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Magnitude and Directionality of Halogen Bond of Benzene with CFX, CHX and CFX (X = I, Br, Cl and F) 6

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Seiji Tsuzuki, Tadafumi Uchimaru, Akihiro Wakisaka, and Taizo Ono J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06295 • Publication Date (Web): 15 Aug 2016 Downloaded from http://pubs.acs.org on August 20, 2016

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The Journal of Physical Chemistry

Magnitude and Directionality of Halogen Bond of Benzene with C6F5X, C6H5X and CF3X (X = I, Br, Cl and F) Seiji Tsuzuki,*a Tadafumi Uchimaru,b Akihiro Wakisakac and Taizo Onod a

Research Center for Computational Design of Advanced Functional Materials (CD-FMat),

National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan. b

Research Institute for Sustainable Chemistry, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan.

c

Environmental Management Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba, 305-8569, Japan.

d

Structural Materials Research Institute, National Institute of Advanced Industrial Science

and Technology (AIST), 2266-98, Anagahora, Shimoshidami, Moriyama-ku, Nagoya, Aichi 463-8560 Japan.

e-mail [email protected]

ACS Paragon Plus Environment

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Abstract Geometries of benzene complexes with C6F5X, C6H5X and CF3X (X is I, Br, Cl, F) were optimized and their interaction energies were evaluated. The CCSD(T) interaction energies at the basis set limit (Eint) of C6F5X (X is I, Br, Cl, F) with benzene were -3.24, -2.88, -2.31, -0.92 kcal mol-1. Eint of C6H5X (X is I, Br, Cl) with benzene were -2.31, -1.97, -1.48 kcal mol-1. The fluorination of halobenzenes slightly enhances the attraction. Eint of CF3X (X is I, Br, Cl, F) with benzene (-3.11, -2.74, -2.22, -0.71 kcal mol-1) were very close to Eint of corresponding C6F5X with benzene. In contrast to the halogen bond of iodine and bromine with pyridine (n-type halogen bond acceptor) where the main cause of the attraction is the electrostatic interactions, that of halogen bond with benzene (p-type acceptor) is dispersion interaction.

In the halogen bonds with p-type acceptors (halogen-π interactions), the

electrostatic interactions and induction interactions are small. The overall orbital-orbital interactions are repulsive. The directionality of halogen bonds with p-type acceptors is very weak owing to the weak electrostatic interactions in contrast to the strong directionality of the halogen bonds with n-type acceptors and hydrogen bonds.

Introduction In the past decade, halogen bond1-12 attracted much attention in many research fields. It has been believed that halogen bond is one of important interactions in the fields of biochemistry13-15 and material science.16-22 Several experimental23-31 and theoretical studies32-44 were reported on the nature of halogen bond. There exists strong attraction between iodine or bromine atom and n-type halogen bond acceptors (such as pyridine). It is believed that the halogen bond with n-type acceptors is important in controlling molecular recognition processes and determining molecular packing in crystals, as the halogen bond with n-type acceptors is sufficiently strong and sufficiently directional.

The halogen bond with p-type acceptors (such as benzene) attracted attention in several research field of chemistry and biochemistry. The halogen bonds with p-type acceptors is often called as halogen-π interactions. The contact of halogen atoms and aromatic ring was often observed in crystals.45-56 The halogen-π interaction is believed as one of the important


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driving forces in the crystal organizations.52-56

The importance of the halogen-π

interactions in molecular recognition processes57-59 and chemical reactions60-63 was also pointed out.

The nature of the halogen-π interactions of alkyl and aryl halides are important for improving our understanding on their roles in determining molecular orientation is crystals and self-assemblies. A few theoretical studies on the nature of the halogen-π interactions were reported.64-74 The halogen-π interactions of I2, ClF and NCX (X = Cl, Br) were reported.64-66,68,69,74 Only a few theoretical studies were reported on the nature of the halogen-π interactions of alkyl and aryl halides. The interaction energies of tyrosine with chloro- and bromo-benzene using CCSD(T) calculations were reported.71 Rezac et al. carried out CCSD(T) calculations and estimated the interaction energies of CH3Br, CH3I, CF3Br, CF3I with benzene at the basis set limit.72 Recent theoretical studies indicate that we have to use a large basis set and carry out CCSD(T) calculations for studying weak interactions of aromatic molecules quantitatively.75-78

Unfortunately, the interaction

energies of halogen-π interactions of alkyl and aryl halides using CCSD(T) method were reported for only limited model systems.71,72 In addition, the comparison of the magnitude of directionality of halogen-π interactions with halogen bond with n-type acceptors was not reported.

Using CCSD(T) method we studied the interactions of C6F5X, C6H5X, CF3X (X = I, Br, Cl, F) with benzene in this work to elucidate the magnitude of halogen-π interactions. The magnitude of halogen-π interactions was studied by changing the orientation of interacting molecules. We compared the halogen-π interactions and the halogen bond with pyridine (ntype acceptor) for elucidating the distinctive features of the halogen-π interactions. We discussed the magnitude of the electrostatic, induction, dispersion interactions in the halogen-π interactions.

Computational method


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For ab initio calculations, the Gaussian 09 program79 was used.

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The MP280,81 and

CCSD(T) methods were used to correct electron correlation.82 Using counterpoise method BSSE was corrected83,84 The MP2/6-311G* calculations with BSSE correction were used for optimization of geometries of complexes.85 The geometries of pyridine complexes were taken from reference 43. For iodine the DGDZVP basis set86 was used. The MP2 and CCSD(T) interaction energies (EMP2 and ECCSD(T)) at the basis set limit (EMP2(limit) and ECCSD(T)(limit)) were estimated. Using Helgaker et al.’s method87 EMP2(limit) was estimated. For estimating EMP2(limit), we employed aug-cc-pVDZ and aug-cc-pVTZ.88,89 From the ∆CCSD(T) calculated using aug-cc-pVDZ basis set, we estimated the ∆CCSD(T) (= ECCSD(T) - EMP2) at the basis set limit [∆CCSD(T)(limit)].89-91 The ∆CCSD(T)(limit) was added to EMP2(limit) to obtain ECCSD(T)(limit). In supporting information, we described the estimation procedure in detail. From the interaction between distributed multipoles of molecules we calculated the electrostatic energy using the ORIENT version 3.2.92,93 Using GDMA program, distributed multipoles of isolated molecules were calculated on all atoms up to hexadecapole using wave functions of MP2/6-311G** level.89,94,95 From atomic polarizabilities and the electric field obtained by the distributed multipole, induction energy was calculated.96

The atomic polarizabilities (α) used for carbon, nitrogen, fluorine,

chlorine, bromine, iodine are 10, 8, 3, 16, 23, 34 au.97,98 We evaluated the interaction energy potentials at the MP2 level using cc-pVTZ basis set.89 The MP2/6-311G** level geometry optimizations of isolated molecules were carried out.

They were used for

calculating potentials without further geometry optimizations. The geometries of C6F5X and C6H5X complexes with benzene, which were employed for the interaction energy potential calculations, have C2v symmetry, if not otherwise noted. The CF3X-benzene complexes have C3v symmetry. The C6 axis of benzene is on the C-X bond in these C2v and C3v complexes. Results and discussion

Interaction energy between C6F5I and benzene The interaction energies between C6F5I and benzene (1) were calculated using various basis sets for studying the basis set effects on calculations of halogen-π interaction (Figure 1). R


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is the distance between halogen atom and center of benzene. The HF level potentials have potential minima. This shows the existence of attractive electrostatic interactions between C6F5I and benzene, as the HF interaction energy is approximately the sum of exchangerepulsion interactions and electrostatic intetactions.43

Compared with the MP2, the

attraction is significantly underestimated by the HF calculations. The significant difference shows that there exist large dispersion interactions. The MP2 level potentials has strong basis set dependences. The attraction was underestimated by small basis sets.

Using several correction procedures of electron correlation interaction energies of 1 were calculated with cc-pVDZ for revealing the effects of correction procedure. Compared with the more accurate CCSD(T) method, the attraction is substantially overestimated by the MP2 method (Figure 2). If we want to evaluate the halogen-π interaction quantitatively, we need to employ a large basis set and carry out the CCSD(T) calculations as well as the evaluation of other weak interactions of aromatic molecules (such as π/π, CH/π interactions).76,77,99-106

The MP2 level interaction energy potentials obtained with several basis sets were compared with the ECCSD(T)(limit) (Figure S1).

Compared with the ECCSD(T)(limit), the attraction is

overestimated by the MP2 method if the basis set used includes diffuse functions. The MP2 potentials with 6-311G* and cc-pVTZ (medium size basis sets) are close to ECCSD(T)(limit) owing to the error cancellation.107

We used the MP2/6-311G* and MP2/cc-pVTZ

calculations for the optimizations of geometries of complexes and qualitatively evaluating the interaction energy potentials (mainly for the comparison of the effects of halogen atoms).

The interaction energy potential for 1 was calculated by DFT method using dispersion corrected functionals (B97D and B2PLYPD) for evaluating their performance (Figure 3). The potential obtained by the B97D method is close to the MP2/aug-cc-pVDZ potential. Compared with ECCSD(T)(limit), the attraction is overestimated by the B97D method as well as the MP2 method,101 while the B2PLYPD method underestimates the attraction.


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The three orientations of 1 (1a-1c) was used for calculating interaction energy potentials. The C-I bond is perpendicular to the interacting benzene ring in 1a-1c (Figure 4). The C-I bond in 1a is on the C6 axis of benzene. The C-I bond points toward a carbon atom of benzene in 1b. The C-I bond points toward the midpoint of C-C bond in 1c. The three interaction energy potentials (1a-1c) have nearly identical potential depth as shown in Figure 4, which shows that the intermolecular interaction energy potential for 1 is very shallow with regard to the displacement of C6F5I parallel to benzene. Therefore, we decided to select the orientation 1a as one of the typical orientations of halogen bond with benzene for studying the halogen dependence of the halogen-π interactions.

Molecular electrostatic potentials The molecular electrostatic potentials were calculated for C6H5Cl, C6F5I, benzene and pyridine by the MP2 method using the cc-pVTZ (Figure S2). The positively charged region of halobenzene has contact with the negatively charged region of benzene in the halogen bond with benzene as well as the halogen bond with pyridine (n-type acceptor).43

Interaction energy between C6F5X and benzene Intermolecular interaction energies of C6F5X (1-4, X is I, Br, Cl, F) with benzene were calculated for studying the effects of halogen atom on the halogen-π interactions. The potential depth depends on the halogen atom strongly (Figure 5). The size of the attraction follows the order I > Br > Cl > F as well as the halogen bond with pyridine (n-type acceptors).

The interaction energy potentials indicate that the attraction decreases slowly with the increase of the intermolecular distance. Even if the molecules are well separated, there exists substantial attraction. This show that long-range interactions are the primary source of the attraction.108

The energies of long-range interactions (electrostatic, induction,

dispersion) behave as some inverse power of the distance (E ~ R-n), as the Coulombic interactions are the origin of the long-range interactions. Orbital-orbital interactions (shortrange interactions: charge-transfer and exchange-repulsion) arise at the distance when the molecular wave functions overlap significantly.92

The energies of orbital-orbital


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interactions decrease rapidly with the increase of distance (E ~ e-αR), as the size of orbitalorbital interactions is nearly proportional to the size of overlap integral. Therefore, the attraction between molecules should decrease rapidly with distance, if the orbital-orbital interactions were the primary source of the attraction.104,109

Interaction energy between C6H5X and benzene Intermolecular interaction energies of C6H5X (5-8, X is I, Br, Cl, F) with benzene were calculated for studying the effects of fluorination of halobenzenes on the halogen-π interactions (Figure 6). The potential depth depends on the halogen atom strongly as well as the interaction of C6F5X with benzene. The size of the attraction follows the same order (I > Br > Cl > F). The calculated potentials show that the fluorination of halobenzenes enhances the attraction, although the attraction in the halogen-π interactions do not necessary need the fluorination of halobenzenes. There exists attraction in the C6H5Xbenzene complexes (5-8), while the attraction in the C6F5X-benzene complexes (1-4) is stronger than that in the corresponding C6H5X-benzene complexes. Interaction energy between CF3X and benzene Intermolecular interaction energies of CF3X (9-12, X is I, Br, Cl, F) with benzene were calculated for studying the halogen-π interactions of haloalkanes (Figure 7). The potential depth calculated for the CF3X-benzene complexes (9-12) is close to the potential depth calculated for the corresponding C6F5X-benzene complexes (1-4).

Interaction energies for halogen-π interactions ECCSD(T)(limit) of C6F5X, C6H5X and CF3X with benzene were estimated for quantitative evaluations of the magnitude of the halogen-π interactions.110 The optimized geometries were used for the estimations.111 Table 1 shows the total interaction energies [Eint = ECCSD(T)(limit)] of the complexes. The Eint depends on the halogen atom strongly. The Eint of C6F5X with benzene (1-4) are -3.24, -2.88, -2.31, -0.92 kcal mol-1. The fluorine atoms on the C6F5X enhance the halogen-π interactions. The Eint of C6H5X with benzene (5-7) are 2.31, -1.97, -1.48 kcal mol-1. The fluorine atoms enhance the attraction nearly the same magnitude (0.93, 0.91, 0.83 kcal mol-1). The Eint of CF3X with benzene (9-12) are -3.11, -


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2.74, -2.22, -0.71 kcal mol-1. The Eint of CF3I and CF3Br with benzene are close to the ECCSD(T)(limit) estimated by Rezac et al. (-3.38 and -2.65 kcal/mol). The Eint of CF3X with benzene (9-12) are very close to the Eint of corresponding C6F5X with benzene (1-4). The differences are smaller than 0.2 kcal mol-1. The Eint of C6F5X and CF3X with benzene (X is I, Br, Cl) are about 50-60 % of that of the water dimer (about -5 kcal mol-1),

The size of the attraction of the halogen-π interactions follows the order (I > Br > Cl > F) as well as the halogen bond with pyridine (n-type acceptor), while the halogen-π interactions are significantly weaker than the corresponding halogen bond with pyridine (13-20) (Table 1). The Eint of C6F5X with pyridine (13-15, X = I, Br and Cl) are -6.29, -4.62, -3.07 kcal mol-1. The halogen-π interactions of fluorine atoms are very weak as well as the halogen bond of fluorine with pyridine. The Eint of C6F6 and CF4 with benzene (4, 12) are -0.92 and -0.71 kcal mol-1. The Eint of C6F6 with is -0.26 kcal mol-1. The halogen dependence of halogen-π interactions is weaker than that of halogen bond with n-type acceptor.

Origin of attraction The size of the electrostatic, induction and dispersion interactions was studied for elucidating the origin of halogen-π interactions. Table 1 compares the electrostatic (Ees) and induction (Eind) energies of C6F5X, C6H5X, CF3X with benzene and those of C6F5X, CF3I, C6H5X with pyridine (halogen bonds with n-type acceptor).43 The interaction energy obtained by the HF method (EHF) is approximately the sum of the electrostatic, induction and orbital-orbital interactions.

Accordingly, the contributions of the orbital-orbital

interactions were discussed based on the Eshort obtained by equation (1)

Eshort = EHF – Ees – Eind (1).89

The effects of electron correlation (Ecorr) was calculated according to equation (2)

Ecorr = Eint – EHF (2),


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where Eint is the interaction energy with the correction of electron correlation. We discuss the magnitude of dispersion interactions based on the size of Ecorr, since the effect of electron correlation (Ecorr) is mainly dispersion energy, although Ecorr includes contributions of some other terms.89,112 The large Ecorr of C6F5X, C6H5X, CF3X with benzene (-0.96 ~ -3.64 kcal mol-1) indicate that the main cause of the attraction in the halogen-π complexes is the dispersion interaction. Compared with the dispersion, the electrostatic and induction interactions are not large. The Ees are 0.63 to -0.29 kcal mol-1 and Eind are -0.02 and -0.35 kcal mol-1. Wallnoefer et al. also suggested the importance of the dispersion in the halogen-π interactions of the C6H5Xtyrosine (X = Br and I) systems.71 On the other hand Rezac et al. concluded that halogen-π interactions were very similar to halogen bond from the calculations of the benzene complexes with CH3Br, CH3I, CF3Br and CF3I.72 The magnitude of dispersion interactions (Ecorr) of C6F5X with benzene (1-4) follows the order I > Br > Cl > F. The same trend is observed in the Ecorr of C6H5X, CF3X with benzene. The order of the magnitude of Ecorr agrees with the order of the size of atomic polarizabilities of halogen atoms. From the comparison of Ees, Eind and Ecorr we can understand that the dispersion is the main source of the halogen dependence of halogen-π interactions.

The comparison of the Ees of C6F5X with benzene (1-3) and that of C6H5X with benzene (57) shows the electron withdrawing fluorine atoms on the halobenzenes enhance the attraction by the electrostatic interactions. The Ecorr of C6F5X with benzene (1-3) are close to those of C6H5X with benzene (5-7). This shows that the change of the electrostatic interaction by the electron withdrawing fluorine atoms is the origin of substituent effects. Analysis of the substituent effects on the interactions of iodobenzenes with pyridine (n-type acceptor) also shows that the electrostatic interactions are the main cause of the substituent effects on halogen bond.44


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The orbital-orbital interactions (Eshort) of C6F5X, C6H5X, CF3X with benzene (X is I, Br, Cl, F) are always repulsive (0.15 to 1.03 kcal mol-1) as well as the halogen bond with n-type acceptor. The Eshort includes exchange-repulsion interactions and attractive charge-transfer interactions. Although the charge-transfer interaction might contribute to the attraction, the overall orbital-orbital interactions in the halogen-π interactions are repulsive. Apparently large contribution of dispersion is the cause of the slow decrease of the attraction in the halogen-π interactions with the increase of the distance.

In contrast to the strong halogen bonds of iodine and bromine with pyridine (n-type acceptor), the primary source of the attraction of the halogen-π interactions is dispersion. The primary source of the attraction in the halogen bonds of C6F5I, C6F5Br with pyridine (13 and 14) is the electrostatic interaction, although the dispersion also contributes to the attraction. The Ees in 13 and 14 are -5.83 and -3.58 kcal mol-1, while the Ecorr are -3.88 and -3.31 kcal mol-1. The Eint (total interaction energy) of C6F5I with benzene and pyridine were calculated with changing the intermolecular distances (Figure 8). The contributions of Ees, Eind, Ecorr and Eshort are also summarized in Figure 8. The Ees and Eind of C6F5I with benzene (Figure 8a) are very small near the equilibrium distance compared with those in the halogen bond of the C6F5I-pyridine complex (Figure 8b). Orientation dependence of interaction The interaction energies of C6F5X (1-3) with benzene were calculated with changing the orientation of molecules for studying the directionality of the halogen-π interactions (Figure 9). The C-X…Y angle (θ) was changed in the calculations. Y is the center of benzene. The intermolecular distance (R) was fixed at the equilibrium intermolecular distance in the calculations. The halogen-π interactions in these complexes show weak directionality. The interaction energies are most negative when θ = 180˚. The interaction energy of C6F5I with benzene at θ = 180˚ is -3.51 kcal mol-1, while that at θ = 120˚ is -2.31 kcal mol-1. The halogen-π interaction of C6F5Br with benzene shows weaker directionality compared with that of C6F5I with benzene. The halogen-π interaction of C6F5Cl with benzene shows negligible directionality. Although the magnitude of the directionality of Eint is very weak, the order of the directionality of Eint (I > Br > Cl) is the same as the order of the magnitude


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of electrostatic interactions. The Ees of C6F5X (X is I, Br, Cl) with benzene are -0.29, -0.20, -0.01 kcal mol-1 (Table 1).

The electrostatic interactions, which are highly directional, are the main cause of the strong orientation dependence of halogen bonds with n-type acceptors and hydrogen bonds.43,113 The electrostatic interaction between neutral molecules can be repulsive or attractive depending on the orientation of molecules, while the dispersion is always attractive. The dependence of the dispersion interaction on molecular orientation is weak in general. The Ees calculated for halogen bonds in the C6F5X-pyridine complexes at the equilibrium distances (X = I, Br and Cl) are -1.94 to -5.83 kcal mol-1, while the Ees for the halogen-π interactions between C6F5X, C6H5X, CF3X and benzene are small (0.63 ~ -0.29 kcal mol-1) (Table 1). Apparently the direction dependence of the halogen-π interactions is weak owing to the weak electrostatic interactions.

The direction dependence of the interaction energy of C6F5X (X is I, Br, Cl) with benzene was compared with that of the halogen bond in the C6F5I-pyridine complex (13) and that of the hydrogen bonds between water and benzene (21) and in the water dimer (22) (Figure 9). The direction dependence of the halogen-π interaction of C6F5I with benzene is slightly weaker than the directionality of the π-hydrogen bond between water and benzene, although the interaction energy of C6F5I with benzene has the strongest direction dependence among the three halogen-π complexes. Compared with the directionality of halogen bond of C6F5I with pyridine and the hydrogen bond in water dimer, the directionality of the interactions in the three halogen-π complexes are significantly weaker.

The directionality of intermolecular interaction is important in determining crystal structures and controlling molecular recognition processes. It is believed that hydrogen bond is one of the important interactions in determining the molecular orientations in molecular assemblies, as the hydrogen bond is sufficiently strong and sufficiently directional.114 Compared with the hydrogen bond of water, the directionality of halogen-π interactions is substantially weak, in contrast to the strong halogen bond of iodine with ntype acceptor (pyridine). These calculations suggest that most of halogen-π interactions are


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not likely to play the dominant role in determining the molecular arrangement in crystals, although the halogen-π interactions observed in crystals increase the stability of crystals associated with other interactions. The directionality of the halogen-π interactions will be enhanced, if the basicity of aromatic ring is increased by electron donating substituents. In such cases the halogen-π interactions may play important roles in determining the crystal structures.

Conclusion Interactions of C6F5X, C6H5X, CF3X with benzene (halogen-π interactions) were studied by CCSD(T) calculations. (1) The interaction energies of C6F5X, CF3X (X = I, Br, Cl) with benzene are -2.31 to -3.24 kcal mol-1, which are about 50-60 % of the hydrogen bond (water dimer). The interaction energy between C6H5X and benzene complexes are weaker (-1.48 to -2.31 kcal mol-1). The halogen-π interactions of fluorine are very weak. (2) The magnitude of halogen-π interactions follows the order I > Br > Cl > F, which is the same as the halogen bond with n-type acceptors. The dispersion interactions mainly determine the magnitude of halogen-π interactions. The dependence of the halogen-π interaction on halogen atom is weaker than that of halogen bond with n-type acceptor. (3) The dispersion interactions in the halogen-π interactions are significant in contrast to the strong halogen bonds between iodine or bromine and n-type acceptors, in which the electrostatic interaction is the main source of the attraction. The electrostatic interactions and induction interactions in the halogen-π interactions are small. The overall orbital-orbital interactions are repulsive.

(4) The dependence of the halogen-π interactions on the molecular

orientation is weak owing to the weak electrostatic interactions. The dependence of the halogen-π interactions of bromine is weaker than that of iodine. The directionality of the halogen-π interactions of chlorine is negligible. (5) The fluorination of halobenzenes enhance the attraction in the halogen-π interactions as well as the halogen bonds with ntype acceptors.

The enhancement of the electrostatic interactions is the cause of the

increase of the attraction.

Acknowledgments


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We are grateful for the provision of the computational facilities from Tsukuba Advanced Computing Center. This work was supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “Advanced Molecular Transformations by Organocatalysts” from The Ministry of Education, Culture, Sports, Science and Technology, Japan.

Supporting Information Available Procedures for estimating the MP2 and CCSD(T) level interaction energies for the halogenπ complexes at the basis set limit. Evaluation of the accuracy of the estimated CCSD(T) level interaction energy at the basis set limit. Interaction energy potentials for the C6F5IC6H6 complex using several methods. This material is available free of charge via the Internet at http://pubs.acs.org.


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(66) Lu, Y.-X.; Zou, J.-W.; Wang, Y.-H.; Yu, Q.-S. Substituent effects on noncovalent halogen/π interactions: Theoretical study  Int. J. Quant. Chem. 2007, 107, 1479-1486. (67) Shishkin, O. V. Evaluation of true energy of halogen bonding in the crystals of halogen derivatives of trityl alcohol Chem. Phys. Lett. 2008, 458, 96-100. (68) Xu, L.; Zou, J.-W.; Lu, Y.-X.; Yu, Q.-S.; Zhang, N. Halogen/π interaction and cooperativity effect between dihalogen molecules and unsaturated hydrocarbons: An ab initio study J. Mol. Struct. THEOCHEM 2009, 897, 12-16. (69) Esrafili, M. D.; Mahdavinia, G.; Javaheri, M.; Sobhi, H. R. A theoretical study of substitution effects on halogen–π interactions Mol. Phys. 2013, 112, 1160-1166. (70) Mebel, A. M.; Lin, H. L.; Lin, S. H. Ab initio molecular orbital and density functional study of the C6H6…I2 complex in the ground and excited electronic states Int. J. Quant. Chem. 1999, 72, 307-318. (71) Wallnoefer, H. G.; Fox, T.; Liedl, K. R.; Tautermann, C. S. Dispersion dominated halogen-π interactions: energies and locations of minima Phys. Chem. Chem. Phys., 2010, 12, 14941-14949. (72) Řezáč, J.; Riley, K. E.; Hobza, P. Benchmark calculations of noncovalent interactions of halogenated molecules J. Chem. Theory Comput. 2012, 8, 4285-4292. (73) Wolters, L. P.; Schyman, P.; Pavan, M. J.; Jorgensen, W. L.; Bickelhaupt, F. M.; Kozuch, S. The many faces of halogen bonding: a review of theoretical models and methods Wiley Interdisciplinary Reviews: Computational Molecular Science, 2014, 4, 523540. (74) Riley, K. E.; Ford Jr., C. L.; Demouchet, K. Comparison of hydrogen bonds, halogen bonds, C-H…π interactions, and C-X…π interactions using high-level ab initio methods Chem. Phys. Lett., 2015, 621, 165-170. (75) Dunning Jr., T. H. A road map for the calculation of molecular binding energies J. Phys. Chem. A, 2000, 104, 9062-9080. (76) Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K. Origin of attraction and directionality of the π/π interaction: Model chemistry calculations of benzene dimer interaction J. Am. Chem. Soc. 2002, 124, 104-112.


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(77) Tsuzuki, S.; Fujii, A. Nature and physical origin of CH/π interaction: significant difference from conventional hydrogen bonds A. Phys. Chem. Chem. Phys. 2008, 10, 25842594. (78) Tsuzuki, S.; Lüthi, H. P. Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory: Assessing the PW91 model J. Chem. Phys. 2001, 114, 3949-3957. (79) Gaussian 09, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; et al. Gaussian, Inc., Wallingford CT, 2009. (80) Mφller, C.; Plesset, M. S. Note on an approximation treatment for many-electron systems Phys. Rev. 1934, 46, 618-622. (81) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. MP2 energy evaluation by direct methods Chem. Phys. Lett. 1988, 153, 503-506. (82) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. Quadratic configuration-interaction A general technique for determining electron correlation energies J. Chem. Phys. 1987, 87, 5968-5975. (83) Ransil, B. J. Studies in molecular structure 4. Potential curve for interaction of 2 helium atoms in single-configuration LCAO SCF approximation J. Chem. Phys. 1961, 34, 2109-2118. (84) Boys, S. F.; Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors Mol. Phys. 1970, 19, 553-566. (85) The depth of the interaction energy potentials calculated for the halogen-π interactions depend on the choice of the basis set. The MP2 level potentials calculated for the C6F5Ibenzene complex (1) is shown in Figure S1 in supporting information. Although the depth of the potential depends on the basis set strongly, the basis set dependence of the equilibrium intermolecular distance is not large. The equilibrium intermolecular distance obtained by the MP2/6-311G* level calculations is close to the equilibrium distance of the potential obtained by the CCSD(T) level interaction energies at the basis set limit (CCSD(T)/limit). It is well known that the MP2 calculations overestimate the dispersion interactions of aromatic molecules compared with more reliable CCSD(T) calculations.


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The MP2 calculations using larger basis sets overestimate the attraction compared with the CCSD(T)/limit.

The medium size 6-311G* basis set underestimates the dispersion

interaction compared with the basis set limit. The MP2/6-311G* level potential is rather close to the CCSD(T)/limit level potential owing to the error cancellation. The geometry optimizations of the halogen-π complexes using CCSD(T) calculations using a large basis set are not practical, as they are highly computationally demanding. Therefore, we used the MP2/6-311G* level optimized geometries of the complexes for the evaluation of the interaction energies. (86) Godbout, N.; Salahub, D. R.; Andzelm, J; Wimmer, E. Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation Can. J. Chem., 1992, 70, 560-571. (87) Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. Basis-set convergence of correlated calculations on water J. Chem. Phys. 1997, 106, 9639-9646. (88) Further improvement of the basis sets does not largely change the MP2 interaction energy at the basis set limit [EMP2(limit)] estimated by Helgaker et al.’s method. The MP2 level interaction energies (EMP2) calculated for the C6F5Br-benzene complex using the augcc-pVDZ, aug-cc-pVTZ and aug-cc-pVQZ basis sets are -3.386, -3.677 and -3.809 kcal/mol, respectively. The EMP2(limit) estimated for the C6F5Br-benzene complex from the EMP2 obtained using the aug-cc-pVDZ and aug-cc-pVTZ basis sets (-3.799 kcal/mol) is very close to the EMP2(limit) estimated from the EMP2 obtained using the aug-cc-pVTZ and aug-ccpVQZ basis sets (-3.905 kcal/mol). The difference is only 0.106 kcal/mol. The basis set effect beyond the aug-cc-pVTZ on the calculated HF level interaction energy (EHF) is negligible. The EHF calculated for the C6F5Br-benzene complex using the aug-cc-pVTZ and aug-cc-pVQZ basis sets are 0.521 and 0.520 kcal/mol, respectively. The aug-cc-pVTZ basis set is nearly saturated for the calculation of EHF.

Therefore, we used the EHF

calculated using the aug-cc-pVTZ basis set as the EHF at the basis set limit. The error of the estimated EMP2(limit) associated with this assumption is not large. (89) Tsuzuki, S.; Sato, N. Origin of attraction in chalcogen-nitrogen interaction of 1,2,5chalcogenadiazole dimers J. Phys. Chem. B 2013, 117, 6849-6855.


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(102) Tsuzuki, S. CH/π interactions; Annual Reports on the progress of Chemistry 2012 Volume 108 Section C (Physical Chemistry), RSC Publishing: Cambridge, 2012. (103) Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M.; Tanabe, K. Origin of the attraction and directionality of the NH/π interaction: Comparison with OH/π and CH/π interactions J. Am. Chem. Soc. 2000, 122, 11450-11458. (104) Tsuzuki, S.; Uchimaru, T.; Mikami, M. Magnitude of CH/O interactions between carbohydrate and water Theor. Chem. Acc., 2012, 131, 1192. (105) Tsuzuki, S.; Uchimaru, T.; Mikami, M. Magnitude and nature of carbohydratearomatic interactions: Ab initio calculations of fucose-benzene complex J. Phys. Chem. B 2009, 113, 5617-5621. (106) Tsuzuki, S.; Uchimaru, T.; Mikami, M. Magnitude and nature of carbohydratearomatic interactions in fucose-phenol and fucose–indole complexes: CCSD(T) level interaction energy calculations J. Phys. Chem. A 2011, 115, 11256-11262. (107) Shibasaki, K.; Fujii, A.; Mikami, N.; Tsuzuki, S. Magnitude of the CH/π interaction in the gas phase: Experimental and theoretical determination of the accurate interaction energy in benzene-methane J. Phys. Chem. A 2006, 110, 4397-4404. (108) Tsuzuki, S.; Mikami, M.; Yamada, S. Origin of attraction, magnitude, and directionality of interactions in benzene complexes with pyridinium cations J. Am. Chem. Soc. 2007, 129, 8656-8662. (109) The energy of short-range interactions depends not only on R but also α. The energy does not decrease rapidly, if α was very small. (110) The geometry optimization of the C6H5F-benzene complex at the MP2/6-311G* level did not succeed owing to the very weak attraction. (111) The geometries for the benzene complexes with halobenzenes were optimized without constraint. However, the optimized geometries for the benzene complexes with C6F5X and C6H5X have C2v symmetry and those for the CF3X-benzene complexes have C3v symmetry, as the initial geometries for the optimizations have C2v or C3v symmetry, respectively. (112) Tsuzuki, S.; Uchimaru, T.; Mikami, M.; Kitagawa, H.; Kobayashi, K. Mechanism of orientational isomerism of unsymmetrical guests in heterodimeric capsule: Analysis by ab initio molecular orbital calculations J. Phys. Chem. B 2010, 114, 335-5341.


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(113) Tsuzuki, S. Origin of attraction and directionality of hydrogen bond and halogen bond: analysis by ab initio MO calculations AIP Conference Proceedings, 2015, 1702, 090044. (114) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond; Oxford University Press: New York, 1999.


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Table 1. Electrostatic, Induction, Short-range and Dispersion Interactions of Halogen-π interactions and Halogen Bonds with Pyridinea C6F5I-benzene (1) C6F5Br-benzene (2) C6F5Cl-benzene (3) C6F6-benzene (4) C6H5I-benzene (5) C6H5Br-benzene (6) C6H5Cl-benzene (7) CF3I-benzene (9) CF3Br-benzene (10) CF3Cl-benzene (11) CF4-benzene (12) C6F5I-pyridine (13)g C6F5Br-pyridine (14)g C6F5Cl-pyridine (15)g C6F6-pyridine (16)g CF3I-pyridine (17)g C6H5I-pyridine (18)g C6H5Br-pyridine (19)g C6H5Cl-pyridine (20)g

Eintb -3.24 -2.88 -2.31 -0.92 -2.31 -1.97 -1.48 -3.11 -2.74 -2.22 -0.71 -6.29 -4.62 -3.07 -0.26 -5.99 -3.57 -2.39 -1.33

Eesc -0.29 -0.20 -0.01 0.31 0.50 0.49 0.63 -0.25 -0.20 -0.09 0.11 -5.83h -3.58h -1.94h 0.25h -5.61h -2.73h -1.22h -0.18h

Eindd -0.34 -0.20 -0.11 -0.03 -0.13 -0.08 -0.05 -0.35 -0.20 -0.11 -0.02 -1.68h -0.95h -0.48h -0.04h -1.55h -0.82h -0.48h -0.26h

Eshorte 1.03 0.92 0.60 0.30 0.66 0.73 0.42 0.65 0.57 0.29 0.15 5.11 3.22 1.72 0.11 4.29 3.30 2.05 1.00

Ecorrf -3.64 -3.40 -2.79 -1.50 -3.34 -3.11 -2.47 -3.17 -2.91 -2.31 -0.96 -3.88 -3.31 -2.36 -0.58 -3.12 -3.31 -2.73 -1.90

a

Energy in kcal mol-1.

b

Estimated CCSD(T) interaction energy at the basis set limit. See text.

c

Electrostatic energy. See text.

d

Induction energy. See text.

e

Short-range (orbital-orbital) interaction energy (= EHF - Ees - Eind). HF/aug-cc-pVTZ level

interaction energy was used as the EHF. Eshort is mainly the sum of the contributions of exchange-repulsion and charge-transfer interactions. See text. f

Contribution of electron correlation on the interaction energy (= Eint - EHF). Ecorr is mainly

dispersion energy. See text. g

Geometries of the complexes were taken from reference 43.

h

Reference 43.


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Figure 1. Effects of basis set on the calculated interaction energies for the C6F5I-benzene complex (1).


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Figure 2. Effects of electron correlation correction procedure on the calculated interaction energies for the C6F5I-benzene complex (1). The cc-pVDZ basis set was used for the calculations. The geometry of the complex is shown in Figure 1.


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Figure 3. The interaction energies calculated for the C6F5I-benzene complex (1) by the DFT methods using dispersion corrected functionals. The geometry of the complex is shown in Figure 1.


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Figure 4. The interaction energies calculated for three orientations of C6F5I-benzene complex (1a-1c). The interaction energies were calculated at the MP2/cc-pVTZ level.


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Figure 5. Interaction energies calculated for the C6F5X-benzene complexes (X = I, Br, Cl and F) (1-4). The interaction energies were calculated at the MP2/cc-pVTZ level.


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Figure 6. Interaction energies calculated for the C6H5X-benzene complexes (X = I, Br, Cl and F) (5-8). The interaction energies were calculated at the MP2/cc-pVTZ level.


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Figure 7. Interaction energies calculated for the CF3X-benzene complexes (X = I, Br, Cl and F) (9-12). The interaction energies were calculated at the MP2/cc-pVTZ level.


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Figure 8. Total interaction energy (int) and contributions of electrostatic (es), induction (ind), correlation (corr) and short-range (short) interactions calculated for a) C6F5I-benzene complex (1) and b) C6F5I-pyridine complex (13). Total interaction energy was calculated at the MP2/cc-pVTZ level.


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Figure 9. Direction-dependence of the interaction energies for the C6F5X-benzene complex (X = I, Br and Cl) (1-3), C6F5I-pyridine complex (13), water-benzene (21) and water dimer (22). The interaction energy potentials were calculated at the MP2/cc-pVTZ level with changing θ. The intermolecular distances (R) for 1, 2, 3, 13, 21 and 22 are fixed at 3.0, 2.2, 3.2, 3.0, 2.4 and 2.0 Å, respectively. These distances correspond to the intermolecular distances at the potential minima. The φ was fixed at 63˚ in the calculations.


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