CX4 (X = Cl, Br

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Halogen-# Interactions Between Benzene and X/CX (X = Cl, Br): Assessment of Various Density Functionals with Respect to CCSD(T) Il-Seung Youn, Dong Yeon Kim, Woo Jong Cho, Jenica Marie L. Madridejos, Han Myoung Lee, Maciej Kolaski, Joonho Lee, Chunggi Baig, Seung Koo Shin, Michael Filatov, and Kwang S. Kim J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09395 • Publication Date (Web): 01 Nov 2016 Downloaded from http://pubs.acs.org on November 2, 2016

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The Journal of Physical Chemistry

Halogen-π Interactions Between Benzene and X2/CX4 (X = Cl, Br): Assessment of Various Density Functionals with Respect to CCSD(T) Il Seung Youn,‡,a Dong Yeon Kim,‡,b Woo Jong Cho,‡,a Jenica Marie L. Madridejos,a Han Myoung Lee,a Maciej Kołaski,c,d Joonho Lee,c,e Chunggi Baig,b Seung Koo Shin,c Michael Filatov,a and Kwang S. Kim*,a

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to) *Corresponding author: [email protected] ‡

a

These authors contributed equally to this work.

Center for Superfunctional Materials, Department of Chemistry, Ulsan National Institute of

Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Korea b

Department of Chemical Engineering, Ulsan National Institute of Science and Technology

(UNIST), 50 UNIST-gil, Ulsan 44919, Korea c

Department of Chemistry, Pohang University of Science and Technology, Pohang 37673,

Korea d

Department of Theoretical Chemistry, Institute of Chemistry, University of Silesia, 9

Szkolna Street, 40-006 Katowice, Poland e

Department of Chemistry, University of California, Berkeley, CA 94720-1460, USA

Supporting Information

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ABSTRACT Various types of interactions between halogen (X) and π moiety (X-π interaction) including halogen bonding play important roles in forming the structures of biological, supramolecular, and nanomaterial systems containing halogens and aromatic rings. Furthermore, halogen molecules such as X2 and CX4 (X = Cl/Br) can be intercalated in graphite and bilayer graphene for doping and graphene functionalization/modification. Due to the X-π interactions, though recently highly studied, their structures are still hardly predictable. Here, using the coupled-cluster with single, double, and non-iterative triple excitations (CCSD(T)), the Møller-Plesset second order perturbation theory (MP2), and various flavors of density functional theory (DFT) methods, we study complexes of benzene (Bz) with halogen-containing molecules X2 and CX4 (X = Cl/Br) and analyze various components of the interaction energy using symmetry adapted perturbation theory (SAPT). As for the lowest energy conformers (S1), X2-Bz is found to have the T-shaped structure where the electro-positive X atom-end of X2 is pointing to the electro-negative midpoint of CC bond of the Bz ring, and CX4-Bz has the stacked structure. In addition to this CX4-Bz (S1), other low energy conformers of X2-Bz (S2/S3) and CX4-Bz (S2) are stabilized primarily by the dispersion interaction, while the electrostatic interaction is substantial. Most of the density functionals show noticeable deviations from the CCSD(T) complete basis set (CBS) limit binding energies, especially in the case of strongly halogen-bonded conformers of X2Bz (S1), while the deviations are relatively small for CX4-Bz where the dispersion is more important. The halogen bond shows highly anisotropic electron density around halogen atoms and the DFT results are very sensitive to basis set. The unsatisfactory performance of many density functionals could be mainly due to less accurate exchange. This is evidenced from the good performance by the dispersion corrected hybrid and double hybrid functionals. B2GPPLYP-D3 and PBE0-TS(Tkatchenko-Scheffler)/D3 are well suited to describe the X-π interactions adequately, close to the CCSD(T)/CBS binding energies (within ~1 kJ/mol). This understanding would be useful to study diverse X-π interaction driven structures such as halogen containing compounds intercalated between 2 dimensional layers.

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INTRODUCTION The halogen bond is a noncovalent interaction between a halogen atom with an electrophilic region and a Lewis base with a nucleophilic region.1,2 Since the discovery of crystal structures showing close contacts between halogen atoms and Lewis bases,3,4 the halogen bond has received considerable attention due to its important role in biological systems,5-12 crystal engineering,13-16 and materials science.17-26 Chemists have regarded halogen atoms as negatively charged atoms in organic molecules because of their electronegativity. Thus, it might seem counter-intuitive that halogens were attracted to other nucleophilic groups in the molecule. To explain this attraction, Politzer et al. have introduced the concept of σ-hole;27-30 which is a region of positive electrostatic potential at the tip of the σ-bond axis in a molecule. In this sense, the halogen bond was considered to be governed mainly by the electrostatic interaction although dispersion, polarization, and charge-transfer effects seem to also play a role in these interactions, based on intermolecular perturbation theory calculations using small basis sets.31 Even though the main contribution to the halogen bonding was considered to be the electrostatic energy, the geometries could be largely determined by not only electrostatics but also exchange repulsion.32 Meanwhile, halogen bonding interactions were also considered to be dispersive in nature, although electrostatic contributions are not negligible.33 In recent studies,34-36 certain inaccuracies of DFT methods in describing halogen bond energies were noted; in particular, the delocalization error of approximate functionals may lead to overestimation of the halogen bond.36 To discuss with diverse interactions between X atom and π moiety, here we denote such general cases as X-π interactions which of course include halogen bond as a special case. The X-π interactions frequently appear in ligand-protein complexes,37-39 supra-molecular systems,40-45 and halogen-adsorbed carbon compounds such as graphene (or graphite)46-52 and nanotubes.53,54 Analyses of the protein database have shown that the X-π interaction plays a crucial role in stabilizing the ligand-protein complexes. Besides, the X-π interaction is a major factor forming the halogen-adsorbed/intercalated carbon compounds. In these cases, the X-π type interaction is the combination of electrostatic and dispersion interactions.37 Matter et al.38 reported that the dispersion interaction (not electrostatic interaction) was the major source of attraction, which also led to a relatively weak angular dependence and short

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binding distance. However, despite the recent effort in investigating the nature of X-π interactions,38,55-57 the origin of these interactions still remains poorly understood. To fill this gap, we have investigated interaction of X2 and CX4 (X = Cl, Br) with benzene (Bz) to analyze the origin of the X–π interactions in these systems. These halogencontaining molecules are non-polar, which simplifies the analysis of X-π interactions, as the relatively strong dipole-quadrupole interactions are not present in these complexes. The binding energies of halogen–benzene complexes were calculated using a variety of ab initio methods and the components of the interaction energy were analyzed using the DFTSAPT58,59 methodology. The exact CCSD(T)/CBS limit binding energies and the SAPT energy decompositions were used to assess the accuracy of various density functionals for the calculation of X-π interactions in organic aromatic systems.

COMPUTATIONAL DETAILS The geometries of the low energy conformers of X2-Bz and CX4-Bz complexes were determined in a two-step procedure, which started from prescreening of possible conformations using relatively inexpensive dispersion-corrected DFT (DFT-D3) geometry optimizations followed by the resolution of identity (RI) MP2 calculations employing the aug-cc-pVNZ (aVNZ; N = D, T, Q) basis sets. Initially, a large number of possible conformations were generated and only a few low energy conformations survived the prescreening, as shown in Figure 1. The vibrational frequency analysis was carried out to ensure that the conformations are global (S1) or local (S2. and S3) minima on the potential energy surface. In the next step, the geometries of the low-energy conformers of X2-Bz (Figure 1a-1c) and CX4-Bz (figure 1d-1e) were optimized using the basis set superposition error (BSSE)-corrected (BSSEc) MP2/aVDZ and MP2/aVTZ methods. At the BSSEc MP2/aVTZ geometries, the MP2 CBS-limit binding energies were obtained by the N-3 extrapolation using the aVNZ (N = T, Q) basis set.60-63 The geometry was further refined by optimization of the distance between X2/CX4 and Bz at the CCSD(T)/aVTZ level. Then the CCSD(T)/CBS binding energy was extrapolated using the CCSD(T)/aVTZ value by adding the change of the MP2/CBS energy from the MP2/aVTZ energy. The CCSD(T)/CBS energies were used as the most accurate reference values when evaluating the accuracy of DFT methods. As the DFT correlation energy does not strictly 4


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follow the N-3 dependence on the aVNZ, the DFT CBS energies were obtained using the least-biased pseudo-interpolation approach which connects the BSSEc energy (Eb) and BSSE-uncorrected (BSSEu) energy (Eu) at 1/N = 0 (i.e., N = ∞).61-63 These asymptotic values are labeled CBS*, and are calculated by the equation ECBS* = (δNεN+1 – δN+1εN) / (δN – δN+1), where εN [= (EbN+EuN)/2] is the median value of Eb and Eu, while δN [= (EbNEuN)] is the BSSE. The pseudo-interpolated energies can be calculated using any other series of basis sets of increasing size as well as aVNZ series. The pseudo-interpolated CBS* energies (which is applicable to any type of calculations using two different basis sets) are typically very close (within 0.1 kJ/mol in the present systems) to the CBS values obtained using a traditional N-3 extrapolation scheme in the cases of MP2 and CCSD(T) calculations.61 To understand the nature of bonding in the X2-Bz and CX4-Bz complexes, decomposition of the interaction energy was carried out using the DFT-SAPT method which is known to yield reliable energy components when employed in connection with the asymptotically corrected PBE0 (PBE0AC)64 exchange-correlation (xc) functional, where adiabatic local density approximation (ALDA)65 xc kernel was applied for induction and dispersion components and their exchange counterparts. Here we use the following notations: Ees (electrostatic energy), Eind* (effective induction energy including the induction-induced exchange energy; Eind*= Eind + Eind-exch, Edisp* (effective dispersion energy including the dispersion-induced exchange energy; Edisp*= Edisp + Edisp-exch), Eexch* (effective exchange repulsion energy with the induction-induced and dispersion-induced exchange energies excluded; Eexch*= Eexch - (Eind-exch +Edisp-exch) = Eexch1), δH (contribution of the third and higher order terms at the uncorrelated level, which could be included into Eind*), and Eint (total interaction energy).62,66 All-electron aVDZ and aVTZ basis sets were employed for the DFTSAPT calculations except Br for which we used aug-cc-pVNZ-pp.67 The following xc density functionals were employed in the DFT calculations: B97

68,69

-D3, TPSS70-D3, PBE71-D3, BLYP72-D3, BP8673-D3, PBE074-D3, HSE0675-D3,

B3LYP76-D3, ωB97X-D,77 M06-2X,78 B2-PLYP79-D3, B2GP-PLYP80-D3, PBE-TS, PBE0TS, OptB86b-vdW-DF,81 and rPW86+vdW-DF2,82,83 where D3 stands for the Grimme’s D3 5



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dispersion correction scheme84 and TS for the Tkatchenko-Scheffler dispersion correction scheme.85 For the case of M06-2X functionals, which are known to have sensitive in accordance with the choice of grid, we used default grid size, FineGrid(75,302), having 75 radical shells and 302 angular points per shell. The calculations were carried out by using the program codes of Turbomole,86 Gaussian09,87 Molpro,88 Fritz Haber Institute ab initio molecular simulations (FHI-AIMS),89 Orca,90 and Vienna Ab-initio Simulation Package (VASP).91,92 FHI-AIMS was used for calculations using the TS dispersion correction with light tier 2 and 3 basis sets (simply denoted as tier 2 and 3 hereafter). VASP was used for vdW-DF, vdW-DF2, B3LYP-D3, PBE-D3, PBE0-D3, HSE06-D3, PBE-TS and PBE0-TS with 30×30×30 unit cell using the kinetic energy cutoff of 500 eV for the plane wave (PW) basis set and the projected augmented wave (PAW) pseudopotentials.93,94 Most of the DFTD3 methods were calculated using Turbomole, and DFT-SAPT analysis was carried out using Molpro. The optimized geometries were drawn using the Posmol molecular visualization and analysis package.95

RESULTS & DISCUSSION Three distinct lowest energy conformers of the X2-Bz complex are shown in Figure 1. In the S1 conformer, the X2 molecule is almost perpendicular to the benzene ring and lies above the center of the C-C bond of the aromatic ring. In this case, the electro-positive X atom-end of X2 is pointing to the electro-negative midpoint of CC bond of the Bz ring along with significant dispersion energy, resulting in forming strong halogen bond. Based on quantum theory of atoms in molecules (QTAIM) analysis,96 the S1 confomer shows the presence of bond critical point ((3,-1) BCP) of the halogen bond (see Figures S2-S3 in Supporting Information). In the S2 conformer, X2 is nearly parallel to the plane of aromatic π-electrons, but displaced from the benzene centroid, showing no halogen bond. In the S3 conformer, X2 is on the lateral position with respect to the aromatic ring, where one might address very weak hydrogen bonding between H atoms and X2 bond instead of halogen bonding. At the CCSD(T)/CBS level, S1 has the largest binding energy for X = Cl/Br (12.73/16.22 kJ/mol) followed by S2 (8.79/10.34 kJ/mol) and S3 (6.48/7.24 kJ/mol) (see Table 1). If only dispersion interaction was considered as the major component of binding between the two molecules, this trend could not be easily explained because the dispersion 6


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interaction in S2 (where both X atoms in X2 face the delocalized π-electrons of benzene) is similar to or smaller than that in S1 (where only one end of X2 is pointing toward the πelectron cloud of benzene) (see the DFT-SAPT energy components in Table 2). Although CX4-Bz may seem to have various low-lying conformers, only two stable conformers (S1 and S2 in Figure 1) out of twelve trial geometries have survived the prescreening procedure described in the previous section. The most stable S1 conformer of CX4-Bz is characterized not by the halogen bond between the C-X bonds and the π-electron cloud of benzene ring (because the angle of CBr···Bz is not linear but almost perpendicular) but by strong dispersion and weak electrostatic interactions. The three X atoms of CX4 is stacked above the Bz ring, while the C atom of CX4 is stacked above the C atom in Bz. One electro-positive region along the X atom-end of CX4 is energetically stabilized in the electronegative potential above the C atom across the above C atom in Bz, while two electronegative regions below two X atoms (due to somewhat perpendicular direction to the C-X bond) are stabilized in the electro-positive outer-surface surrounding the H atoms of the Bz ring (see Figure 2 and Figures S4-S5). The S2 conformation of CX4-Bz does not form any halogen bond, but shows very weak H···X hydrogen bond. Thus, the S1 conformer has much larger electrostatic energy than the S2, while both S1 and S2 have very large dispersion energies (see the DFT-SAPT energy components in Table 2). As in the case of X2-Bz, the S1 structure of CX4-Bz shows relatively large CCSD(T)/CBS binding energy of 13.64/14.99 kJ/mol for X=Cl/Br, while the S2 structure shows somewhat smaller binding energy of 8.13/9.41 kJ/mol (Table 1). For all the conformations of X2-Bz and CX4-Bz, DFT-SAPT reproduces the CCSD(T)/CBS interaction energies reasonably well (Table 2). The dispersion energy gives the largest contribution to the attractive interaction for all the conformers, except for the S1 conformer of X2-Bz where the electrostatic component is as large as the dispersion component. The electrostatic attraction increases as X changes from Cl to Br, and the induction term cannot be neglected for X = Br. In the S1 conformation of CX4-Bz, the electrostatic interaction component is weaker than the dispersion energy; however it is still comparable in magnitude to the overall interaction energy.

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As both X2 and CX4 do not have dipole moments and cannot properly establish significant hydrogen bonds (except for very weak ones) with Bz, the only plausible reason for the strong electrostatic interaction is the halogen bond in the case of X2-Bz. In the present model systems, the σ-hole (positive electrostatic potential) on the tips of X2 and CX4 molecules attracts the π electron cloud of the benzene ring, as shown in the plots of electrostatic potentials (Figure 2). It is well-known that the strength of the halogen bond depends on (i) the kind of X, (ii) the chemical environment surrounding X, and (iii) the bond directionality. If the s-contribution to the σ orbital is very small and X is bonded to an electron-withdrawing group, the positive potential part on the tip of the halogen atom is pronounced.30 The halogen bonding, which originates from the interaction of the σ-hole on the tips of X2 with the π electrons of the benzene ring, is present in the lowest conformer S1(X2-Bz). As the Br atom is less electronegative and has a more diffuse valence charge distribution than Cl, it provides a more pronounced σ-hole that leads to stronger halogen bonding in the case of Br. In the S1 conformers, both electrostatic interaction (mainly due to halogen bond) and dispersion interaction contribute equivalently to the overall interaction energy, and the bonding in this conformer is sensitive to the orientation of σ hole with respect to the benzene ring. In the S2 and S3 conformers, the dispersion energy becomes more important, and consequently the halogen bond weakens by losing the optimally oriented conformation; thus, much of the orientation dependence is lost compared to the S1 conformation. As the σ-hole orientation is not favorable in the CX4-Bz complexes, the halogen bond does not exist. The origin of the strong electrostatic interaction (Ees) in X2-Bz (S1) can be partly explained with multipole interactions which strongly reflect the electrostatic nature of halogen bonding. We derived an equation to evaluate quadrupole-quadrupole (Q-Q) interaction energy to compare with the DFT-SAPT Ees for Cl2-Bz (S1) (see Figure S1 in Supporting Information). If centers of mass of two monomers are separated far enough (over ~6 Å), the electrostatic interactions can be simply represented as Q-Q interaction energies; two results are very close to each other in the long distance range. At the minimum energy point (where the distance between the centers of mass of monomers is ~4.28 Å), the deviation between Q-Q interaction energies and DFT-SAPT Ees is only ~5 kJ/mol, indicating that the Q-Q interaction is the major contribution to the Ees of the halogen bond in X2-Bz systems. 8


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Likewise, we can expect that the quadrupole-octopole (Q-O) interaction is not negligible in CX4-Bz where both dipole and quadrupole moments of CX4 are zero. The above concept can also provide a plausible explanation why the directionality is significant in halogen bond. For stronger electrostatic interactions, both quadrupoles should align along the z-axis, which corresponds to the vertical X2 molecule on the Bz plane. Namely, the halogen bond is favored when the σ hole is pointing directly to the π electron cloud. Consequently, the strongest halogen interaction is observed in X2-Bz, whereas the orientation of σ holes at the tips of C-X bonds in CX4-Bz is not so favorable (see Figures 1 and 2). Hence, the relative contribution of electrostatic interaction in comparison with dispersion is less significant for CX4-Bz than for X2-Bz (see Table 2). The dispersion energy produced by the DFT-SAPT calculations is larger in S1 than in any other conformations of X2-Bz. This seems unexpected because in S2 conformation, X2 is parallel to the benzene molecule and has a larger surface area facing the π-electron cloud than in S1. However, the greater attraction due to the halogen bond in S1 causes a shortening of the X2···Bz distance, which in turn results in strengthening of the dispersion interaction. This strengthening however is outweighed by the increase in exchange repulsion. The binding energies of Cl2-Bz, Br2-Bz, CCl4-Bz, and CBr4-Bz computed by DFT methods along with the deviations from the reference CCSD(T)/CBS values are collected and described in Supporting Information (Tables S1–S5). For most density functionals, the errors in binding energies are huge for the X2-Bz (S1) conformers involving in strong halogen bonding, while small for X2-Bz (S2, S3) conformers and CX4-Bz (S1, S2) conformers. In addition, despite that the BSSE in DFT is generally small in most chemical systems, very large BSSEs are noticed in halogen-bonded complexes. In view of overall energy analysis for all the conformers of X2-Bz (S1, S2, S3) and CX4-Bz (S1, S2) studied here, Figure 3 displays the deviations (∆∆E = ∆EDFT - ∆ECCSD(T)/CBS) of various DFT binding energies (based on CBS* for the Gaussian basis sets, tier3 for TS dispersion correction, or 500eV-cut-off for PW) from the CCSD(T)/CBS binding energies. Also, to compare the performances of diverse DFT functionals based on various basis sets, Table 3 shows the mean absolute deviation (MAD) and root-mean-squared deviation (RMSD) in kJ/mol in the case of five conformers of X2-Bz (S1, S2, S3) and CX4-Bz (S1, S2) and in 9



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the case of two global minimum energy conformers of X2-Bz (S1) and CX4-Bz (S1). The double hybrid functional of B2GP-PLYP-D3 (MAD/RMSD in kJ/mol = 0.51/0.65 for CBS*) and the hybrid functional of PBE0-TS (0.44/0.61 for the PW with the 500 eV cut off energy; 0.52/0.74 and 0.54/0.75 for the tier3 and tier2 basis sets) perform very well. PBE0/D3 (0.65/0.79 for CBS*) and B2-PLYP-D3 (0.69/0.84 for CBS*) also perform well. These are followed by HSE06-D3 (0.73/0.97 for PW/500eV, 0.77/0.97 for CBS*), B3LYP-D3 (0.95/1.08 for CBS*, 1.39/1.71 for PW/500eV using PAW pseudopotentials). The good performance of double hybrid and hybrid functionals indicates that exchange is critical in describing X-π interactions accurately. Highly time-consuming calculation methods of M06-2X (1.32/1.42) and ωB97X-D (1.90/2.20) functionals based on CBS* perform moderately. However, though BSSEc M062X (1.36/1.42 for aVTZ) and BSSEu M06-2X (4.04/4.16 for aVDZ) behave poorly, it is interesting to note that BSSEu M06-2X (0.43/0.49 for aVTZ) and BSSEc M06-2X (0.84/0.91 for aVDZ) perform very well, as equivalent as B2GP-PLYP-D3/CBS*. Thus this less timeconsuming calculation approach using small basis sets could be a useful choice for the study of complex systems, though such close agreements could be rather fortuitous because the accuracy arises from the cancellation of errors. Among the GGAs tested here, PBE-TS (1.17/1.49 for tier3, 1.19/1.73 for tier2, 1.24/1.78 for PW) performs the best despite its small basis set size. It is followed by PBE-D3 (1.53/2.08), TPSS-D3 (1.55/2.17), and B97-D3 (1.59/2.29) based on CBS*. These fast calculation methods using typical GGA-D3 behave better than time-consuming calculation methods of vdW-DF2 (1.75/2.70) and vdW-DF (2.47/3.69). However, well-known BLYP-D3 (2.76/3.18) and BP86-D3 (4.15/4.76) based on CBS* perform rather poorly. A somewhat interesting performance in GGA functional PBE-TS which shows less basis set dependency than PBE-D3 can be noted because it performs comparably to the hybrid functional B3LYP-D3 using PW since the TS is able to properly take into account the anisotropic effect of electron density using either light tier 2/3 or PW basis sets. As the basis set size increases, the results based on GGA-D3, B3LYP-D3, and PBE0-D3 improve, while the M06-2X (1.32/1.42) and ωB97X-D (1.90/2.20) results become worse, which could be due to the parameter fitting made at rather small basis sets. 10


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An observation from the obtained results is that the errors in binding energy of X2-Bz and CX4-Bz become larger for X = Br for which a more positive σ-hole yields stronger halogen bond. The errors are the largest for the S1 conformers of X2-Bz where the contribution of halogen bond interaction is the largest, while they are relatively small for CX4-Bz where the electrostatic interaction is less significant than the dispersion interaction. This clearly shows that the halogen bond is unsatisfactorily described by the conventional GGA functionals. Due to the high anisotropy of the electron density around the halogen atom involved in halogen bond, calculations with small basis sets cannot reproduce the highly anisotropic effect of electron density around each atom and tend to exaggerate the binding energies. Hence, either large basis sets or BSSE correction are required to obtain reasonably accurate binding energies. Nevertheless, most GGA functionals do not accurately reproduce the halogen bond driven binding energies even with large basis sets. This requires a further improvement of density functionals to properly describe the highly anisotropic electron density around halogen atoms in molecular systems. Such high anisotropic electron density which cannot be described adequately without exact exchange, appears not only in halogen bond but also in other types of noncovalent bonding (such as dimers of N2, dimers of CO, and aromatic systems involving in π-interactions in the presence of polar environments or high electric fields, which show anisotropic dispersion).97-100 To deal with such highly anisotropic electron density around atoms in molecular systems, the improved density functionals with less delocalized electron density by using accurate exchange are highly desirable. Finally, in Figure 4 we show the interaction energy profiles of Cl2-Bz (S1) for several types of density functional with respect to the distance from the benzene centroid to the nearest Cl atom (energies at the complete basis limit). A good performance comparable to CCSD(T)/CBS is noted from PBE0-D3, followed by B2GP-PLYP-D3, and by B3LYP-D3, while M06-2X gives somewhat smaller binding energy in the region longer than the equilibrium distance, as it is known to suffer from insufficient long range electron correlation.101

CONCLUDING REMARKS

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We have assessed a variety of density functional comparing with the CCSD(T)/CBS results for the low-lying energy conformations of the X2-Bz and CX4-Bz (X = Cl, Br) complexes. Of the density functionals studied here, B2GP-PLYP-D3, B2-BLYP-D3, PBE0TS, PBE0-D3/CBS, and HSE06-D3/CBS provide particularly good results in terms of the overall performance reflected in MAD/RMSD, followed by M06-2X/CBS and PBE-TS. However, double hybrid functionals, though showing very good performance, may not be exploited for large systems because of their heavy computation. For large systems, one would be inclined to use small basis sets such as aVDZ, but most calculation methods using aVDZ give serious overestimated binding energies even with BSSE correction (let alone without BSSE correction). The GGA-D3 binding energies based on small basis sets such as aVDZ are highly overestimated; the overestimation is especially large for the S1 conformers that yield a strong halogen bond. Although the overestimation is somewhat reduced with the use of larger basis sets, the description of systems with strong halogen bond still remains unsatisfactory. The DFT description of halogen bond, despite that the D3 correction itself does not depend on the basis set, shows noticeable sensitivity to the quality of the basis set. Especially, it is highly sensitive for Br-containing molecules for which halogen bond is relatively strong due to the pronounced σ-hole of Br. The unsatisfactory description of halogen bond is likely to be caused by the delocalization error arising from less accurate exchange of density functionals which lead to large overestimation of electrostatic interaction. Thus, hybrid functionals such as the BSSEc PBE0-D3, HSE06-D3, B3LYP-D3, M06-2X, and ωB97X-D provide somewhat reliable values even with using aVDZ. When the aVTZ basis set is used, the BSSEu M06-2X gives only small errors. Thus, BSSEc M06-2X/aVDZ and BSSEu M06-2X/aVTZ perform very well. However, the aVQZ and CBS* provide less accurate values, which could imply that the relevant parameters for M06-2X were optimized for aVTZ without BSSE correction. At the level of aVTZ or larger basis sets, regardless of BSSE correction or not, PBE0-D3 gives reliable values. Overall, PBE0/plane-wave, PBE0TS/tier, and PBE0-D3/aVTZ provide very reliable values (< 1 kJ/mol), followed by BSSEc B3LYP-D3/aVTZ (~1 kJ/mol). For medium-sized systems, the use of the BSSEu M062X/aVTZ method can be a viable alternative; however, the BSSE correction underestimates the binding energies. It also imposes certain limitations on its use, as it requires much more computation time than other GGA functionals and it suffers from insufficient long range 12


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electron correlation. Meanwhile, such an overestimation problem tends to be less serious in DFT calculations using Tkatchenko-Scheffler (TS) dispersion correction. PBE0-TS/lighttier2 and PBE0-TS/plane-wave which are free from BSSE, tend to give small errors (within 1 kJ/mol), as the tier2 basis set results are similar to the tier3 results. We believe that the results obtained in this work help in better understanding the nature of X-π interactions in halogen-containing supramolecular and biomolecular systems and halogen-adsorbed/intercalated graphene/graphite systems.

ASSOCIATED CONTENT

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca. Binding energies of the X2-Bz and CX4-Bz conformers at various levels of DFT. Comparison between Quadrupole-Quadrupole (Q-Q) interaction and DFT-SAPT Ees. QTAIM analysis of the X2-Bz and CX4-Bz conformers. Computed geometries at each computation level (PDF).

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This work was supported by NRF (National Honor Scientist Program: 2010-0020414) and KISTI (KSC-2015-C3-059, KSC-2015-C3-061). MF was supported by the Korean Ministry of Science within the framework of the Brain Pool program.

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Kim, H.; Doan, V. D.; Cho, W. J.; Valero, R.; Tehrani, Z. A.; Madridejos, J. M. L.;

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Table 1. CCSD(T)/CBS binding energies (kJ/mol) of the chosen conformers. For Br, the CRENBL ECP basis set was used. Conformer

MP2/ aVTZ

MP2/ aVQZ

CCSD(T)/ aVTZa

CCSD(T) /CBS

Cl2-Bz S1 16.82 17.78 11.08 12.73 S2 11.89 12.57 7.61 8.79 S3 7.11 7.60 5.64 6.48 Br2-Bz S1 21.26 22.21 14.57 16.22 S2 13.98 14.76 8.99 10.34 S3 8.16 8.55 6.60 7.24 CCl4-Bz S1 18.24 19.17 12.03 13.64 S2 9.16 9.50 7.55 8.13 CBr4-Bz S1 20.29 21.31 13.23 14.99 S2 11.35 11.50 9.15 9.41 a X2-Bz intermolecular distance optimized at the CCSD(T)/aVTZ level for the BSSEc-MP2/aVTZ geometry

22


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Table 2. DFT-SAPT interaction energy components (kJ/mol). Conformer

E es

* E ind

* E disp

PBE0AC/aVDZ at the BSSEc-MP2/aVDZ geometry Cl2-Bz S1 -15.36 -2.26 -17.29 S2 -6.58 -0.58 -15.74 S3 -2.78 -0.21 -8.98 Br2-Bz S1 -22.45 -10.25 -21.30 S2 -7.44 -1.75 -17.72 S3 -3.29 -0.51 -10.12 CCl4-Bz S1 -10.31 -0.71 -24.29 S2 -4.13 -0.32 -13.42 CBr4-Bz S1 -9.12 -1.98 -23.32 S2 -4.93 -0.74 -14.73 PBE0AC/aVTZ at the BSSEc-MP2/aVTZ geometry Cl2-Bz S1 -13.10 -1.76 -18.52 S2 -6.21 -0.46 -18.06 S3 -3.83 -0.31 -12.49 Br2-Bz S1 -24.59 -11.70 -26.57 S2 -9.23 -1.91 -22.48 S3 -4.10 -0.72 -13.34

* E exch

δH

Eint

30.61 17.80 7.41

-6.89 -1.32 -0.38

-11.19 -6.42 -4.94

36.18 18.77 8.10

2.69 0.83 -0.04

-15.12 -7.31 -5.86

27.18 11.69

-1.89 -0.63

-10.02 -6.81

22.17 12.48

0.84 -0.11

-11.41 -8.07

26.69 17.62 11.67

-5.52 -1.12 -0.63

-12.21 -8.22 -5.59

41.85 22.95 11.21

4.89 0.90 -0.02

-16.12 -9.77 -6.97

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Table 3. MAD/RMSD in kJ/mol of various DFT methods (BSSEu values without parentheses and BSSEc values in parentheses) with respect to CCSD(T)/CBS for the cases of (a) all the conformers

of X2-Bz (S1, S2, S3) and CX4-Bz (S1, S2) and (b) only the global minimum energy conformers (S1) of X2-Bz and CX4-Bz.a (a) All conformers B97-D3 TPSS-D3 PBE-D3 BLYP-D3 BP86-D3 PBE0-D3 HSE06-D3 B3LYP-D3 ωB97X-D M06-2X B2-PLYP-D3 B2GP-PLYP-D3

aVTZ 2.05/2.86 (1.65/2.52) 2.14/2.97 (1.54/2.18) 1.77/2.57 (1.56/2.21) 3.44/3.89 (2.71/3.24) 5.16/5.74 (4.19/4.87) 0.98/1.17 (0.65/0.81) 1.20/1.45 (0.77/0.98) 1.24/1.51(1.01/1.15) 1.03/1.34 (1.54/1.88) 0.43/0.49 (1.36/1.42) 1.86/2.00 (0.62/0.77) 1.75/1.85 (0.59/0.79) light tier3 1.17/1.49 0.52/0.74

aVQZ 1.85/2.65 (1.62/2.41) 1.88/2.67 (1.55/2.18) 1.59/2.32 (1.55/2.15) 3.02/3.48 (2.75/3.22) 4.46/5.10 (4.17/4.80) 0.71/0.91 (0.65/0.79) 0.85/1.09 (0.77/0.98) 1.05/1.21 (0.97/1.10) 1.59/1.93 (1.80/2.10) 1.02/1.13 (1.36/1.43) 1.06/1.25 (0.62/0.76) 0.88/0.98 (0.49/0.66)

CBS* 1.59/2.29 1.55/2.17 1.53/2.08 2.76/3.18 4.15/4.76 0.65/0.79 0.77/0.97 0.95/1.08 1.90/2.20 1.32/1.42 0.69/0.84 0.51/0.65

PBE-D3 PBE-TS PBE0-TS PBE0-D3 HSE06-D3 B3LYP-D3 OptB86B-vdW-DF rPW86-vdW-DF2

aVDZ 4.43/5.56 (2.35/3.87) 5.39/6.15 (2.24/3.62) 4.33/5.32 (2.12/3.40) 5.40/6.12 (2.89/4.01) 8.02/8.74 (4.93/6.05) 4.16/4.34 (1.09/1.53) 4.22/4.48 (1.21/1.83) 3.22/3.69 (1.47/1.81) 2.10/2.43 (0.94/1.08) 4.04/4.16 (0.84/0.91) 4.54/4.77 (1.14/1.37) 4.65/4.85 (1.58/1.91) light tier2 1.19/1.73 0.54/0.75 PW/500 eV 1.70/2.56 1.24/1.78 0.44/0.61 0.65/0.84 0.73/0.97 1.39/1.71 2.47/3.69 1.75/2.70

(b) S1 conformers B97-D3 TPSS-D3 PBE-D3 BLYP-D3

aVDZ 6.20/7.73 (4.81/6.02) 7.56/8.35 (4.33/5.58) 6.09/7.33 (4.20/5.27) 7.14/7.92 (4.82/5.90)

aVQZ 3.32/3.95 (3.01/3.68) 3.23/3.94 (2.60/3.20) 2.66/3.41 (2.64/3.20) 4.09/4.56 (3.78/4.28)

CBS* 2.87/3.44 2.57/3.16 2.58/3.06 3.70/4.15

BP86-D3 PBE0-D3 HSE06-D3 B3LYP-D3 ωB97X-D M06-2X B2-PLYP-D3 B2GP-PLYP-D3

11.07/11.56 (7.98/8.75)

aVTZ 3.53/4.23 (3.16/3.86) 3.48/4.33 (2.64/3.24) 2.85/3.72 (2.72/3.33) 4.62/5.06 (3.84/4.40) 7.35/7.70 (6.33/6.75) 1.00/1.16 (0.73/0.90) 1.34/1.65 (0.96/1.18) 1.68/1.96 (1.35/1.44) 1.71/1.96 (2.38/2.60) 0.35/0.43 (1.17/1.20) 2.25/2.37 (0.93/1.03) 1.94/2.04 (0.76/1.05) light tier3 1.49/1.83 0.79/1.01

6.55/6.94 (6.20/6.60) 0.78/0.94 (0.73/0.87) 1.11/1.32 (0.93/1.15) 1.36/1.49 (1.20/1.29) 2.41/2.65 (2.68/2.87) 0.81/0.88 (1.15/1.18) 1.36/1.53 (0.98/1.01) 1.14/1.18 (0.70/0.93)

6.13/6.51 0.73/0.86 0.91/1.12 1.10/1.20 2.83/3.01 1.15/1.19 1.02/1.04 0.81/0.92

PBE-TS PBE0-TS

PBE-TS PBE0-TS PBE-D3 PBE-TS PBE0-TS PBE0-D3 HSE06-D3 B3LYP-D3 OptB86B-vdW-DF rPW86-vdW-DF2 a

4.62/4.85 (1.74/2.15) 5.07/5.39 (2.14/2.72) 3.85/4.22 (2.08/2.41) 1.85/2.39 (1.27/1.36) 4.58/4.69 (1.12/1.15) 4.17/4.76 (2.09/2.84) 4.77/4.87 (1.80/2.33) light tier2 1.71/2.44 0.82/1.02 PW/500 eV 3.12/3.91 1.81/2.44 0.53/0.68 0.80/1.01 0.92/1.19 1.93/2.30 4.76/5.65 3.09/4.02

The values of deviation less than 1 kJ/mol are highlighted in bold. 24


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Figure Captions

Figure 1. Low energy conformers of (a-c) X2-Bz and (d-e) CX4-Bz (X = Cl and Br). The right and left pairs are top and side views, respectively, in each structure.

Figure 2. Electrostatic potential (ESP) map of structures of X2, CX4 and X2-Bz (S1) and CX4-Bz (S1) complexes (X = Cl and Br) on the 0.001 electrons/bohr3 surfaces obtained at the M06-2X/aVTZ level (C: grey; H: white; Cl: green; Br: red).

Figure 3. Interaction energy deviations (∆∆E = ∆EDFT - ∆ECCSD(T)/CBS) of the DFT methods (based on CBS* for the Gaussian basis sets, tier3 for TS dispersion correction, or 500eV-cutoff for PW) from the CCSD(T)/CBS binding energies for all the conformers of X2-Bz (S1, S2, S3) and CX4-Bz (S1, S2).

Figure 4. Interaction energy profile of Cl2-Bz (S1) with respect to the distance from the benzene centroid to the nearest Cl atom (energies at the complete basis limit).

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Figure 1. Low energy conformers of (a-c) X2-Bz and (d-e) CX4-Bz (X = Cl and Br). The right and left pairs are top and side views, respectively, in each structure.

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Figure 2. Electrostatic potential (ESP) map of structures of X2, CX4 and X2-Bz (S1) and CX4-Bz (S1) complexes (X = Cl and Br) on the 0.001 electrons/bohr3 surfaces obtained at the M06-2X/aVTZ level (C: grey; H: white; Cl: green; Br: red).

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Figure 3. Interaction energy deviations (∆∆E = ∆EDFT - ∆ECCSD(T)/CBS) of the DFT methods (based on CBS* for the Gaussian basis sets, tier3 for TS dispersion correction, or 500eV-cutoff for PW) from the CCSD(T)/CBS binding energies for all the conformers of X2-Bz (S1, S2, S3) and CX4-Bz (S1, S2).

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Figure 4. Interaction energy profile of Cl2-Bz (S1) with respect to the distance from the benzene centroid to the nearest Cl atom (energies at the complete basis limit).

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TOC

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CX4 (X = Cl, Br

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