A heuristic approach to evaluate peri interactions versus intermolecular interactions in an overcrowded naphthalene

An electron density study on sterically overcrowded octachloronaphthalene is performed using an extensive combination of high-resolution single crystal X-ray diffraction and ab initio single-point and periodic DFT calculations. The unusual asymmetry in the crystalline geometry as opposed to symmetric solvated phase geometry is investigated and the role of steric forces, contributed primarily by the peri interactions in imparting unique ‘localized double bond’ character in the naphthalene ring, is rationalized.


Introduction
The term 'overcrowding' in chemistry is synonymous with the presence of non-bonded intramolecular interactions often referred to as steric hindrance. These steric factors influenced by the presence of exocyclic bonds invoke in-plane or out-ofplane deviations from the ideal geometry of aromatic molecules. Consequently, the molecules undergo geometrical manifestation to release the strain in the system which in turn modulates the -electron delocalization. This results in an alteration in the reactivity and property of the molecule, a factor of significant interest to chemists. The synthesis of sterically congested polyaromatic hydrocarbons (PAHs) has remained a challenge due to their elusiveness often resulting in low yields. The design of convex, bowl-shaped PAHs akin to fullerenes and also as synthetic precursors for the synthesis of carbon nanotubes has been a matter of interest to chemists for decades (Wu & Siegel, 2006;Scott et al., 2012). PAHs have garnered considerable attention in recent times due to their potential applications in organic electronics (Tannaci et al., 2007;Pascal, 2006). In addition, highly symmetric PAHs form cavities in a supramolecular assembly with the potential to encapsulate and trap guest molecules (Downing et al., 1994). Overcrowded bistricyclic aromatic enes (BAEs) show thermochromic and photochromic properties which qualify them as candidates for chiroptical molecular switches and molecular motors (Biedermann et al., 2001). Overcrowding in aromatic molecules such as naphthalene, acenaphthylenes, acenaphthene and pyrene are uniquely characterized by peri interac-tions (Balasubramaniyan, 1966;Diamond et al., 2014;Knight et al., 2012). In the case of compounds wherein atoms or groups other than H atoms are at the peri positions like in naphthalene and related PAHs, the 'ideal' peri distance (ca 2.5 Å ) between respective atoms or groups becomes shorter than the sum of their van der Waals radii. This causes the atoms or groups to crave for space leading to steric congestion in the molecule. In order to minimize these steric strains the rigid carbon framework undergoes distortion that generally leads to extended distances. The extent of distortions or the degree of strain in these systems depends upon the number, size and the nature of the functional groups present at the peri positions and also the type of aromatic backbone involved. Several synthetic routes have been suggested for the preparation of peri substituted naphthalene, acenaphthylenes and acenaphthene, and efforts have been made on exploring the nature of weak non-bonded intramolecular interactions in the peri substituted species (Hoefelmeyer et al., 2002;Dominiak et al., 2005;Kilian et al., 2011;Matta et al., 2005). The transannular interactions between substituents in 1,8-and 5,6-positions can either be repulsive due to steric congestion which result from the direct overlap of orbitals (lone pair-lone pair interactions for Groups 15,16,17) or attractive due to n(lonepair) ! *(antibonding) orbital interactions. The majority of these studies were made based on crystal structure analysis and routine gas-phase calculations. Indeed, a very limited number of experimental electron density studies involving peri interactions are reported in the literature (Mallinson et al., 1999;Lyssenko et al., 2004;Farrugia et al., 2009;Hoser et al., 2010). However, all such studies are devoid of detailed quantitative and qualitative discussion on the nature of these non-conventional intramolecular interactions and their influence on the molecular geometry and -electron distribution.
Halogenated naphthalenes show anomalous gradation in intra-and intermolecular interactions and associated crystal packing based on the size of the halogen atom. The degree of polarization in a halogen atom and its supramolecular effects has been a topic of intense investigations towards understanding intermolecular interactions and rational design of molecular crystals (Gilday et al., 2015). An analysis based on the Cambridge Structural Database (CSD; Version 5.37, November 2015) reveals an interesting trend in the crystal structures of the octahalo derivatives of naphthalene. The smaller size of fluorine (isosteric to hydrogen) has no overcrowding effect in the octafluoronaphthalene such that the molecule remains planar with a centre of symmetry passing through the centre of the molecule in the crystal structure (Ilott et al., 2010). Octabromonaphthalene understandably exhibits an out-of-plane twisted conformation because of larger bromine atoms giving rise to steric effects; although it is non-planar, the twisted conformation is symmetrical making the molecule symmetrical such that it too sits on a twofold rotation axis (Brady et al., 1982). However, in sharp contrast, octachloronaphthalene (hereafter referred as OCN) shows a twisted conformation which is asymmetric in nature, i.e. the molecular geometry is asymmetric (Fig. 1), and therefore the molecule sits on a general position in the crystal structure.
These features prompted us to closely investigate the anomalous behaviour of OCN to gain insight into the overcrowding phenomenon and its effects on geometry, aromaticity and supramolecular assembly. It is noteworthy that the current study on OCN is the first X-ray electron density study on an overcrowded molecule and the results are expected to provide a fundamental understanding of the overcrowding phenomenon. In addition, the importance of this study comes from the fact that OCN, which belongs to the class of polychlorinated naphthalenes (PCNs), is a serious environmental pollutant (Falandysz, 1998). Toxicological studies of OCN based on metabolic reactivity on living cells (Campbell et al., 1981) and thermal degradation of OCN (Su et al., 2014) are of huge relevance in the context of environmental protection. Further, nucleophilic substitution reactions of OCN produces ansubstituted product contrary to the -substituted product obtained in the case of octafluoronaphthalene (Brady et al., 1984). To gain a clear perception on the nature of these properties/reactivities of OCN and their correlation with its structure, understanding of the electron density distribution is deemed significant.
OCN in its reported room-temperature (Herbstein, 1979) structure displays remarkably shorter distances (nearly 17% shorter than the sum of van der Waals radii) between peri Cl atoms on either side of the molecule. The influence of such transannular ClÁ Á ÁCl interactions at the 1,8 and 4,6 peri substituted positions further triggered by the overcrowding of the other Cl atoms is suggested to possibly cause the molecule to deviate from the plane of symmetry.
In this work the nature of the peri interactions is analyzed and the impact of the conflict/contest between such intramolecular peri interactions with other intermolecular interactions on the molecular geometry as well as on the crystal packing is investigated. The multipole model derived at high-resolution X-ray data (Hansen & Coppens, 1978), along with topological analysis based on Bader's QTAIM (Bader, 2002)   quantitative inputs to the properties exhibited in crystals. It is of interest to note that an unusual difference in the out-ofplane displacements occurs in the OCN molecule. Analysis of the packing features in terms of the nature of electron density distribution in the crystal structure both from theory and experiment provides an explanation. The degree of aromaticity lost in the molecule because of out-of-plane deformations is evaluated in terms of the ellipticity profile (Farrugia et al., 2009) and Nuclear Independent Chemical Shift (NICS) studies (Chen et al., 2005).

Synthesis
The compound octachloronaphthalene (OCN) was synthesized according to the method reported in the literature (Jacobsson et al., 2007).

Crystallization
The purified solid was kept for crystallization in a saturated solution of benzene at low temperature (278 K). Yellow needle crystals were obtained after 2 weeks of solvent evaporation.

Data collection and structure refinement details
The high-resolution charge-density data on OCN were collected on an Oxford Xcalibur (Mova) diffractometer equipped with an EOS CCD detector using Mo K radiation ( = 0.71073 Å ). A crystal of dimensions 0.34 Â 0.21 Â 0.06 mm, was cooled to 100 K with a liquid nitrogen stream using an Oxford cobra open stream non-liquid nitrogen cooling device. The crystal-to-detector distance was fixed at 45 mm, and the scan width (Á!) was 1 per frame during the data collection. The data collection strategy was chosen in such a way to yield a high resolution X-ray data set (d = 0.46 Å ) with high redundancy and completeness to 100%. Cell refinement, data integration and reduction were carried out using the program CrysAlisPro (Oxford Diffraction, 2011). Face indexing was done for the accurate numerical absorption correction. Sorting, scaling and merging of the data sets were carried out using the program SORTAV (Blessing, 1997). The crystal structure was solved by direct method using SHELXS2014 (Sheldrick, 2014) and refined based on the spherical-atom approximation (based on F 2 ) using SHELXL2014 included in the WinGX package suite (Farrugia, 2012).

Multipole modelling
The charge density modelling and multipolar aspherical atom refinements for OCN were performed based on the Hansen and Coppens multipole formalism using XD2015 (Koritsanszky et al., 2015). The function AEw[|F o | 2 À |F c | 2 ] 2 was minimized for all reflections with I > 2(I). Weights (w) were taken as 1/ 2 (F o 2 ), and the convergence criterion of the refinement was set to a maximal shift/e.s.d. of < 10 À10 . From the list of scattering factor wavefunctions available in the XD package, the basis functions and single-values were taken from the databank file of SuÀCoppensÀMacchi (Su & Coppens, 1998). The scale factor was refined against the whole resolution range of diffraction data in the first refinement step. The scatterplot depicting the variation of F obs with F calc and variation of F 2 obs /F 2 calc with (sin)/ (supporting information, Fig. S1) is indicative of the good quality of the data after scaling. The positional and anisotropic displacement parameters of all the atoms were refined against the whole resolution of data. The multipolar populations were constrained to obtain a reasonable data-to-parameter ratio. Further scale, positional and anisotropic displacement parameters, P val , P lm , , and 0 , on all atoms were refined in a stepwise manner, until the convergence criterion was reached. Separate and 0 parameters were used to define different atom types based on their chemical environments. The multipole expansion was extended to hexadecapoles in the case of the chlorine atoms (l = 4) and were truncated at the octupole level for carbon atoms (l = 3). The residual electron density peaks in the final model are À0.44 and 0.47 e Å À3 with an r.m.s. value of 0.09 e Å À3 for minimum and maximum values, respectively, at full resolution (1.08 Å À1 , supporting information, Fig. S2). The fractal dimension plot (Meindl & Henn, 2008) which provides the overall distribution of residual electron density in the unit cell is symmetric in nature and parabolic in shape (sin / 0.8 Å À1 ) (supporting information, Fig. S3 À0.44, 0.47/ À0.27,0.24 analysis of the electron-density topology and related properties was performed using the XDPROP (Volkov et al., 2000) module of the XD software suite. The relevant crystallographic and refinement details are listed in Table 1 and the multipole population parameters are provided in the supporting information (Tables S1-S5).

Results and discussion
The outcomes from the high-resolution X-ray diffraction data at 100 K, experimental charge-density modeling and gas-phase DFT calculations are organized into four sections. In x3.1, the crystal structure is discussed in detail. x3.2 describes the nature of intramolecular peri interactions, while in x3.3 the effect of overcrowding on -electron distribution and consequently on aromaticity is determined. x3.4 focuses on the investigation of the observed asymmetric twisted conformation (differences in dihedral angles) in the crystal and also establishes the importance of interplay between intramolecular steric forces and intermolecular interactions in directing the conformation as well as crystal packing.
3.1. Crystal structure at 100 K OCN crystallizes in the monoclinic space group P2 1 /n. The salient features of the crystal structure are the presence of two distinct short intramolecular peri ClÁ Á ÁCl interactions (1,8 = 2.994 Å and 4,6 = 3.025 Å ) and two different dihedral values of angles 1 and 2 at the peri substituted positions 1 (Cl4-C4-C6-Cl5 = 36.80 ) and 2 (Cl1-C1-C9-Cl8 = 24.42 ) (Fig. 2a). This confirms the asymmetry between the upper and lower halves of the molecule. In the intermolecular space, the molecules aggregate along the 2 1 screw axes parallel to the b axis in parallel-displaced geometries (Fig. 2b). However, due to the twisted conformation of OCN,stacking is inefficient as vertical separation between centres of the corresponding fused benzene rings (in the individual naphthalene moiety) are significantly longer (4.097 and 4.559 Å , respectively) than the optimum intermolecular distance of $ 3.75 Å between two benzene rings in a parallel displaced configuration generally observed in crystal structures (Sinnokrot et al., 2002). The presence of Cl atoms at all positions of overcrowded naphthalene molecule gives rise to various types of interesting intermolecular ClÁ Á ÁCl interactions (supporting information, Figs. S4 and S5).
A Cambridge Structural Database (CSD) analysis was carried out to estimate the abundance of intramolecular ClÁ Á ÁCl interactions in molecular crystals. The search was done on the basis of the ClÁ Á ÁCl contact distance being restricted to the sum of the van der Waals radii (Batsanov, 2001) and the corresponding intramolecular contacts are separated by at least four covalent bonds. The search resulted in 421 hits (supporting information, Fig. S6), out of which 35 have intramolecular peri ClÁ Á ÁCl interactions. The distances found for the peri ClÁ Á ÁCl interactions in OCN are in agreement with the average value of 3.000 AE 0.025 Å derived from the histo-gram of the number of hits versus distance (supporting information, Fig. S7).

Nature of intramolecular ClÁ Á ÁCl peri interactions
In order to unequivocally establish the nature of peri interactions and their possible influence on the deviation from planarity and unusual molecular geometry, Bader's topological and RDG-based NCI analysis have been performed and are outlined below.
Three-dimensional deformation and Laplacian maps were plotted to recognize the nature of the intramolecular peri   interactions. From both deformation maps of individual peri interactions it is observed that the lone pairs of Cl atoms signified by the blue electron dense region (supporting information, Fig. S8a and S8c) are displaced from another. This observation is corroborated in the three-dimensional Laplacian maps which show the VSCCs (valence shell concentrated regions) of one Cl atom is facing the cavity (electron depleted site) of the other Cl atom (supporting information, Figs. S8b and S8d). This can be interpreted as reduced repulsion between respective atoms which minimizes the strain in the molecule.
3.2.2. NCI analysis. A NCI (non-covalent interaction) descriptor (Johnson et al., 2010;Saleh et al., 2012), based on two scalar field quantities, electron density () and reduced density gradient (RDG), allows for the extraction of additional information on ClÁ Á ÁCl peri interactions. RDG is a dimensionless quantity [s = 1/2(3 2 ) 1/3 )|r|/ 4/3 ] used in DFT to describe the deviation from a homogeneous electron distribution. Generally non-covalent interactions are characterized by low and low RDG values. The sign of the second largest eigenvalue ( 2 ) of Hessian matrix is utilized to characterize NCI at each RDG isosurface points. Mapping of the sign( 2 )(r) on RDG isosurfaces categorizes the nature of non-covalent interactions as either stabilizing ( 2 < 0) or destabilizing ( 2 > 0). Herein the RDG (reduced density gradient) based NCI descriptor is applied to experimental electron density determined from multipole modeling of Xray data at 100 K.
The three-dimensional RDG isosurfaces mapped with the sign( 2 )(r) (Fig.  4) reflect riveting details about these hitherto unexplored peri intramolecular interactions. The three-dimensional surfaces depict the characteristics of all interaction types -attractive (red), dispersive (yellow-green) and repulsive (blue) in the interaction zone between peri Cl atoms. The excess of the red region at the centre of the surface implies the dominance of attractive factors over the dispersive (yellow and green area) and repulsive ones (blue region present at the periphery of the surface). Therefore, these observations strengthen the argument provided by the three-dimensional Laplacian maps (supporting information, Figs. S8b and d). However, the blue region present at the bottom of the surface has contributions from the electron density of the ring critical points (3, +1) (denoted by blue dots in Fig. 3) where the 2 value is positive. Thus, it can be hypothesized that when the molecule is in an ideal planar conformation, a severe destabilizing interaction between lone pairs of peri-substituted Cl atoms dominates. In order to lessen these forces, the molecule adopts a twisted conformation to enable the ClÁ Á ÁCl peri interactions to possess excess attractive components over repulsion. It may be claimed that this   description from NCI analysis is the first of its kind in the fundamental understanding of steric hindrance between perisubstituted groups.

Probe of aromaticity
The influence on the aromaticity of OCN due to distortions by the overcrowding of Cl atoms is evaluated from NICS (Nuclear Independent Chemical Shift) index and QTAIM theory.
3.3.1. NICS calculation. The nucleus independent chemical shift (NICS) is a robust and simple technique to examine aromaticity based on the measurement of magnetic shielding due to the ring current produced by -electron delocalization (Chen et al., 2005). Negative NICS values (in p.p.m.) refer to a diatropic ring current, suggesting aromaticity, while positive NICS values refer to a paratropic ring current, indicating antiaromaticity. NICS values are calculated by placing a dummy atom at the geometric centre of the ring as well as at 1 Å above the centre. The NICS value at 0 Å [NICS (0)] is essentially dominated by the contribution from the bonds in the ring. The value at 1.0 Å above the plane of the molecule [NICS (1 Å )] therefore gives a better measure for examining the aromaticity (Frash et al., 2001;von Ragué Schleyer et al., 2001).
In the present study, the calculated values of NICS (1 Å ) of each ring marked as A and B in Table 3 are compared with the corresponding values calculated for naphthalene at the same level of theory. The NICS (1 Å ) value associated with the molecule OCN is less negative compared with that of naphthalene and the consequent percentage difference in NICS (1 Å ) values suggests an appreciable loss in aromaticity for the molecule OCN. However, the primary reason for the reduction in aromaticity for OCN could not be deciphered from NICS values as they do not provide information on the preferential accumulation of electron density in the molecular plane due to the formation of a bond. This can be obtained from ellipticity profile analysis and is discussed as follows.
3.3.2. Ellipticity profiles. Ellipticity [" = ( 1 / 2 )À1] is defined as the ratio of the eigenvalues 1 and 2 of the Hessian matrix that corresponds to the negative curvature of electron density along two perpendicular directions to the bond path as per the QTAIM theory (Bader, 2002). Evaluation of the ellipticity for the entire bond path rather than at BCPs reveals subtle information of -bonding effects (Cheeseman et al., 1988). In the ellipticity profile plots, ref is defined as the angle between the major axis of the ellipticity, 2 (least negative curvature perpendicular to the 3 along the bond axis) and a reference vector normal to the -plane. Generally for a homopolar bond near the BCP region, ref is ideally zero as the two vectors are parallel and at a distance of 0.5 Å approximately from the atomic nuclei, and ref assumes the value of 90 as the major axis 2 lies in the -plane.
Bond ellipticity profiles computed from experimental charge-density analysis of OCN provide an account of nature of -electron distribution. The common attribute observed in all the 11 C-C bond ellipticity profiles (Fig. 5a-k) is the asymmetric double-hump shape in contrast to a symmetrical one for C-C bonds in naphthalene (Farrugia et al., 2009;Fig. 5l). Such behaviour of C-C bonds is somewhat puzzling since for typical C-C aromatic bonds, " is relatively large in the region near the BCPs. A careful investigation of these profiles brings out the peculiarity in the -electron delocalization between C atoms. The asymmetric double hump signifies the concentration of -electron density at C centres and the extent of -electron density concentration varies severely in all the C atoms. This establishes the 'localized double bond'-like nature in the naphthalene ring instead of a continuous delocalizedsystem and can be correlated with the ineffective overlap of p z orbitals of the respected C atoms. Indeed, this factor is the cause for reduced aromaticity in OCN, also corroborated from NICS values.

Unraveling the differences in dihedral angles
Having established the nature of peri interactions between two pairs of Cl atoms (Cl1Á Á ÁCl8/Cl4Á Á ÁCl5) and its influence on the conformation of the molecule, the unusual difference in dihedral angles ( 1 = 36.80 and 2 = 24.42 , Fig. 2a) at the peri substituted region of OCN needs to be probed.
3.4.1. Geometry optimization. The remarkable difference of 12.38 observed specifically with chlorine substitution in naphthalene has been addressed via energy optimization of OCN (taking the initial geometry from crystalline phase minima) using the integral equation formalism (IEF) version of the polarizable continuum solvation model (PCM; Tomasi et al., 2005) at the wB97XD/6-311+g* level. The result of the outcome is quite noteworthy as there is a significant change in  conformation of the overcrowded OCN molecule from the crystal geometry to the optimized geometry in solution (Fig.  6). The energy difference between the optimized solvated phase and the crystalline phase is À5.26 kJ mol À1 . The prominent feature observed in the optimized conformer is that the dihedral angles are nearly equal ( 1 ' 2 ' 38 ) at the peri substituted positions. This ensures that the dihedral angle 2 involving the peri interaction between Cl1 and Cl8 reverts from 24.42 to 38.03 in solution.
3.4.2. Electrostatic potential isosurfaces. Molecular electrostatic potentials (MESP) allow for the description of chemical reactivity and assist in exploring molecular aggregation in an isolated phase, whereas in a crystal these surfaces provide perspectives regarding electrostatic complementarity between interacting molecules leading to packing of the molecules in the lattice. The electrostatic potential (ESP) maps are drawn at isodensity surfaces of 0.  striking contrast with each other (Fig. 7). The electropositive isosurface regions are indicated in violet, while the electronegative regions are displayed in red. Due to the symmetric nature of the optimized solvated geometry of the OCN molecule, the electrostatic features on the isosurface are uniform. However, in the crystal geometry the ESP isosurface around the peri substituted Cl1 and Cl8 is positive (violet and blue) compared with the negative regions (red) of the other pair of peri substituted Cl4 and Cl5. This exceptional observation in the crystal geometry is backed by a similar trend seen in Bader charges (supporting information, Table S6; Bader, 2002) and the electrostatic potential values calculated at the nuclear sites of each atom from the experimental multipole model (supporting information, Table S7; Volkov et al., 2006). The inhomogeneity in electrostatic features on the isosurface of the crystal geometry can be mainly attributed to the difference in the dihedral angle at the peri substituted region. 3.4.3. Conformational analysis. An elementary dihedral scan was performed to estimate the energy change in the molecule when individual dihedral angles ( 1 and 2 ) move from the solvated optimized geometry to the arrested conformation in the crystal lattice using the PCM model in benzene solvent. The energy difference of 2.65 kJ mol À1 for 2 change from 38.03 to 24.42 at Cl1Á Á ÁCl8 (supporting information, Fig. S9a) is much higher than the energy difference of 0.026 kJ mol À1 for the 1 change from 38.11 to 36.80 at Cl4Á Á ÁCl5 (supporting information, Fig. S9b). This analysis establishes the higher destabilizing effect of intramolecular  ESP map drawn at the isoelectron density surface at 0.001 a.u. for (a) crystalline geometry and (b) for solvated optimized geometry.

Figure 8
Molecular graph depicting the various intermolecular ClÁ Á ÁCl interactions involving (a) peri interaction pair Cl1 and Cl8; (b) peri interaction pair Cl4 and Cl5.  corresponding pairs of peri substituted C-Cl bonds which adjust to the crystal forces, obviously bringing the intermolecular interactions to the fore. Clearly molecular electrostatic potential surfaces activated by the crystal symmetry bring in the differences in intermolecular interactions depending on the top and bottom peri ClÁ Á ÁCl contacts.

Influence of intermolecular interactions of individual
peri Cl atoms on molecular geometry. Analysis of the role of the individual intermolecular interactions involving the peri substituted Cl atoms using a highresolution charge density analysis is deemed essential to account for the observed difference in dihedral angles. The absence of any type of hydrogen-bonding motifs in OCN makes this study quite fascinating. The topological analysis of (r) illustrates (3,À1) BCPs for ClÁ Á ÁCl and ClÁ Á Á as two major intermolecular interactions present in the crystal structure.
From the molecular graph ( Fig.  8) it is quite evident that the nature of ClÁ Á ÁCl interactions associated with the peri interacting pair Cl1/ Cl8 is strikingly different from that of Cl4/Cl5 (shown as red circles). Cl1 and Cl8 participate in typical type II halogen bonding (Bui et al., 2009;Hathwar & Row, 2010) with Cl6 and Cl3, respectively [Cl1Á Á ÁCl6 = 3.460 (2) Å , /C1-Cl1Á Á ÁCl6 = 176.08 ; Cl3Á Á ÁCl8 = 3.514 (3) Å , /C9-Cl8Á Á ÁCl3 = 174.54 ]. The near linearity in the angles indicates conventional electrophile-nucleophile pairing. However, although the linearity is retained, the distances hover around the van der Waals limit (3.6 Å ) preventing a robust overlap of electron density due to the interference of Cl4 and Cl5, which enter the interaction sphere. Figs. 9 and 10 show the two-dimensional deformation and Laplacian maps depicting the intermolecular space associated with the peri pairs Cl1/ Cl8 and Cl4/Cl5, respectively. The    -hole (red dots) along the C-Cl bond axis facing the lone pair density (blue solid) on the Cl atom is depicted in Figs. 9(a) and (c). The two-dimensional Laplacian plots ( Fig. 9b and d) characterize the 'polar flattening' on the respective Cl atoms in accordance with the lump (red solid)-hole (blue dash) interaction at the valence shell charge concentration (VSCC) region .
On the other hand, the other peri pair, Cl4 and Cl5 interacts with Cl8 and Cl1 in a trans type I ClÁ Á ÁCl contact as evident from the interaction geometry [Cl1Á Á ÁCl5 = 3.4780 (3)  In addition, atom Cl4 interacts with Cl6 in a quasi type I/type II contact (Mukherjee et al., 2014) [Cl4Á Á ÁCl6 Molecular graph showing various intermolecular interactions between molecular units packed along the 2 1 screw axis parallel to the b axis. Only the peri interacting pair Cl1 and Cl8 exhibits ClÁ Á Á interactions.

Figure 12
Molecular graphs showing intramolecular and various intermolecular bond paths of different dimers in the crystal structure.
It is notable that ClÁ Á Á contacts are exclusively found to be associated with the peri-pair Cl1/Cl8 as can be seen from the molecular graph (Fig. 11). These occur between molecular units packed along the 2 1 screw axis parallel to the b axis. It can be surmised that the differences in top and bottom dihedral angles in the OCN molecule might be a consequence of such ClÁ Á Á contacts limited to one half of the molecule.
3.4.5. Interaction energies. In order to evaluate the contribution of the intermolecular ClÁ Á ÁCl and ClÁ Á Á interactions involving the peri substituted Cl atoms towards crystal packing, the crystal structure of OCN is dissected into six dimers (Fig. 12). The electrostatic contribution to the interaction energy of the individual dimers is calculated from the exact potential/multipole moment hybrid method (EPMM; Volkov et al., 2004). The values are listed in Table 4 corresponding to individual dimers. The positive electrostatic energies obtained for dimers (III) and (IV) support the earlier observation that the interactions involving atoms Cl4Á Á ÁCl6 and Cl3Á Á ÁCl5 are weak and can be considered only as structure-directed contacts. Indeed, the negligible energy rise in the molecule due to the change in 1 (supporting information, Fig.  S9a) from the optimized solvated geometry to the crystalline phase is in support of this observation. On the other hand, the electrostatic energies associated with dimer (I) and dimer (II), pertaining to the peri substituted pair Cl1 and Cl8, are substantially negative, thus validating the attractive type (II) intermolecular ClÁ Á ÁCl interactions.
Pairwise interactions between molecules in dimers (V) and (VI) organized by several interactions including ClÁ Á Á results in a highly negative electrostatic interaction energy. The resulting supramolecular assembly thus compensates for the destabilizing peri interactions between Cl1 and Cl8. This concurs with the somewhat steep energy rise in the molecule (2.65 kJ mol À1 ) due to the change in 2 (supporting information, Fig. S9b) from the optimized solvated geometry to the crystalline phase. It is to be noted that the electrostatic energy associated with the ClÁ Á Á interaction alone is not discernible from this analysis. Hence it is still uncertain from these interaction energy values whether the ClÁ Á ÁCl or ClÁ Á Á interaction is causing the in-plane bending of C-Cl bonds that leads to asymmetry in the crystal geometry of OCN.   3.4.6. Trimer optimization. To settle this issue, restricted gas-phase optimization of a pair of trimers, T1 and T2 (Fig.  13), was performed at the wB97XD/6-31g(d) level. Restricted optimization was carried out to mimic the environment in a condensed phase. T1 involves the peri substituted pair Cl1/Cl8 in molecule A interacting with molecules B and C primarily through intermolecular ClÁ Á ÁCl interactions, whereas in T2, molecule D is sandwiched between E and F forming ClÁ Á Á interactions.
Initial coordinates of all atoms for both T1 and T2 are from the multipole refined structural values (T1 and T2 , Figs. 13ab), except that the dihedral angle 2 associated with molecules A and D are fixed corresponding to the optimized solvated geometry value (38.03 ). Thus, during optimization which includes only those atoms (Cl1, C1, C10, C9, Cl8) marked in red are allowed to change in both T1 and T2 (Fig. 13c and 13e). This approach is expected to allow for the study of the respective control through ClÁ Á ÁCl and ClÁ Á Á interactions in directing the molecules A and D, respectively, close to planarity by causing in-plane bending of exocylic C-Cl bonds. The optimized conformations of T1 and T2 are referred to as T1 0 and T2 0 , respectively ( Fig. 13d and 13f). Upon optimization of T1 (Fig. 13a), 2 reduces marginally to 33.75 in T1 0 (Fig. 13b), whereas in T2 optimization, 2 results in a value of 24.68 in T2 0 (Fig. 13d). It is remarkable to observe that the value matches the final crystal geometry value 2 (24.42 , Fig.  2a), confirming the exclusive role of ClÁ Á Á in the control of crystal geometry.
This observation can be justified by the following arguments. The angular geometries of the individual type II interactions in the following trimers -T1 , T1, T1 0 are listed in Table 5. The reduced directionality (deviation from linearity, 1 = 166.53 , 2 = 165.30 ) associated with a starting geometry of A in T1 hampers effective type II ClÁ Á ÁCl interactions with B and C. (The angular geometries of the type II ClÁ Á ÁCl interactions in trimer T1 is shown in the supporting information, Fig. S12, the corresponding angular geometries of the type II ClÁ Á ÁCl interactions in the crystal geometry of trimer T1 and optimized geometry of trimer T1 0 are shown in the supporting information, Figs. S13 and S14, respectively.) As a result, the -hole interaction involving the nucleophilic Cl atoms in B and C is unable to drive the in-plane bending of the corresponding Cl1 and Cl8 close to the crystal geometry. On the contrary, the ClÁ Á Á interactions, being non-directional in nature, are more effective in causing the in-plane deviations of the exocyclic C-Cl bonds and hence they control the crystal packing. Additionally, under these changes, the type II ClÁ Á ÁCl interactions benefit as they are ushered closer to the crystal geometry as seen in T2 0 . This rationalizes the symbiotic relation between ClÁ Á Á and type II ClÁ Á ÁCl interactions, which induces crystal packing by perturbing the molecular geometry of OCN and consequently the asymmetry becomes incorporated in the molecular shape.

Conclusions
The present work documents a unique quantitative estimate of the influence of intra-and intermolecular interactions in an overcrowded molecule, OCN, in controlling the molecular conformation. A hitherto less explored intramolecular interaction between peri-substituted halogen atoms which contributes to the steric hindrances is characterized from Bader topological analysis. The RDG-based NCI descriptor applied to multipole electron densities reveals interesting details about peri interactions; the confronting lone-pair density reorganizes in such a way that the interaction zone has more attractive than repulsive features so that the strain in the molecule is minimized, a description so far missing in the literature. Perhaps the formation of an -substituted product in nucleophilic substitution reactions as opposed to theproduct in OCN can thus be attributed to the reduction in steric forces, contributed primarily by the peri interactions, in transition state geometry. Additionally we have described the impact of these steric hindrances in imparting localized character to the electron density. The reduced aromatic character in the naphthalene ring of OCN due to this phenomenon of localized -electrons is estimated from NICS calculation.
Understanding of the discrepancy in dihedral angles in the crystal phase pinpoints the individual role of major intermolecular interactions (ClÁ Á Á and ClÁ Á ÁCl) against the opposing peri interactions in stabilizing the high-energy conformer. This study brings out the novelty in gauging the modification in electron density of overcrowded molecules when they undergo a transition from the solvated to the crystalline phase and hence the findings from this study could be further extended in establishing the relationship between solid-state properties of organic functional materials (for example, semiconductors, fullerenes) and crystal structures.