The nature of the I⋯I interactions and a comparative study with the nature of the π⋯π interactions

Accepted Manuscript The nature of the I· · ·I interactions and a comparative study with the nature of the π · · · π interactions Weizhou Wang, Yan Zhao, Yu Zhang, Yi-bo Wang PII: DOI: Reference:

S2210-271X(13)00550-1 http://dx.doi.org/10.1016/j.comptc.2013.12.021 COMPTC 1344

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Computational & Theoretical Chemistry

Please cite this article as: W. Wang, Y. Zhao, Y. Zhang, Y-b. Wang, The nature of the I· · ·I interactions and a comparative study with the nature of the π · · · π interactions, Computational & Theoretical Chemistry (2014), doi: http://dx.doi.org/10.1016/j.comptc.2013.12.021

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The nature of the I···I interactions and a comparative study with the nature of the π···π interactions Weizhou Wang a,*, Yan Zhao b, Yu Zhang a, Yi-bo Wang c,* a

College of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang 471022,

China b

College of Physics and Electronic Information, Luoyang Normal University, Luoyang 471022,

China c

Department of Chemistry, and Key Laboratory of Guizhou High Performance Computational

Chemistry, Guizhou University, Guiyang 550025, China

ABSTRACT The I···I interactions play an important role in molecular self-assembly. In the present study, the nature of the I···I interactions has been investigated and compared with the nature of the π···π interactions by using the I2 dimer and benzene dimer as the prototypes of these interactions. The CCSD(T) interaction energies in the complete basis set limit at the equilibrium distances are -1.51, -2.04, and -3.08 kcal/mol for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer, respectively. These energy values are little different from the corresponding ones of the benzene dimer. In addition to accurate interaction energies, we have also performed symmetry adapted perturbation theory analyses for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer and benzene dimer. The dispersion interaction was found to be the major source of attraction in the

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sandwich and parallel-displaced configurations of the I2 dimer and benzene dimer. Different from the T-shaped configuration of the benzene dimer in which the dispersion interaction is still the major source of attraction, electrostatic, induction and dispersion interactions play equal role for the stabilization of the T-shaped configuration of the I2 dimer. On the other hand, potential energy curves for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer were obtained employing different wave function and density functional theories with several large basis sets. It was noted that, for the T-shaped configuration of the I2 dimer, all the theory methods considered in this work cannot give comparable results to the CCSD(T) ones in the complete basis set limit. Relationships between the nature of the I···I and π···π interactions and the performance of theory methods were discussed.

Keywords: I···I interactions; π···π interactions; CCSD(T)/CBS; SAPT; New computational methods

* Corresponding authors. Tel. +86 379 65515113; fax: +86 379 65523821. E-mail address: [email protected] (W. Wang); [email protected] (Y.-b. Wang).

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1. Introduction Great attention is paid to the halogen···halogen interactions due to their key roles in crystal engineering, molecular recognition, functional materials, biomolecular systems, and biomedical applications [1-13]. Most of the halogen atoms carry both an electrophilic (electron-poor) region and a nucleophilic (electron-rich) region [14]. However, the halogen···halogen interaction can not be simply defined as “a halogen···halogen interaction occurs when there is evidence of a net attractive interaction between an electrophilic region on a halogen atom and a nucleophilic region on the other halogen atom”. Note that the halogen···halogen stacking interactions were often found in the crystal structures [1-13]. The directional preferences of the halogen···halogen interactions were noticed many years ago and classified as Type I and Type II (Scheme 1) [1,2]. The nature of the halogen···halogen interactions has been extensively studied by crystallographic and theoretical methods [1-13]. It was generally accepted that the halogen···halogen interaction strength decreases in the order I···I > Br···Br > Cl···Cl > F···F [5]. The electric dipole polarizabilities for I, Br, Cl and F are 5.35, 3.05, 2.18 and 0.557 Å3, respectively [15]. Evidently, the trend in halogen···halogen interaction strength parallels the polarizability of the electronic charge around the halogen atom. At the same time, some studies showed that the halogen···halogen interactions are controlled by electrostatic forces and indeed display directional preferences [5]. Although these results are very important for the understanding of the nature of the halogen···halogen interactions, there are still many fundamental questions that need to

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be addressed. First, the halogen bond has been defined by the International Union of Pure and Applied Chemistry (IUPAC) as “a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity” [16]. Can some special halogen···halogen interactions, such as the Type II contacts, also be classified as the halogen bond? Second, the π···π interactions are largely dependent on the dispersion interactions [17-29] and the halogen bonds are largely dependent on both electrostatic and dispersion type interactions [30]. Here, for the halogen···halogen interactions, the contribution of different components to the total interaction energy deserves more attention and needs to be studied further. Third, It was observed that the geometries of the halogen···halogen interactions are very similar to the geometries of the π···π interactions. As shown in Fig. 1, both the halogen···halogen interactions and the π···π interactions have three typical geometries: the sandwich (S), parallel-displaced (PD), and T-shaped (T) configurations. For a better understanding of the nature of the halogen···halogen interactions, it is significant and important to compare it with the nature of the π···π interactions. Another important issue unsettled is the accurate stabilization and structure calculations of the halogen···halogen interactions. In recent years, there are many new quantum chemical methods, either wave function theory (WFT) or density functional theory (DFT) based, which are stated to achieve the accuracy of intermolecular interaction energies similar to that of the coupled-cluster calculation covering the single and double electron excitations iteratively and the triple electron excitations perturbatively (CCSD(T)) in combination with the complete

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basis set (CBS) limit extrapolations at a very small fraction of computational costs [31-33]. Do these newly developed methods still work for the study of the halogen···halogen interactions? In order to address the above-mentioned questions, in the present study, the I···I interactions were studied in detail using the state-of-the-art quantum chemistry methods. We did not consider the F···F, Cl···Cl and Br···Br interactions due to the following three reasons. (i) The nature of these interactions should be the same although the I···I interactions are much stronger than the other halogen···halogen interactions. (ii) In contrast to the F···F, Cl···Cl and Br···Br interactions, the I···I interactions are studied with the pseudo-potential basis sets not the all-electron basis sets. (iii) Just like the C6H6 dimer which was always considered as a prototype of the π···π interactions, in this wok, the I2 dimer was selected as a prototype of the I···I interactions. The molecular polarizability of I2 is 10.33(28) Å3 [34], which is close to the value of 10.32 Å3 for the benzene [35]. Both I2 and C6H6 have no dipole moment. Quadrupole moment is the lowest order of non-vanished electric multipole moment of I2 and C6H6. The quadrupole moments of I2 (4.65 au) and C6H6 (-6.60 au) have a similar order of magnitude but with their different signs [36,37]. Fig. 2 shows that the molecular electrostatic potential maps of I2 and C6H6 are also very similar to each other. Similar properties of I2 and C6H6 indicate that, among the halogen···halogen interactions, only the I···I interactions are comparable to the π···π interactions.

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2. Theoretical methods Potential energy curves as a function of intermonomer distances for different configurations of the I2 dimer were systematically calculated via CCSD(T) [38], MP2 [39], B3-LYP [40,41], B3-LYP-D [40-42], B3-LYP-D3 [40,41,43], TPSS [44], TPSS-D [42,44], TPSS-D3 [43,44], M06-2X [45], M06-2X-D3 [43,45], SCS-MP2 [46] and MP2.5 [47] methods, respectively. The intermonomer distances for the I2 dimer are defined in Fig. 1. The vertical R1 and horizontal R2 are the intermonomer distances between the centers of mass. CCSD(T), MP2, SCS-MP2 and MP2.5 computations were performed using Dunning’s correlation-consistent split valence basis

sets

aug-cc-pVTZ-PP

(AVTZ-PP),

aug-cc-pVQZ-PP (AVQZ-PP)

and

aug-cc-pV5Z-PP (AV5Z-PP) [48], and DFT computations were carried out with Ahlrichs’s def2-TZVP basis sets [49]. All calculations were performed with the experimental I2 monomer geometry (rI-I = 2.6663 Å) [50], and this geometry was kept rigid in the calculations. At the CCSD(T)/AVQZ-PP level of theory, we found that the values of the equilibrium intermonomer separation and interaction energy of the I2 dimer obtained by full geometry optimization are almost the same as those obtained by partial optimization (freezing the monomer geometry), which indicates that the effect of freezing the monomer geometry on both the equilibrium geometry and interaction energy can be negligible. The interaction energies of all the dimers were calculated using the supermolecule method. Hence, a negative interaction energy refers to a bound complex and a positive interaction energy indicates repulsion. The interaction energies are corrected for basis set superposition error using the

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counterpoise (CP) method of Boys and Bernardi [51]. It is well known that the accuracy of DFT calculations also depends on the number of points used in the numerical integration. In the present study, an “ultrafine” integration grid (99 radial, 590 angular points) was used for all the DFT calculations to avoid the possible integration grid errors. The CCSD(T)/CBS interaction energies were calculated by using the three-point scheme of Feller and co-workers [52,53]. According to Feller’s extrapolation scheme, the interaction energies at the complete basis set can be calculated with A(n) = A(∞) + αе-βn, where A(n) and A(∞) are the interaction energies at the AVnZ-PP (n = T, Q, 5) and CBS limit, respectively, and α and β are the fitting parameters. Besides the CCSD(T)/CBS interaction energies, we also calculated the estimated CCSD(T)/CBS interaction energies. The estimated CCSD(T)/CBS interaction energies were calculated as follows: ΔECCSD(T)/CBS = ΔEMP2/CBS + δ δ = ΔECCSD(T)/AVTZ-PP – ΔEMP2/AVTZ-PP MP2 calculations were performed with the basis sets AVTZ-PP, AVQZ-PP and AV5Z-PP, and extrapolated to the CBS limit using the same extrapolation procedure. To better understand the nature of I···I interaction, we have also carried out symmetry adapted perturbation theory (SAPT) calculations on the different configurations of the homogeneous dimers of I2 and C6H6. Let us add here that SAPT provides a means of directly computing the noncovalent interaction between two

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molecules and a decomposition of the interaction energy into physically meaningful components: i.e., electrostatic (Eelec), exchange (Eexch), induction (Eind), and dispersion (Edisp) terms [54]. The SAPT interaction energy is given as SAPT = Epol1 + Eex1 + Eind2 + Eex-ind2 + Edisp2 + Eex-disp2 + δHF Eint

= Eelec + Eexch + Eind + Edisp + δHF δHF is a Hartree-Fock correction for higher order contributions to the interaction energy. SAPT computations were performed with MOLPRO quantum chemistry package [55], using the AVQZ-PP basis set for the I2 dimer and the AVTZ basis set for the C6H6 dimer [56]. The geometries of the C6H6 dimer were taken from the work of Sherrill et al [27]. Other electronic structure calculations were carried out using the Gaussian 09 suite of programs [57]. The newest version of the dispersion correction (DFT-D3) was calculated using the stand-alone code of Grimme et al [43].

3. Results and discussion 3.1. Geometries and interaction energies for different configurations of the I2 dimer The potential energy curves for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer are plotted in Figs. 3-6. There are two geometrical parameters (R1 and R2) for the parallel-displaced configuration. Fig. 4 gives the equilibrium intermonomer distances of R1 = 4.3 Å and R2 = 1.6 Å. Tables 1 and 2 list the equilibrium geometries and corresponding interaction energies for the three configurations of the I2 dimer.

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It can be clearly seen from Table 1 that the effect of the basis sets on the equilibrium geometries can be negligible either at the MP2 theory level or at the CCSD(T) theory level. The difference between the CCSD(T) and the MP2 equilibrium geometries is also not large. In general, the CCSD(T) equilibrium distances are found to be about 0.1 Å larger than the MP2 ones. These results show that the equilibrium geometries can be accurately predicted using smaller basis sets at the MP2 level. This is in good accord with the results of the benzene dimer, in which the CCSD(T) equilibrium distances were found to be 0.1-0.3 Å larger than the MP2 ones.33 The van der Waals radius of the I atom is 1.98 Å [58]. The sum of van der Waals radii of two I atoms is 3.96 Å. It is clear from Table 1 that, in the sandwich and parallel-displaced configurations of the I2 dimer, the interatomic distances between two I atoms are all larger than the sum of their van der Waals radii. Hence, according to the IUPAC definition of the halogen bond [16], the I···I interactions in these configurations can not be categorized as the halogen bond. At the CCSD(T)/CBS level of theory, the equilibrium intermonomer distance of R = 3.65 Å is smaller than the sum of van der Waals radii of two I atoms in the T-shaped configuration of the I2 dimer. Considering that, at the same time, the electrophilic region on one I atom points to the nucleophilic region on the other I atom in the T-shaped configuration (Figs. 1 and 2), it is reasonable to conclude that here the I···I interaction is of the halogen bond. Table 2 shows that, at the equilibrium geometries, the CCSD(T)/CBS interaction

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energies for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer are found to be -1.51, -2.04, and -3.08 kcal/mol, respectively. For the benzene dimer, the CCSD(T)/CBS interaction energies at the equilibrium geometries are -1.64, -2.70, and -2.69 kcal/mol for the sandwich, parallel-displaced, and T-shaped configurations, respectively [21]. The interaction energies for various configurations of the I2 dimer are 0.13-0.66 kcal/mol larger than the corresponding ones of the benzene dimer. Table 2 also shows that, at the equilibrium geometries, MP2 calculations systematically overestimate the interaction energies of the three configurations of the I2 dimer. The best MP2/CBS interaction energies differ from the more accurate CCSD(T)/CBS values by up to 1.16 kcal/mol. It can be seen from Figs. 3, 5 and 6 that overestimation of MP2 calculations is still noticeable at the other intermonomer distances. This result, combined with the similar result of the benzene dimer [27], highlights the importance of going beyond MP2 to achieve higher accuracy in stabilization calculations for noncovalent interactions. In Figs. 3, 5 and 6, besides the CCSD(T)/CBS potential energy curves, we also give the estimated CCSD(T)/CBS potential energy curves. The two curves are almost overlaying each other for each configuration. On the other hand, from Table 2, we can see that the difference between the estimated CCSD(T)/CBS and the CCSD(T)/CBS interaction energies is smaller than 0.2 kcal/mol at equilibrium geometries. These results support the assumption that the difference between the CCSD(T) and MP2 interaction energies depends only negligibly on the basis set size and can thus be determined with small or medium basis set only.

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3.2. The nature of the I···I interactions and a comparative study with the nature of the π···π interactions Table 3 gives the symmetry adapted perturbation theory interaction energy decomposition results for various configurations of the I2 dimer. SAPT calculations were performed at the CCSD(T)/CBS equilibrium geometries. For the sandwich and parallel-displaced configurations of the I2 dimer, dispersion forces represent about 69% and 65% of the total attractive forces, respectively. In contrast, the electrostatic components of these interactions account for about 18% and 22% of the overall attraction, while induction contributes 13% and 13% to the stability of the two configurations. Although small in numbers, the induction contribution (-0.59 and -0.63 kcal/mol) cannot be neglected. Thus, the I···I interactions in these configurations are dependent on all three stabilizing interaction energy components, that is, electrostatic, induction and dispersion, with dispersion playing the dominant role for their stability. For the T-shaped configuration of the I2 dimer, dispersion accounts for only 37% of the attractive interaction. The electrostatic term and induction play a larger role in the T-shaped configuration than in the sandwich and parallel-displaced configurations; the electrostatic term represents about 31% of the attractive forces, while induction accounts for about 32% of the overall attractive interaction. As mentioned above, the I···I interaction in the T-shaped configuration of the I2 dimer can be categorized as the halogen bond. Riley and Hobza found that halogen bonds are largely dependent on both electrostatic and dispersion type interactions [30]. Here, the induction

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contribution to the interaction energy (-4.29 kcal/mol) is a little larger than the electrostatic contribution (-4.17 kcal/mol) and slightly smaller than the dispersion contribution (-5.04 kcal/mol). The structures and interaction energies of the I···I interactions and the π···π interactions are very similar. Here it is interesting to compare the SAPT interaction energy decomposition results for the two types of noncovalent interactions. Table 3 also gives the SAPT interaction energy decomposition values for the three configurations of the benzene dimer. As clearly shown in Table 3, the π···π interactions are all of the dispersion type. The π···π interaction in the sandwich configuration of the benzene dimer is very dispersion in nature, and the dispersion component is responsible for 97% of the attractive interaction! Also different from the I2 dimer, the induction contributions are only about 3% of the overall attractive interaction in the three configurations of the benzene dimer. Generally, it can be said that the I···I interactions in the sandwich and parallel-displaced configurations of the I2 dimer are similar to the π···π interactions in the sandwich and parallel-displaced configurations of the benzene dimer because they are all of the dispersion type. However, the nature of the I···I interaction in the T-shaped configuration of the I2 dimer is totally different from the nature of the π···π interaction in the T-shaped configuration of the benzene dimer. Electrostatic, induction and dispersion interactions play equal role for the stabilization of the I···I interaction in the T-shaped configuration of the I2 dimer, while the π···π interaction in the T-shaped configuration of the benzene dimer is still of the dispersion type.

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The SAPT interaction energies for various configurations of the homogeneous dimers of I2 and C6H6 are in excellent agreement with those obtained at the CCSD(T)/CBS theory level. Note that, in the case of the T-shaped configuration of the I2 dimer, the third and higher-order terms (δHF) become more important. The potential of the dispersion interaction is often truncated to -C6R-6 because it was believed that the higher-order contribution is small in comparison to this term. Figs. 7 and 8 are the least squares fitting of the tail of the potential energy curve for the sandwich and T-shaped configurations using the equation -C6R-6, where C6 is a constant to be determined from the fit. We can see from Figs. 7 and 8 that the tail of the potential energy curve for the sandwich configuration can be well described by a function of the form -C6R-6, even when points close to equilibrium are included in the fit, but for the T-shaped configuration of the I2 dimer the deviation of the tail of the potential energy curve from -C6R-6 is very clear. This can be explained by the different nature of the I···I interactions. The I···I interaction in the sandwich configuration is of the dispersion type, while, for the T-shaped configuration of the I2 dimer, in addition to dispersion other energy components such as electrostatic and induction also contribute largely to the overall interaction energy. 3.3. Relationships between the nature of the I···I and π···π interactions and the performance of theory methods Figs. 9-11 display the potential energy curves for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer obtained by employing different wave function and density functional theories with several large basis sets. It is not

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surprising to find that standard density functionals B3-LYP and TPSS fail to accurately describe interaction energies of the I···I interactions in the three configurations of the I2 dimer. The curves of the functionals M06-2X and M06-2X-D3 are almost identical in all three configurations and both of them underestimate the I···I interaction energies. This is unusual because these functionals are always recommended for studying equilibrium configurations of dispersion bound complexes. The physical reason for the poor performance of M06-2X and M06-2X-D3 is, however, difficult to assess due to their complex functional forms. The benzene dimer has been quite extensively studied. Almost all the dispersion-corrected DFT (DFT-D or DFT-D3) methods were claimed to produce reasonable interaction energies for the equilibrium or near-equilibrium configurations of the benzene dimer. Similar results are found in the sandwich configuration of the I2 dimer (Fig. 9). For the parallel-displaced configuration of the I2 dimer, Fig. 10 shows that B3-LYP-D and TPSS-D3 still performs very well, while B3-LYP-D3 and TPSS-D overestimate the interaction energies significantly. It is interesting to note that DFT-D3 works much better than DFT-D for the TPSS functional, while DFT-D works much better than DFT-D3 for the B3-LYP functional. We believe that much more accurate parameters for the heavier element iodine will make the case better. The excellent performance of the dispersion-corrected DFT methods for both the three configurations of the benzene dimer and the two configurations of the I2 dimer strongly correlate with the dispersion nature of noncovalent interactions in these configurations.

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The I···I interaction in the T-shaped configuration of the I2 dimer is not of the dispersion type. As expected, all the dispersion-corrected DFT methods fail to accurately predict either the equilibrium geometries or the interaction energies (Fig. 11). We also investigate the performance of two very popular WFT-based methods SCS-MP2 and MP2.5. As shown in Fig. 11, SCS-MP2 underestimates greatly the interaction energies and MP2.5 overestimates greatly the interaction energies. All these results demonstrate that, for the I···I interaction in the T-shaped configuration of the I2 dimer, the achievement of an accurate description is highly challenging. The inclusion of only long-range dispersion correction is not enough for a better description of van der Waals complexes. Accurate treatment of short-range repulsion and medium-range exchange and correlation is also very important for the development of new computational methods. There are many van der Waals complexes in which electrostatic, induction and dispersion forces contribute equally to the overall attraction. We are now developing new methods to accurately calculate these challenging systems.

4. Conclusions In this work, we have performed MP2, CCSD(T), DFT, DFT-D, DFT-D3, SCS-MP2 and MP2.5 calculations on the I2 dimer and SAPT calculations on both the I2 dimer and the C6H6 dimer, using different extended basis sets (especially with diffuse and polarization functions). The CCSD(T)/CBS interaction energies for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer are found to

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be -1.51, -2.04, and -3.08 kcal/mol, respectively, which are little different from the corresponding values of the benzene dimer. Just as the case of the C6H6 dimer, MP2 calculations systematically overestimate the interaction energies of the three configurations of the I2 dimer. Again, the result highlights the importance of going beyond MP2 to achieve higher accuracy in stabilization calculations for noncovalent interactions. Additionally, the difference between the estimated CCSD(T)/CBS and the CCSD(T)/CBS interaction energies are found to be negligible, which supports the assumption that the difference between the CCSD(T) and MP2 interaction energies can be determined with small or medium basis set only. SAPT analyses of the interaction energies reveals that dispersion is the dominant stabilizing contribution to the total interaction energy, but electrostatic and induction contributions are also not negligible for the sandwich and parallel-displaced configurations at their equilibrium geometries. For the T-shaped configuration of the I2 dimer, electrostatic, induction and dispersion contributions play equal role to the total interaction energy, which is different from the T-shaped configuration of the benzene dimer in which the dispersion interaction is still the major source of attraction. Correspondingly, the tail of the potential energy curve for the sandwich configuration can be well described by a function of the form -C6R-6, even when points close to equilibrium are included in the fit, but for the T-shaped configuration of the I2 dimer the deviation of the tail of the potential energy curve from -C6R-6 is obvious. According to the IUPAC definition of the halogen bond, the I···I interaction in the

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T-shaped configuration of the I2 dimer is of the halogen bond type because there is evidence of a net attractive interaction between an electrophilic region on one I atom and a nucleophilic region on the other I atom. However, the I···I interactions in the sandwich and parallel-displaced configurations of the I2 dimer are of the dispersion type of interactions and can not be categorized as the halogen bond because the interatomic distance between two I atoms is larger than the sum of their van der Waals radii in each configuration. Potential energy curves for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer were obtained employing different wave function and density functional theories with several large basis sets. The performance of the tested DFT DFT-D and DFT-D3 methods is very diverse and only some of the DFT-D and DFT-D3 methods perform extremely well for the sandwich and parallel-displaced configurations of the I2 dimer. For the T-shaped configuration of the I2 dimer, all the theory methods considered in this study cannot give comparable results to the CCSD(T)/CBS benchmark. Evidently, the performance of theory methods depends strongly on the nature of the I···I interactions to be calculated, and more accurate and well-balanced functionals are needed for the study of the I···I interactions. As Metrangolo and Resnati pointed out, “despite its 200 years of history, iodine is still very much part of recent developments in diverse areas of chemistry, and there is little doubt that it will continue to attract attention in the forthcoming decades” [59]. Correspondingly, the I···I interactions must also continue to attract attention in the future. The nature of the I···I interactions presented in this work will be helpful for

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future studies.

Acknowledgements The authors gratefully acknowledge financial support from the Natural Science Foundation of China (21173113). This work was also sponsored by the Program for Science & Technology Innovation Talents in Universities of Henan Province (13HASTIT015).

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Table 1 Equilibrium geometries (Å) for different configurations of the I2 dimer. method

I2···I2 (S)

I2···I2 (PD)

I2···I2 (T)

R

R1

R2

R

MP2/AVTZ-PP

4.50

4.30

1.60

3.65

MP2/AVQZ-PP

4.40

4.30

1.50

3.55

MP2/AV5Z-PP

4.40

4.30

1.50

3.55

MP2/CBS

4.40

4.30

1.50

3.55

Est. CCSD(T)/CBS

4.50

4.30

1.60

3.65

CCSD(T)/AVTZ-PP

4.60

4.30

1.60

3.76

CCSD(T)/AVQZ-PP

4.50

4.30

1.60

3.70

CCSD(T)/AV5Z-PP

4.50

4.30

1.60

3.65

CCSD(T)/CBS

4.50

4.30

1.60

3.65

Table 2 Interaction energies (kcal/mol) for different configurations of the I2 dimer at the equilibrium geometries. method

I2···I2 (S)

I2···I2 (PD)

I2···I2 (T)

MP2/AVTZ-PP

-1.78

-2.23

-3.49

MP2/AVQZ-PP

-2.15

-2.48

-3.94

MP2/AV5Z-PP

-2.31

-2.57

-4.12

MP2/CBS

-2.43

-2.62

-4.24

Est. CCSD(T)/CBS

-1.68

-2.02

-3.00

CCSD(T)/AVTZ-PP

-1.18

-1.65

-2.45

CCSD(T)/AVQZ-PP

-1.37

-1.90

-2.84

CCSD(T)/AV5Z-PP

-1.46

-1.99

-2.99

CCSD(T)/CBS

-1.51

-2.04

-3.08

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Table 3 SAPT decomposition of the interaction energies (kcal/mol) for the homogeneous dimers of I2 and C6H6 at the equilibrium geometries. I2···I2 (S)

I2···I2 (PD)

I2···I2 (T)

Eelec

-0.77

-1.13

-4.17

0.19

-0.99

-1.72

Eind

-0.59

-0.63

-4.29

-0.16

-0.22

-0.23

Edisp

-3.06

-3.27

-5.04

-4.78

-5.85

-4.01

3.46

4.79

3.28

14%

29%

Eexch

C6H6···C6H6 (S) C6H6···C6H6 (PD) C6H6···C6H6 (T)

2.16

2.14

6.77

a

18%

22%

31%

a

13%

13%

32%

3%

3%

4%

a

Edisp%

69%

65%

37%

97%

83%

67%

E1

1.39

1.01

2.61

3.65

3.79

1.56

E2

-3.65

-3.90

-9.33

-4.94

-6.08

-4.24

δHF

0.82

0.75

3.47

-0.08

-0.35

-0.32

SAPT Eint

-1.43

-2.13

-3.25

-1.36

-2.63

-2.99

Eelec% Eind%

a

Contribution to the total attractive interactions.

26

C

X

X

X

Type I X C Trans geometry C

C C Cis geometry

X

Type II

X

C

Scheme 1. Schematic representation of Type I (cis and trans geometries) and Type II halogen···halogen interactions.

Fig. 1. Sandwich, parallel-displaced, and T-shaped configurations of the homogeneous dimers of I2 and C6H6.

27

Fig. 2. Electrostatic potentials of I2 (top) and C6H6 (bottom) with a scale of -3.77 (red) to 3.77 (blue) kcal/mol.

28

Fig. 3. MP2 and CCSD(T) potential energy curves for the sandwich configuration of the I2 dimer.

29

Fig. 4. CCSD(T)/CBS potential energy curves for the parallel-displaced configuration of the I2 dimer.

30

Fig. 5. MP2 and CCSD(T) potential energy curves for the parallel-displaced configuration of the I2 dimer.

31

Fig. 6. MP2 and CCSD(T) potential energy curves for the T-shaped configuration of the I2 dimer.

32

Fig. 7. Asymptotic 1/R6 fit of the CCSD(T)/CBS potential energy curve for the sandwich configuration of the I2 dimer.

33

Fig. 8. Asymptotic 1/R6 fit of the CCSD(T)/CBS potential energy curve for the T-shaped configuration of the I2 dimer.

34

Fig. 9. Potential energy curves for the sandwich configuration of the I2 dimer at different levels of theory.

35

Fig. 10. Potential energy curves for the parallel-displaced configuration of the I2 dimer at different levels of theory.

36

Fig. 11. Potential energy curves for the T-shaped configuration of the I2 dimer at different levels of theory.

37

►CCSD(T)/CBS potential energy curves as a benchmark. ► The nature of the I···I interactions has been investigated by symmetry adapted perturbation theory analyses. ► The nature of the I···I interactions has been compared with the nature of the π···π interactions. ► The relationship between the nature of the I···I and π···π interactions and the performance of theory methods are studied in detail.