Does the occurrence of resonance (by the delocalization of radical/cationic/anionic charges) induce the existence of intramolecular halogen–halogen contacts?

Abstract

Exotic intramolecular homo/hetero dihalogen bonding (C–X⋯X–C: X = Br, Cl and F) in radical, cationic and anionic five-membered ring systems was analyzed using wave functional theory (MP2/aug-cc-pVTZ) analysis. The six types (Br–Br, Cl–Cl, F–F, Br–Cl, Cl–F and Br–F) of C–X⋯X–C interactions, stabilized by resonance, were created using delocalized radical/cationic/anionic carbon atoms in corresponding five-membered ring structures. The above interactions fall under the group of ‘resonance assisted noncovalent interactions’, where the impact of resonance is to induce the existence of intramolecular dihalogen bonding, even without electrostatic interaction. Further, the paper focuses on NCI bond length and stability, as these can be tuned through substitution effects. 3D-NCI plots and the presence of Bond Critical Points (BCP) clearly confirm the existence of dihalogen bonding. Natural bond orbital (NBO) analysis reveals that the dihalogen bonding in radical/cationic/anionic systems lacks charge transfer and orbital overlapping through non-interacting lobes. Specifically, σ- and π-holes exist not only for the electron depleted regions (positive regions) but also for the electron enriched regions (negative regions). The σ- and π-holes were not utilized for the C–X⋯X–C interactions because the interactions considered were not assisted by electrostatic interactions; instead, they were only assisted by resonance. Overall, this study clearly reveals that the impact of resonance formation (by delocalization of radical, cation, and anion charges) enhances the chance of occurrence of intramolecular halogen–halogen contacts.

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Introduction

A σ-hole bond, the interaction between a nucleophilic region and a charge-depletion hole (σ-hole) of a polarizable electronegative atom,^1–3 has many applications, mainly in the halogen–Lewis base interactions referred to as halogen bonds.^4–8 This σ-hole is an electron depletion region on a polarizable atom (specifically group IV to VII atoms) along with a sigma covalent bond. The π-hole is the same concept, but perpendicular to a molecular framework with pi unsaturated covalent bonds. This was studied by Politzer et al.⁹ through computational analysis for 13 complexes containing HCN, NH₃, etc. A polarizable halogen atom, having both nucleophilic and electrophilic nature, tends to act as a donor and acceptor for inter- and intramolecular non-covalent interactions (NCI) simultaneously or individually.^10–13 Hence, halogen–halogen contacts are more possible and more valuable. Many C–X⋯X–C interactions derived and reported to date^14–17 are associated only with intermolecular interactions. Even though intramolecular interactions are important to decide the structure orientation of molecules and properties, theoretical studies on the above interactions are still rare. Moreover, it is too complicated to analyze and characterize the NCIs within the molecule. Recently, more unusual bonding situations have been discovered;¹⁸ further, intramolecular NCIs are enhanced for unsaturated compounds by the charge delocalization (conjugative resonance) within the system, termed resonance-assisted intramolecular non-covalent interaction. This indicates that resonance-assisted intramolecular interactions cannot be properly described by the electrostatic model alone, since their strength is associated with π delocalization.^19–21

In our previous paper,²² intramolecular halogen bonds (Br–O, Cl–O, F–O, Br–O, Cl–S and F–S) with conjugative resonance in the singlet system of X–C₁R₁=C₃R₂–C₂R₃=Y were reported. The σ-hole fails to describe the existence of intramolecular interactions in the abovementioned structures; however, it is confirmed through the electrostatic interaction between the opposite charges of the cusp points and two corresponding atoms (X = Br, Cl and F; Y = O and S). Among other factors which contribute to NCIs, resonance plays a major role for the stabilization of the structures; also, the systems lack charge transfer and orbital overlapping. In continuation of our previous work,²² this work focuses on the intramolecular interactions existing between two same/different halogen atoms (dihalogen bonding) for five membered ring structures of radical/cationic/anionic systems (X–C^{δ*/δ+/δ−}₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^{δ*/δ+/δ−}₂R₃–Y). We have analyzed and compared six types of halogen–halogen contacts, Br–Br, Cl–Cl, F–F, Br–Cl, Cl–F and Br–F, through quantum chemical calculations. The electrostatic interactions were primarily checked and visualized by molecular electrostatic potential maps. The existence of intramolecular interactions is confirmed by deep troughs in the 2D-NCI plots, isosurface regions in the 3D-NCI plots and the presence of the (3, −1) bond critical point (BCP) in QTAIM analysis. In order to derive the strength of the NCIs, the electron density, Laplacian, ellipticity and energy of the corresponding BCPs were analyzed. The charge transfer mechanisms and orbital overlapping were analyzed by natural bond orbital analysis.

The present study aims to gain in-depth knowledge about intramolecular halogen–halogen contacts in radical/cationic/anionic systems through answering the following questions. (1) The first issue is the impact of σ-holes and π-holes in intramolecular halogen–halogen contacts. (2) Also, whether similar effects of halogen bonding by conjugative resonance may be responsible for the intramolecular halogen–halogen contact by the corresponding resonance (formed by partial radical/cationic/anionic atoms through the wobbling of electrons within the structures in radical/cationic/anionic systems). (3) Another issue is whether these corresponding resonance types are responsible for the enhancement or existence of intramolecular halogen–halogen contacts. Furthermore, this work aims to report the existence of exotic interactions with resonance dependent intramolecular homo and hetero halogen–halogen contacts in radical, cationic and anionic systems.

Computational details

All the computations in the present study were performed using the Gaussian 09W program.²³ The calculations were carried out in the framework of the MP2/aug-cc-pVTZ level of theory. All the optimized model structures correspond to the minima in the potential energy surface, because no imaginary frequencies were observed. Bader's theory of atoms in molecules (AIM) was employed to find the critical points and to analyze the electron densities and their Laplacians. The properties of the bond critical points (BCPs) were studied, including the electron density (ρ), its Laplacian (Δ²ρ) and the ellipticity at a BCP. The AIM calculations were carried out using the AIM2000 package.²⁴ The NCI PLOT program, developed by Contreras-Garcia et al.,²⁵ was used to identify and visualize non-covalent interactions. It analyzes the reduced density gradient (S) of the electron density (r) obtained by single-point energy calculations at low densities that are related to the weakest interaction. Therefore, a density cutoff of ρ < 0.1 a.u. was chosen because it includes the region of interest. Natural bond orbital (NBO) analysis was used to examine the stabilizing interactions in the ground state.

The electrostatic potential map was generated for the five-membered closed structures in order to gain insight into the nature and directionality of the halogen-bond interactions being considered here. The electrostatic potentials have been computed on molecular surfaces, with a surface being defined as the 0.001 a.u. (electrons per bohr³) outer contour of the electron density, as proposed by Bader et al. The most positive value of the potential (the maximum value) is referred to as V_s,max.¹⁴

Results and discussion

The halogen–halogen contact is analyzed by considering molecule 1 as a radical system (X–C₁R₁=C₃R₂–C^*₂R₃–Y or X–C^*₁R₁–C₃R₂=C₂R₃–Y: X = Br, Cl and F and Y = Br, Cl and F). The resonance is formed by the partial radical character of two carbon atoms, such as C^*₁ and C^*₂. The structure X–C^δ*₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^δ*₂R₃–Y (Scheme 1; system 1) has three types of homo halogen–halogen contacts (X = Y: Br–Br, Cl–Cl, F–F) and three types of hetero halogen–halogen contacts (X ≠ Y: Br–Cl, Br–F, Cl–F). All the above structures involve comparatively weaker pi bonds, which is responsible for stabilizing the radicals. In general, radical stabilization can be described through three-electron bonding with well identified free radicals, especially when the radical centre is attached to another atom; it has an unshared electron pair. Molecules 2 and 3 are cationic and anionic systems (X–C₁R₁=C₃R₂–C^+/−₂R₃–Y or X–C^+/−₁R₁–C₃R₂=C₂R₃–Y) with the same types of X and Y substituents. These systems are stabilized with resonance by partial cationic or anionic atoms (X–C^δ+/δ−₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^δ+/δ−₂R₃–Y) as like radical systems having homo/hetero halogen–halogen contacts (Scheme 1; system 2 and 3). Among these three systems, system 1 has partial radical carbon atoms, with each having a partial unpaired electron; system 2 has partial carbo-cation atoms, but without lone-pair carbon atoms; and system 3 has partial carbo-anion atoms, with each having one unpaired electron stabilized by resonance.

Scheme 1 System 1 for the sketch of possible radical system, System 2 for the sketch of possible cationic system and System 3 for the sketch of possible anionic system. Inside box is the structure which is used for this study.

The paper also focuses on NCI bond length interactions and stability, as these can be tuned through substitution effects. To explain the mechanism of the bonding characteristics, the substituents R₁, R₂, and R₃ in X–C^δ*₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^δ*₂R₃–Y are preferred as electron-withdrawing groups (EWGs), inductively and by resonance [NO₂], and an electron-donating group (EDG) is preferred only by inductive effects [CH₃]. The substitution effect was handled in four ways: (I) the hydrogen atom was substituted for all Rs (Hs), (II) the EWG was only substituted for one of the Rs (EWGs), (III) the EDG was substituted for one of the Rs (EDGs) and (IV) both an EWG and an EDG were simultaneously substituted in two of the Rs (EWDGs). These substituted systems are clearly given in Scheme S1.† All these substituted methods were analyzed only for a radical system (X–C^δ*₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^δ*₂R₃–Y) at the MP2/aug-cc-pVTZ level of theory in order to understand the enhancement effect of intramolecular halogen–halogen contacts through substitutions.

To visualize the interaction (as electrostatic) between two halogen atoms, an MESP map has been plotted with a contour value of 0.03 a.u. Fig. 1 clearly shows a positive depletion hole (blue color) and a negative electron enriched hole (red color) for each σ- and π-hole. In the cationic systems (X–C^δ+₁R₁[horiz bar, triple dot above]C₃R₂[horiz bar, triple dot above]C^δ+₂R₃–Y), the Br and Cl atoms are observed to have positive σ-holes; the V_s,max value of the bromine atom is 0.419 and the V_s,max value of the chlorine atom is very small. The electrostatic interaction between the positive σ-hole and the negative electron donor is responsible not only for the stability but also for the high directionality of the bonds. However, in the present study, the electrostatic interaction in halogen bonds is repulsive; thus, all the attraction comes from the dispersion energy. The stabilisation energy in the halogen bonds is dominated by the dispersion energy and the halogen bond angle is below 100° for all the studied structures. This is not surprising, because the heavier halogens with large polarizabilities are close to each other, which increases the dispersion energy.¹⁴ This is supported by the concept that halogen–halogen contacts (type I) are generally considered to be dispersive, are associated with crystallographic inversion centers, and are not halogen bonds. Furthermore, it shows that halogen bonds are more stable than the respective halogen–halogen contacts; however, the difference is small.¹⁴ Furthermore, the fluorine atom is observed with a negative σ-hole along the C–X bond with a V_s,_min value of 0.249. Interestingly, partial cationic carbon atoms have a positive π-hole with a V_s,max value of 0.419 and partial anionic carbon atoms have a negative π-hole with a V_s,max value of −0.241, which is perpendicular to the molecular framework in the cationic and anionic systems (Fig. 1F and I), respectively. The V_s,max values of the σ-hole for a halogen atom were observed for EWG and EWDG systems, whose values are close to each other with slight variations in the corresponding interactions (figure/table). Similarly, the V_s,max values of H- and EDG-substituted systems are also found to be nearer, which is clearly revealed in Table S1.† On the other hand, the V_s,max values of EWG- and EWDG-substituted systems are higher (by approximately 0.05) than those of H- and EDG-substituted systems. This indicates that the NO₂-substituted method (EWG/EWDG) is more favorable for the occurrence of σ-holes. A graphically visualized MESP also proves the efficiency of the NO₂ substitution, because the positivity in the cusp region is higher for this method than for the other two methods (H/EDG). A large variation in the σ-hole size between the bromine and chlorine atoms is observed in the five-membered ring radical/cationic/anionic structures.

Fig. 1 The electrostatic potential (in a.u.) mapped on the 0.001 a.u. isodensity surface for the selected structure, computed at the MP2/aug-cc-pVTZ level of theory. All systems are H, H, H order of substituted structures. (A), (B), (C) = Br⋯Br, F⋯F, Br⋯Cl for the radical system, respectively. (D), (E), (F) = Br–Br, F–F, Br–Cl for cationic system, respectively. (G), (H), (I) = Br–Br, F–F, Br–Cl for anionic system, respectively.

In general, the existence of a negative σ-hole in the surroundings¹ is not sufficient to describe a charged anisotropic halogen atom.⁹ In the present study, the negative σ-hole present in the fluorine atom is bonded with partial characteristics of the radical/cationic/anionic carbon atom. On the other hand, this negative σ-hole does not exist in the true conjugative resonance five-membered ring neutral system (F–C₁R₁=C₃R₂–C₂R₃=O) as observed in our previous results.²² Therefore, it is expected that the partial characteristic existing in the radical/cationic/anionic carbon atoms is due to the negative σ-hole in the fluorine atom. In a cationic system, the negative σ-hole of the fluorine atom exists with a positive V_s,max value (of approximately 0.2). This is comparable with our previous study¹⁴ for the anionic system of I₃⁻, where the positive σ-hole is observed with a negative V_s,max value of −0.109. Similarly, in the present study for the cationic system, the negative σ-hole is observed with positive V_s,max values. The range of the σ-hole V_s,max values for the cationic system is 0.41 to 0.47, the range for the anionic system is 0.07 to 0.04 and the range for the radical system is 0.10 to 0.20 for all substitutions, respectively. For the cationic system, the range of the positive π-holes is 0.41 to 0.47 and that of the negative π-holes is −0.24 to −1.6. However, the presence of π-holes does not contribute to the intramolecular interactions. The V_s,max values of the σ-holes for all molecules are given in Table S1.†

The σ-hole present in all halogens is found along the C–X bond axis and away from the interacting region, where the halogen bond angle plays a major role. This in turn reveals the lesser impact of the σ-hole on intramolecular interactions. Fig. 1 shows that the electrostatic potential on the halogen facing regions between two halogen atoms is identical; however, at the same time, it has a close contact within the ring system. Johansson et al.¹⁸ reported that close contacts minimized the electrostatic repulsion, which is also evident in the halogen–halogen contact. In the present study, the σ-hole is not responsible for this type of interaction, but any one of the fluorine atoms in the hetero halogen–halogen contact (Br–F and Cl–F) associated with the opposite charges of the cusp point facing the interaction region plays a key role. Thus, in five-membered ring closed radical/cationic/anionic systems with halogen–halogen contacts, if one of the halogens is a fluorine atom which has electrostatic interactions, the other halogen–halogen contacts do not have electrostatic interactions.

From the ESP map, it is concluded that although the contribution of electrostatic interactions to form strong NCIs is much lower, the close contact for all the abovementioned interactions is shorter than the sum of the van der Waals (VDW) radii of the corresponding atoms, except the F–F interaction of the anionic system. Most of the halogen–halogen contacts considered in the present study are not close to the ideal geometric arrangement, with Br–Br, Cl–Cl, F–F, Br–Cl, Cl–F and Br–F angles less than 100°; however, the X–Y (X, Y = I, Br, Cl, F) distance is smaller than the sum of the van der Waals radii. This sum for Br–Br, Cl–Cl, F–F, Br–Cl, Cl–F and Br–F amounts to 3.70, 3.50, 2.94, 3.60, 3.22 and 3.32 Å, respectively. The greater the difference between the X–Y distance and the sum of the van der Waals radii, the stronger the expected binding. The halogen bonds are shorter than the sum of the van der Waals radii of a halogen and an electron donor or two halogens.¹⁴ ΣVDW − L (the difference between the bond length and the sum of the VDW radii) is important evidence for the presence of halogen bonding.

The halogen–halogen close contact observed in the F–F interaction for the anionic system is 3.01 Å, resulting in the absence of an intramolecular halogen bond. 2.55 to 3.60 Å is the bond-length range of all the exotic intramolecular NCIs. Overall, the intramolecular X–X interaction of the cationic system is very strong when compared with the radical and cationic systems, and the anionic system is weak. While comparing the radical, cationic and anionic systems with the common substituted method (Hs), the NCIs strength decreases in the order of anionic < radical < cationic systems for each type of interaction because the C[horiz bar, triple dot above]C[horiz bar, triple dot above]C angle is the crucial factor. The large variations in the angle between the cationic/radical/anionic systems indicate the contribution of full or partial unpaired electrons of the carbon atoms.

The discussion reveals that the intramolecular halogen–halogen contacts cannot exist without these delocalized charges and radicals of resonance. For example, Fig. 2A–C show the substitutions for X = Br and Y = Br, where the Br–Br interaction bond lengths are 3.36 Å, 3.46 Å and 3.60 Å for resonance-associated cationic/radical/anionic systems, respectively. Fig. 2D has the same X and Y substitutions as above; however, the resonance is neglected in order to solve the carbon tetravalent properties (the neutral singlet system). The structures (between Br and Br) are observed with a distance of 4.38 Å, indicating the lack of an intramolecular halogen–halogen contact. In neutral systems for all halogen–halogen contacts, the bond critical point (BCP) is lacking between the Br and Br atoms. This in turn reveals that resonance (formed by partial radical/cationic/anionic delocalized charges) plays a major role in the existence of intramolecular halogen–halogen contacts (including fluorine-atom-containing interactions). Meanwhile, in the case of five membered cationic/anionic/radical ring systems, the role of resonance is to induce the existence of halogen–halogen contact even in the identical region between two halogen atoms, which lacks the electrostatic interaction. Thus, the third question in the aim has also been addressed.

Fig. 2 The structures of the five-membered and five-membered closed systems of Br⋯Br interactions represents (A) the cationic system, (B) the radical system, (C) the anionic system and (D) the singlet neutral system.

Concerning substitution analysis for the radical system, all halogen–halogen contacts, bond lengths for the Hs method, halogen bond ranges and changes in halogen–halogen contact through EWG, EDG and EWDG substitutions are shown in Table 1. Hs-substituted structures associated with weak interactions have longer bonds than other types of substitutions. Stronger intramolecular halogen–halogen contacts are observed for EWDG than for EDG and EWG. The NO₂, CH₃, H order of substitutions, associated with the strongest interactions, has shorter bonds for all types of halogen–halogen contacts. The above substitution has stronger halogen–halogen contact when compared with another 12 orders of interactions and also with respect to the corresponding cationic system. The halogen–halogen contact bond lengths for 90 structures (6 for cations, 6 for anions, and 78 for radicals with their corresponding substituted structures) are reported in Table S2.† It is thus concluded that intramolecular X–X interactions can be stronger for a radical system and for a cationic system if suitable substitutions in the proper order are selected. The bond-length range of the radical system is between the range of the cationic and anionic systems except for the EWDGs method. All these types of halogen–halogen contact have much smaller bond angles, which are given in Table S4.†

Table 1 The bond-length variations of all substitutional groups

R1, R2, R3	Br⋯Br	Cl⋯Cl	F⋯F	Br⋯Cl	Br⋯F	Cl⋯F
a Cationic system.b Anionic system.c Radical system.
ΣVDW	3.70	3.50	2.94	3.60	3.32	3.22
H, H, H^a	3.36	3.17	2.61	3.26	2.97	2.88
H, H, H^b	3.60	3.44	3.01	3.52	3.26	3.20
H, H, H^c	3.46	3.27	2.76	3.36	3.08	3.00
EWG only^c	3.42–3.44	3.23–3.24	2.70–2.73	3.32–3.34	3.03–3.06	2.95–2.98
EDG only^c	3.40–3.42	3.21–3.23	2.69–2.72	3.30–3.33	3.02–3.05	2.93–2.96
Both simultaneously^c	3.35–3.40	3.13–3.21	2.55–2.68	3.23–3.34	2.90–3.02	2.81–2.93

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Moreover, the presence of anti-aromaticity and aromaticity due to delocalization of radical/cationic/anionic charges, as well as changes in the resonance due to substitution effects, can be examined by NICS analysis. The NICS (1) value is more suitable for analyzing the resonance, because the maximum of the diatropic ring current effect of the π-bond is counterbalanced by a paratropic contribution of σ-bonds. This paratropic effect decreases with the distance from the centre. Specifically, at 1.0 Å above the centre, the σ-bonds vanish. The negative value of NICS (1) confirms the presence of resonance, which originates from delocalized radical/cationic/anionic charges, and the large value shows its high efficiency. The values of NICS (1) in Table 2 clearly express the presence of resonance in all substituted radical systems. The reference molecule benzene (aromaticity by conjugative resonance) is a model of aromaticity whose NICS value is −11.5; however, here, few systems are observed to have high values. Generally, the H, CH₃, H order of the substituted systems has high NICS values compared with the other order of substitutions. Finally, the NCISs value clearly indicates that the corresponding resonance is responsible for the close contact of the donor and acceptor in halogen–halogen bonding.

Table 2 Nucleus independent chemical shift NICS (1) values (in ppm) for radical system

R1, R2, R3	Br⋯Br	Cl⋯Cl	F⋯F	Br⋯Cl	Br⋯F	Cl⋯F
H, H, H	−10.42	−10.42	−9.60	−10.41	−9.92	−9.97
NO2, H, H	−11.18	−8.98	−8.80	−11.11	−10.79	−10.54
H, NO2, H	−8.95	−11.11	−9.50	−6.92	−6.60	−8.48
H, H, NO2	−11.18	−8.98	−8.80	−12.38	−12.03	−11.18
CH3, H, H	−13.11	−12.41	−8.52	−10.34	−9.73	−12.46
H, CH3, H	−13.24	−12.80	−11.03	−10.65	−8.71	−12.44
H, H, CH3	−13.11	−12.41	−8.52	−11.53	−6.63	−10.20
NO2, H, CH3	−7.84	−7.47	−6.63	−11.00	−6.68	−6.91
H, NO2, CH3	−9.32	−7.06	−8.87	−9.48	−4.50	−6.35
CH3, H, NO2	−7.84	−7.47	−6.63	−9.61	−11.99	−7.67
NO2, CH3, H	−12.99	−8.65	−7.12	−9.38	−10.45	−7.55
CH3, NO2, H	−9.32	−7.06	−8.87	−7.01	−4.64	−9.06
H, CH3, NO2	−12.99	−8.65	−7.12	−9.99	−9.11	−8.89

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The (3, −1) BCP is the essential evidence to confirm, analyze and characterize the interaction properties and to describe the strength of the BCP between two halogen atoms using the Atoms In Molecules (AIM) theory. All the intramolecular halogen–halogen contact has an electron density range of 0.0088 to 0.0155 a.u and a Laplacian electron density range of 0.0800 to 1.0300 a.u. The values of less than 0.1 a.u for the electron density and the positive values for the Laplacian of electron density in the non-covalent interactions indicate the presence of interactions. The above ranges reveal that the halogen–halogen contacts are stronger than the hydrogen bonds. All the topological parameters (ρ(r), Δ²ρ(r), E_BCP, ε) indicate that the halogen–halogen contacts for the cationic systems are stronger than for other systems, as compared with the fundamental order of the H, H, H type; this is clearly revealed in Table S5–S8,† respectively. Similarly, ρ(r), Δ²ρ(r), E_BCP, and ε clearly show that the NO₂, CH₃, H order of radical systems has stronger halogen–halogen contact than the cationic system of the H, H, H order of substitution.

The halogen-bonded radii through the mutual penetration of electron density reported for the halogen–halogen contacts are 3.05 to 3.22, 2.93 to 3.11 and 2.41 to 2.61 a.u for the bromine, chlorine and fluorine atoms, respectively (Table 3). Further, the substitution method reveals that the halogen-bonded radii for the halogen atoms may vary within the molecules. Also, not all the halogen–halogen bond strengths can be compared through their bond lengths; however, this can be calculated through their ΣVDW − L parameters.²⁶ There is a linear correlation between electron density and the ΣVDW − L parameter with the correlation equation of ρ = 0.0045 + 0.0273ΣVDW − L (R = 0.92), as shown in Fig. 3. The strength of the interactions thus depends on how many halogen atoms are immersed into the other halogen atoms.

Table 3 Halogen bonded radius of halogen atoms in halogen–halogen interactions for cation/anionic systems and radical system with substituted systems

R1, R2, R3	Br⋯Br	Cl⋯Cl	F⋯F	Br⋯Cl	Br⋯F	Cl⋯F
a Cation system.b Radical system.c Anionic system.
H, H, H^a	3.17	3.00	2.47	3.01	2.47	2.45
	3.17	3.00	2.47	3.16	3.15	3.01
H, H, H^b	3.41	3.26	—	3.24	2.73	2.74
	3.41	3.26		3.41	3.43	3.31
H, H, H^c	3.27	3.10	2.61	3.11	2.60	2.57
	3.27	3.10	2.61	3.25	3.22	3.11
NO2, H, H	3.24	3.07	2.58	3.09	2.54	2.54
	3.26	3.07	2.59	3.22	3.25	3.09
H, NO2, H	3.24	3.06	2.55	3.07	2.52	2.52
	3.24	3.06	2.55	3.21	3.22	3.06
H, H, NO2	3.26	3.07	2.58	3.08	2.54	2.55
	3.24	3.07	2.59	3.24	3.21	3.09
CH3, H, H	3.24	3.07	2.58	3.08	2.54	2.54
	3.23	3.06	2.57	3.22	3.18	3.07
H, CH3, H	3.22	3.04	2.54	3.06	2.52	2.51
	3.22	3.04	2.54	3.19	3.15	3.04
H, H, CH3	3.23	3.07	2.58	3.07	2.54	2.54
	3.24	3.06	2.57	3.21	3.23	3.08
NO2, H, CH3	3.22	3.04	2.53	3.05	2.54	2.50
	3.21	3.05	2.54	3.19	3.16	3.05
H, NO2, CH3	3.20	3.02	2.49	3.03	2.49	2.48
	3.21	3.03	2.50	3.18	3.17	3.02
CH3, H, NO2	3.21	3.04	2.53	3.10	2.54	2.52
	3.22	3.05	2.54	3.22	3.17	3.04
NO2, CH3, H	3.16	2.97	2.41	2.99	2.42	2.40
	3.17	2.97	2.41	3.12	3.05	2.91
CH3, NO2, H	3.21	3.02	2.49	3.04	2.49	2.43
	3.20	3.03	2.50	3.18	3.16	2.93
H, CH3, NO2	3.16	2.97	2.41	2.99	2.52	2.42
	3.17	2.97	2.41	3.15	3.15	2.93

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Fig. 3 The graph of linear correlation between ΣVDW − L (Å) and electron density (ρ).

The 2D-NCI plot (plotting the reduced gradient S as a function of the electron density r, oriented by the sign of λ₂) analysis formulates the potential to understand the presence of a weak interaction between atoms, as well as its strength.²⁵ The reduced density gradient, (RDG) S = |Δρ|/(2(3π²)^1/3ρ^4/3), is one of the three components of electron-density distribution. The presence of interactions (hydrogen bonding, attraction, van der Waals, repulsive, steric clashes) and their strengths are identified from the depth of the peak (plot between low sign(λ₂)ρ and low RDG) in the 2D-NCI plot, and the bonding or non-bonding characteristics can also be identified. Therefore, these plots provide clear fingerprints of inter- and intramolecular interactions. Fig. 4a shows the 2D-NCI plots for the interaction of F–F with cationic and anionic systems, respectively. The red-color region belongs to the cationic system and the violet-color region belongs to the anionic system, while the mixed red and violet colors represent common data between them. The depth trough of the color red clearly indicates the presence of intramolecular F–F contact, and the value of −0.025 a.u (sign(λ₂)ρ) shows the strength of the interaction, which is stronger than the weak hydrogen bonds.

Fig. 4 A 2D-NCI plot of a reduced density gradient (RDG) vs. sign(λ₂)ρ (A) combined with the F⋯F interactions of cationic (red color) and anionic (violet color) systems; (B) combined with the Cl⋯F interactions of NO₂, CH₃ and H substitutes in the radical system (red color) and anionic system (violet color).

The halogen bonds have dual characteristics with attraction/repulsion interactions, which are shown by the double-like depth troughs with opposite signs. The bottom blue trough thoroughly shows the lack of F–F contact in the anionic system. Fig. 4b compares the Cl–F contacts for the NO₂, CH₃, H order of substitution in the radical system (the red region) and in the anionic system (the violet region). This proves that both systems experience halogen bonding between the chlorine and fluorine atoms. The figure reveals that their strength is comparable by the negative value of sign(λ₂)ρ for the anionic system, which is smaller than that of the corresponding radical system. All the interaction strengths could be described through this trough between the RDG and sign(λ₂)ρ. The dual characteristics (attraction/repulsion) of halogen–halogen contacts are also shown in the isosurface region with the bicolor region (light blue/red curved in green) of the 3D-NCI plot in the ESI.† Therefore, this analysis confirms the presence of exotic interactions.

Moreover, the charge-transfer mechanism and its stabilization energies have been verified by the second-order perturbation term using NBO analysis. For these five-membered ring molecules, the charge transfer between the lone pair (n) of the acceptor atom and the anti-bonding orbital (σ*) of the donor atom was not observed for any of these resonance-assisted intramolecular halogen–halogen contacts, such as intramolecular halogen bonding. Also, the NBO view for analyzing the orbital overlap shown in Fig. 5 (H, NO₂, H order of radical structure with Cl–Cl interaction) was calculated. It indicates non-interacting lobes between two halogen atoms (Cl–Cl contact) when it reaches the minimum or it almost vanishes. Non-interacting lobes imply the absence of orbital overlapping. These concepts were identical to the intramolecular halogen bonding in the singlet neutral system.²¹ Furthermore, interacting lobes are present for the hydrogen bonding between an oxygen and hydrogen atom; these are clearly visualized in Fig. 5.

Fig. 5 The major second order perturbation interaction energies obtained from NBO analysis for H, NO₂, H order of substitution in radical system.

Comparison of the results of intramolecular halogen bonding in neutral systems and intramolecular halogen–halogen contacts in radical/cationic/anionic systems reveals that these dihalogen bonding interactions are the same, with bond angles below 100°. The ΣVDW − L parameter clearly describes the strength of the corresponding halogen–halogen contacts. Although the concept of VDW is not necessary for intermolecular halogen bonding, it has more effect in intramolecular halogen–halogen contacts. However, the linear-probability correlation plotted between the difference of the sum of the van der Waals radius and the non-covalent bond length (ΣVDW − L) and the electron density of corresponding interactions reveals the impact of the halogen–halogen contact bond length. This was also found for intramolecular halogen bond contacts through the same correlation in a previous report. The presence of the BCP, the lack of charge transfer and orbital overlapping are also same for both intramolecular halogen bonding and halogen–halogen contact. The strength of halogen–halogen contact in the cationic system is stronger than other intramolecular halogen bonding. The study of NICS without resonance structures and with different substituted radical systems reveals the impact of resonance alone in intramolecular halogen–halogen contacts, which automatically provides an answer for questions 2 and 3 that we raised.

Conclusion

In conclusion, this work reports the existence of exotic intramolecular halogen–halogen contacts. These interactions were surprisingly stabilized by resonance alone and also occur through delocalized radical/cationic/anionic carbon atoms. The answers to three questions asked above have been examined. (1) The effect of forming halogen bonding by conjugative resonance is similar to that of forming halogen–halogen contacts by resonance. This is formed by partial radical/cationic/anionic atoms through delocalization in radical/cationic/anionic systems. (2) In this study, the impact of resonance on intramolecular interactions (formed by partially delocalized radical/positive/negative charges) does not enhance the intramolecular halogen–halogen contacts, but is responsible for the existence of halogen–halogen contacts even without electrostatic interactions. (3) Positive and negative σ-holes were reported for the radical system; however, the σ-hole was not utilized for halogen–halogen contact. More specifically, the existence of the positive π-hole in cationic systems and, for the first time, the existence of the negative π-hole in anionic systems was reported in these five membered ring systems. Overall, the following results have been acquired to satisfy the aim of the present work.

When comparing these radical, cationic and anionic systems associated with delocalized resonance structures, the cationic system has shorter halogen–halogen cutoffs with stronger noncovalent interactions due to the absence of lone pairs in the cationic carbon atoms. Interestingly, for the radical system, the strength of the halogen–halogen contact in the NO₂, CH₃, H order of substitution competes with the high strength of the cationic halogen–halogen contact. Overall, this study reveals the impact of various substituent orders on electron withdrawing and electron donating groups in order to enhance the intramolecular halogen–halogen contact. The homo/hetero halogen–halogen contacts are the most remarkable, because there is no electrostatic interaction except for the fluorine atom. The interactions were neither charge transfer nor orbital overlapping. Nevertheless, the ΣVDW − L, the topological parameters and the NCI plot confirm the presence of these exotic interactions and demonstrate their strengths and properties. Although exotic interactions are continually being discovered, this different type of resonance-dependent exotic interactions is the most notable. An extension of this work can be carried out with the synthesis of salts, including cationic or anionic five membered ring systems. This is also very useful to understand and analyze intermolecular interactions using σ-holes and π-holes with positive and negative regions.

Acknowledgements

This work was part of the Research Project RVO: 61388963 of the Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic. It was also supported by the Czech Science Foundation [P208/12/G016] and the operational program Research and Development for Innovations of the European Social Fund (CZ 1.05/2.1.00/03/0058).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra14270b

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