2-({[(Pyridin-1-ium-2-ylmeth­yl)carbamo­yl]form­amido}­meth­yl)pyridin-1-ium bis­­(3,5-di­carb­­oxy­benzoate): crystal structure and Hirshfeld surface analysis

The asymmetric unit of the title salt, C₁₄H₁₆N₄O₂²⁺·2C₉H₅O₆⁻, comprises half a dication, being located about a centre of inversion, and one anion, in a general position. The central C₄N₂O₂ group of atoms in the dication are almost planar (r.m.s. deviation = 0.009 Å), and the carbonyl groups lie in an anti disposition to enable the formation of intra­molecular amide-N—H⋯O(carbon­yl) hydrogen bonds. To a first approximation, the pyridinium and amide N atoms lie to the same side of the mol­ecule [N_py—C—C—N_amide torsion angle = 34.8 (2)°], and the anti pyridinium rings are approximately perpendicular to the central part of the mol­ecule [dihedral angle = 68.21 (8)°]. In the anion, one carboxyl­ate group is almost coplanar with the ring to which it is connected [C_ben—C_ben—C_q—O torsion angle = 2.0 (3)°], whereas the other carboxyl­ate and carb­oxy­lic acid groups are twisted out of the plane [torsion angles = 16.4 (3) and 15.3 (3)°, respectively]. In the crystal, anions assemble into layers parallel to (10-4) via hy­droxy-O—H⋯O(carbon­yl) and charge-assisted hy­droxy-O—H⋯O(carboxyl­ate) hydrogen bonds. The dications are linked into supra­molecular tapes by amide-N—H⋯O(amide) hydrogen bonds, and thread through the voids in the anionic layers, being connected by charge-assisted pyridinium-N—O(carboxyl­ate) hydrogen bonds, so that a three-dimensional architecture ensues. An analysis of the Hirshfeld surface points to the importance of O—H⋯O hydrogen bonding in the crystal structure.

1. Chemical context

Of the isomeric N,N′-bis­(pyridin-n-ylmeth­yl)ethanedi­amides, n = 2, 3 or 4, the mol­ecule with n = 2 appears to have attracted the least attention in co-crystallization studies; for the chemical structure of the diprotonated form of the n = 2 isomer see Scheme 1. By contrast, the n = 3 and 4 mol­ecules have attracted inter­est from the crystal engineering community in terms of their ability to form co-crystals with iodo-containing species leading to aggregates featuring N⋯I halogen bonding (Goroff et al., 2005; Jin et al., 2013) as well as carb­oxy­lic acids (Nguyen et al., 2001). It is the latter that has formed the focus of our inter­est in co-crystallization experiments of these mol­ecules which has led to the characterization of both co-crystals (Arman, Kaulgud et al., 2012; Arman, Miller et al., 2012) and salts (Arman et al., 2013). It was during the course of recent studies in this area (Syed et al., 2016) that the title salt was isolated from the 1:1 co-crystallization experiment between the n = 2 isomer and trimesic acid. The crystal and mol­ecular structures as well as a Hirshfeld surface analysis of this salt is described herein.

2. Structural commentary

The title salt, Fig. 1, was prepared from the 1:1 reaction of trimesic acid and N,N′-bis­(pyridin-2-ylmeth­yl)ethanedi­amide conducted in ethanol. The harvested crystals were shown by crystallography to comprise (2-pyridinium)CH₂N(H)C(=O)C(=O)CH₂N(H)(2–pyridinium) dications and 3,5-di­carb­oxy­benzoate anions in the ratio 1:2; as the dication is located about a centre of inversion, one anion is found in the asymmetric unit. The confirmation for the transfer of protons during the co-crystallization experiment is found in (i) the pattern of hydrogen-bonding inter­actions as discussed in Supra­molecular features, and (ii) the geometric characteristics of the ions. Thus, the C—N—C angle in the pyridyl ring has expanded by over 3° cf. that found in the only neutral form of N,N′-bis­(pyridin-2-ylmeth­yl)ethanedi­amide characterized crystallographically in an all-organic mol­ecule, i.e. in a 1:2 co-crystal with 2-amino­benzoic acid (Arman, Miller et al., 2012), Table 1. The observed angle is in agreement with the sole example of a diprotonated form of the mol­ecule, i.e. in a 1:2 salt with 2,6-di­nitro­benzoate (Arman et al., 2013), Table 1. Further, the experimental equivalence of the C14—O2, O3 bond lengths, i.e. 1.259 (2) and 1.250 (2) Å is consistent with deprotonation and the formation of a carboxyl­ate group, and contrasts the great disparity in the C15—O4, O5 [1.206 (2) and 1.320 (2) Å] and C16—O6, O7 [1.229 (2) and 1.315 (2) Å] bond lengths.

Table 1
Selected geometric details (Å, °) for an N,N′-bis­(pyridin-2-ylmeth­yl)ethanedi­amide mol­ecule and protonated forms^a

Coformer	C—Npy—C	C4N2O2/N-ring	C(=O)—C(=O)	Npy—C—C—Namide	Refcode^b	Ref.
2-NH2C6H4CO2H^c	119.01 (11)	69.63 (6)	1.54119 (16)	165.01 (10)	DIDZEX	Arman, Miller et al. (2012)
2,6-(NO2)2C6H3CO2^−^d	123.00 (12)	72.92 (5)	1.5339 (18)	73.84 (15)	TIPHEH	Arman et al. (2013)
3,5-(CO2H)2C6H3CO2^−	122.36 (18)	68.21 (8)	1.538 (3)	34.8 (2)	–	This work
Notes: (a) All di­amide mol­ecules/dianions are centrosymmetric; (b) Groom & Allen (2014); (c) 1:2 co-crystal with 2-amino­benzoic acid; (d) 1:2 salt with 2,6-di­nitro­benzoate in which both pyridyl-N atoms are protonated.

Figure 1 The mol­ecular structures of the ions comprising the title salt, showing the atom-labelling scheme and displacement ellipsoids at the 50% probability level: (a) 2-({[(pyridin-1-ium-2-ylmeth­yl)carbamo­yl]formamido}­meth­yl)pyridin-1-ium, and (b) 3,5-di­carb­oxy­benzoate; unlabelled atoms are related by the symmetry operation −x, 1 − y, 1 − z.

In the dication, the central C₄N₂O₂ chromophore is almost planar, having an r.m.s. deviation of 0.009 Å and, from symmetry, the carbonyl groups are anti. An intra­molecular amide-N—H⋯O(carbon­yl) hydrogen bond is noted, Table 2. The pyridinium-N1 and amide-N2 atoms are approximately syn as seen in the value of the N1—C1—C6—N2 torsion angle of 34.8 (2)°. This planarity does not extend to the terminal pyridinium rings which are approximately perpendicular to and lying to either side of the central chromophore, forming dihedral angles of 68.21 (8)°. The central C7—C7ⁱ bond length of 1.538 (4) Å is considered long for a C—C bond involving sp²-hybridized atoms (Spek, 2009). Geometric data for the two previously characterized mol­ecules (Arman, Miller et al., 2012; Arman et al., 2013) related to the dication are collected in Table 1. To a first approximation, the three mol­ecules present the same features as described above with the notable exception of the relative disposition of the pyridinium-N1 and amide-N2 atoms. Thus, in the neutral form of the mol­ecule, these are anti, the N1—C1—C6—N2 torsion angle being 165.01 (10) Å, and almost perpendicular in the salt, with N1—C1—C6—N2 being 73.84 (15)°. These differences are highlighted in the overlay diagram shown in Fig. 2.

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N2—H2N⋯O1^i	0.88 (2)	2.38 (2)	2.704 (2)	102 (1)
O7—H7O⋯O6^ii	0.85 (2)	1.77 (2)	2.614 (2)	178 (2)
O5—H5O⋯O2^iii	0.85 (2)	1.69 (2)	2.5352 (19)	175 (2)
N2—H2N⋯O1^iv	0.88 (2)	2.01 (2)	2.816 (2)	153 (2)
N1—H1N⋯O3^v	0.89 (2)	1.73 (2)	2.604 (2)	169 (2)
C5—H5⋯O4^vi	0.95	2.46	3.019 (3)	117
C6—H6A⋯O4^vi	0.99	2.55	3.362 (3)	140
C2—H2⋯O2^i	0.95	2.50	3.251 (3)	136
C3—H3⋯O6^vii	0.95	2.59	3.068 (2)	112
Symmetry codes: (i) -x, -y+1, -z+1; (ii) -x, -y+1, -z; (iii) ; (iv) x-1, y, z; (v) -x+1, -y+1, -z+1; (vi) x-2, y, z; (vii) .

Figure 2 Overlay diagram of the dication in the title compound (red image), the neutral mol­ecule in its co-crystal (green), and dication in the literature salt (blue). The mol­ecules have been overlapped so that the O=C—C=O residues are coincident. The ring N atoms are indicated by an asterisk.

In the anion, the C13—C8—C14—O2 and C9—C10—C15—O4 torsion angles of 15.3 (3) and 16.4 (3)°, respectively, indicate twisted conformations between these residues and the ring to which they are attached whereas the C11—C12—C16—O6 torsion angle of 2.0 (3)° shows this carb­oxy­lic acid group to be co-planar with the ring. The conformational flexibility in 3,5-di­carb­oxy­benzoate anions is well illustrated in arguably the four most closely related structures in the crystallographic literature (Groom & Allen, 2014), identified from approximately 35 organic salts containing this anion. Referring to Scheme 2, the most closely related structure features the dication C_I with two protonated pyridyl N atoms (Santra et al., 2009). Here, with two crystallographically independent anions, twists are noted from the mean-plane data collated in Table 3. For one anion, all groups are twisted out of the least-squares plane through the benzene ring but, in the second anion, the carboxyl­ate group is effectively co-planar with the ring with up to a large twist noted for one of the carb­oxy­lic acid groups. In the other example with a diprotonated cation, C_II (Singh et al., 2015), both independent anions exhibit twists of less than 8° with all three residues effectively co-planar in one of the anions. In the example with a single protonated pyridyl residue, C_III (Ferguson et al., 1998), twists are evident for one of the carb­oxy­lic acid groups and for the carboxyl­ate but, the second carb­oxy­lic acid residue is effectively co-planar. Finally, in the mono-protonated species related to C_I, i.e. C_IV (Basu et al., 2009), twists are evident for all groups with the maximum twists observed in the series for the carboxyl­ate residue, i.e. 25.13 (10)°, and for one of the carb­oxy­lic acid groups, i.e. 22.50 (10)°.

Table 3
Dihedral angles (°) for the 3,5-di­carb­oxy­benzoate anion in the title salt and in selected literature precedents^a

Cation	C6/CO2	C6/CO2H	C6/CO2H	CSD Refcode^b	Ref.
C_I^c	8.6 (2)	4.96 (19)	12.82 (16)	QUFYIA	Santra et al. (2009)
	1.6 (2)	8.9 (2)	19.13 (15)
C_II^c	4.5 (3)	7.5 (4)	3.43 (18)	LUBJAV	Singh et al. (2015)
	2.1 (4)	2.0 (4)	2.6 (3)
C_III	5.92 (11)	1.69 (14)	10.38 (10)	NIFGOY	Ferguson et al. (1998)
C_IV	25.13 (10)	22.50 (10)	11.60 (7)	CUMQUX	Basu et al. (2009)
dication	15.70 (13)	16.34 (12)	1.99 (10)	–	This work
Notes: (a) Refer to Scheme 2 for chemical structures; (b) Groom & Allen (2014); (c) Two independent anions.

3. Supra­molecular features

The mol­ecular packing may be conveniently described in terms of O—H⋯O hydrogen bonding to define an anionic network which is connected into a three-dimensional architecture by N—H⋯O hydrogen bonds; Table 2 collates geometric data for the inter­molecular inter­actions discussed in this section. Thus, centrosymmetrically related C—O6,O7 carb­oxy­lic acid groups associate via hy­droxy-O—H⋯O(carbon­yl) hydrogen bonds to form a familiar eight-membered {⋯HOCO}₂ synthon. These are connected by charge-assisted hy­droxy-O—H⋯O(carboxyl­ate) hydrogen bonds that form C(8) chains. The result is a network of anions lying parallel to (10) and having an undulating topology, Fig. 3a. The dications also self-associate to form supra­molecular tapes via C(4) chains featuring pairs of amide-N—H⋯O(amide) hydrogen bonds and 10-membered {⋯HNC₂O}₂ synthons, Fig. 3b. The tapes are aligned along the a axis and, in essence, thread through the voids in the anionic layers to form a three-dimensional architecture, Fig. 3c. The links between the anionic layers and cationic tapes are hydrogen bonds of the type charge-assisted pyridinium-N—O(carboxyl­ate). In this scheme, no apparent role for the carbonyl-O4 atom is evident. However, this atoms accepts two C—H⋯O inter­actions from pyridyl- and methyl­ene-H to consolidate the mol­ecular packing. Additional stabilization is afforded by pyridyl-C—H⋯O(carboxyl­ate, carbon­yl) inter­actions, Table 2.

Figure 3 Mol­ecular packing in the title salt: (a) supra­molecular layers mediated by O—H⋯O hydrogen bonds, (b) supra­molecular tapes mediated by N—H⋯O hydrogen bonds, and (c) a view of the unit-cell contents shown in projection down the a axis, whereby the supra­molecular layers, illustrated in Fig. 3(a), are linked by charge-assisted N—H⋯O(carboxyl­ate) hydrogen bonds to consolidate a three-dimensional architecture. The O—H⋯O and N—H⋯O hydrogen bonds are shown as orange and blue dashed lines, respectively.

4. Analysis of the Hirshfeld surfaces

Crystal Explorer 3.1 (Wolff et al., 2012) was used to generate Hirshfeld surfaces (Spackman & Jayatilaka, 2009) mapped over d_norm, d_e and electrostatic potential for the title salt. The electrostatic potentials were calculated using TONTO (Spackman et al., 2008; Jayatilaka et al., 2005) integrated with Crystal Explorer, and mapped on the Hirshfeld surfaces using the STO-3G basis set at the Hartree–Fock level theory over the range ±0.25 au. The contact distances d_i and d_e from the Hirshfeld surface to the nearest atom inside and outside, respectively, enable the analysis of the inter­molecular inter­actions through the mapping of d_norm. The combination of d_e and d_i in the form of two-dimensional fingerprint plots provides a summary of inter­molecular contacts in the crystal (Rohl et al., 2008).

Views of the Hirshfeld surface mapped over d_norm in the title salt are given in Fig. 4. The formation of charge-assisted hydroxyl-O—H⋯O(carboxyl­ate) and pyridinium-N—H⋯O(carboxyl­ate) hydrogen bonds in the crystal appear as distinct dark-red spots near the respective donor and acceptor atoms. In Fig. 5, the blue and red colouration are the corres­ponding regions on the surface mapped over the electrostatic potential. The dark-red spots on the Hirshfeld surface of the dication corresponds to a pair of amide-N—H⋯O(amide) hydrogen bonds leading to the supra­molecular tape. Inter­molecular C—H⋯O and N—H⋯O inter­actions, representing weak hydrogen bonds over and above those discussed above in Supra­molecular features, result in light-red spots near some of the carbon, nitro­gen and oxygen atoms, Fig. 4. Hence, the contribution to the surface from these inter­actions involve not only O⋯H/H⋯O contacts but also C⋯O/O⋯C and N⋯O/O⋯N contacts, Table 4. The relative contributions of the different contacts to the Hirshfeld surfaces are collated in Table 5 for the entire structure and also delineated for the dication and anion. The linkage of ions through the formation of hydrogen bonds is illustrated in Fig. 6.

Table 4
Short inter­atomic contacts (Å) in the title salt

Contact	Distance	Symmetry operation
C1⋯O1	3.096 (2)	−1 + x, y, z
C7⋯O3	3.072 (3)	1 − x, 1 − y, 1 − z
C11⋯O4	3.141 (3)	−1 + x, y, z
C14⋯H1N	2.74 (2)	1 − x, 1 − y, 1 − z
C10⋯H6A	2.77	1 + x, y, z
C14⋯H5O	2.631 (17)	-x, − + y,  − z
C16⋯H7O	2.70 (2)	-x, 1 − y, −z

Table 5
Percentage contribution of the different inter­molecular inter­actions to the Hirshfeld surfaces for the dication, anion and salt

Contact	Dication	Anion	Salt
O⋯H/H⋯O	41.6	47.2	43.2
H⋯H	25.1	16.7	23.7
C⋯H/H⋯C	20.2	17.4	17.3
C⋯O/O⋯C	6.6	12.8	10.2
N⋯H/H⋯N	2.3	0.3	1.1
C⋯C	0.2	3.0	2.2
O⋯O	1.2	2.0	1.0
N⋯O/O⋯N	2.3	0.1	1.2
N⋯C/C⋯N	0.5	0.5	0.1

Figure 4 Views of the Hirshfeld surface mapped over dnorm in the title salt: (a) dication, (b) and (c) anion.

Figure 5 View of the Hirshfeld surface mapped over the calculated electrostatic potential the tri-ion aggregate in the title salt.

Figure 6 Views of the Hirshfeld surfaces mapped over dnorm in the title salt emphasizing the inter­actions between (a) dianions and (b) the environment about the anion.

The overall two-dimensional fingerprint plot (FP) of the salt together with those of the dication and anion, and FP's delineated into H⋯H, O⋯H/H⋯O, C⋯H/H⋯C and C⋯O/O⋯C contacts are illustrated in Fig. 7. The O⋯H/H⋯O contacts have the largest overall contribution to the Hirshfeld surface, i.e. 43.2%, and these inter­actions dominate in the crystal structure. The prominent spike with green points appearing in the lower left region in the FP for the anion at d_e + d_i ∼ 1.7 Å has a major contribution, i.e. 47.2%, from O⋯H contacts; the spike at the same d_e + d_i distance is due to a small contribution, 10.0%, from H⋯O contacts. The different contributions from O⋯H and H⋯O contacts to the Hirshfeld surface of the dication, i.e. 6.8 and 34.8%, respectively, lead to asymmetric peaks at d_e + d_i ∼ 1.8 and 2.0 Å, respectively, indicating the varying strength of these inter­actions. However, the overall FP of the salt delineated into O⋯H/H⋯O contacts shows a symmetric pair of spikes at d_e + d_i ∼ 1.7 Å with nearly equal contributions from O⋯H and H⋯O contacts. A smaller contribution is made by the H⋯H contacts, Table 1, and these appear as the scattered points without a distinct peak, Fig. 7. The presence of short inter­atomic C⋯H/H⋯C contacts, Table 4, result in a 17.3% overall contribution to the surface, although there are no C—H⋯π contacts within the acceptance distance criteria for such inter­actions (Spek, 2009). These are represented by a pair of symmetrical wings at d_e + d_i ∼ 2.9 Å in the FP plot, Fig. 7. The contribution from C⋯O/O⋯C contacts to the Hirshfeld surface is also evident from the presence of inter­molecular C—H⋯O inter­actions as well as short inter­atomic C⋯O/O⋯C contact, Table 4. These appear as cross-over wings in the (d_e, d_i) region between 1.7 and 2.7 Å. A small but significant contribution to the Hirshfeld surface of the dication due to N⋯O/O⋯N contacts is the result of inter­molecular amide-N—H⋯O(amide) inter­actions.

Figure 7 The two-dimensional fingerprint plots for the title salt: (a) dication, (b) anion, and (c) full structure, showing contributions from different contacts, i.e. H⋯H, O⋯H/H⋯O, C⋯H/H⋯C, and C⋯O/O⋯C.

The inter­molecular inter­actions were further analysed using a recently reported descriptor, the enrichment ratio, ER (Jelsch et al., 2014), which is based on Hirshfeld surface analysis and gives an indication of the relative likelihood of specific inter­molecular inter­actions to form; the calculated ratios are given in Table 6. The relatively poor content of hydrogen atoms in the salt and the involvements of many hydrogen atoms in the inter­molecular inter­actions, as discussed above, reduces the ER value of non-bonded H⋯H contacts to a value less unity, i.e. 0.8, due to a 23.7% contribution from the 54.5% available Hirshfeld surface and anti­cipated 29.7% random contacts. The ER value of 1.4 corresponding to O⋯H/H⋯O contacts results from a relatively high 43.2% contribution by O—H⋯O, N—H⋯O and C—H⋯O inter­actions. The carbon and oxygen atoms involved in the inter­molecular C—H⋯O inter­actions and short inter C⋯O/O⋯C contacts are at distances shorter than the sum of their respective van der Waals radii, hence they also have a high formation propensity, so the ER value is > 1. The C⋯H/H⋯C contacts in the crystal are enriched due to the poor nitro­gen content and the presence of short inter­atomic C⋯H/H⋯C contacts so the ratio is close to unity, i.e. 0.99. Finally, the ER value of 1.68 corresponding to N⋯O/O⋯N contacts for the surface of dication is the result of the charge-assisted N—H⋯O inter­actions consistent with their high propensity to form.

Table 6
Enrichment ratios (ER) for the dication, anion and salt

Contact	Dication	Anion	Salt
O⋯H/H⋯O	1.37	1.50	1.40
H⋯H	0.77	0.69	0.80
C⋯H/H⋯C	1.27	0.96	0.99
C⋯O/O⋯C	0.90	1.09	1.13
N⋯H/H⋯N	0.77	0.68	0.88
N⋯O/O⋯N	1.68	–	–

5. Database survey

As mentioned in the Chemical context, N,N′-bis­(pyridin-2-ylmeth­yl)ethanedi­amide (LH₂), has not been as well studied as the n = 3 and 4 isomers. This notwithstanding, the coordin­ation chemistry of LH₂ is more advanced and diverse. Thus, co-crystals have been reported with a metal complex, i.e. [Mn(1,10-phenanthroline)₃][ClO₄]₂·(LH₂) (Liu et al., 1999). Monodentate coordination via a pyridyl-N atom was found in mononuclear HgI₂(LH₂)₂ (Zeng et al., 2008). Bidentate, bridging via both pyridyl-N atoms has been observed in binuclear {[Me₂(4-HO₂CC₆H₄CH₂)Pt(4,4′-di-t-butyl-2,2′-bipyrid­yl]₂(LH₂)}₂²⁺ (Fraser et al., 2002) and in a polymeric silver salt, {AgBF₄(LH₂)·H₂O}_n (Schauer et al., 1998). In the analogous triflate salt {Ag₂(O₃SCF₃)₂(LH₂)₃}_n (Arman et al., 2010), one LH₂ bridges as in the BF₄ salt (Schauer et al., 1998) but the other two LH₂ mol­ecules bridge one Ag⁺ via a pyridyl-N atom and another via the second pyridyl-N atom as well as a carbonyl-O atom, i.e. are tridentate. In a variation, tetra­dentate, bridging coordination via all four nitro­gen atoms is found in polymeric [CuL(LH₂)(OH₂]_n (Lloret et al., 1989). Deprotonation of LH₂ leads to a tetra­dentate ligand coordinating via all four nitro­gen atoms in PdL (Reger et al., 2003). There are several examples of hexa­dentate-N₄O₂ coordination in copper(II) chemistry, as in the aforementioned [CuL(LH₂)(OH₂]_n (Lloret et al., 1989) and, for example, in polymeric [CuL(μ₂-4,4′-bipyridyl-)(OH₂)]₂ (Zhang et al., 2001).

6. Synthesis and crystallization

The di­amide (0.25 g), prepared in accord with the literature procedure (Schauer et al., 1997), in ethanol (10 ml) was added to a ethanol solution (10 ml) of trimesic acid (Acros Organic, 0.18 g). The mixture was stirred for 2 h at room temperature. After standing for a few minutes, a white precipitate formed which was filtered off by vacuum suction. The filtrate was then left to stand under ambient conditions, yielding pale-yellow crystals after 2 weeks.

7. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 7. The carbon-bound H atoms were placed in calculated positions (C—H = 0.95–0.99 Å) and were included in the refinement in the riding-model approximation, with U_iso(H) set to 1.2U_eq(C). The oxygen- and nitro­gen-bound H atoms were located in a difference Fourier map but were refined with distance restraints of O—H = 0.84±0.01 Å and N—H = 0.88±0.01 Å, and with U_iso(H) set to 1.5U_eq(O) and 1.2U_eq(N).

Table 7
Experimental details

Crystal data
Chemical formula	C14H16N4O2^2+·2C9H5O6^−
Mr	690.56
Crystal system, space group	Monoclinic, P21/c
Temperature (K)	100
a, b, c (Å)	5.0436 (3), 18.4232 (10), 16.0796 (9)
β (°)	95.878 (5)
V (Å^3)	1486.25 (15)
Z	2
Radiation type	Mo Kα
μ (mm^−1)	0.12
Crystal size (mm)	0.30 × 0.10 × 0.05
Data collection
Diffractometer	Agilent SuperNova Dual diffractometer with an Atlas detector
Absorption correction	Multi-scan (CrysAlis PRO; Agilent, 2014)
Tmin, Tmax	0.580, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections	17686, 3410, 2656
Rint	0.069
(sin θ/λ)max (Å^−1)	0.650
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.051, 0.134, 1.07
No. of reflections	3410
No. of parameters	238
No. of restraints	4
Δρmax, Δρmin (e Å^−3)	0.46, −0.26
Computer programs: CrysAlis PRO (Agilent, 2014), SHELXS97 (Sheldrick, 2008), SHELXL2014 (Sheldrick, 2015), ORTEP-3 for Windows (Farrugia, 2012), QMol (Gans & Shalloway, 2001), DIAMOND (Brandenburg, 2006) and publCIF (Westrip, 2010).

Supporting information

S1. Chemical context

Of the isomeric N,N'-bis­(pyridin-n-yl­methyl)­ethanedi­amides, n = 2, 3 or 4, the molecule with n = 2 appears to have attracted the least attention in co-crystallization studies; for the chemical structure of the diprotonated form of the n = 2 isomer see Scheme 1. By contrast, the n = 3 and 4 molecules have attracted inter­est from the crystal engineering community in terms of their ability to form co-crystals with iodo-containing species leading to aggregates featuring N···I halogen bonding (Goroff et al., 2005; Jin et al., 2013) as well as carb­oxy­lic acids (Nguyen et al., 2001). It is the latter that has formed the focus of our inter­est in co-crystallization experiments of these molecules which has led to the characterization of both co-crystals (Arman, Kaulgud et al., 2012; Arman, Miller et al., 2012) and salts (Arman et al., 2013). It was during the course of recent studies in this area (Syed et al., 2016) that the title salt was isolated from the 1:1 co-crystallization experiment between the n = 2 isomer and trimesic acid. The crystal and molecular structures as well as a Hirshfeld surface analysis of this salt is described herein.

S2. Structural commentary

The title salt, Fig. 1, was prepared from the 1:1 reaction of trimesic acid and N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide conducted in ethanol. The harvested crystals were shown by crystallography to comprise (2-pyridinium)CH₂N(H)C(═O)C(═O)CH₂N(H)(2–pyridinium) dications and 3,5-di­carb­oxy­benzoate anions in the ratio 1:2; as the dication is located about a centre of inversion, one anion is found in the asymmetric unit. The confirmation for the transfer of protons during the co-crystallization experiment is found in i) the pattern of hydrogen-bonding inter­actions as discussed in Supra­molecular features, and ii) the geometric characteristics of the ions. Thus, the C—N—C angle in the pyridyl ring has expanded by over 3° cf. that found in the only neutral form of N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide characterized crystallographically in an all-organic molecule, i.e. in a 1:2 co-crystal with 2-amino­benzoic acid (Arman, Miller et al., 2012), Table 1. The observed angle is in agreement with the sole example of a diprotonated form of the molecule, i.e. in a 1:2 salt with 2,6-di­nitro­benzoate (Arman et al., 2013), Table 1. Further, the experimental equivalence of the C14—O2, O3 bond lengths, i.e. 1.259 (2) and 1.250 (2) Å is consistent with deprotonation and the formation of a carboxyl­ate group, and contrasts the great disparity in the C15—O4, O5 [1.206 (2) and 1.320 (2) Å] and C16—O6, O7 [1.229 (2) and 1.315 (2) Å] bond lengths.

In the dication, the central C₄N₂O₂ chromophore is almost planar, having an r.m.s. deviation of 0.009 Å and, from symmetry, the carbonyl groups are anti. An intra­molecular amide-N—H···O(carbonyl) hydrogen bond is noted, Table 2. The pyridinium-N1 and amide-N2 atoms are approximately syn as seen in the value of the N1—C1—C6—N2 torsion angle of 34.8 (2)°. This planarity does not extend to the terminal pyridinium rings which are approximately perpendicular to and lying to either side of the central chromophore, forming dihedral angles of 68.21 (8)°. The central C7—C7ⁱ bond length of 1.538 (4) Å is considered long for a C—C bond involving sp²-hybridized atoms (Spek, 2009). Geometric data for the two previously characterized molecules (Arman, Miller et al., 2012; Arman et al., 2013) related to the dication are collected in Table 1. To a first approximation, the three molecules present the same features as described above with the notable exception of the relative disposition of the pyridinium-N1 and amide-N2 atoms. Thus, in the neutral form of the molecule, these are anti, the N1—C1—C6—N2 torsion angle being 165.01 (10) Å, and almost perpendicular in the salt, with N1—C1—C6—N2 being 73.84 (15)°. These differences are highlighted in the overlay diagram shown in Fig. 2.

In the anion, the C13—C8—C14—O2 and C9—C10—C15—O4 torsion angles of 15.3 (3) and 16.4 (3)°, respectively, indicate twisted conformations between these residues and the ring to which they are attached whereas the C11—C12—C16—O6 torsion angle of 2.0 (3)° shows this carb­oxy­lic acid group to be co-planar with the ring. The conformational flexibility in 3,5-di­carb­oxy­benzoate anions is well illustrated in arguably the four most closely related structures in the crystallographic literature (Groom & Allen, 2014), identified from approximately 35 organic salts containing this anion. Referring to Scheme 2, the most closely related structure features the dication C_I with two protonated pyridyl N atoms (Santra et al., 2009). Here, with two crystallographically independent anions, twists are noted from the mean-plane data collated in Table 2. For one anion, all groups are twisted out of the least-squares plane through the benzene ring but, in the second anion, the carboxyl­ate group is effectively co-planar with the ring with up to a large twist noted for one of the carb­oxy­lic acid groups. In the other example with a diprotonated cation, C_II (Singh et al., 2015), both independent anions exhibit twists of less than 8° with all three residues effectively co-planar in one of the anions. In the example with a single protonated pyridyl residue, C_III (Ferguson et al., 1998), twists are evident for one of the carb­oxy­lic acid groups and for the carboxyl­ate but, the second carb­oxy­lic acid residue is effectively co-planar. Finally, in the mono-protonated species related to C_I, i.e. C_IV (Basu et al., 2009), twists are evident for all groups with the maximum twists observed in the series for the carboxyl­ate residue, i.e. 25.13 (10)°, and for one of the carb­oxy­lic acid groups, i.e. 22.50 (10)°.

S3. Supra­molecular features

The molecular packing may be conveniently described in terms of O—H···O hydrogen bonding to define an anionic network which is connected into a three-dimensional architecture by N—H···O hydrogen bonds; Table 3 collates geometric data for the inter­molecular inter­actions discussed in this section. Thus, centrosymmetrically related C—O6,O7 carb­oxy­lic acid groups associate via hy­droxy-O—H···O(carbonyl) hydrogen bonds to form a familiar eight-membered {···HOCO}₂ synthon. These are connected by charge-assisted hy­droxy-O—H···O(carboxyl­ate) hydrogen bonds that form C(8) chains. The result is a network of anions lying parallel to (104) and having an undulating topology, Fig. 3a. The dications also self-associate but, to form supra­molecular tapes via C(4) chains featuring pairs of amide-N—H···O(amide) hydrogen bonds and 10-membered {···HNC₂O}₂ synthons, Fig. 3b. The tapes are aligned along the a axis and, in essence, thread through the voids in the anionic layers to form a three-dimensional architecture, Fig. 3c. The links between the anionic layers and cationic tapes are hydrogen bonds of the type charge-assisted pyridinium-N—O(carboxyl­ate). In this scheme, no apparent role for the carbonyl-O4 atom is evident. However, this atoms accepts two C—H···O inter­actions from pyridyl- and methyl­ene-H to consolidate the molecular packing. Additional stabilization is afforded by pyridyl-C—H···O(carboxyl­ate, carbonyl) inter­actions, Table 3.

S4. Analysis of the Hirshfeld surfaces

Crystal Explorer 3.1 (Wolff et al., 2012) was used to generate Hirshfeld surfaces (Spackman & Jayatilaka, 2009) mapped over d_norm, d_e and electrostatic potential for the title salt. The electrostatic potentials were calculated using TONTO (Spackman et al., 2008; Jayatilaka et al., 2005) integrated with Crystal Explorer, and mapped on the Hirshfeld surfaces using the STO-3G basis set at the Hartree–Fock level theory over the range ±0.25 au. The contact distances d_i and d_e from the Hirshfeld surface to the nearest atom inside and outside, respectively, enable the analysis of the inter­molecular inter­actions through the mapping of d_norm. The combination of d_e and d_i in the form of two-dimensional fingerprint plots provides a summary of inter­molecular contacts in the crystal (Rohl et al., 2008).

Views of the Hirshfeld surface mapped over d_norm in the title salt are given in Fig. 4. The formation of charge-assisted hydroxyl-O—H···O(carboxyl­ate) and pyridinium-N—H···O(carboxyl­ate) hydrogen bonds in the crystal appear as distinct dark-red spots near the respective donor and acceptor atoms. In Fig. 5, the blue and red colouration are the corresponding regions on the surface mapped over the electrostatic potential. The dark-red spots on the Hirshfeld surface of the dication corresponds to a pair of amide-N—H···O(amide) hydrogen bonds leading to the supra­molecular tape. Inter­molecular C—H···O and N—H···O inter­actions, representing weak hydrogen bonds over and above those discussed above in Supra­molecular features, result in light-red spots near some of the carbon, nitro­gen and oxygen atoms, Fig. 4. Hence, the contribution to the surface from these inter­actions involve not only O···H/H···O contacts but also C···O/O···C and N···O/O···N contacts, Table 4. The relative contributions of the different contacts to the Hirshfeld surfaces are collated in Table 5 for the entire structure and also delineated for the dication and anion. The linkage of ions through the formation of hydrogen bonds is illustrated in Fig. 6.

The overall two-dimensional fingerprint plot (FP) of the salt together with those of the dication and anion, and FP's delineated into H···H, O···H/H···O, C···H/H···C and C···O/O···C contacts are illustrated in Fig. 7. The O···H/H···O contacts have the largest overall contribution to the Hirshfeld surface, i.e. 43.2%, and these inter­actions dominate in the crystal structure. The prominent spike with green points appearing in the lower left region in the FP for the anion at d_e + d_i ~ 1.7 Å has a major contribution, i.e. 47.2%, from O···H contacts; the spike at the same d_e + d_i distance is due to a small contribution, 10.0%, from H···O contacts. The different contributions from O···H and H···O contacts to the Hirshfeld surface of the dication, i.e. 6.8 and 34.8 %, respectively, lead to asymmetric peaks at d_e + d_i ~ 1.8 and 2.0 Å, respectively, indicating the varying strength of these inter­actions. However, the overall FP of the salt delineated into O···H/H···O contacts shows a symmetric pair of spikes at d_e + d_i ~ 1.7 Å with nearly equal contributions from O···H and H···O contacts. A smaller contribution is made by the H···H contacts, Table 1, and these appear as the scattered points without a distinct peak, Fig. 7. The presence of short inter­atomic C···H/H···C contacts, Table 5, result in a 17.3% overall contribution to the surface, although there are no C—H···π contacts within the acceptance distance criteria for such inter­actions (Spek, 2009). These are represented by a pair of symmetrical wings at d_e + d_i ~ 2.9 Å in the FP plot, Fig. 7. The contribution from C···O/O···C contacts to the Hirshfeld surface is also evident from the presence of inter­molecular C—H···O inter­actions as well as short inter­atomic C···O/O···C contact, Table 5. These appear as cross-over wings in the d_e, d_i region between 1.7 and 2.7 Å. A small but significant contribution to the Hirshfeld surface of the dication due to N···O/O···N contacts is the result of inter­molecular amide-N—H···O(amide) inter­actions.

The inter­molecular inter­actions were further analysed using a recently reported descriptor, the enrichment ratio, ER (Jelsch et al., 2014), which is based on Hirshfeld surface analysis and gives an indication of the relative likelihoods of specific inter­molecular inter­actions to form; the calculated ratios are given in Table 6. The relatively poor content of hydrogen atoms in the salt and the involvements of many hydrogen atoms in the inter­molecular inter­actions, as discussed above, reduces ER value of non-bonded H···H contacts to a value less unity, i.e. 0.8, due to a 23.7% contribution from the 54.5% available Hirshfeld surface and anti­cipated 29.7% random contacts. The ER value of 1.4 corresponding to O···H/H···O contacts results from a relatively high 43.2% contribution by O—H···O, N—H···O and C—H···O inter­actions. The carbon and oxygen atoms involved in the inter­molecular C—H···O inter­actions and short inter C···O/O···C contacts are at distances shorter than the sum of their respective van der Waals radii, hence they also have a high formation propensity, so the ER value is > 1. The C···H/H···C contacts in the crystal are enriched due to the poor nitro­gen content and the presence of short inter­atomic C···H/H···C contacts so the ratio is close to unity, i.e. 0.99. Finally, the ER value of 1.68 corresponding to N···O/O···N contacts for the surface of dication is the result of the charge-assisted N—H···O inter­actions consistent with their high propensity to form.

S5. Database survey

\ As mentioned in the Chemical context, N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide (LH₂), has not been as well studied as the n = 3 and 4 isomers. This notwithstanding, the coordination chemistry of LH₂ is more advanced and diverse. Thus, co-crystals have been reported with a metal complex, i.e. [Mn(1,10-phenanthroline)₃][ClO₄]₂.(LH₂) (Liu et al., 1999). Monodentate coordination via a pyridyl-N atom was found in mononuclear HgI₂(LH₂)₂ (Zeng et al., 2008). Bidentate, bridging via both pyridyl-N atoms has been observed in binuclear {[Me₂(4-HO₂CC₆H₄CH₂)Pt(4,4'-di-t-butyl-2,2'-bi­pyridyl]\ ₂(LH₂)}₂²⁺ (Fraser et al., 2002) and in a polymeric silver salt, {AgBF₄(LH₂)·H₂O}_n (Schauer et al., 1998). In the analogous triflate salt {Ag₂(O₃SCF₃)₂(LH₂)₃}_n (Arman et al., 2010), one LH₂ bridges as in the BF₄ salt (Schauer et al., 1998) but the other two LH₂ molecules bridge one Ag⁺ via a pyridyl-N atom and another via the second pyridyl-N atom as well as a carbonyl-O atom, i.e. are tridentate. In a variation, tetra­dentate, bridging coordination via all four nitro­gen atoms is found in polymeric [CuL(LH₂)(OH₂]_n (Lloret et al., 1989). Deprotonation of LH₂ leads to a tetra­dentate ligand coordinating via all four nitro­gen atoms in PdL (Reger et al., 2003). There are several examples of hexadentate-N₄O₂ coordination in copper(II) chemistry, as in the aforementioned [CuL(LH₂)(OH₂]_n (Lloret et al., 1989) and, for example, in polymeric [CuL(µ₂-4,4'-bi­pyridyl-)(OH₂)]₂ (Zhang et al., 2001).

S6. Synthesis and crystallization

The di­amide (0.25 g), prepared in accord with the literature procedure (Schauer et al., 1997), in ethanol (10 ml) was added to a ethanol solution (10 ml) of trimesic acid (Acros Organic, 0.18 g). The mixture was stirred for 2 h at room temperature. After standing for a few minutes, a white precipitate formed which was filtered off by vacuum suction. The filtrate was then left to stand under ambient conditions, yielding pale-yellow crystals after 2 weeks.

S7. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 7. The carbon-bound H atoms were placed in calculated positions (C—H = 0.95–0.99 Å) and were included in the refinement in the riding-model approximation, with U_iso(H) set to 1.2U_eq(C). The oxygen- and nitro­gen-bound H atoms were located in a difference Fourier map but were refined with distance restraints of O—H = 0.84±0.01 Å and N—H = 0.88±0.01 Å, and with U_iso(H) set to 1.5U_eq(O) and 1.2U_eq(N).

Related literature

For related literature, see:

Structure description

Of the isomeric N,N'-bis­(pyridin-n-yl­methyl)­ethanedi­amides, n = 2, 3 or 4, the molecule with n = 2 appears to have attracted the least attention in co-crystallization studies; for the chemical structure of the diprotonated form of the n = 2 isomer see Scheme 1. By contrast, the n = 3 and 4 molecules have attracted inter­est from the crystal engineering community in terms of their ability to form co-crystals with iodo-containing species leading to aggregates featuring N···I halogen bonding (Goroff et al., 2005; Jin et al., 2013) as well as carb­oxy­lic acids (Nguyen et al., 2001). It is the latter that has formed the focus of our inter­est in co-crystallization experiments of these molecules which has led to the characterization of both co-crystals (Arman, Kaulgud et al., 2012; Arman, Miller et al., 2012) and salts (Arman et al., 2013). It was during the course of recent studies in this area (Syed et al., 2016) that the title salt was isolated from the 1:1 co-crystallization experiment between the n = 2 isomer and trimesic acid. The crystal and molecular structures as well as a Hirshfeld surface analysis of this salt is described herein.

The title salt, Fig. 1, was prepared from the 1:1 reaction of trimesic acid and N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide conducted in ethanol. The harvested crystals were shown by crystallography to comprise (2-pyridinium)CH₂N(H)C(═O)C(═O)CH₂N(H)(2–pyridinium) dications and 3,5-di­carb­oxy­benzoate anions in the ratio 1:2; as the dication is located about a centre of inversion, one anion is found in the asymmetric unit. The confirmation for the transfer of protons during the co-crystallization experiment is found in i) the pattern of hydrogen-bonding inter­actions as discussed in Supra­molecular features, and ii) the geometric characteristics of the ions. Thus, the C—N—C angle in the pyridyl ring has expanded by over 3° cf. that found in the only neutral form of N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide characterized crystallographically in an all-organic molecule, i.e. in a 1:2 co-crystal with 2-amino­benzoic acid (Arman, Miller et al., 2012), Table 1. The observed angle is in agreement with the sole example of a diprotonated form of the molecule, i.e. in a 1:2 salt with 2,6-di­nitro­benzoate (Arman et al., 2013), Table 1. Further, the experimental equivalence of the C14—O2, O3 bond lengths, i.e. 1.259 (2) and 1.250 (2) Å is consistent with deprotonation and the formation of a carboxyl­ate group, and contrasts the great disparity in the C15—O4, O5 [1.206 (2) and 1.320 (2) Å] and C16—O6, O7 [1.229 (2) and 1.315 (2) Å] bond lengths.

In the dication, the central C₄N₂O₂ chromophore is almost planar, having an r.m.s. deviation of 0.009 Å and, from symmetry, the carbonyl groups are anti. An intra­molecular amide-N—H···O(carbonyl) hydrogen bond is noted, Table 2. The pyridinium-N1 and amide-N2 atoms are approximately syn as seen in the value of the N1—C1—C6—N2 torsion angle of 34.8 (2)°. This planarity does not extend to the terminal pyridinium rings which are approximately perpendicular to and lying to either side of the central chromophore, forming dihedral angles of 68.21 (8)°. The central C7—C7ⁱ bond length of 1.538 (4) Å is considered long for a C—C bond involving sp²-hybridized atoms (Spek, 2009). Geometric data for the two previously characterized molecules (Arman, Miller et al., 2012; Arman et al., 2013) related to the dication are collected in Table 1. To a first approximation, the three molecules present the same features as described above with the notable exception of the relative disposition of the pyridinium-N1 and amide-N2 atoms. Thus, in the neutral form of the molecule, these are anti, the N1—C1—C6—N2 torsion angle being 165.01 (10) Å, and almost perpendicular in the salt, with N1—C1—C6—N2 being 73.84 (15)°. These differences are highlighted in the overlay diagram shown in Fig. 2.

In the anion, the C13—C8—C14—O2 and C9—C10—C15—O4 torsion angles of 15.3 (3) and 16.4 (3)°, respectively, indicate twisted conformations between these residues and the ring to which they are attached whereas the C11—C12—C16—O6 torsion angle of 2.0 (3)° shows this carb­oxy­lic acid group to be co-planar with the ring. The conformational flexibility in 3,5-di­carb­oxy­benzoate anions is well illustrated in arguably the four most closely related structures in the crystallographic literature (Groom & Allen, 2014), identified from approximately 35 organic salts containing this anion. Referring to Scheme 2, the most closely related structure features the dication C_I with two protonated pyridyl N atoms (Santra et al., 2009). Here, with two crystallographically independent anions, twists are noted from the mean-plane data collated in Table 2. For one anion, all groups are twisted out of the least-squares plane through the benzene ring but, in the second anion, the carboxyl­ate group is effectively co-planar with the ring with up to a large twist noted for one of the carb­oxy­lic acid groups. In the other example with a diprotonated cation, C_II (Singh et al., 2015), both independent anions exhibit twists of less than 8° with all three residues effectively co-planar in one of the anions. In the example with a single protonated pyridyl residue, C_III (Ferguson et al., 1998), twists are evident for one of the carb­oxy­lic acid groups and for the carboxyl­ate but, the second carb­oxy­lic acid residue is effectively co-planar. Finally, in the mono-protonated species related to C_I, i.e. C_IV (Basu et al., 2009), twists are evident for all groups with the maximum twists observed in the series for the carboxyl­ate residue, i.e. 25.13 (10)°, and for one of the carb­oxy­lic acid groups, i.e. 22.50 (10)°.

The molecular packing may be conveniently described in terms of O—H···O hydrogen bonding to define an anionic network which is connected into a three-dimensional architecture by N—H···O hydrogen bonds; Table 3 collates geometric data for the inter­molecular inter­actions discussed in this section. Thus, centrosymmetrically related C—O6,O7 carb­oxy­lic acid groups associate via hy­droxy-O—H···O(carbonyl) hydrogen bonds to form a familiar eight-membered {···HOCO}₂ synthon. These are connected by charge-assisted hy­droxy-O—H···O(carboxyl­ate) hydrogen bonds that form C(8) chains. The result is a network of anions lying parallel to (104) and having an undulating topology, Fig. 3a. The dications also self-associate but, to form supra­molecular tapes via C(4) chains featuring pairs of amide-N—H···O(amide) hydrogen bonds and 10-membered {···HNC₂O}₂ synthons, Fig. 3b. The tapes are aligned along the a axis and, in essence, thread through the voids in the anionic layers to form a three-dimensional architecture, Fig. 3c. The links between the anionic layers and cationic tapes are hydrogen bonds of the type charge-assisted pyridinium-N—O(carboxyl­ate). In this scheme, no apparent role for the carbonyl-O4 atom is evident. However, this atoms accepts two C—H···O inter­actions from pyridyl- and methyl­ene-H to consolidate the molecular packing. Additional stabilization is afforded by pyridyl-C—H···O(carboxyl­ate, carbonyl) inter­actions, Table 3.

Crystal Explorer 3.1 (Wolff et al., 2012) was used to generate Hirshfeld surfaces (Spackman & Jayatilaka, 2009) mapped over d_norm, d_e and electrostatic potential for the title salt. The electrostatic potentials were calculated using TONTO (Spackman et al., 2008; Jayatilaka et al., 2005) integrated with Crystal Explorer, and mapped on the Hirshfeld surfaces using the STO-3G basis set at the Hartree–Fock level theory over the range ±0.25 au. The contact distances d_i and d_e from the Hirshfeld surface to the nearest atom inside and outside, respectively, enable the analysis of the inter­molecular inter­actions through the mapping of d_norm. The combination of d_e and d_i in the form of two-dimensional fingerprint plots provides a summary of inter­molecular contacts in the crystal (Rohl et al., 2008).

Views of the Hirshfeld surface mapped over d_norm in the title salt are given in Fig. 4. The formation of charge-assisted hydroxyl-O—H···O(carboxyl­ate) and pyridinium-N—H···O(carboxyl­ate) hydrogen bonds in the crystal appear as distinct dark-red spots near the respective donor and acceptor atoms. In Fig. 5, the blue and red colouration are the corresponding regions on the surface mapped over the electrostatic potential. The dark-red spots on the Hirshfeld surface of the dication corresponds to a pair of amide-N—H···O(amide) hydrogen bonds leading to the supra­molecular tape. Inter­molecular C—H···O and N—H···O inter­actions, representing weak hydrogen bonds over and above those discussed above in Supra­molecular features, result in light-red spots near some of the carbon, nitro­gen and oxygen atoms, Fig. 4. Hence, the contribution to the surface from these inter­actions involve not only O···H/H···O contacts but also C···O/O···C and N···O/O···N contacts, Table 4. The relative contributions of the different contacts to the Hirshfeld surfaces are collated in Table 5 for the entire structure and also delineated for the dication and anion. The linkage of ions through the formation of hydrogen bonds is illustrated in Fig. 6.

The overall two-dimensional fingerprint plot (FP) of the salt together with those of the dication and anion, and FP's delineated into H···H, O···H/H···O, C···H/H···C and C···O/O···C contacts are illustrated in Fig. 7. The O···H/H···O contacts have the largest overall contribution to the Hirshfeld surface, i.e. 43.2%, and these inter­actions dominate in the crystal structure. The prominent spike with green points appearing in the lower left region in the FP for the anion at d_e + d_i ~ 1.7 Å has a major contribution, i.e. 47.2%, from O···H contacts; the spike at the same d_e + d_i distance is due to a small contribution, 10.0%, from H···O contacts. The different contributions from O···H and H···O contacts to the Hirshfeld surface of the dication, i.e. 6.8 and 34.8 %, respectively, lead to asymmetric peaks at d_e + d_i ~ 1.8 and 2.0 Å, respectively, indicating the varying strength of these inter­actions. However, the overall FP of the salt delineated into O···H/H···O contacts shows a symmetric pair of spikes at d_e + d_i ~ 1.7 Å with nearly equal contributions from O···H and H···O contacts. A smaller contribution is made by the H···H contacts, Table 1, and these appear as the scattered points without a distinct peak, Fig. 7. The presence of short inter­atomic C···H/H···C contacts, Table 5, result in a 17.3% overall contribution to the surface, although there are no C—H···π contacts within the acceptance distance criteria for such inter­actions (Spek, 2009). These are represented by a pair of symmetrical wings at d_e + d_i ~ 2.9 Å in the FP plot, Fig. 7. The contribution from C···O/O···C contacts to the Hirshfeld surface is also evident from the presence of inter­molecular C—H···O inter­actions as well as short inter­atomic C···O/O···C contact, Table 5. These appear as cross-over wings in the d_e, d_i region between 1.7 and 2.7 Å. A small but significant contribution to the Hirshfeld surface of the dication due to N···O/O···N contacts is the result of inter­molecular amide-N—H···O(amide) inter­actions.

The inter­molecular inter­actions were further analysed using a recently reported descriptor, the enrichment ratio, ER (Jelsch et al., 2014), which is based on Hirshfeld surface analysis and gives an indication of the relative likelihoods of specific inter­molecular inter­actions to form; the calculated ratios are given in Table 6. The relatively poor content of hydrogen atoms in the salt and the involvements of many hydrogen atoms in the inter­molecular inter­actions, as discussed above, reduces ER value of non-bonded H···H contacts to a value less unity, i.e. 0.8, due to a 23.7% contribution from the 54.5% available Hirshfeld surface and anti­cipated 29.7% random contacts. The ER value of 1.4 corresponding to O···H/H···O contacts results from a relatively high 43.2% contribution by O—H···O, N—H···O and C—H···O inter­actions. The carbon and oxygen atoms involved in the inter­molecular C—H···O inter­actions and short inter C···O/O···C contacts are at distances shorter than the sum of their respective van der Waals radii, hence they also have a high formation propensity, so the ER value is > 1. The C···H/H···C contacts in the crystal are enriched due to the poor nitro­gen content and the presence of short inter­atomic C···H/H···C contacts so the ratio is close to unity, i.e. 0.99. Finally, the ER value of 1.68 corresponding to N···O/O···N contacts for the surface of dication is the result of the charge-assisted N—H···O inter­actions consistent with their high propensity to form.

\ As mentioned in the Chemical context, N,N'-bis­(pyridin-2-yl­methyl)­ethanedi­amide (LH₂), has not been as well studied as the n = 3 and 4 isomers. This notwithstanding, the coordination chemistry of LH₂ is more advanced and diverse. Thus, co-crystals have been reported with a metal complex, i.e. [Mn(1,10-phenanthroline)₃][ClO₄]₂.(LH₂) (Liu et al., 1999). Monodentate coordination via a pyridyl-N atom was found in mononuclear HgI₂(LH₂)₂ (Zeng et al., 2008). Bidentate, bridging via both pyridyl-N atoms has been observed in binuclear {[Me₂(4-HO₂CC₆H₄CH₂)Pt(4,4'-di-t-butyl-2,2'-bi­pyridyl]\ ₂(LH₂)}₂²⁺ (Fraser et al., 2002) and in a polymeric silver salt, {AgBF₄(LH₂)·H₂O}_n (Schauer et al., 1998). In the analogous triflate salt {Ag₂(O₃SCF₃)₂(LH₂)₃}_n (Arman et al., 2010), one LH₂ bridges as in the BF₄ salt (Schauer et al., 1998) but the other two LH₂ molecules bridge one Ag⁺ via a pyridyl-N atom and another via the second pyridyl-N atom as well as a carbonyl-O atom, i.e. are tridentate. In a variation, tetra­dentate, bridging coordination via all four nitro­gen atoms is found in polymeric [CuL(LH₂)(OH₂]_n (Lloret et al., 1989). Deprotonation of LH₂ leads to a tetra­dentate ligand coordinating via all four nitro­gen atoms in PdL (Reger et al., 2003). There are several examples of hexadentate-N₄O₂ coordination in copper(II) chemistry, as in the aforementioned [CuL(LH₂)(OH₂]_n (Lloret et al., 1989) and, for example, in polymeric [CuL(µ₂-4,4'-bi­pyridyl-)(OH₂)]₂ (Zhang et al., 2001).

For related literature, see:

Synthesis and crystallization

The di­amide (0.25 g), prepared in accord with the literature procedure (Schauer et al., 1997), in ethanol (10 ml) was added to a ethanol solution (10 ml) of trimesic acid (Acros Organic, 0.18 g). The mixture was stirred for 2 h at room temperature. After standing for a few minutes, a white precipitate formed which was filtered off by vacuum suction. The filtrate was then left to stand under ambient conditions, yielding pale-yellow crystals after 2 weeks.

Refinement details

Crystal data, data collection and structure refinement details are summarized in Table 7. The carbon-bound H atoms were placed in calculated positions (C—H = 0.95–0.99 Å) and were included in the refinement in the riding-model approximation, with U_iso(H) set to 1.2U_eq(C). The oxygen- and nitro­gen-bound H atoms were located in a difference Fourier map but were refined with distance restraints of O—H = 0.84±0.01 Å and N—H = 0.88±0.01 Å, and with U_iso(H) set to 1.5U_eq(O) and 1.2U_eq(N).

Computing details

Data collection: CrysAlis PRO (Agilent, 2014); cell refinement: CrysAlis PRO (Agilent, 2014); data reduction: CrysAlis PRO (Agilent, 2014); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012), QMol (Gans & Shalloway, 2001) and DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures

	Fig. 1. The molecular structures of the ions comprising the title salt, showing the atom-labelling scheme and displacement ellipsoids at the 50% probability level: (a) 2-({[(pyridin-1-ium-2-ylmethyl)carbamoyl]formamido}methyl)pyridin-1-ium, and (b) 3,5-dicarboxybenzoate; unlabelled atoms are related by the symmetry operation -x, 1 - y, 1 - z.
	Fig. 2. Overlay diagram of the dication in the title compound (red image), the neutral molecule in its co-crystal (green), and dication in the literature salt (blue). The molecules have been overlapped so that the O═C—C═O residues are coincident. The ring N atoms are indicated by an asterisk.
	Fig. 3. Molecular packing in the title salt: (a) supramolecular layers mediated by O—H···O hydrogen bonds, (b) supramolecular tapes mediated by N—H···O hydrogen bonds, and (c) a view of the unit-cell contents shown in projection down the a axis, whereby the supramolecular layers, illustrated in Fig. 3(a), are linked by charge-assisted N—H···O(carboxylate) hydrogen bonds to consolidate a three-dimensional architecture. The O—H···O and N—H···O hydrogen bonds are shown as orange and blue dashed lines, respectively.
	Fig. 4. Views of the Hirshfeld surface mapped over dnorm in the title salt: (a) dication, (b) and (c) anion.
	Fig. 5. View of the Hirshfeld surface mapped over the calculated electrostatic potential the tri-ion aggregate in the title salt.
	Fig. 6. Views of the Hirshfeld surfaces mapped over the calculated electrostatic potential in the title salt emphasizing the interactions between the: (a) dianions, and (b) the environment about the anion.
	Fig. 7. The two-dimensional fingerprint plots for the title salt: (a) dication, (b) anion, and (c) full structure, showing contributions from different contacts, i.e. H···H, O···H/H···O, C···H/H···C, and (e) C···O/O···C.

2-({[(Pyridin-1-ium-2-ylmethyl)carbamoyl]formamido}methyl)pyridin-1-ium bis(3,5-dicarboxybenzoate)

Crystal data

C14H16N4O2^2+·2C9H5O6^−	F(000) = 716
Mr = 690.56	Dx = 1.543 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
a = 5.0436 (3) Å	Cell parameters from 6152 reflections
b = 18.4232 (10) Å	θ = 3.4–29.2°
c = 16.0796 (9) Å	µ = 0.12 mm^−1
β = 95.878 (5)°	T = 100 K
V = 1486.25 (15) Å^3	Prism, pale-yellow
Z = 2	0.30 × 0.10 × 0.05 mm

Data collection

Agilent SuperNova Dual diffractometer with an Atlas detector	3410 independent reflections
Radiation source: SuperNova (Mo) X-ray Source	2656 reflections with I > 2σ(I)
Mirror monochromator	Rint = 0.069
Detector resolution: 10.4041 pixels mm^-1	θmax = 27.5°, θmin = 3.4°
ω scan	h = −6→6
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	k = −23→23
Tmin = 0.580, Tmax = 1.000	l = −20→20
17686 measured reflections

Refinement

Refinement on F^2	4 restraints
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.051	w = 1/[σ^2(Fo^2) + (0.0563P)^2 + 0.8519P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.134	(Δ/σ)max < 0.001
S = 1.07	Δρmax = 0.46 e Å^−3
3410 reflections	Δρmin = −0.26 e Å^−3
238 parameters

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
O1	0.2441 (3)	0.56058 (7)	0.47153 (9)	0.0231 (3)
N1	−0.3956 (3)	0.69095 (9)	0.53385 (11)	0.0198 (4)
H1N	−0.285 (4)	0.6629 (11)	0.5665 (12)	0.024*
N2	−0.2089 (3)	0.56875 (9)	0.45086 (11)	0.0194 (4)
H2N	−0.364 (3)	0.5516 (12)	0.4615 (14)	0.023*
C1	−0.3894 (4)	0.69266 (10)	0.45027 (12)	0.0187 (4)
C2	−0.5582 (4)	0.73355 (11)	0.57322 (13)	0.0226 (4)
H2	−0.5589	0.7300	0.6321	0.027*
C3	−0.7242 (4)	0.78235 (11)	0.52887 (13)	0.0241 (4)
H3	−0.8446	0.8113	0.5562	0.029*
C4	−0.7117 (4)	0.78821 (11)	0.44357 (13)	0.0234 (4)
H4	−0.8184	0.8231	0.4122	0.028*
C5	−0.5438 (4)	0.74330 (10)	0.40389 (13)	0.0209 (4)
H5	−0.5349	0.7472	0.3453	0.025*
C6	−0.2190 (4)	0.63885 (10)	0.40966 (13)	0.0208 (4)
H6A	−0.2906	0.6325	0.3504	0.025*
H6B	−0.0358	0.6584	0.4107	0.025*
C7	0.0204 (4)	0.53666 (11)	0.47870 (12)	0.0197 (4)
O2	0.8690 (3)	0.32072 (7)	0.27064 (9)	0.0253 (3)
O3	1.1233 (3)	0.39299 (8)	0.35861 (9)	0.0298 (4)
O4	1.2729 (3)	0.64690 (8)	0.25738 (10)	0.0260 (3)
O5	0.9119 (3)	0.69980 (7)	0.19086 (9)	0.0243 (3)
H5O	0.994 (5)	0.7391 (9)	0.2034 (16)	0.036*
O6	0.2374 (3)	0.55161 (7)	0.03570 (9)	0.0220 (3)
O7	0.1837 (3)	0.43588 (7)	0.07250 (9)	0.0217 (3)
H7O	0.049 (3)	0.4407 (14)	0.0370 (13)	0.033*
C8	0.8550 (4)	0.44714 (10)	0.24689 (12)	0.0183 (4)
C9	0.9905 (4)	0.51294 (10)	0.25715 (12)	0.0178 (4)
H9	1.1439	0.5167	0.2964	0.021*
C10	0.9018 (4)	0.57340 (10)	0.20997 (12)	0.0171 (4)
C11	0.6784 (4)	0.56752 (10)	0.15260 (12)	0.0180 (4)
H11	0.6170	0.6086	0.1205	0.022*
C12	0.5438 (4)	0.50196 (10)	0.14184 (12)	0.0178 (4)
C13	0.6305 (4)	0.44181 (10)	0.18970 (12)	0.0180 (4)
H13	0.5360	0.3972	0.1832	0.022*
C14	0.9579 (4)	0.38131 (10)	0.29671 (12)	0.0197 (4)
C15	1.0500 (4)	0.64353 (10)	0.22231 (12)	0.0191 (4)
C16	0.3081 (4)	0.49865 (10)	0.07891 (12)	0.0184 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0151 (7)	0.0200 (7)	0.0337 (8)	−0.0005 (5)	−0.0001 (6)	0.0019 (6)
N1	0.0211 (9)	0.0166 (8)	0.0204 (9)	−0.0001 (6)	−0.0033 (7)	0.0019 (7)
N2	0.0166 (8)	0.0145 (8)	0.0264 (9)	0.0000 (6)	−0.0006 (7)	0.0020 (7)
C1	0.0193 (9)	0.0160 (9)	0.0197 (10)	−0.0030 (7)	−0.0031 (7)	0.0000 (8)
C2	0.0266 (11)	0.0206 (10)	0.0197 (10)	−0.0036 (8)	−0.0014 (8)	−0.0006 (8)
C3	0.0276 (11)	0.0176 (10)	0.0272 (11)	−0.0007 (8)	0.0027 (8)	−0.0034 (8)
C4	0.0274 (11)	0.0145 (9)	0.0270 (11)	0.0008 (8)	−0.0032 (8)	0.0008 (8)
C5	0.0252 (10)	0.0166 (9)	0.0201 (10)	−0.0018 (8)	−0.0024 (8)	0.0006 (8)
C6	0.0221 (10)	0.0176 (10)	0.0221 (10)	−0.0002 (7)	−0.0006 (8)	0.0021 (8)
C7	0.0188 (9)	0.0191 (10)	0.0207 (10)	−0.0003 (7)	−0.0002 (7)	−0.0034 (8)
O2	0.0290 (8)	0.0153 (7)	0.0298 (8)	0.0007 (6)	−0.0060 (6)	0.0020 (6)
O3	0.0359 (9)	0.0218 (8)	0.0281 (8)	0.0010 (6)	−0.0140 (7)	0.0031 (6)
O4	0.0214 (7)	0.0204 (7)	0.0341 (9)	−0.0014 (6)	−0.0071 (6)	−0.0030 (6)
O5	0.0260 (8)	0.0135 (7)	0.0313 (8)	−0.0026 (6)	−0.0074 (6)	0.0017 (6)
O6	0.0220 (7)	0.0185 (7)	0.0234 (7)	−0.0015 (5)	−0.0072 (6)	0.0036 (6)
O7	0.0210 (7)	0.0163 (7)	0.0256 (8)	−0.0035 (5)	−0.0084 (6)	0.0020 (6)
C8	0.0220 (10)	0.0154 (9)	0.0171 (9)	0.0028 (7)	0.0009 (7)	0.0000 (7)
C9	0.0186 (9)	0.0192 (9)	0.0149 (9)	0.0011 (7)	−0.0012 (7)	−0.0019 (7)
C10	0.0178 (9)	0.0148 (9)	0.0185 (9)	−0.0003 (7)	0.0016 (7)	−0.0013 (7)
C11	0.0204 (10)	0.0146 (9)	0.0185 (10)	0.0037 (7)	−0.0004 (8)	0.0013 (7)
C12	0.0175 (9)	0.0169 (9)	0.0184 (10)	0.0010 (7)	−0.0001 (7)	0.0001 (7)
C13	0.0194 (9)	0.0150 (9)	0.0196 (10)	0.0000 (7)	0.0013 (7)	−0.0018 (7)
C14	0.0206 (9)	0.0164 (9)	0.0214 (10)	0.0021 (7)	−0.0010 (8)	0.0016 (8)
C15	0.0226 (10)	0.0166 (9)	0.0176 (9)	−0.0001 (7)	0.0000 (8)	−0.0015 (7)
C16	0.0199 (10)	0.0162 (9)	0.0186 (10)	−0.0001 (7)	−0.0001 (8)	0.0002 (7)

Geometric parameters (Å, º)

O1—C7	1.227 (2)	O3—C14	1.250 (2)
N1—C2	1.340 (3)	O4—C15	1.206 (2)
N1—C1	1.348 (3)	O5—C15	1.320 (2)
N1—H1N	0.892 (10)	O5—H5O	0.848 (10)
N2—C7	1.335 (3)	O6—C16	1.229 (2)
N2—C6	1.450 (2)	O7—C16	1.315 (2)
N2—H2N	0.878 (10)	O7—H7O	0.847 (10)
C1—C5	1.384 (3)	C8—C13	1.387 (3)
C1—C6	1.504 (3)	C8—C9	1.393 (3)
C2—C3	1.377 (3)	C8—C14	1.516 (3)
C2—H2	0.9500	C9—C10	1.395 (3)
C3—C4	1.384 (3)	C9—H9	0.9500
C3—H3	0.9500	C10—C11	1.385 (3)
C4—C5	1.385 (3)	C10—C15	1.496 (3)
C4—H4	0.9500	C11—C12	1.388 (3)
C5—H5	0.9500	C11—H11	0.9500
C6—H6A	0.9900	C12—C13	1.394 (3)
C6—H6B	0.9900	C12—C16	1.481 (3)
C7—C7^i	1.538 (4)	C13—H13	0.9500
O2—C14	1.259 (2)
C2—N1—C1	122.36 (17)	C15—O5—H5O	110.7 (18)
C2—N1—H1N	116.1 (15)	C16—O7—H7O	107.8 (17)
C1—N1—H1N	121.5 (15)	C13—C8—C9	119.82 (17)
C7—N2—C6	122.43 (17)	C13—C8—C14	120.39 (17)
C7—N2—H2N	122.4 (15)	C9—C8—C14	119.77 (17)
C6—N2—H2N	114.8 (15)	C8—C9—C10	120.28 (17)
N1—C1—C5	118.93 (18)	C8—C9—H9	119.9
N1—C1—C6	119.35 (17)	C10—C9—H9	119.9
C5—C1—C6	121.71 (18)	C11—C10—C9	119.56 (17)
N1—C2—C3	120.45 (19)	C11—C10—C15	121.15 (17)
N1—C2—H2	119.8	C9—C10—C15	119.29 (17)
C3—C2—H2	119.8	C10—C11—C12	120.34 (17)
C2—C3—C4	118.52 (19)	C10—C11—H11	119.8
C2—C3—H3	120.7	C12—C11—H11	119.8
C4—C3—H3	120.7	C11—C12—C13	120.10 (17)
C3—C4—C5	120.13 (19)	C11—C12—C16	117.97 (16)
C3—C4—H4	119.9	C13—C12—C16	121.92 (17)
C5—C4—H4	119.9	C8—C13—C12	119.89 (17)
C1—C5—C4	119.44 (19)	C8—C13—H13	120.1
C1—C5—H5	120.3	C12—C13—H13	120.1
C4—C5—H5	120.3	O3—C14—O2	127.13 (18)
N2—C6—C1	112.55 (17)	O3—C14—C8	116.59 (17)
N2—C6—H6A	109.1	O2—C14—C8	116.27 (17)
C1—C6—H6A	109.1	O4—C15—O5	124.63 (17)
N2—C6—H6B	109.1	O4—C15—C10	122.39 (17)
C1—C6—H6B	109.1	O5—C15—C10	112.98 (16)
H6A—C6—H6B	107.8	O6—C16—O7	123.05 (17)
O1—C7—N2	125.63 (19)	O6—C16—C12	121.29 (17)
O1—C7—C7^i	121.6 (2)	O7—C16—C12	115.66 (16)
N2—C7—C7^i	112.8 (2)
C2—N1—C1—C5	4.2 (3)	C10—C11—C12—C13	1.0 (3)
C2—N1—C1—C6	−174.80 (18)	C10—C11—C12—C16	−179.31 (17)
C1—N1—C2—C3	−1.2 (3)	C9—C8—C13—C12	1.0 (3)
N1—C2—C3—C4	−2.4 (3)	C14—C8—C13—C12	−177.46 (18)
C2—C3—C4—C5	2.9 (3)	C11—C12—C13—C8	−1.4 (3)
N1—C1—C5—C4	−3.5 (3)	C16—C12—C13—C8	178.90 (18)
C6—C1—C5—C4	175.42 (18)	C13—C8—C14—O3	−165.39 (18)
C3—C4—C5—C1	0.0 (3)	C9—C8—C14—O3	16.1 (3)
C7—N2—C6—C1	−125.7 (2)	C13—C8—C14—O2	15.3 (3)
N1—C1—C6—N2	34.8 (2)	C9—C8—C14—O2	−163.19 (18)
C5—C1—C6—N2	−144.13 (19)	C11—C10—C15—O4	−163.64 (19)
C6—N2—C7—O1	−1.8 (3)	C9—C10—C15—O4	16.4 (3)
C6—N2—C7—C7^i	179.1 (2)	C11—C10—C15—O5	16.2 (3)
C13—C8—C9—C10	−0.2 (3)	C9—C10—C15—O5	−163.84 (17)
C14—C8—C9—C10	178.26 (17)	C11—C12—C16—O6	2.0 (3)
C8—C9—C10—C11	−0.2 (3)	C13—C12—C16—O6	−178.26 (18)
C8—C9—C10—C15	179.80 (17)	C11—C12—C16—O7	−178.40 (17)
C9—C10—C11—C12	−0.2 (3)	C13—C12—C16—O7	1.3 (3)
C15—C10—C11—C12	179.82 (18)

Symmetry code: (i) −x, −y+1, −z+1.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N2—H2N···O1^i	0.88 (2)	2.38 (2)	2.704 (2)	102 (1)
O7—H7O···O6^ii	0.85 (2)	1.77 (2)	2.614 (2)	178 (2)
O5—H5O···O2^iii	0.85 (2)	1.69 (2)	2.5352 (19)	175 (2)
N2—H2N···O1^iv	0.88 (2)	2.01 (2)	2.816 (2)	153 (2)
N1—H1N···O3^v	0.89 (2)	1.73 (2)	2.604 (2)	169 (2)
C5—H5···O4^vi	0.95	2.46	3.019 (3)	117
C6—H6A···O4^vi	0.99	2.55	3.362 (3)	140
C2—H2···O2^i	0.95	2.50	3.251 (3)	136
C3—H3···O6^vii	0.95	2.59	3.068 (2)	112

Symmetry codes: (i) −x, −y+1, −z+1; (ii) −x, −y+1, −z; (iii) −x+2, y+1/2, −z+1/2; (iv) x−1, y, z; (v) −x+1, −y+1, −z+1; (vi) x−2, y, z; (vii) x−1, −y+3/2, z+1/2.

 

Footnotes

‡Additional correspondence author, e-mail: [e-mail].