-Y bond is dominated by a contraction of F toward each nucleus, as it is usual in closed-shell interactions. It is also important to note that in isolated interhalogenated molecules, the X-Y bonds had the same characteristics (see Figure 6c), so it cannot be attributed to the complexes formation. From Table 2a-c it can also be observed that, in line with the elongation of X-Y bond, the electron density at X-Y BCP, in general, decreases upon complexation. In contrast, in H2S...BrF, H2O...IF, H2S...IF, and H2S...ICl complexes, the electron density at X-Y BCP increased, probably because of

Amezaga et al.

Figure 6. Contour maps of ∇2F for (a) H3N...HF and (b) H3N...BrF complexes and (c) BrF isolated. Each map is for a plane containing the N, Br, or H, and F nucleus. The diagrams are overlaid with the bond paths and interatomic surfaces as determined by the gradient vector field of F. Bond critical point in ∇Fare denoted by black circles. Red contours denote negative, black contours positive values of ∇2F. Note that the H-Y bond critical point occurs at a region of charge concentration (region of negative values of 32F) while the B...X, B...H, and X-Y bond critical points are found in regions of charge depletion (region of positive values of 32F).

the withdrawing effect produced by Y over X. In hydrogen complexes, on the other hand, in turn with the elongation of H-Y bond, the electron density at BCP decreased upon complex formation in all cases. Integrated Atomic Properties. Table 3a,b shows the changes in the integrated atomic properties for the three atoms involved in the halogen bonds and hydrogen bonds interactions, respectively. Such properties are the electronic population, N, the total energy of the atom, E, the dipolar polarization, M, and the atomic volume, V. The changes were calculated subtracting the property value of the atom in the isolated compound to the value of the corresponding property in the complex. The criteria37,38 for hydrogen bonding, based on the integrated properties of the hydrogen atom, involves loss of charge, (∆N > 0), energetic destabilization, (∆E < 0), decrease of dipolar polarization (∆M < 0), and decrease of the hydrogen atoms volume (∆V > 0). As can be seen in Table 3b, these criteria were satisfied for the hydrogen complexes studied here; with

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TABLE 3: (a) Comparison of Atomic Properties for Three Atoms Involved in the Halogen Bonding, and (b) Comparison of Atomic Properties for Three Atoms Involved in the Hydrogen Bondinga,b complex

atom

∆N

∆E

∆M

∆V

H3N...Cl-F

N Cl F O Cl F S Cl F N Br F O Br F S Br F N I F O I F S I F N Br Cl O Br Cl S Br Cl N I Cl O I Cl S I Cl N I Br O I Br S I Br

-0.061 0.108 0.108 -0.019 0.025 0.047 -0.102 0.130 0.062 -0.040 0.093 0.107 -0.010 0.021 0.055 -0.094 0.127 0.067 -0.005 0.069 0.077 0.014 0.005 0.044 -0.058 0.097 0.049 -0.034 0.008 0.159 -0.003 -0.024 0.072 -0.069 0.051 0.092 -0.009 0.009 0.125 0.015 -0.028 0.064 -0.049 0.248 0.072 -0.008 -0.019 0.150 0.014 -0.042 0.074 -0.046 0.028 0.083

0.0951 -0.1890 -0.0368 0.0842 -0.1077 -0.0293 -0.2454 0.1289 0.0425 0.1780 -1.0333 -0.0242 0.1911 -0.5430 -0.0209 0.1131 -0.8141 -0.0116 0.2386 -0.3504 -0.0221 0.2714 -0.4222 -0.0181 0.5379 -0.6795 -0.0184 0.1822 0.1565 -0.0112 0.1907 -0.1226 -0.0306 0.0769 0.1672 0.0032 0.2408 4.3609 -0.0219 0.2677 0.8886 -0.0322 0.5094 2.6323 -0.0441 0.2371 3.9114 1.9617 0.2644 0.2397 0.7282 0.4613 2.8308 0.8738

-0.218 -0.246 0.039 0.102 -0.146 0.017 -0.126 -0.108 0.032 -0.238 -0.254 0.043 0.096 -0.177 0.019 -0.140 -0.090 0.033 -0.165 -0.328 -0.041 0.076 -0.245 -0.019 -0.130 -0.114 -0.03 -0.223 -0.195 0.009 0.079 -0.143 0.002 -0.109 -0.058 0.010 -0.165 -0.299 -0.043 0.067 -0.223 -0.013 -0.107 -0.101 -0.032 -0.164 -0.250 -0.003 0.063 -0.200 0.001 -0.097 -0.076 0.000

-28.381 -8.777 12.592 -16.629 -10.048 6.487 -31.827 -4.810 9.661 -28.730 -8.760 8.073 -17.979 -10.036 3.795 -32.988 -4.394 5.726 -26.764 -12.152 6.382 -16.404 -13.333 3.163 -29.422 -8.392 4.250 -24.772 -14.150 15.525 -12.540 -9.993 6.103 -25.290 -6.318 9.663 -24.237 -12.315 14.235 -12.097 -12.573 7.064 -24.033 -5.548 8.836 -22.541 -11.830 15.348 -10.613 -10.167 7.056 -21.755 -4.024 8.733

H2O...Cl-F H2S...Cl-F H3N...Br-F H2O...Br-F H2S...Br-F H3N...I-F H2O...I-F H2S...I-F H3N...Br-Cl H2O...Br-Cl H2S...Br-Cl H3N...I-Cl H2O...I-Cl H2S...I-Cl H3N...I-Br H2O...I-Br H2S...I-Br

comparison of atomic properties for three atoms involved in the hydrogen bondinga,b H3N...H-F H2O...H-F H2S...H-F H3N...H-Cl H2O...H-Cl H2S...H-Cl H3N...H-Br H2O...H-Br H2S...H-Br

a

complex

atom

∆N

∆E

∆M

N H F O H F S H F N H Cl O H Cl S H Cl N H Cl O H Br S H Br

0.004 0.012 0.073 0.018 -0.012 0.055 -0.005 0.023 0.040 -0.004 -0.112 0.203 0.020 -0.085 0.111 -0.006 -0.023 0.070 -0.011 -0.185 0.299 0.018 -0.103 0.128 -0.007 -0.037 0.082

0.0154 0.0068 -0.0941 -0.0111 0.0115 -0.0538 -0.1769 0.0015 0.1419 0.0959 0.0633 -0.2445 0.0807 0.0389 -0.1753 -0.2108 0.0217 0.1545 0.1779 0.0902 -0.7112 0.1979 0.0425 -0.6011 0.1342 0.0243 -0.4241

-0.143 -0.029 -0.060 0.083 -0.031 -0.023 -0.077 0.000 -0.009 -0.152 -0.063 -0.011 0.066 -0.053 -0.036 -0.068 -0.016 -0.030 -0.171 -0.057 -0.866 0.063 -0.050 -0.745 -0.073 -0.012 -0.705

-19.488 -6.932 1.091 -12.718 -7.480 1.352 -16.039 -3.087 2.342 -18.462 -15.046 9.547 -8.983 -12.246 7.395 -12.347 -10.613 6.307 -19.528 -19.658 17.483 -8.586 -13.199 7.927 -11.371 -4.994 5.877

All quantities are in atomic units. b Symbols are explained in the text.

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TABLE 4: NBO Analysis of Halogen and Hydrogen Complexes: Occupation Numbers for the σ*X-Y Antibonds and the nN, nO, and nS Lone Pairs, and the Second-Order Perturbation Energies E2 (Donorf Acceptor) Involving the σ*X-Y Antibonda H3N...Cl-F H2O...Cl-F H2S...Cl-F H3N...Br-F H2O...Br-F H2S...Br-F H3N...I-F H2O...I-F H2S...I-F H3N...Br-Cl H2O...Br-Cl H2S...Br-Cl H3N...I-Cl H2O...I-Cl H2S...I-Cl H3N...I-Br H2O...I-Br H2S...I-Br

H3N...H-F H2O...H-F H2S...H-F H3N...H-Cl H2O...H-Cl H2S...H-Cl H3N...H-Br H2O...H-Br H2S...H-Br

nBb

∆nBc

E2(nBfσ*X-Y)

σ*X-Yd

∆σ*X-Ye

1.77032 1.91963 1.79254 1.77985 1.91046 1.78246 1.82294 1.92745 1.82994 1.81743 1.93992 1.84443 1.83997 1.94430 1.86357 1.84839 1.94979 1.87560

0.22634 0.07594 0.20654 0.21681 0.08513 0.21248 0.17372 0.06888 0.16755 0.17923 0.05592 0.15254 0.15669 0.05178 0.13375 0.14827 0.04632 0.12185

39.88 12.68 26.54 42.02 16.34 31.63 32.72 14.00 23.32 28.08 9.42 17.34 25.77 9.74 16.15 23.58 8.57 14.18

0.21060(0.00000) 0.07264 0.19160 0.20066(0.00016) 0.08168 0.20100 0.15609(0.00069) 0.06436 0.15122 0.17175(0.00006) 0.05472 0.14561 0.14524(0.00028) 0.04942 0.12401 0.13911(0.00027) 0.04469 0.11426

0.21060 0.07264 0.19160 0.20050 0.08152 0.20084 0.15540 0.06367 0.15053 0.17169 0.05466 0.14555 0.14496 0.04914 0.12373 0.13884 0.04442 0.11399

nB

∆nB

E2(nBfσ*H-Y)

σ*H-Y

∆σ*H-Y

1.92275 1.96318 1.95901 1.89535 1.96276 1.95419 1.86725 1.96085 1.95104

0.07391 0.03318 0.03910 0.10131 0.03360 0.04440 0.12941 0.03551 0.04645

34.70 17.84 12.27 35.64 13.44 10.30 44.91 12.90 10.04

0.07374(0.00000) 0.03493 0.03756 0.09976(0.00000) 0.00047 0.04237 0.12801(0.00036) 0.03699 0.04590

0.07374 0.03493 0.03756 0.09976 0.00047 0.04237 0.12765 0.03663 0.04554

a Energies in kcal/mol. b For H2O and H2S, only the population of lone pair involved in the charge transfer interaction is reported. Occupation numbers for nitrogen, oxygen, and sulfur lone pair in isolated compounds are nN: 1.99667e; nO: 1.99559 e and nS: 1.99697 e respectively. ∆nB represents the change in population of donor atom lone pair of Lewis base. d The corresponding values in isolated compounds are given in parentheses. e ∆σX* - Y denote the change in population of σ*X-Y antibonds respect to the isolated compound. c

the exceptions noted in the H3N...HF and H2S...HF complexes, where the hydrogen atom gained charge instead of losing it. In addition, on the other two atoms involved in the hydrogen bonds, B and Y atoms, it was not possible to generalize, because of the one property that varied regularly, the atomic volume. The atomic volume decreased on the B atom and increased on the Y atom. In halogen complexes (Table 3a), the general trend on the bridged halogen atom was the gain of charge, the decrease of the dipolar polarization, the decrease of the atomic volume, and perhaps the most important, the energetic stabilization. Furthermore, in almost all cases, the Y halogen atom was energetically stabilized. Exceptions were found in weaker halogen complexes. Thus, the fact that the two halogens were stabilized in the complexes may explain the greater strength of these bonds with respect to that of hydrogen. 3.3. Natural Bond Orbitals (NBO) Analysis. The results of NBO analysis carried out on halogen and hydrogen complexes are given in Table 4. The values reported in this table are the NBO occupation numbers for the σ*X-Y, σ*H-Y antibonds and the nitrogen, nN, oxygen, nO, and sulfur, nS, lone pairs. Additionally, the second-order perturbation energies E(2) (donor f acceptor) that involve the σ*X-Y are reported. The occupation number data are indicative of the values for the isolated molecules (numerical data between parentheses). Observation of the results given in Table 4 shows that the lone pair occupation number differs from the ideal occupation number by an important amount. Moreover, upon complexes formation, the σ*X-Y, σ*H-Y antibonds occupation number increased notably, as indicated by the high values of ∆σ*X-Y, which

ranged from 0.044 to 0.21 e in halogen complexes, and the ∆σ*H-Y values, that ranged from 0.0005 to 0.128 e in hydrogen complexes. These results should be interpreted in terms of the charge transfer interactions orbitals. In strong intermolecular charge transfer interactions, nB f σ*X-Y or nB f σ*H-Y, the lone pair of the B atom of the Lewis base acts as a donor and the σ*X-Y or σ*H-Y antibonds act as acceptors. Moreover, as reflected in the ∆nB versus ∆σ*X-Y, ∆nB versus ∆σ*H-Y plots, all of the charge that the donor orbital lost was consequently gained by the acceptor orbital (see Figure 7a,b). It is also important to note that, in line with the calculated binding energy, the highest values of nB f σ*X-Y interactions are those in which the nitrogen is the donor atom, and the lowest values of nB f σ*X-Y interactions are those in which the oxygen is the donor atom. In hydrogen complexes, on the other hand, the hyperconjugative energy of charge transfer followed the order nN f σ*H-Y > nO f σ*H-Y > nS f σ*H-Y. Thus, the oxygen atom, with a higher electronegativity compared with nitrogen and sulfur atoms, showed a greater tendency of binding to the hydrogen atom instead of binding to the halogen atom. Finally, as shown in Figure 8, a fairly good correlation was found between the charge transfer interactions and the binding energies of halogen bonds. 4. Conclusions In this work, a systematic theoretical study at B3LYP/6311++G** level of halogen bond was carried out on a series of binary complexes formed between Lewis bases and Lewis acids. The AIM theory and the NBO analysis was applied to

Halogen Bonding

J. Phys. Chem. A, Vol. 114, No. 1, 2010 561 points, indicating that this topological parameter can be considered as a good descriptor of the strength of these interactions. In addition, the AIM analysis has also revealed the different nature of the H-Y and X-Y bonds involved in the intermolecular interactions. While, the HY bond is essentially covalent, the X-Y bond is partially covalent and partially electrostatic. The analysis of the Laplacian distribution of the charge density has allowed us to understand the origin of the halogen bond. The halogen-bonded complexes result from the interaction between the charge density provided by the lone pair of donor atom of Lewis base (N, O, and S atoms) and the charge density depletion localized on the outermost portion of the X halogen atom centered on the X-Y axis bonds (σ-hole). Such charge depletion, on the X atom, results from the electron density withdrawing of the Y atom. This generates a decrease of the charge density in the front part of the X atom, which makes this atom more prone to uptake of the charge density provided by the lone pair of B. Finally, from NBO analysis, it was inferred that the charge transfer interactions play an important role in the formation of the complexes. Acknowledgment. The authors acknowledge SECYT-UTN for financial support. S.C.P. is a fellowship researcher of SECYT-UTN, and N.M.P. is career researcher of CONICET, Argentina. N.M.P. and G.L.S. acknowledge Grant PICTOUNNE 089.

Figure 7. (a) Change in the occupation numbers of lone pair of B atom of the Lewis base, ∆nB, vs change in the occupation numbers of ∆σ*H-Yantibond of Lewis acid. (b) Change in the occupation numbers of lone pair of B atom of the Lewis base, ∆nB, vs change in the occupation numbers of ∆σ*X-Yantibond of Lewis acid.

Figure 8. Correlation between the second-order perturbation stabilization energy, nBfσ*X-Y and the interaction energy.

analyze the electron density distribution of these complexes and, primarily, to understand the underlying reason for any similarities or differences to conventional hydrogen bonds. It was shown that the halogen bonding energies vary in a wide range between 4.36 and 18.87 kcal/mol and were generally stronger than hydrogen bonds. Additionally, it was observed that the water shows a higher affinity for hydrogen rather than for a halogen. Consequently, hydrogen bonds formed with water should prevail over those formed with halogen. A linear relationship was established between the interaction energies and the electron densities at halogen bond critical

References and Notes (1) Cole, G. C.; Legon, A. C.; Ottaviani, P. J. Chem. Phys. 2002, 117, 2790–2799. (2) Poleshchuk, O. Kh.; Branchadell, V.; Brycki, B.; Legon, A. C. J. Mol. Struct.(Theochem) 2006, 760, 175–182. (3) Loc Nguyen, H.; Horton, P. N.; Hursthouse, M. B.; Legon, A. C.; Bruce, D. W. J. Am. Chem. Soc. 2004, 126, 16–17. (4) Wang, Z. X.; Zheng, B. S.; Yu, X. Y.; Yi, P. G. J. Mol. Struct. (Theochem) 2008, 857, 13–19. (5) Wang, F.; Ma, N.; Chen, Q.; Wang, W.; Wang, L. Langmuir 2007, 23, 9540–9542. (6) Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703– 2707. (7) Mulliken, R. S.; Pearson, W. B. Molecular Complexes: A Lecture and Reprint Volume;Wiley Interscience: New York, 1969. (8) Hassel, O.; Rømming, C. Q. ReV. Chem. Soc. 1962, 16, 1–18. (9) Hassel, O., In Nobel Lectures, Chemistry 1963-1970; Elsevier: Amsterdan, 1972. (10) Legon, A. C. Angew. Chem., Int. Ed. 1999, 38, 2687–2714. (11) Auffinger, P.; Hays, F. A.; Westhof, E.; Shing Ho, P. Proc. Natl. Acad. Sci. USA (PNAS) 2004, 101, 16789–16794. (12) Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Acc. Chem. Res. 2005, 38, 386–395. (13) Cardillo, P.; Corradi, E.; Lunghi, A.; Meille, S. V.; Messina, M. T.; Metrangolo, P.; Resnati, G. Tetrahedron 2000, 56, 5535–5550. (14) Metrangolo, P. and; Resnati, G. Chem.sEur. J. 2001, 7, 2511– 2519. (15) Liantonio, R.; Metrangolo, P.; Pilati, T.; Resnati, G.; Stevenazzi, A. Cryst. Growth Des. 2003, 3, 799–803. (16) Caronna, T.; Liantonio, R.; Logothis, T. A.; Metrangolo, P.; Pilati, T.; Resnati, G. J. Am. Chem. Soc. 2004, 126, 4500–4501. (17) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon: Oxford, 1990. (18) Wojtulewski, S.; Grabowski, S. J. J. Mol. Struct. 2002, 605, 235– 240. (19) Sosa, G. L.; Peruchena, N. M.; Contreras, R. H.; Castro, E. A. J. Mol. Struct. (Theochem) 2002, 577, 219–228. (20) Fidanza, N. G.; Sosa, G. L.; Lobayan, R. M.; Peruchena, N. M. J. Mol. Struct. (Theochem) 2005, 722, 65–78. (21) Parthasarathi, R.; Subramanian, V.; Sathyamurthy, N. J. Phys. Chem. A 2006, 110, 3349–3351. (22) Grabowski, S. J.; Sokalski, W. A.; Dyguda, E.; Leszczynski, J. J.Phys. Chem. B 2006, 110, 6444–6446. (23) Pakiari, A. H.; Eskandari, K. J. Mol. Struct.(Theochem) 2006, 759, 51–60.

562

J. Phys. Chem. A, Vol. 114, No. 1, 2010

(24) Politzer, P.; Lane, P.; Concha, M. C.; Ma, Y.; Murray, J. S. J. Mol. Model. 2007, 13, 305–311. (25) Reed, A. E.; Curtis, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899–926. (26) Weinhold, F., Natural bond orbital methods. Encyclopedia Comput. Chem.; Schleyer, P.v.R., Ed.; Wiley: Chichester, U.K., 1988, 1793-1810. (27) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T. ; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (28) Karpfen, A. Theor. Chem. Acc. 2003, 110, 1–91,. and references therein. (29) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (30) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785–789. (31) (a) Glukhovtsev, M. N.; Pross, A.; McGrath, M. P.; Radom, L. J. Chem. Phys. 1995, 103, 1878–1885. (b) Glukhovtsev, M. N.; Pross, A.; McGrath, M. P.; Radom, L. J. Chem. Phys. 1996, 104, 3407. (32) Begovic, N.; Markovkic, Z.; Anic, S.; Kolar-Anic, L. J. Phys. Chem. A 2004, 108, 651–657.

Amezaga et al. (33) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553–559. (34) NBO Versio´n 3.1, Glendening, E. D.; Reed, A. E., Eds. (35) Blieger-Ko¨nig, F.; Scho¨nbohn, J. AIM2000, Version 2.0; chemical adviser, Bader, R. F. W.; Bu¨ro fur Innovative Software Streibel BliegerKo¨nig: Germany, 2002. (36) Bader, R. F. W. AIMPAC, a suite of program for the Theory of Atoms in Molecules; McMaster University, Hamilton Ontario, Canada. (37) Bondi, A. J. Phys. Chem. 1964, 68, 441–451. (38) Wang, W.; Wong, N. B.; Zheng, W.; Tiang, A. J. Phys. Chem. A 2004, 108, 1799–1805. (39) (a) Carroll, M. T.; Bader, R. F. W. Mol. Phys. 1988, 65, 695–722. (b) Carroll, M. T.; Bader, R. F. W. Mol. Phys. 1988, 63, 387–405. (40) Koch, U.; Popelier, P. A. L. J. Phys. Chem. 1995, 99, 9747–9754. (41) Bader, R. F. W.; Esse´n, H. J. Chem. Phys. 1984, 80, 1943–1960. (42) Valerio, G.; Raos, G.; Meille, S. V.; Metrangolo, P.; Resnati, G. J. Phys. Chem. A 2000, 104, 1617–1620. (43) Grabowski, S. J.; Bilewicz, E. Chem. Phys. Lett. 2006, 427, 51– 55. (44) Lu, Y. X.; Zou, J. W.; Yu, Q. S.; Jiang, Y. J.; Yu, Q. S.; Zhao, W. N. Chem. Phys. Lett. 2007, 449, 6–10. (45) Lu, Y. X.; Zou, J. W.; Wang, Y. H.; Jiang, Y. J.; Yu, Q. S. J. Phys. Chem. A 2007, 111, 10781–10788. (46) Pakiari, A. H.; Eskandari, K. J. Mol. Struct. (Theochem) 2006, 759, 51–60. (47) Cremer, D.; Kraka, E. Angew. Chem. 1984, 23, 627–628. (48) Espinosa, E.; Alkorta, I.; Elguero, J.; Molins, E. J. Chem. Phys. 2002, 117, 5529–5542. (49) Lu, Y. X.; Zou, J. W.; Wang, Y. H.; Zhang, H. X.; Yu, Q. S.; Jiang, Y. J. J. Mol. Struct. (Theochem) 2006, 766, 119–124.

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