Enhancing Effects of Electron-Withdrawing Groups and Metallic Ions

Article pubs.acs.org/JPCA

Enhancing Effects of Electron-Withdrawing Groups and Metallic Ions on Halogen Bonding in the YC6F4X···C2H8N2 (X = Cl, Br, I; Y = F, CN, NO2, LiNC+, NaNC+) Complex Na Han, Yanli Zeng,* Xiaoyan Li, Shijun Zheng, and Lingpeng Meng* Institute of Computational Quantum Chemistry, College of Chemistry and Material Science, Hebei Normal University, Shijiazhuang 050024, PR China ABSTRACT: Halogen-bonding interactions are highly directional intermolecular interactions that are often important in crystal engineering. In this work, the second-order Møller−Plesset perturbation theory (MP2) calculations and the quantum theory of “atoms in molecules” (QTAIM) and noncovalent interaction (NCI) studies were carried out on a series of X···N halogen bonds between substituted haloperfluoroarenes C6F4XY (X = Cl, Br, I; Y = F, CN, NO2) as bond donors and 1,2-diaminoethane as bond acceptor. Our research supports earlier work that electron-withdrawing substituents produce an enhancement effect on the size of the σ-hole and the maximum positive electrostatic potentials (VS,max), which further strengthens the halogen bonding. The metallic ion M+ (M+ = Li+, Na+) has the ability to enhance the size of both the σ-hole and VS,max value with the formation of [MNCC6F4X]+, resulting in more electronic charge transfer away from the halogen atom X and an increase in the strength of the halogen bond. It is found that the values of VS,max at the σ-holes are linear in relation to the halogen-bonded interaction energies and the halogen-bonding interaction distance, indicating that the electrostatic interaction plays a key role in the halogen-bonding interactions. The values of VS,max at the σ-holes are also linear in relation to the electron density ρb, its Laplacian ∇2ρb, and −Gb/Vb of XB, indicating that the topological properties (ρb, ∇2ρb) and energy properties (Gb, Vb) at the BCPs are correlated with the electrostatic potentials.

1. INTRODUCTION Halogen bonding (XB) is a typical intermolecular noncovalent interaction1 that has applications in many fascinating fields,2−8 such as crystal engineering,9 materials chemistry,10 and drugs discovery.11−13 Recently, these interactions have been the focus of research into the solid state synthesis of organic molecules14 in the field of supramolecular chemistry.15−17 Halogen bonding18,19 refers to the noncovalent interactions between electron deficient halogen atoms and electronegative sites, for instance, a lone pair of Lewis bases. According to this definition, halogen bonding can be depicted as R−X···B,20 where X is the halogen atom, the donor of the halogen bonding, and B acts as the halogen-bonding acceptor.21 Theoretical studies of halogen bonding have been reported22−31 and according to these studies, the outermost portion of the halogen surface has a region of positive electrostatic potential,3 and this positive region has been labeled the “σ-hole”.32−36 According to reports from Legon18 and Ibrahim,37 the strength of halogen bonding is correlated with the magnitude of VS,max36,38 (the most positive electrostatic potential at the σ-hole). Experimental studies39 and theoretical studies34,40 predicted that the size of the σ-hole is related to the mass number of the halogen, and it is also related to the electron-withdrawing power of the substituent group (R), which is covalently bonded to the halogen atom (X). Upon the formation of XB, if the electronic charge transfers away from X, the halogen surface will become more positive and the strength © 2013 American Chemical Society

of halogen bonding will increase. This has important implications in crystal engineering and organic material design.41 The goal of crystal engineering is to develop new materials with desired crystal architectures and expected molecular properties. Halogen bonding is a highly directional interaction42 that is an effective driving force. In crystal engineering, X···N halogen bonding is a very effective building block for obtaining halogen-bonding complexes.43 In an earlier experimental study,44 iodoperfluoroarenes were used to orient the halogen bond to a nitrogen-substituted hydrocarbon template (1,2-diaminoethane) and to achieve a level of halogen bonding driven supramolecular reactivity that directs their function. Metal cations play a key role in crystal engineering because of their effectiveness in driving self-assembly processesmainly as a result of their strong tendency to function as electron-pair acceptors in the presence of a variety of Lewis bases.16 The cation binding has been used experimentally to the formation of an XB, showed its effectiveness for the full separation of the ion pair on coordination with alkali-metal halides.45 In this work, the complexes formed by substituted haloperfluoroarenes C6F4XY (X = Cl, Br, I; Y = F, CN, NO2) and the 1,2-diaminoethane Lewis base were studied to Received: August 14, 2013 Revised: November 13, 2013 Published: November 15, 2013 12959

dx.doi.org/10.1021/jp408151t | J. Phys. Chem. A 2013, 117, 12959−12968

The Journal of Physical Chemistry A

Article

Figure 1. Molecular surface electrostatic potential (MEP) of C6F5Cl (a), C6F5Br (b), C6F5I (c), NCC6F4I (d), and C2H8N2 (e) on the 0.001 au (electrons/bohr3) contours of the molecule’s electronic density. Color ranges, in kcal/mol: red, more positive than 18; yellow, 8−18; green, 0−8; blue, negative. Position of VS,max is indicated in black and VS,min in blue.

investigate the factors that influence the size of the σ-hole and achieve very positive electrostatic potentials (VS,max) (i.e., the mass number of the halogen atom and the electron-withdrawing power of substituent Y). To take into account the influences of metallic ions on halogen bonding, the [MNCC6F4X]+···C2H8N2 (M = Li, Na; X = Cl, Br, I) complexes were also investigated.

suite,56 calculated on the 0.001 au (electrons/bohr3) contour of the molecule’s electronic density.57 Subsequently, noncovalent interaction (NCI) index calculations were performed using the Multiwfn program58 and visualized with the VMD program.59

3. RESULTS AND DISCUSSION 3.1. Molecular Electrostatic Potentials, Geometries, and Halogen-Bonded Interaction Energies. 3.1.1. Molecular Electrostatic Potentials (MEPs). Figure 1 shows the MEPs of C6F5Cl (a), C6F5Br (b), C6F5I (c), NCC6F4I (d), and C2H8N2 (e) on the 0.001 au contours of the molecule’s electronic density. From (a) to (d) of Figure 1, the positive electrostatic potential region (σ-hole) is on the outer surface of the X (X = Cl, Br, I) atom, around the extension of the C−X bond. For C2H8N2, the lone-pair electron region outside the nitrogen atom has an obvious negative electrostatic potential. From (a) to (c) of Figure 1, the size of the σ-hole becomes larger in the sequence of Cl < Br < I. Comparing (d) and (c) of Figure 1 shows the electron-withdrawing substituent can produce an enhancement effect on the size of the σ-hole. The metallic ion has the ability to enhance the size of the σhole upon the formation of [MNCC6F4I]+ (M = Li, Na), compared with the case of YC6F4I. Their MEP contours are not included in Figure 1 because the positive MEP values of [MYC6F4I]+ are much larger and the contours could not be incorporated into Figure 1. The most positive electrostatic potentials of the σ-hole (VS,max) associated with the halogen atoms of C6F4XY (X = Cl, Br, I; Y = F, CN, NO2) and [MNCC6F4X]+ (M = Li, Na) are listed in Table 1. It can be observed that the VS,max values correlate with the halogen polarizability (mass number of the atom). For the same substituent groups Y, the VS,max value

2. COMPUTATIONAL DETAILS The geometries were calculated with ab initio calculations using second-order Møller−Plesset perturbation theory (MP2) with a mixed basis set. The aug-cc-pVDZ-PP basis set, which uses small-core energy-consistent relativistic pseudopotentials to account for relativistic effects,46 was used for iodine, whereas for all other atoms the aug-cc-pVDZ47−49 basis set was used. The harmonic vibrational frequencies were then computed at the same level to confirm that these equilibrium geometries were local minima on their potential energy surfaces. To correct the inherent basis set superposition error (BSSE), the counterpoise corrected interaction energies (ΔE) were obtained with the counterpoise procedure proposed by Boys and Bernardi.50 Solvent calculations were performed the polarizable continuum model (PCM)51−53 at the B3LYP level of theory and computed at the same basis set. The optimized geometries in the solvent phase were utilized in water continuous media. The above calculations of the monomers and the complexes were performed using the Gaussian 03 program package.54 The electron density topological properties and energy properties for the halogen bonding were computed by the AIM 2000 program5 and AIMALL program.55 The electrostatic potentials were computed with the WFA surface analysis 12960



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Table 1. Most Positive σ-Hole Potentials (VS,max, kcal/mol) Associated with the Halogen Atoms C6F5Cl C6F5Br C6F5I NCC6F4Cl NCC6F4Br NCC6F4I O2NC6F4Cl O2NC6F4Br O2NC6F4I [LiNCC6F4Cl]+ [LiNCC6F4Br]+ [LiNCC6F4I]+ [NaNCC6F4Cl]+ [NaNCC6F4Br]+ [NaNCC6F4I]+

bond producing VS,max

VS,max

C−Cl C−Br C−I C−Cl C−Br C−I C−Cl C−Br C−I C−Cl C−Br C−I C−Cl C−Br C−I

20.5 25.8 36.2 26.4 32.4 42.2 26.7 31.9 42.4 71.7 77.3 87.3 68.3 74.0 83.9

3.1.3. Halogen-Bonded Interaction Energies. The halogenbonded interaction energies of the complexes, which were corrected with the BSSE and zero-point vibrational energies, are listed in Table 2. For the same substituent group Y, ΔE follows the increasing sequence of X = Cl, Br, I. For example, the ΔE values of NCC6F4Cl···C2H8N2, NCC6F4Br···C2H8N2, and NCC6F4I···C2H8N2 are −14.81, −21.10, and −31.77 kJ· mol−1, respectively. For the same halogen atom X, ΔE increases with the electron-withdrawing group; for example, the ΔE values of C6F5I···C2H8N2, NCC6F4I···C2H8N2, and O2NC6F4I··· C2H8N2 are −29.44, −31.77, and −32.35 kJ·mol−1, respectively. With the addition of Li+ and Na+, the halogen-bonded interaction energies become much greater. Compared with the −31.77 kJ·mol−1 of NCC6F4I···C2H8N2, the ΔE of [LiNCC6F4I]+···C2H8N2 and [NaNCC6F4I]+···C2H8N2 become −48.10 and −45.90 kJ·mol−1, respectively. The halogen-bonded interaction energies of C6F5I···C2H8N2, NCC6F4I···C2H8N2, O2NC6F4I···C2H8N2, [LiNCC6F4I]+··· C2H8N2, and [NaNCC6F4I]+···C2H8N2 are correlated with their respective VS,max values at the σ-holes of C6F5I, NC− C6F4I, O2NC6F4I, [LiNCC6F4I]+, and [NaNCC6F4I]+, respectively. The linear correlation coefficient is 0.9987, as shown in Figure 3. Similarly, linear relationships also exist when X = Cl and Br, with correlation coefficients of 0.9971 and 0.9973, respectively. Accompanied with the VS,max value as the halogen atom increases, the halogen-bonded interaction energies become greater, and the halogen-bonding interactions become stronger, which has been demonstrated as well in earlier works.60,61 Particularly, for the metallic ion system, the polarity of environment should have an obvious effect on the halogenbonded interaction. To consider this effect, the optimizations of the complexes in the water environments were carried out. The computed Br···N interaction energies for NCC6F4Br···C2H8N2, [LiNCC6F4Br]+···C2H8N2, and [NaNCC6F4Br]+···C2H8N2 are −0.53, −2.22, and −1.49 kJ·mol−1, respectively. It is observed

follows the order Cl < Br < I. For example, the VS,max values of NCC6F4Cl, NCC6F4Br, and NCC6F4I are 26.4, 32.4, and 42.2 kcal·mol−1, respectively. For the same halogen atom X, the VS,max increases as the capacity of the electron-withdrawing group Y increases, which shifts the electronic charge far from the halogen atom X. For example, the VS,max values of C6F5I, NCC6F4I, and O2NC6F4I are 36.2, 42.2, and 42.4 kcal·mol−1, respectively. With the formation of [MNCC6F4X]+, more electronic charge transfers away from the halogen atom X, and the VS,max values increases greatly. 3.1.2. Geometries. The optimized geometries of C6F5X··· C2H8N2 and [MNCC6F4X]+···C2H8N2 (M = Li, Na) are displayed in Figure 2. The σ-hole of C6F5X points to the negative electrostatic potential region of C2H8N2, the angle of R-X···N is approximately 180°, indicating that the halogenbonding interaction is highly directional.

Figure 2. Optimized geometries of the C6F5X···C2H8N2 (X = Cl, Br, I) (a) and [MNCC6F4X]+···C2H8N2 (M = Li, Na; X = Cl, Br, I) (b) complexes. 12961



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Table 2. Halogen-Bonded Interaction Energies, Interaction Distances, and Vibrational Frequencies complex

ΔEa

d(X···N)b

Δd(X···N)c

ν(X···N)d

d(M−N)e

C6F5Cl···C2H8N2 C6F5Br···C2H8N2 C6F5I···C2H8N2 NCC6F4Cl···C2H8N2 NCC6F4Br···C2H8N2 NCC6F4I···C2H8N2 O2NC6F4Cl···C2H8N2 O2NC6F4Br···C2H8N2 O2NC6F4I···C2H8N2 [LiNCC6F4Cl]+···C2H8N2 [LiNCC6F4Br]+···C2H8N2 [LiNCC6F4I]+···C2H8N2 [NaNCC6F4Cl]+···C2H8N2 [NaNCC6F4Br]+···C2H8N2 [NaNCC6F4I]+···C2H8N2

−14.17 −19.86 −29.44 −14.81 −21.10 −31.77 −15.63 −22.01 −32.35 −23.76 −33.32 −48.10 −22.50 −31.67 −45.90

3.0522 2.9672 2.9157 3.0208 2.9401 2.8911 3.0225 2.9401 2.8890 2.9025 2.8051 2.7540 2.9169 2.8215 2.7690

0.2479 0.4328 0.6143 0.2792 0.4599 0.6390 0.2776 0.4599 0.6410 0.3975 0.5949 0.7760 0.3831 0.5785 0.7610

64.72 82.42 91.45 65.38 94.42 112.60 85.98 94.39 112.62 86.05 102.80 133.83 81.45 94.33 127.48

1.9474 (1.896)f 1.9445(1.896) 1.940 (1.896) 2.3298(2.250) 2.3263(2.250) 2.3209(2.250)

ΔE denotes the halogen-bonded interaction energies, in kJ/mol. bd(X···N) denotes the halogen-bonded distances, in angstrom (Å). cΔd(X···N) denotes the difference between d(X···N) and the sums of the van der Waals radii of X and N, in Å. dν(X···N) denotes vibrational frequencies, in cm−1. ed(M−N) denotes the M−N bond distance, in Å. fValues in parentheses denote the sums of the single-bond covalent radii of N and M, in Å. a

Figure 4. Linear relationships between the halogen-bonded interaction distance d(X···N) versus the most positive electrostatic potentials VS,max of X.

Figure 3. Linear relationships between the halogen-bonded interaction energies ΔE versus the most positive electrostatic potentials VS,max of X.

Table 1, with correlation coefficients 0.9959, 0.9986, and 0.9990 for X = Cl, Br, and I, respectively (Figure 4). The M−N bond distances, d(M−N), are also collected in Table 2. It can be seen that the d(M−N) values are somewhat smaller than the sums of the single-bond covalent radii of N and M, indicating that the M−N bond is very strong, close to the covalent bond. 3.2. QTAIM Analyses of the XB. The quantum theory of “Atoms in Molecules”63−65 has constituted a useful methodology to assess intermolecular interactions, such as halogen bonding.66−70 In this section, topological and energy parameters of electron density distribution, local parameters of the Lacplacian of electron density distribution, and the atomic integral properties are discussed to insight into the XB. 3.2.1. Topological and Energy Parameters of Electron Density Distribution. By means of a topological analysis of electron density distribution, features such as critical points and paths of maximum electron density (atomic interaction lines) can be studied; the “molecular graph” is a representation of the

that, comparing with the results in the gas phase, the strength of the halogen-bonded interaction energies conspicuously weakens under solvent effects. But more than that, with the addition of the metallic ion M+ (M+ = Li+, Na+), the strengths have an order similar to those in the gas phase, the interaction energies also become greater by the addition of the metallic ion. 3.1.4. Geometrical Parameters and Vibrational Frequencies. The geometrical parameters and vibrational frequencies are collected in Table 2. The halogen-bonded interaction distance, d(X···N), decreases in the order Cl···N, Br···N, and I···N. The X···N interaction distances are all shorter than the sum of the van der Waals radii of the X and N atoms.62 The difference, Δd(X···N), becomes more and more obvious along the sequence of X = Cl, Br, and I. The vibrational frequency of the halogen bond, v(X···N), increases in the sequence Cl···N, Br···N, and I···N. These are in accordance with the halogenbonded interaction energies. The halogen-bonded interaction distances d(X···N) are linearly related to the VS,max of X of 12962



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Figure 5. QTAIM molecular graphs for NCC6F4I···C2H8N2 and [LiNCC6F4I]+···C2H8N2 complexes.

Table 3. Topological Properties and Energy Properties at the Halogen Bond Critical Points (BCPs) (All Values in au) complex

ρb

λ1

λ2

λ3

∇2ρb

Gb

Vb

Hb

−Gb/Vb


0.0111 0.0156 0.0212 0.0119 0.0164 0.0223 0.0119 0.0163 0.0224 0.0152 0.0216 0.0292 0.0148 0.0209 0.0284

−0.0078 −0.0107 −0.0141 −0.0085 −0.0115 −0.0151 −0.0085 −0.0114 −0.0151 −0.0116 −0.0164 −0.0213 −0.0112 −0.0157 −0.0205

−0.0076 −0.0103 −0.0136 −0.0082 −0.0110 −0.0144 −0.0082 −0.0109 −0.0145 −0.0111 −0.0156 −0.0203 −0.0107 −0.0150 −0.0195

0.0552 0.0717 0.0887 0.0591 0.0759 0.0929 0.0589 0.0760 0.0931 0.0763 0.0999 0.1196 0.0740 0.0966 0.1164

0.0398 0.0507 0.0610 0.0424 0.0533 0.0633 0.0422 0.0536 0.0635 0.0536 0.0679 0.0781 0.0521 0.0660 0.0764

0.0086 0.0114 0.0148 0.0092 0.0120 0.0156 0.0092 0.0120 0.0156 0.0118 0.0157 0.0204 0.0114 0.0152 0.0198

−0.0073 −0.0100 −0.0144 −0.0078 −0.0107 −0.0153 −0.0077 −0.0105 −0.0153 −0.0101 −0.0145 −0.0213 −0.0098 −0.0139 −0.0205

0.0014 0.0013 0.0004 0.0014 0.0013 0.0003 0.0014 0.0014 0.0003 0.0016 0.0013 −0.0009 0.0016 0.0013 −0.0007

1.1860 1.1324 1.0285 1.1811 1.1247 1.0181 1.1814 1.1359 1.0173 1.1611 1.0868 0.9586 1.1640 1.0924 0.9658

covalent in nature.72,73 Taking −Gb/Vb as the balance between the positive value of Gb and the negative value of Vb may indicate the regions corresponding to covalent or noncovalent interactions. That is, if −Gb/Vb is greater than 1, then the interaction is noncovalent. If the ratio is between 0.5 and 1, the interaction is partly covalent in nature, and when this ratio is less than 0.5, the interaction is a shared covalent interaction. From Table 3, for the halogen-bonded BCPs of the YC6F4X···C2H8N2 (X = Cl, Br, I; Y = F, CN, NO2) complexes, the values of ∇2ρb and Hb at the X···N BCPs are all positive and the −Gb/Vb values are larger than 1, indicating that the halogen-bonded interactions of these complexes display the characteristics of “closed-shell” noncovalent interactions. In the [MNCC6F4X]+···C2H8N2 (X = Cl, Br) complexes, ∇2ρb > 0, Hb > 0, and −Gb/Vb > 1, so the halogen-bonded interactions of these complexes also display the characteristics of “closed-shell” noncovalent interactions. In the [LiNCC6F4I]+···C2H8N2 and [NaNCC6F4I]+···C2H8N2 complexes, ∇2ρb > 0, Hb < 0, and −Gb/Vb are between 0.5 and 1, so the halogen-bonded

bonding interactions. As examples of the halogen-bonded complexes, the molecular graphs of NCC6F4I···C2H8N2 and [LiNCC6F4I]+···C2H8N2 are displayed in Figure 5. The X···N bond critical points (BCPs) indicate the existence of halogenbonded intermolecular interactions in these complexes. The value of ρb is a good estimate of XB strength.63,71 The larger the ρb value, the stronger the halogen bond is. From Table 3, the electron density (ρb) at the BCP ranges from 0.0111 to 0.0292 au, with a sequence consistent with the halogen-bonded interaction energies of Table 2. The larger the ρb at the BCPs of XB, the greater the interaction energies are. The kinetic electron energy density Gb, the potential electron energy density Vb, the electron energy density Hb, and −Gb/Vb at the BCPs of the XBs are also listed in Table 3. The values of ∇2ρb and Hb indicate the nature of the interaction. A negative value of ∇2ρb indicates that there is a shared interaction like in a covalent bond, whereas a positive value of ∇2ρb indicates closed-shell system interactions, that is, ionic interactions, van der Waals forces, or hydrogen bonding.63 On the other hand, if ∇2ρb is positive but Hb is negative, then the interaction is partly 12963



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interactions in these two complexes are partly covalent in nature. From Table 3, with the increasing atomic mass number of X and with the addition of electron-withdrawing group Y, especially with the addition of M+, ρb, ∇2ρb, and Gb become larger and Vb, Hb, and −Gb/Vb become smaller, indicating that accompanied with the XB becoming stronger, both the electrostatic and covalent character of the XB become obvious. Figure 6a presents the linear relationships between electron density ρb of XB and VS,max of the X atoms. Large VS,max values of X lead to larger ρb values of XB and the stronger XB. Figure 6b presents the linear relationships between the electron density Laplacian ∇2ρb and VS,max of the X atom. Larger VS,max values of X result in more positive values of ∇2ρb, which results in stronger electrostatic character of the XB. Figure 6c shows the relationship between −Gb/Vb and the VS,max of the X atom. Larger VS,max values of X correlate with smaller values of −Gb/ Vb, indicating the more covalent character of the XB. These relations show that the topological properties (ρb, ∇2ρb) and the energy properties (Gb, Vb) at the BCPs are correlated with the electrostatic potentials. 3.2.2. Local Parameters of the Laplacian of Electron Density Distribution. The L(r) = −1/4∇2ρ(r) function is of particular interest to study XB because its topology shows the regions of the space where the electron density is locally concentrated or depleted.74 For the valence shell of an atom, the inner region is where L(r) > 0 signifies a local concentration of electron density and the outer region is where L(r) < 0 signifies a local depletion of electron density. The first one is named the valence shell charge concentration (VSCC). From a topological viewpoint, the extremes or CPs in the distribution of the L(r) function easily provide the precise localization of different reactivity zones. A (3, −3) critical point (CP) corresponds to a local maximum in L(r), indicating a local electronic charge concentration (CC), a (3, +3) CP corresponds to a local minimum in L(r), indicating a local depletion of the electronic charge (CD). On the other hand, (3, −1) and (3, +1) CPs are saddle points.70,74,75 The analysis of the distributions of the ∇2ρ(r) (or of the L(r) function) by Duarte et al.70 has shown that the presence of a depletion of electron density in the direction of the in the formation of XB interaction, the (3, +1) CPs of the L(r) function corresponds to the positive σ-hole. In this work, the complexes YC6F4Cl···C2H8N2 (Y = F, CN, NO2, LiNC+, NaNC+) were taken as example, the (3, +1) CPs of the L(r) function (σ-hole) were found, and the electron densities at the (3, +1) CPs of the L(r) function, namely ρ(rhole), were calculated, with values 0.2008, 0.2008, 0.2004, 0.1985, and 0.1987 for C 6 F 5 Cl···C 2 H 8 N 2 , NCC 6 F 4 Cl···C 2 H 8 N 2 , O 2 NC 6 F 4 Cl···C 2 H 8 N 2 , [LiNCC 6 F 4 Cl] + ···C 2 H 8 N 2 , and [NaNCC6F4Cl]+···C2H8N2, respectively. Comparing the above values with the corresponding VS,max values of Table 1, one can see that the greater the VS,max value outside the chlorine atom, the smaller the ρ(rhole) values. The relation is displayed in Figure 7 with the linear coefficient 0.9924. That is, the greater the value of VS,max, the more depletion of the electron density over the σ-hole, which results in the smaller value of the electron density at the (3, +1) critical point of the L(r) function. 3.2.3. Integral Characteristics. In QTAIM, the molecules could be divided into atoms by the zero-flux surface. The integration of electron density over the zero-flux surface could provide useful bonding information for the interacting atoms.

Figure 6. Linear relationships between the topological properties (ρb, ∇2ρb) and energy properties (−Gb/Vb) versus the most positive electrostatic potentials VS,max.

In this work, the integration of atom charges and volumes of X atom were considered. Upon the complex formation, the X atom charge and volume have changed; the changes Δq(X) and ΔV(X) are collected in Table 4. 12964



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Figure 7. Linear relationship between the ρ(rhole) values and VS,max values outside the chlorine atom.

Figure 8. Linear relationships between the halogen-bonded interaction energies and ΔV(X).

Table 4. Atom Integral Properties for Halogen Atoms Involved in the Halogen-Bonded Complexesa complex

atom

Δq(X)

ΔV(X)


Cl Br I Cl Br I Cl Br I Cl Br I Cl Br I

0.0410 0.0623 0.0628 0.0444 0.0651 0.0619 0.0438 0.0629 0.0614 0.0509 0.0720 0.0598 0.0494 0.0714 0.0613

−5.8411 −10.3165 −13.8410 −6.3068 −10.6760 −13.2838 −6.2612 −10.5339 −13.2837 −7.6827 −11.8608 −15.4174 −7.4750 −11.7035 −14.8460

3.3. Noncovalent Interactions (NCI) Index of the XB. The noncovalent interaction (NCI) index based on the relationship between the electron density and the reduced density gradient has been introduced by Yang and coworkers.76−78 The reduced density gradient

s=

|∇ρ| 1 2 1/3 4/3 2(3π ) ρ

is a fundamental dimensionless quantity in DFT used to describe the deviation from a homogeneous electron distribution.77,79−81 To a certain extent, the NCI analysis method can be regarded as an extension of AIM.78 Not only can the location of the pairwise atoms connected along the bond path be identified, but also the properties around BCPs can be visualized using NCI. The reduced density gradient is able to be used to identify the noncovalent interactions and covalent interactions in real space.12 Therefore, the NCI index is a useful tool to distinguish and visualize different types of noncovalent interactions as regions of real space. In QTAIM, the value of ρ is a good estimate of the strength of an interaction.82 Moreover, the three eigenvalues λi of the electron density Hessian Matrix are a widely used tool to distinguish different interactions.63 ρ and sign(λ2),77 where sign(λ2) is the sign of λ2, are capable of distinguishing the types and strength values of the interactions. According to the definition from Yang and co-workers,76−78 if the ρ value is large and sign(λ2) is negative, the interaction is attractive, and if the ρ value is large and sign(λ2) is positive, the interaction is nonbonding. Figure 9 shows the s(ρ) vs sign(λ2)ρ in the C6F5Br···C2H8N2, NCC6F4I···C2H8N2, and [LiNCC6F4I]+··· C2H8N2 complexes. On the basis of the scatter plots in Figure 9, when sign(λ2) = −1 and the vicinity of ρ is low-density (0.005 au < ρ < 0.05 au), the reduced density gradient, s(ρ), has one low-gradient spike, and the value of s(ρ) at the spike is close to zero;22 these characteristic peaks are indicative of the weak noncovalent interactions of the XB. From C6F5Br··· C2H8N2 to NCC6F4I···C2H8N2, and to [LiNCC6F4I]+··· C2H8N2, the characteristic peaks directed toward the sign(λ2)ρ values are 0.019, 0.028, and 0.035, respectively, indicating the XB interactions become stronger from C6F5Br···C2H8N2 to NCC6F4I···C2H8N2, and to [LiNCC6F4I]+···C2H8N2. The

a Δq(X) and ΔV(X) represent the difference of the properties between the complexes and the monomers; all values in a.u.

From Table 4, it can be observed that the values of Δq(X) ranges from 0.0410 to 0.0720 au, indicating that the charge transfer occurs from C2H8N2 to the X atom of YC6F4X. For C6F5Cl···C2H8N2, C6F5Br···C2H8N2, and C6F5I···C2H8N2, the Δq(X) value follows the order Cl < Br < I, which is consistent with the interaction energies. The greater the interaction energy, the more charge transfer. On the other hand, for the same halogen atom X, Δq(X) increases with the stronger electron-withdrawing group Y. For example, Δq(Cl) values of the C6F5Cl···C2H8N2, NCC6F4Cl···C2H8N2, O2NC6F4Cl··· C2H8N2, [LiNCC6F4Cl]+···C2H8N2, and [NaNCC6F4Cl]+··· C2H8N2 are 0.0410, 0.0444, 0.0438, 0.0509, and 0.0494, respectively. The changes of atom volumes, ΔV(X), are all negative, indicating that the halogen atom volumes contract in the complexes. The ΔV(X) values are linearly related to the halogen-bonded interaction energies ΔE, with correlation 0.9881, 0.9909, and 0.9271 for X = Cl, Br, and I, respectively (Figure 8). The greater the interaction energy, the more volume contraction of the X atom. 12965



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Figure 9. Plots of the reduced density gradient versus the electron density multiplied by the sign of the second Hessian eigenvalue (above) and isosurfaces were generated for s = 0.05 au (below) for C6F5Br···C2H8N2 (a), NCC6F4I···C2H8N2, (b) and [LiNCC6F4I]+···C2H8N2 (c).

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ACKNOWLEDGMENTS Thanks for International Science Editing to edit this paper. This project was supported by the National Natural Science Foundation of China (Contract Nos.: 21371045, 21102033, 21171047, 21073051), the Natural Science Foundation of Hebei Province (Contract No.: B2011205058), and the Education Department Foundation of Hebei Province (ZH2012106, ZD2010126).

reduced gradient isosurface (s = 0.05 au) of Figure 9 agrees with the analysis of the scatter plots. In the middle region of the halogen and nitrogen atoms, there is a bonding isosurface. The color coding of these bonding isosurfaces is from green to blue, indicating that these XB interactions are becoming stronger in the sequence C6F5Br···C2H8N2, NCC6F4I···C2H8N2, and [LiNCC6F4I]+···C2H8N2.

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4. CONCLUSIONS In this work, MP2 calculations, QTAIM, and NCI studies were carried out on a series of X···N halogen-bonding types in the YC6F4X···C2H8N2 (X = Cl, Br, I; Y = F, CN, NO2, LiNC+, NaNC+) complexes. (1) Our research supports earlier work that the electronwithdrawing capacity of substituents will produce an enhancement effect on the size of the σ-hole as well as increase the maximum positive electrostatic potential (VS,max), which further strengthens the halogen bonding. (2) The metallic ion M+ (M+ = Li+, Na+) has the ability to enhance the size of the σ-hole and VS,max value with the formation of [MNCC6F4X]+, resulting in more electronic charge transfer away from the halogen atom X and an increase in the strength of the halogen bonding. (3) The values of VS,max at the σ-holes are linearly related to the halogen-bonded interaction energies and the halogen-bonding interaction distance, indicating that the electrostatic interaction plays a key role in the halogen-bonding interactions. (4) The values of VS,max at the σ-holes are linearly related to the electron density ρb, its Laplacian ∇2ρb, and −Gb/Vb of XB, showing that the topological properties (ρb, ∇2ρb) and energy properties (Gb, Vb) at the BCPs are correlated with the electrostatic potentials.

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AUTHOR INFORMATION

Corresponding Authors

*Y. Zeng: e-mail, [email protected]. *L. Meng: e-mail, [email protected]. Notes

The authors declare no competing financial interest. 12966



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