Crystal structures of the hexafluoridophosphate salts of the isomeric 2-, 3- and 4-cyano-1-methylpyridinium cations and determination of solid-state interaction energies

Metathesis of 2-, 3- and 4-cyano-1-methylpyridinium iodide with KPF6 in water generated the corresponding hexafluoridophosphate salts, C7H7N2 +·PF6 −, whose crystal structures were determined. They feature a variety of weak interactions (C—H⋯F hydrogen bonds and P—F⋯π interactions). Dispersion-corrected density functional theory (DFT-D) calculations were carried out in order to elucidate some of the energetic aspects of the solid-state structures.

The synthesis and crystal structures of the isomeric molecular salts 2-, 3-and 4-cyano-1-methylpyridinium hexafluoridophosphate, C 7 H 7 N 2 + ÁPF 6 À , are reported. In 2-cyano-1-methylpyridinium hexafluoridophosphate, C-HÁ Á ÁF hydrogen bonds form chains extending along the c-axis direction, which are associated through C-HÁ Á ÁF hydrogen bonds and P-FÁ Á Á(ring) interactions into stepped layers. For 3-cyano-1-methylpyridinium hexafluoridophosphate, corrugated sheets parallel to [001] are generated by C-HÁ Á ÁF hydrogen bonds and P-FÁ Á Á(ring) interactions. The sheets are weakly associated by a weak interaction of the cyano group with the six-membered ring of the cation. In 4-cyano-1-methylpyridinium hexafluoridophosphate, C-HÁ Á ÁF hydrogen bonds form a more open three-dimensional network in which stacks of cations and of anions are aligned with the b-axis direction. Dispersion-corrected density functional theory (DFT-D) calculations were carried out in order to elucidate some of the energetic aspects of the solid-state structures. The results indicate that the distribution of charge within a molecular ionic cation can play a large role in determining the strength of a cation-anion interaction within a crystal structure. Crystals of 2-cyano-1-methylpyridinium hexafluoridophosphate are twinned by a 180 rotation about the c* axis. The anion in 3-cyano-1methylpyridinium hexafluoridophosphate is rotationally disordered by 38.2 (1) in an 0.848 (3):0.152 (3) ratio.

Chemical context
Our interest in the structural features of salts of the cyano-1methylpyridinium cations (CMP) was generated by the significantly different melting behaviors of 3-CMP chloride and iodide (Koplitz et al., 2003). This was attributed to a greater amount of C-HÁ Á ÁN and C-HÁ Á ÁX (X = Cl À , I À ) hydrogen bonding in the former, in part because all ions lie on mirror planess in the chloride salt while the cation planes are not parallel in the iodide. As a result, it was estimated that the stabilization is at least 1.9 kcal mol À1 more in the chloride than in the iodide. At that time, relatively few crystal structures of CMP salts had been published so in order to investigate the packing and non-covalent interactions for these cations in the solid state, structures of salts of the 2-, 3-and 4-CMP + cations with a variety of anions including Br À (Kammer et al., 2012b;Mague et al., 2005;Nguyen et al., 2015b), I 3 À (Nguyen et al., 2016), I À (Kammer et al., 2012a(Kammer et al., , 2013 (McCormick et al., 2013;Koplitz et al., 2012) and BF 4 À (Vaccaro et al., 2015) were determined. In addition to structures with parallel sheets as for 3-CMP chloride, ones with interpentrating layers, wrinkled sheets and three-dimensional networks are found. We report here on the hexafluoridophosphate salts of all three cations. More broadly, a better understanding of the manifestations of non-covalent interactions in crystalline organic salts will lead to improved predictions for useful substances in a variety of fields, including materials engineering and targeted drug design. Mapping the crystal structure space for heterocyclic cations in a variety of salts is a very important early step in this overall context.

Structural commentary
The molecular structures of 1-3 are unexceptional in that all three feature essentially planar cations and octahedral anions (Figs. 1, 2 and 3, respectively). The interest lies in their differing solid-state structures and interionic interactions. First, 1 crystallizes in the centrosymmetric space group P2 1 /n while 2 and 3 are in the non-centrosymmetric space group P2 1 2 1 2 1 . Second, the number of interionic interactions per asymmetric unit is six in 1, five in 2 and four in 3. With no mirror planes present, layer structures are not possible and the cation planes are canted with respect to [100] by AE63.19 (9) in 1, AE62.29 (8) in 2 and AE31.41 (8) in 3. In 2 there is a close approach of the cyano group to the six-membered ring of the cation at x À 1 2 , Ày + 1 2 , Àz + 1 with an N2Á Á Ácentroid distance of 3.322 (4) Å and a C7-N2Á Á Ácentroid angle of 114.4 (3) .

Supramolecular features
In 1, one cation and one anion are associated through C4-H4Á Á ÁF6 and C5-H5Á Á ÁF5 hydrogen bonds (Table 1)  Perspective view of 2 with labeling scheme and 50% probability ellipsoids. Only the major orientation of the disordered anion is shown. The cation-anion interaction is indicated by a dashed line.

Figure 3
Perspective view of 3 with labeling scheme and 50% probability ellipsoids.
are joined by the close interaction of F1 with the sixmembered rings of the cations [F1Á Á Ácentroid = 3.186 (3) Å , P1-F1Á Á Ácentroid = 123.67 (12) , forming corrugated sheets parallel to [001]. These sheets are associated through the weak interaction of the cyano group with the six-membered ring of the cation mentioned in the preceding section (Fig. 7).
In 3, a relatively open, three-dimensional network structure in which stacks of cations and of anions are aligned with the baxis direction is generated by C1-H1CÁ Á ÁF1, C3-H3Á Á ÁF3 and C5-H5Á Á ÁF5 hydrogen bonds (Table 3 and Figs. 8 and 9).

Figure 4
Side view of two cation and anion columns in 1 projected onto (021). C-HÁ Á ÁF hydrogen bonds are shown as black dashed lines and P-FÁ Á Á(ring) interactions by blue dashed lines.

Figure 6
View of two adjacent cation-anion chains in 2 along the c-axis direction with C-HÁ Á ÁF hydrogen bonds shown by black dashed lines.

Figure 7
Packing of 2 viewed along the b-axis direction. C-HÁ Á ÁF hydrogen bonds and P-FÁ Á Á(ring) and C NÁ Á Á(ring) interactions are shown, respectively, by black, blue and purple dashed lines.
were carried out at the !B97X-D/def2-TZVP level of theory (Jurečka et al., 2007;Chai & Head-Gordon, 2008;Grimme, 2006;Schrö der et al., 2017). Here, all computations are carried out using the SMD (solvation model based on density) model in order to approximate the effect of the crystal environment (Marenich et al., 2009). The dielectric constant of the CMP-PF 6 crystals is currently unknown, so a dielectric constant of 4.0 was chosen as a generic value (as has been done in previous studies; Nguyen et al., 2016). Although the interactions under consideration are between molecular cations and anions, and complex stabilization is therefore attributable mainly to electrostatic forces, it is important that all attractive and repulsive forces (induction, dispersion, exchange) be modeled as well as possible. As DFT is known to describe dispersion interactions very poorly, here we have used a model incorporating an empirical dispersion term (-D2) in order to account for this shortcoming (Grimme, 2006). Dispersion plays a substantial role in stabilizing all non-covalent complexes (Riley et al., 2010;Johnson et al., 2010) and is known to be especially important in larger aliphatic and aromatic molecules (Sedlak et al., 2013). It has been shown that the parameterizations of empirical dispersion terms, which are generally established from gas-phase benchmark data, remain essentially unchanged when implicit solvent models, such as SMD, are used (Riley et al., 2007). Electrostatic potentials for the three CMP molecular cations ( Fig. 10) and the PF 6 À anion ( Fig. 11) were obtained at the B3LYP/6-311+G** level of theory. It has been shown that the quality of an electrostatic potential does not strongly depend on the level of theory (DFT or HF) or on the particular basis set used, so long as the basis set is sufficiently large (at least 6-31G*; Riley et al., 2016). The most interesting aspect of these electrostatic potentials concerns the molecular cations, for which there are seen to be large shifts in charge density from one part of the molecular ion to another, with the most positive regions having potential values of 140 (1), 109 (2), and 108 (3) kcal mol À1 and the least positive regions having values of 529 (1), 533 (2), and 531 (3) kcal mol À1 . This large shift in charge from one region to another is principally attributable to the high electron-withdrawing capacity of the cyano group, resulting in a less positive partial charge in that region of the molecular ion. For all three molecular cations, the most positively charged regions are those neighboring the CMP methyl groups (i.e. the H atoms that are ortho-to the methyl groups), with the exception of the region located between the methyl and cyano groups in 1. As will be discussed below, the anisotropic distribution of charge throughout these molecular cations has significant effects on the strengths of the interactions ( View of two adjacent cation-anion chains in 3 along the a-axis direction with C-HÁ Á ÁF hydrogen bonds shown by black dashed lines.

Figure 9
Packing of 3 viewed along the b-axis direction. C-HÁ Á ÁF hydrogen bonds are shown by black dashed lines.

Figure 10
Electrostatic potential maps (kcal mol À1 ) for the 4-CMP + (left), 3-CMP + (center) and 2-CMP + (right) cations. Note the large range of 440 kcal mol À1 . The strong electron-withdrawing ability of the cyano group results in a significantly less positive partial charge for that part of the molecular ion.

Figure 11
Electrostatic potential map (kcal mol À1 ) for the hexafluoridophosphate anion. Note the relatively small range of 50 kcal mol À1 .
The shortest cation-anion contacts within the crystal structure of 1 are shown in Fig. 12. Here it is seen that three of the molecular cations (shown in cyan, pink, and yellow) have aromatic rings that are coplanar with each other and are quasicoplanar with three fluorine atoms from the PF 6 À anion. In each case, two contacts are made between a cation H atom and one of the quasi-coplanar PF 6 À fluorine atoms, although it should be noted that the longest contact in the interaction involving the pink cation (3.59 Å ) is substantially longer than all other contacts (2.40-2.62 Å ). Two of the shorter contacts involving aromatic hydrogen atoms (cyan, yellow) and one involving a methyl hydrogen atom (purple). The fourth close contact (green) is a stacking interaction involves a 2-CMP cation located in a plane below PF 6 À (as depicted), with a short C-HÁ Á ÁF contact occurring between a methyl H atom and an anion F atom.
Unsurprisingly, among the four cation-anion pairs given in Fig. 12, the stacking contact (green) represents the strongest interaction, with a binding energy of À19.0 kcal mol À1 . The strength of this interaction is mainly due to the large area of contact between cation and ion, with three F atoms within a distance of 3.4 Å from the cation. Without knowledge of the electronic density distribution, as reflected in the electrostatic potential, it might be assumed that the strongest interaction among the PF 6 À contacts with the three coplanar molecular cations would be that involving the yellow cation, which exhibits the shortest contact distances with the PF 6 À anion. Thus, it is somewhat surprising that this interaction is actually predicted to be the weakest among the coplanar interactions, with an interaction energy of À15.7 kcal mol À1 . Surprisingly, even the coplanar interaction with only one short H + Á Á ÁF À contact (purple) exhibits slightly stronger attraction (À15.9 kcal mol À1 ), while the strongest interaction (À16.9 kcal mol À1 ) occurs for the cyan cation, whose contact distances are slightly longer than those of the interaction involving the yellow cation.
The counter-intuitive results described above can be explained by considering the distribution of charge on 2-CMP + , as reflected in the electrostatic potential. The most positive region of the 2-CMP + cation encompasses the hydrogen neighboring the methyl group and the N-CH 3 bond. Each of the two stronger complexes (cyan, purple) includes a contact between this strongly positive region of the electrostatic potential and a negative F atom. Conversely the shortest contact in the weaker of these complexes (yellow) involves the H atom that is para-to the methyl group, the least positively charged of the aromatic hydrogen atoms.
The details of cation charge distribution are again seen to be important in determining interaction strengths within the crystal structure of 3. In Fig. 13 it is seen that the strongest interaction involves the green 4-CMP + molecular cation (À16.7 kcal mol À1 ), whose shortest H + Á Á ÁF À contact (involving a methyl H atom) is the longest (2.51 Å ) among the three interactions considered here. The enhanced strength of this interaction, relative to the other two contacts, can be explained by the orientation of the 4-CMP + cation relative to the PF 6 À anion. As seen in Fig. 10, the regions neighboring the methyl group on the 4-CMP + cation are significantly more positive than other regions of the molecular ion. It is this highly positive region that forms contact with the PF 6 À anion, 1326 Mague et al. C 7 H 7 N 2 + ÁPF 6 À , C 7 H 7 N 2 + ÁPF 6 À and C 7 H 7 N 2 + ÁPF 6 À Acta Cryst. (2018). E74, 1322-1329 research communications Table 4 Cation-anion interaction energies (kcal mol À1 ).
The ordering of the interaction strengths for the two complexes involving the 3-CMP + cations, shown in Fig. 14, are also counter-intuitive. The interaction with the shorter H + Á Á ÁF À distances (cyan) represents the weaker of the two interactions. The stronger of the two interactions (green) involves the aromatic H atom that is para-to the cyano group, located on the most positive region of the cation. The proximity of this positive region to the anion is likely responsible for the stronger binding of this cation.
Results presented here indicate that the distribution of charge within a molecular ionic cation can play a large role in determining the strength of a cation-anion interaction within a crystal structure. It is presumed that careful inspection of electrostatic potentials becomes more important as the size of a cation increases and as strong electron-withdrawing groups, such as cyano groups, are introduced. Although not investigated here, similar trends are likely observed for larger molecular anions.

Database survey
In addition to those compounds cited in the Chemical context section, there are 14 other structures in the CSD (Version 5.39; Groom et al., 2016) containing cyano-1-methyl pyridinium cations. Of these, ten contain the 4-CMP cation and the other four the 3-CMP cation. Both 3-and 4-CMP[N(SO 2 CF 3 ) 2 ] are described with the former having a layer structure formed from cation chains involving C-HÁ Á ÁN interactions between a ring hydrogen atom and the cyano group, which are bound to anion chains by C ring -HÁ Á ÁO and C methyl -HÁ Á ÁN hydrogen bonds. The layers have the trifluoromethyl groups protruding from one face and the para ring hydrogens from the other. The latter has a three-dimensional network structure in which only the ring hydrogen atoms form C-HÁ Á ÁO hydrogen bonds, leading to channels along the a-axis direction with the cyano, methyl and trifluoromethyl groups forming the inner edges (Hardacre et al., 2008). The co-crystal of 4-CMP[N(SO 2 CF 3 ) 2 ] with 1-methylnapthalene has corrugated layers of alternating cations and anions with trifluromethyl groups protruding from both faces interspersed with layers of 1-methylnapthalene (Hardacre et al., 2010). In 4-CMP[CH 3 OSO 3 ], C-HÁ Á ÁO hydrogen bonds involving both aromatic and aliphatic H atoms form cation-anion chains along the c-axis direction, which are joined into double layers having the anion methyl groups protruding from both faces by C methyl -HÁ Á ÁO hydrogen bonds (Hardacre et al., 2008). A different structure is found in 4-CMP[Co(CO) 4 ] where pairwise C ring -HÁ Á ÁN interactions form dimers that are expanded into cross-linked zigzag chains by C ring -HÁ Á ÁO hydrogen bonds with the anions (Bockman & Kochi, 1989). Cross-linked, zigzag chains are also found in 4-CMP[ZnI 4 ], but here the chains are only cations and are formed by C methyl -HÁ Á ÁN interactions. The anions serve to cross-link them through C ring -HÁ Á ÁI and C methyl -HÁ Á ÁI interactions (Glavcheva et al., 2004). Another example of a layer structure is in [4-CMP] 2 {Cu[S 2 C 2 (CN) 2 ] 2 } where alternating cation-anion chains are formed with half of the cations and the anions through C ring -HÁ Á ÁN hydrogen bonds. The remaining cations use C ring -HÁ Á ÁN hydrogen bonds to both cations and anions in the chains to form a three-dimensional network .

Synthesis and crystallization
potassium hexafluoridophosphate with stirring. The white solid that precipitated was washed with a small quantity of icecold, deionized water and recrystallized from deionized water by slow evaporation under a gentle stream of nitrogen. M.p. 379 K.

Refinement details
Crystal data, data collection and structure refinement details are summarized in Table 5. Crystals of 1 are twinned by a 180 rotation about the c* axis. Trial refinements of this structure with the single-component reflection file extracted from the twinned data set with TWINABS (Sheldrick, 2009) and the full 2-component reflection file showed the former to be more satisfactory. The anion in 2 is rotationally disordered by 38.2 (1) about the F1-P1-F4 axis in an 0.848 (3):0.152 (3) ratio. The two components of the disorder were refined with restraints that their geometries be comparable. H atoms were placed in calculated positions and refined using a riding model: C-H = 0.98 Å with U iso (H) = 1.5U eq (C) for methyl H atoms, C-H = 0.95 Å with U iso (H) = 1.2U eq (C) for all other H atoms.

Funding information
The support of NSF-MRI grant No. 1228232 for the purchase of the diffractometer and Tulane University for support of the Tulane Crystallography Laboratory are gratefully acknowledged. LVK acknowledges generous support from the Earl and Gertrude Vicknair Distinguished Professorship in Chemistry at Loyola University.

3-Cyano-1-methylpyridinium hexafluoridophosphate (2)
Crystal data C 7 H 7 N 2 + ·PF 6 − M r = 264.12 Orthorhombic, P2 1 2 1 2 1 a = 7.8484 (2) (6) Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > 2sigma(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger. Hatoms were placed in calculated positions (C-H = 0.95 -0.98 Å) and included as riding contributions with isotropic displacement parameters 1.2 -1.5 times those of the attached carbon atoms. The anion is rotationally disordered over two resolved sites about the F1···F4 axis in a 85/15 ratio. The disorder was refined with restraints that the two components have the same geometry.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 )
x y z U iso */U eq Occ. (

Special details
Experimental. The diffraction data were obtained from 3 sets of 400 frames, each of width 0.5° in ω, colllected at φ = 0.00, 90.00 and 180.00° and 2 sets of 800 frames, each of width 0.45° in φ, collected at ω = -30.00 and 210.00°. The scan time was 15 sec/frame. Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > 2sigma(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger. Hatoms attached to carbon were placed in calculated positions (C-H = 0.95 -0.98 Å). All were included as riding contributions with isotropic displacement parameters 1.2 -1.5 times those of the attached atoms.