Shape and Geometry Corrected Statistical Analysis on Halogen

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Shape and Geometry Corrected Statistical Analysis on Halogen···Halogen Interactions Binoy K. Saha,* Arijit Saha,‡ and Sumair A. Rather‡ Department of Chemistry, Pondicherry University, Puducherry-605014, India S Supporting Information *

ABSTRACT: Two new corrections, namely, area and shape corrections, have been introduced in the statistical analysis of halogen···halogen interactions. Before geometrical corrections, all the halogens show a clear preference for type 1 contact, but after the geometrical corrections the type 2 interaction has taken over type 1 contact for Cl, Br, and I for the Δθ ≠ 0 contacts. In the case of iodine, the population with type 1 contact becomes negligible and the directionality of the contacts increases dramatically after the area along with shape corrections. Without geometrical corrections, F shows a very high preference for lower Δθ, but after the correction it does not show much preference for any angle. Therefore, we anticipate that these corrections would bring a significant change in the concept about the halogen···halogen interactions.

S

Scheme 1. Geometry of Type 1 and Type 2 C−X···X−C Interactions Are Shown (X Is Halogen)a

tatistical analysis plays an important role in understanding intermolecular interactions, such as hydrogen bonds, C− X···Y (X = halogen, Y = O, N, S, C, halogen) interactions, and so forth.1−6 It is more helpful especially for weaker interactions. But very often, normal statistical analysis is biased by geometrical preferences. In that case, it is essential to nullify these preferences by incorporating some geometrical corrections into the statistical analysis.7−13 Halogen···halogen interactions are among the most fascinating types of interactions studied in supramolecular chemistry.14−23 Halogens are known to polarize in such a way that a partial positive electrostatic potential in the polar region (along the C−X bond axis, X is halogen) and partial negative electrostatic potential in the equatorial region (perpendicular to C−X bond axis) are developed.24−27 The order of polarizability among the four halogens is F < Cl < Br < I.28,29 Based on the geometry, halogen···halogen interactions are known to be of two types, type 1 and type 2 (Scheme 1).1,2,5 Type 1 contacts are mainly a result of dispersion interaction, whereas the type 2 interactions are driven by electrostatic interactions between the polar and equatorial regions.14,18 However, Awwadi et al. have reported the presence of a small contribution of electrostatic interaction to the type 1 contacts too.5 Statistical analysis without geometrical corrections shows a clear preference for type 1 contacts.3,13 In our previous report we applied double cone and combination corrections in the statistical analysis of halogen···halogen interactions which reduced the population with type 1 geometry and increased it with type 2 geometry.13 In the present work we have introduced two new corrections, namely, area and shape corrections in the statistical analysis of C−I···I−C interactions. We have used the area correction on the other halogen···halogen interactions too to compare different halogen···halogen interactions. © XXXX American Chemical Society

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The contact line between two halogens is going through angle range θx1 to θx1 − 10 in one halogen and θx2 to θx2 − 10 in another halogen (below). The surface area (shaded with gray) within two circles drawn at angles θx1, θx1 − 10, and θx2, θx2 − 10 on two halogens in area correction are shown.

CSD (version 5.37, November 2015) structural data search was confined to only organic compounds with 3D coordinates available and R factor ≤0.1. The geometrical constraints were applied using ConQuest 1.18. The ∠CXX angle (θ1 and θ2; θ2 ≥ θ1, Scheme 1) range in the C−X···X−C interactions considered is 80−180°. The upper cutoff of X···X distances for spherical halogens used here is the sum of van der Waals radii × 1.1. The radii of the spherical atoms have been taken from Bondi.30 According to Nyburg and Faerman, halogens are Received: December 18, 2016 Revised: March 18, 2017 Published: March 29, 2017 A

DOI: 10.1021/acs.cgd.6b01854 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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oblate shape, the surface area has been calculated using the web based calculator.32 Next, we have calculated the ratios, OP/CP. It has been noted that the population at the point Δθ = 0 is much higher (I 33.8%, Br 32.8%, Cl 27.3%, F 13.3% with respect to the total population) than the population at 0 < Δθ < 10 range (I 12.1%, Br 11.8%, Cl 13.6%, F 20.8% with respect to the total population) which spans over 10°, though the chemical nature of these two geometries are very similar. Therefore, the overwhelming population at Δθ = 0 is not because of energetically favorable interaction geometry but mainly because of favorable inversion symmetry.13 Therefore, these sets of data should be treated and analyzed differently, and accordingly, the population at Δθ = 0 to 10 has been distributed over two sets, Δθ = 0 and 0 < Δθ ≤ 10. Nevertheless, the very high population of Δθ = 0 contacts suggests that this geometry is not energetically unfavorable, and from the order of % population, I > Br > Cl ≫ F, it is clear that dispersion force plays a very big role in this contact geometry. OP/CPΔθ≠0 vs Δθ has been plotted for C−X···X−C interactions (Δθ ≠ 0) (Figure 1a). A comparison of the shapes of the graphs shows that at 0 < Δθ < 10 the population is relatively higher in the lower Δθ region in the case of Δθ ≠ 0 contacts, then it gradually decreases until somewhere in the region at Δθ = 10° to 40° and then again increases to a maximum which is followed by a fall in population until the end. The regions before and after this minimum, found at Δθ = 10° to 40°, may be referred to as type 1 and type 2 geometries, respectively.3 The OP/CPΔθ=0 values are 1 value indicates a higher population density than the average and, hence, energetically favorable interaction geometry, whereas an OP/CP < 1 value indicates a lower population density than the average and hence energetically relatively less favorable (need not be repulsive) interaction geometry. We have calculated probabilities of interactions based on the surface area of the halogens (area correction) (Scheme 1). In area correction, we have calculated the surface area at 10° interval from 180° to 80° for the spherical or oblate-shaped halogen (Scheme 1). The higher the contact area is, the higher the probability. Therefore, based on random distribution, the calculated population of the C−X···X−C contacts with θ1 = θx1 to θx1 − 10 on halogen 1 and θ2 = θx2 to θx2 − 10 on halogen 2 for Δθ ≠ 0 is CPΔθ ≠ 0 = PΔθ ≠ 0 × NΔθ ≠ 0 =

n × Sθx1 → (θx1 − 10) × Sθx2 → (θx2 − 10) 2 S180 → 80

× NΔθ ≠ 0

PΔθ≠0 is the probability of X···X contacts with θ1 = θx1 to θx1 − 10 and θ2 = θx2 to θx2 − 10, NΔθ≠0 = total number of hits with Δθ ≠ 0 obtained from CCDC search, S θx1→(θx1−10) , Sθx2→(θx2−10), and S180 → 80 are the surface areas for the angle ranges θx1 to θx1 − 10 on halogen 1, θx2 to θx2 − 10 on halogen 2, and total surface area on each halogen in the angle range 180−80°, respectively, n = 1 if θx1 = θx2 and n = 2 if θx1 ≠ θx2. The values of θx1 and θx2 are 180°, 170°, ..., 90°. In the case of spherical objects, the surface area for an angle range θx1 to θx1 − 10 is 2πr2[cos(θx1 − 10) − cos θx1] and the surface area for the total angle range (180−80°) under concern is 2πr2(cos 80 − cos 180) = 2πr2 × 1.174. Therefore CPΔθ ≠ 0 =

n[cos(θx1 − 10) − cos θx1][cos(θx 2 − 10) − cos θx 2] (1.174)2 × NΔθ ≠ 0

On the other hand, for the Δθ = 0 geometry (θ1 = θ2), the C− X groups in C−X···X−C interactions almost always reside around the inversion center, which forces the two C−X groups to adopt identical geometries and hence only single area correction is required. In the case of single area correction (for Δθ = 0) the value of calculated population, CPΔθ=0, would be PΔθ ≠ 0 × NΔθ = 0 = =

Sθx1 → (θx1 − 10) S180 → 80

× NΔθ = 0

cos(θx1 − 10) − cos θx1 × NΔθ = 0 1.174

PΔθ=0 is the probability of hits with θ1 = θ2 = θx1 to θx1 − 10, NΔθ=0 is the total number of hits with Δθ = 0. In the case of B

DOI: 10.1021/acs.cgd.6b01854 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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the Figure 1b and c. The population which is highest (17.6− 24.0%) before correction (Figure 1c) is only 3.9−11.1% after correction (Figure 1b) at 0 < Δθ < 10 in the cases of all four halogens. After the shape and double area corrections this population is found to be even smaller (1.9%). It also can be noted here that the most probable regions with type 2 geometry are shifted by 20−30° toward the ideal type 2 geometry (Δθ = 90°) after the area correction. The order of population in the range 0 < Δθ ≤ 50 is F > Cl > Br > I (reverse to that at Δθ = 0), whereas it is F < Cl < Br < I in the range 70 < Δθ ≤ 100 after area correction (Figure 1b). Therefore, at lower Δθ the lighter halogens dominate, but at higher Δθ the heavier halogens dominate due to their preference for type 2 geometry. In contrast to the flat population distribution after geometrical correction, the % population vs Δθ plot without correction incorrectly suggests a high preference for lower Δθ values in the case of C−F···F−C interactions. The population distribution before correction is more uniformly diffused throughout the whole region, whereas the distribution is quite narrow around the maximum at type 2 region after area correction and especially after shape along with area corrections (for I), indicating a high directionality of the C−X···X−C interactions. The OP/CPΔθ=0 ratio vs θ plot for the hits with Δθ = 0 geometry has been shown in Figure 1d. Here also it can be seen that the distribution is relatively more uniform for F. The most probable population density is found in the region θ1 = θ2 = 140−150° for I, 150−160° for Br as well as Cl, and 170−180° for F. It is worth mentioning here that based on theoretical calculations Awwadi et al. predicted this angle to be around 150° for the three heavier halogens, and this angle decreases with increasing polarizability of the halogens.5 The preferred contact areas of the halogens in the θ1 = θ2 interaction geometry are expected to be those where the electrostatic potentials of the contact surfaces on both halogens are neutral rather than positive or negative. Therefore, this shift toward 180° is expected, because as the polarizability of the halogen decreases, the positive electrostatic potential in the polar part of the halogen also decreases and the neutral electrostatic part shifts toward 180°. At 160−180° the population for I is very small because the electrostatic potential in this polar region is significantly positive for I and hence two polar regions repel each other. On the other hand, F is expected to possess a relatively smaller negative electrostatic potential at the polar region compared to other parts of the surface and hence have the highest population in this range. All these facts indicate that the overall population with type 1 geometry for the three heavier halogens is very small, and it is in fact negligible in I after the two corrections (for Δθ ≠ 0). This is because, in this geometry, there is no electrostatic or other enthalpically favorable strong interactions; merely dispersion interactions due to close packing14,18 are present; rather at some angles the interactions could be repulsive due to the close proximity of similar electrostatic potential (positive or negative) on the halogens. In contrast, the % population in this range before correction is quite high which had been misleading the interpretation of C−X···X−C interactions and could not be explained from the type 1 contact geometry. This implies the importance of these corrections in the statistical analysis of X··· X interactions. On the other hand, type 2 interactions are enthalpically favorable due to high electrostatic interactions between the equatorial part with negative electrostatic potential of one halogen and polar part with positive electrostatic

Figure 1. (a) Observed/calculated population of C−X···X−C interactions vs Δθ for Δθ ≠ 0 hits. (b) % Population of C−X···X− C interactions vs Δθ after area correction for Δθ ≠ 0 hits. (c) % Population of C−X···X−C interactions vs Δθ without any correction for Δθ ≠ 0 hits. (d) Observed/calculated population of C−X···X−C interactions vs θ for Δθ = 0 hits. C

DOI: 10.1021/acs.cgd.6b01854 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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potential of another halogen.18 As a result, a very high population is expected with this interaction geometry which is observed only after the geometric corrections but not with the usually practiced spherical halogen without any corrections. A 3D plot of % population vs θ1 and θ2 provides a more detailed picture of the preference for interaction geometries with respect to θ1 and θ2.13 When the 3D plots of the shapedouble area corrected % population distribution at different θ1 and θ2 is compared with that without any correction, a large number of interesting differences are observed (Figure 2). Even though the θ2 = 170−180° region possesses the highest positive electrostatic potential and hence is expected to be the maximum populated region, the populations at the θ2 = 160− 170° range are higher than that at the θ2 = 170−180° range in the case of I before correction. In the shape-double area corrected 3D plot, the highest populated region (24.0%) is found at the θ2 = 170−180° and θ1 = 100−110° region (type 2) and almost the entire population is located within a very small area around this maximum. This indicates a very high directionality of this interaction. This is also the region for highest population density, though with almost half the population (12.8%), in the case of only double area corrected C−I···I−C population distribution, and the distribution is also slightly more diffuse compared to the shape-double area corrected one. In the cases of other three halogens, at the θ2 = 170−180° range there are two maximaone at lower angle of θ1 (100− 130°) and another at higher angle of θ1 (170−180°). The population at maxima, in the range of θ1 = 170−180° referring to type 1 contact, is negligible in the case of iodine but very high for other halogens. The populations at the maxima at lower angle of θ1 increase and moves toward 90° as the halogens (spherical) become more polarizable (F 120−130°, 3.1%; Cl 120−130°, 5.9%; Br 110−120°, 6.8%; and I 100− 110°, 12.8%). This indicates that, as the halogens become more polarizable, type 2 interactions become more favorable and the geometry moves toward θ2 ≈ 180° and θ1 ≈ 90°. Comparison of the 3D graphs also reveals that the similarity between Br and Cl is more than that between I and Br which is in line with our previous report on isostructurality among the halogenated compounds (Br/Cl isostructurality 70.3% vs I/Br isostructurality 59.4%).33 In summary, we have introduced two new corrections, namely, area and shape corrections, and then applied these corrections in the statistical analysis of halogen···halogen interactions. Our analysis shows that there is a dramatic change in the population distribution after adopting these corrections, which also correctly interpret the nature of halogen···halogen interactions. Statistical analysis without these corrections shows a high preference for type 1 contacts over type 2 interactions in all four halogens. However, it is clear from this analysis that the existence of type 1 contacts in C−I···I−C is due to geometrical bias; otherwise, they are not energetically significant, though the population is not so negligible in the cases of other three halogens. After shape and geometrical corrections, the C−I···I− C interaction is found to be highly directional. Apart from F, which does not show any angular preference in the C−F···F−C interaction, for the other three heavier halogens type 2 geometry is more favorable than type 1 geometry. The geometrical corrections used here can also be used in several other interactions to understand their true chemical nature. We anticipate that this study would be able to modify the concept about the nature of halogen···halogen interactions, and this

Figure 2. 3D plots of % population of C−X···X−C interactions vs θ1 and θ2 before and after corrections (OP = observed population and CP = calculated).

method of geometrical corrections would be applied to many other interactions. D

DOI: 10.1021/acs.cgd.6b01854 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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(26) Rajput, L.; Mukherjee, G.; Biradha, K. Cryst. Growth Des. 2012, 12, 5773−5782. (27) Dey, A.; Jetti, R. K. R.; Boese, R.; Desiraju, G. R. CrystEngComm 2003, 5, 248−252. (28) Metrangolo, P.; Meyer, F.; Pilati, T.; Resnati, G.; Terraneo, G. Angew. Chem., Int. Ed. 2008, 47, 6114−6127. (29) Cavallo, G.; Metrangolo, P.; Milani, R.; Pilati, T.; Priimagi, A.; Resnati, G.; Giancarlo Terraneo, G. Chem. Rev. 2016, 116, 2478−2601. (30) Bondi, A. J. Phys. Chem. 1964, 68, 441−451. (31) Nyburg, S. C.; Faerman, C. H. Acta Crystallogr., Sect. B: Struct. Sci. 1985, B41, 274−279. (32) http://keisan.casio.com/exec/system/1358171752. (33) Bhattacharya, S.; Saha, B. K. Cryst. Growth Des. 2012, 12, 169− 178.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b01854. Relevant tables of data used in analysis (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Binoy K. Saha: 0000-0002-4384-8023 Author Contributions ‡

A.S. and S.A.R. contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS B.K.S. thanks CSIR, India for research funding (No. 02(0026)/ 11/EMR-II, dated 16/12/11). A.S. and S.A.R. thank Pondicherry University for fellowship.

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DOI: 10.1021/acs.cgd.6b01854 Cryst. Growth Des. XXXX, XXX, XXX−XXX