Crystal structure and Hirshfeld surface analysis of [FeCl₄(LH)₂] (LH = 1H-imidazo[4,5-b]pyridin-4-ium)

The title coordination complex tetra­chlorido­bis­(1H-imidazo[4,5-b]pyridin-4-ium-κN³)iron(II), [FeCl₄(C₆H₆N₃)₂] or [FeCl₄(LH)₂], was synthesized and structurally characterized by single-crystal X-ray diffraction. The complex crystallizes in the triclinic space group P1. The iron atom (site symmetry ) is hexa-coordinated, adopting a slightly distorted octa­hedral geometry defined by two 1H-imidazo[4,5-b]pyridinium ligands and four chloride anions. In the crystal, N—H⋯Cl hydrogen bonds generate two-dimensional layers parallel to the ab plane, while the three-dimensional supra­molecular framework is further consolidated by C—H⋯Cl inter­actions. In addition, π–π stacking inter­actions contribute to the overall cohesion of the crystal structure. Hirshfeld surface analysis indicates the significance of various inter­molecular contacts in the crystal packing, with major contributions from Cl⋯H/H⋯Cl (43.2%), H⋯H (22.5%), C⋯H/H⋯C (16.4%), H⋯N/N⋯H (4.4%), N⋯C/C⋯N (3.7%), C⋯C (3.6%), Cl⋯N/N⋯Cl (3.2%), Cl⋯C/C⋯Cl (2.4%), and N⋯N (0.6%) inter­actions.

1. Chemical context

The coordination chemistry of iron has attracted great inter­est due to the importance of iron-based coordination compounds and their applications in various fields such as catalysis (Sheldon & Kochi, 1981; Meunier et al., 2000), magnetism (Toftlund, 1989; Gütlich, 1981) and bioinorganic chemistry, particularly in simulating the behaviour of enzymes involved in electron transfer and oxygen transfer processes (Reedijk & Bouwman, 1999). Iron is frequently hexa­coordinated in its coordination complexes; it is important to note that the number, type, and geometric arrangement of ligands around the metal centre significantly influence the previously mentioned properties (Börzel et al., 2002).

Nitro­gen-containing heterocycles, which feature one or more nitro­gen atoms within their ring structures, represent important and distinctive categories of heterocycles (Li et al., 2023). These heterocycles play an important role in coordination chemistry as N-donor ligands. Among them, benzimidazole is particularly well known and widely used as a nitro­gen-donor ligand (Ana, 2019).

Benzimidazole contains two N-donor atoms that can coordinate transition metals (Sundberg & Martin, 1974). The imidazole ring consists of two nitro­gen atoms, one of which is pyrrole-like, with its lone pair electrons contributing to the aromatic sextet. The second N atom is pyridine-like, with a non-delocalized lone pair that imparts basic properties (Haga, 2003). The substitution of a CH group in the benzene ring with a nitro­gen atom, which is necessarily pyridine-like, imparts a basicity similar to that of nitro­gen in the imidazole ring. This modification enhances the ligand's basic properties by introducing a second pyridine-like nitro­gen atom, thereby increasing its binding affinity to metal ions (Zapata et al., 2008). Thus, 4-aza­benzimidazole consists of a fused imidazole and pyridine system. The positioning of its basic nitro­gen atoms enables the potential for chelation with metal ions, facilitating the formation of four-membered rings (Korabik et al., 1998). The three nitro­gen atoms in 4-aza­benzimidazole, each with distinct characteristics, provide versatility to the ligand, allowing it to coordinate with metal ions in various modes, including monodentate, bidentate, chelating, and bridging arrangements.

2. Structural commentary

The title complex crystallizes with the Fe²⁺ atom located on a crystallographic centre of symmetry, generating the complete mol­ecule by inversion symmetry. As a result, the structure consists of two symmetry-related halves forming a discrete mononuclear complex with an octa­hedral geometry and a trans configuration for the N atoms. The Fe²⁺ centre is coordinated by two nitro­gen atoms from two N-donor 1H-imidazo[4,5-b]pyridinium ligands in the axial positions and four chloride ions in the equatorial plane (Fig. 1), resulting in an N₂Cl₄ coordination environment. The bond lengths and angles (Table 1) are consistent with a slightly distorted octa­hedral geometry. The axial Fe1—N1 bond length is 2.2256 (9) Å, whereas the equatorial Fe1—Cl1 and Fe1—Cl2 bond lengths are 2.5845 (2) and 2.4564 (2) Å, respectively. These values fall within the expected range for Fe²⁺ octa­hedral complexes reported in the literature (Rettig et al., 2000; Rusbridge et al., 2018). The bond angles around the metal centre are close to the ideal values of 90°, with only minor deviations, confirming a near-ideal octa­hedral coordination geometry. Moreover, the iron(II) atom lies within the equatorial plane, while the five-membered imidazole and six-membered pyridine rings of the chelating ligand are approximately coplanar, allowing for efficient coordination and contributing to the overall planarity of the ligand framework. The cohesion of the mol­ecular structure is achieved through an intra­molecular N—H⋯Cl hydrogen bond formed between the nitro­gen atom of the imidazole ring and a chloride ion acceptor [N3—H3⋯Cl1ⁱ; symmetry code: (i) −x, −y, −z).

Table 1
Selected geometric parameters (Å, °)

Fe1—Cl1	2.5845 (2)	Fe1—N1	2.2256 (9)
Fe1—Cl2	2.4564 (2)
Cl1—Fe1—Cl2	89.75 (1)	Cl1—Fe1—N1^i	92.41 (2)
Cl1—Fe1—N1	87.59 (2)	Cl2—Fe1—N1	92.50 (2)
Cl1—Fe1—Cl2^i	90.25 (1)	Cl2—Fe1—N1^i	87.50 (2)
Symmetry code: (i) .

Figure 1 ORTEP view of the structure of the title complex showing the atom-labelling scheme. Displacement ellipsoids are drawn at the 50% probability level. Symmetry code: (i) −x, −y, −z.

3. Supra­molecular features

The crystal structure of the title compound is consolidated by various supra­molecular inter­actions, including classical and non-classical hydrogen bonds, as well as π–π stacking inter­actions. All N—H and C—H groups of the 1H-imidazo[4,5-b]pyridinium ligand, except for the C4—H4 group, act as hydrogen-bond donors, while the chloride ions serve as acceptors, forming N—H⋯Cl and C—H⋯Cl inter­actions (Table 2). Furthermore, N2—H2⋯Cl2ⁱⁱ hydrogen bonding links the mol­ecules into chains along the [110] direction. These chains adopt a ribbon-like arrangement featuring R²₂(12) ring motifs (Fig. 2; Bernstein et al., 1995). These chains are further connected via classical hydrogen bonds (N2—H2⋯Cl2ⁱⁱⁱ) into a two-dimensional network lying parallel to the (001) plane, based on alternating R²₂(4) and R²₂(12) ring motifs (Fig. 3). Extension into a three-dimensional network occurs via non-classical C—H⋯Cl hydrogen bonds C5—H5⋯Cl2^v and C6—H6⋯Cl1^iv, forming R²₂(14), R⁴₂(14) and R³₂(11) graph-set motifs (Fig. 4).

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N2—H2⋯Cl2^ii	0.86 (2)	2.66 (2)	3.3061 (10)	133.0 (17)
N2—H2⋯Cl2^iii	0.86 (2)	2.56 (2)	3.1862 (9)	130.4 (17)
N3—H3⋯Cl1^i	0.89 (2)	2.15 (2)	2.9944 (10)	160.7 (19)
C1—H1⋯Cl1	0.942 (15)	2.702 (15)	3.2841 (10)	120.7 (11)
C5—H5⋯Cl2^iv	0.958 (15)	2.725 (15)	3.6357 (10)	159.1 (12)
C6—H6⋯Cl1^v	0.954 (15)	2.641 (15)	3.5932 (11)	176.2 (13)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) .

Figure 2 Network propagation along the [110] direction through N2—H2⋯Cl2^ii hydrogen bonds, forming R^22(12) graph-set motifs (highlighted in purple).

Figure 3 Two-dimensional network of the title compound parallel to the ab plane, showing N—H⋯Cl hydrogen bonds and associated ring motifs.

Figure 4 (a) Fragment of the supra­molecular crystal structure packing of the title compound, (b) hydrogen-bonding patterns. Hydrogen bonds are indicated by dashed blue lines.

Overall, the crystal packing is reinforced by π–π stacking inter­actions involving both the six-membered pyridine rings (Cg6) and the five-membered imidazole rings (Cg5) of neighbouring mol­ecules in a parallel-displaced arrangement (Fig. 5) with centroid–centroid distances of 3.591 (1) and 3.459 (1) Å, respectively

Figure 5 π–π stacking inter­actions in the title complex. Cg(5) and Cg(6) are the centroids of imidazole rings (pink) and pyridine rings (blue), respectively, [symmetry codes: (i) 1 − x, 1 − y, 1 − z; (ii) 1 − x, 1 − y, −z].

To gain a deeper insight into the inter­molecular inter­actions responsible for the cohesion and stability of the supra­molecular structure, a Hirshfeld surface (HS) analysis was performed using Crystal Explorer 21 (Spackman & Jayatilaka, 2009; Spackman et al., 2021). The two-dimensional fingerprint plots (Fig. 6; Spackman & McKinnon, 2002) show that Cl⋯H/H⋯Cl contacts are the most significant (43.2%), followed by H⋯H (22.5%) and C⋯H/H⋯C (16.4%). Minor contributions arise from H⋯N/N⋯H (4.4%), C⋯N/N⋯C (3.7%), C⋯C (3.6%), and Cl⋯N/N⋯Cl (3.2%), while Cl⋯C/C⋯Cl (2.4%) and N⋯N (0.6%) are negligible. Overall, the HS analysis emphasizes the role of hydrogen bonding and van der Waals inter­actions (Hökelek et al., 2018; Hathwar et al., 2015) in consolidating the packing, together with π–π stacking. In addition, it confirms the absence of halogen–halogen contacts, as the Cl⋯Cl contribution is 0% (Moon et al., 2020).

Figure 6 Two-dimensional fingerprint plots for the title compound with the corresponding Hirshfeld surface dnorm for all contacts and those delineated into specific contacts. The di and de values represent the nearest inter­nal and external distances from specific points on the Hirshfeld surface (in Å).

4. Database survey

A Cambridge Structural Database (CSD, version 5.45, November 2023 update; Groom et al., 2016; Bruno et al., 2002) search revealed only one reported iron complex with 4-aza­benzimidazole, where the ligand acts in a bridging mode via the two imidazole N atoms generating a three-dimensional diamond-like framework (refcode XASGON; Rettig et al., 2000). A zinc analogue with the same coordination mode has also been described (MIHHOB; Hayashi et al., 2007).

In contrast, several copper complexes display diverse coordination behaviours. In some cases, the ligand coordinates in a monodentate fashion via the amine nitro­gen [GEZCOF (Domínguez-Martín et al., 2013); BUNZEQ (Choquesillo-Laza­rte et al., 2010)], while in others, coordination occurs through the imine nitro­gen, as in the title compound (GEZCIZ; Domínguez-Martín et al., 2013). Alternatively, 4-aza­benzimidazole can act as a bridging ligand through both the imine and pyridinic nitro­gen atoms, affording dinuclear Cu^II paddlewheel-like architectures (TETGIJ and TETGOP; van Albada et al., 2006).

To date, no structures have been reported with 4-aza­benzimidazole protonated at the pyridinic nitro­gen atom, until the present compound.

5. Experimental

All chemicals were commercially available, purchased from Sigma-Aldrich, and used as received without purification.

5.1. Synthesis and crystallization

FeCl₂·4H₂O (0.198 g, 1 mmol) was dissolved in 10 mL of methanol in the presence of a few drops of ascorbic acid. A solution of 4-aza­benzimidazole (0.238 g, 2 mmol) in 10 mL of aceto­nitrile was then added, resulting in a brown mixture, which was heated under stirring until boiling. The solution was left to evaporate slowly over several days, yielding green crystals of the title compound, suitable for single-crystal X-ray diffraction analysis.

5.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3. All hydrogen atoms were located from difference Fourier maps and refined freely with isotropic displacement parameters.

Table 3
Experimental details

Crystal data
Chemical formula	[FeCl4(C6H6N3)2]
Mr	437.93
Crystal system, space group	Triclinic, P
Temperature (K)	100
a, b, c (Å)	6.9242 (2), 7.5223 (2), 8.6704 (2)
α, β, γ (°)	106.967 (2), 98.665 (2), 109.174 (2)
V (Å^3)	392.51 (1)
Z	1
Radiation type	Mo Kα
μ (mm^−1)	1.65
Crystal size (mm)	0.10 × 0.09 × 0.08
Data collection
Diffractometer	Nonius KappaCCD
No. of measured, independent and observed [I > 2σ(I)] reflections	30304, 2818, 2650
Rint	0.026
(sin θ/λ)max (Å^−1)	0.764
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.019, 0.049, 1.07
No. of reflections	2818
No. of parameters	130
H-atom treatment	All H-atom parameters refined
Δρmax, Δρmin (e Å^−3)	0.51, −0.27
Computer programs: APEX2 and SAINT (Bruker, 2024), SHELXT (Sheldrick, 2015a), SHELXL2018/3 (Sheldrick, 2015b) and OLEX2 (Dolomanov et al., 2009).

Supporting information

Computing details

Tetrachloridobis(1H-imidazo[4,5-b]pyridin-4-ium-κN³)iron(II)

Crystal data

[FeCl4(C6H6N3)2]	Z = 1
Mr = 437.93	F(000) = 220
Triclinic, P1	Dx = 1.853 Mg m^−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 6.9242 (2) Å	Cell parameters from 30213 reflections
b = 7.5223 (2) Å	θ = 3.1–32.9°
c = 8.6704 (2) Å	µ = 1.65 mm^−1
α = 106.967 (2)°	T = 100 K
β = 98.665 (2)°	Prism, green
γ = 109.174 (2)°	0.1 × 0.09 × 0.08 mm
V = 392.51 (1) Å^3

Data collection

Nonius KappaCCD diffractometer	Rint = 0.026
Radiation source: fine-focus sealed tube	θmax = 32.9°, θmin = 3.1°
ω scans	h = −10→10
30304 measured reflections	k = −11→11
2818 independent reflections	l = −12→13
2650 reflections with I > 2σ(I)

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.019	All H-atom parameters refined
wR(F^2) = 0.049	w = 1/[σ^2(Fo^2) + (0.0225P)^2 + 0.1909P] where P = (Fo^2 + 2Fc^2)/3
S = 1.07	(Δ/σ)max = 0.001
2818 reflections	Δρmax = 0.51 e Å^−3
130 parameters	Δρmin = −0.26 e Å^−3

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All su's are estimated from the variances of the (full) variance-covariance matrix. The cell esds are taken into account in the estimation of distances, angles and torsion angles

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

	x	y	z	Uiso*/Ueq
Fe1	0.00000	0.00000	0.00000	0.0091 (1)
Cl1	0.11270 (3)	−0.15421 (3)	−0.26126 (3)	0.0118 (1)
Cl2	0.10569 (3)	−0.21585 (3)	0.12967 (3)	0.0112 (1)
N1	0.32581 (13)	0.24252 (12)	0.09987 (10)	0.0104 (2)
N2	0.65992 (13)	0.42459 (12)	0.10840 (10)	0.0110 (2)
N3	0.30049 (13)	0.49999 (12)	0.33328 (10)	0.0116 (2)
C1	0.48880 (15)	0.24861 (14)	0.03344 (12)	0.0112 (2)
C2	0.40177 (14)	0.42778 (13)	0.22624 (11)	0.0096 (2)
C3	0.61149 (14)	0.54528 (14)	0.23671 (11)	0.0101 (2)
C4	0.72138 (15)	0.73656 (14)	0.35954 (12)	0.0127 (2)
C5	0.61028 (16)	0.80452 (15)	0.46871 (12)	0.0142 (2)
C6	0.40167 (16)	0.68616 (15)	0.45319 (12)	0.0136 (2)
H1	0.486 (2)	0.141 (2)	−0.0572 (18)	0.014 (3)*
H2	0.779 (3)	0.447 (3)	0.084 (2)	0.025 (4)*
H3	0.169 (3)	0.421 (3)	0.324 (2)	0.028 (4)*
H4	0.867 (2)	0.817 (2)	0.3706 (19)	0.018 (4)*
H5	0.676 (2)	0.934 (2)	0.5580 (19)	0.019 (4)*
H6	0.320 (2)	0.728 (2)	0.5245 (19)	0.018 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Fe1	0.0081 (1)	0.0083 (1)	0.0104 (1)	0.0026 (1)	0.0036 (1)	0.0031 (1)
Cl1	0.0110 (1)	0.0115 (1)	0.0125 (1)	0.0038 (1)	0.0055 (1)	0.0035 (1)
Cl2	0.0110 (1)	0.0109 (1)	0.0127 (1)	0.0049 (1)	0.0048 (1)	0.0043 (1)
N1	0.0098 (3)	0.0095 (3)	0.0113 (3)	0.0034 (3)	0.0035 (3)	0.0030 (3)
N2	0.0089 (3)	0.0120 (3)	0.0127 (3)	0.0042 (3)	0.0048 (3)	0.0044 (3)
N3	0.0112 (3)	0.0114 (3)	0.0131 (3)	0.0043 (3)	0.0058 (3)	0.0047 (3)
C1	0.0105 (4)	0.0112 (4)	0.0121 (4)	0.0045 (3)	0.0037 (3)	0.0038 (3)
C2	0.0092 (4)	0.0092 (4)	0.0108 (3)	0.0033 (3)	0.0034 (3)	0.0042 (3)
C3	0.0095 (4)	0.0109 (4)	0.0106 (4)	0.0040 (3)	0.0033 (3)	0.0047 (3)
C4	0.0117 (4)	0.0112 (4)	0.0131 (4)	0.0022 (3)	0.0023 (3)	0.0046 (3)
C5	0.0161 (4)	0.0109 (4)	0.0133 (4)	0.0041 (3)	0.0033 (3)	0.0030 (3)
C6	0.0166 (4)	0.0125 (4)	0.0127 (4)	0.0069 (3)	0.0058 (3)	0.0036 (3)

Geometric parameters (Å, º)

Fe1—Cl1	2.5845 (2)	N3—C6	1.3488 (14)
Fe1—Cl2	2.4564 (2)	C2—C3	1.4030 (15)
Fe1—N1	2.2256 (9)	N2—H2	0.86 (2)
Fe1—Cl1^i	2.5845 (2)	N3—H3	0.89 (2)
Fe1—Cl2^i	2.4564 (2)	C3—C4	1.3877 (14)
Fe1—N1^i	2.2256 (9)	C4—C5	1.3944 (15)
N1—C1	1.3360 (14)	C5—C6	1.3871 (16)
N1—C2	1.3686 (13)	C1—H1	0.942 (15)
N2—C1	1.3469 (14)	C4—H4	0.964 (15)
N2—C3	1.3774 (13)	C5—H5	0.958 (15)
N3—C2	1.3418 (13)	C6—H6	0.954 (15)
Cl1—Fe1—Cl2	89.75 (1)	N1—C2—N3	127.71 (9)
Cl1—Fe1—N1	87.59 (2)	N1—C2—C3	111.74 (9)
Cl1—Fe1—Cl1^i	180.00	N3—C2—C3	120.54 (9)
Cl1—Fe1—Cl2^i	90.25 (1)	C3—N2—H2	128.4 (13)
Cl1—Fe1—N1^i	92.41 (2)	C1—N2—H2	124.0 (13)
Cl2—Fe1—N1	92.50 (2)	N2—C3—C4	134.70 (10)
Cl1^i—Fe1—Cl2	90.25 (1)	C2—C3—C4	121.25 (9)
Cl2—Fe1—Cl2^i	180.00	N2—C3—C2	104.04 (8)
Cl2—Fe1—N1^i	87.50 (2)	C2—N3—H3	118.1 (12)
Cl1^i—Fe1—N1	92.41 (2)	C6—N3—H3	122.1 (12)
Cl2^i—Fe1—N1	87.50 (2)	C3—C4—C5	116.15 (10)
N1—Fe1—N1^i	180.00	C4—C5—C6	121.22 (10)
Cl1^i—Fe1—Cl2^i	89.75 (1)	N3—C6—C5	121.01 (10)
Cl1^i—Fe1—N1^i	87.59 (2)	N1—C1—H1	123.8 (9)
Cl2^i—Fe1—N1^i	92.50 (2)	N2—C1—H1	122.6 (9)
Fe1—N1—C1	126.40 (7)	C3—C4—H4	122.1 (9)
Fe1—N1—C2	129.89 (7)	C5—C4—H4	121.7 (9)
C1—N1—C2	103.25 (9)	C4—C5—H5	121.1 (9)
C1—N2—C3	107.32 (9)	C6—C5—H5	117.6 (9)
C2—N3—C6	119.81 (9)	N3—C6—H6	115.3 (9)
N1—C1—N2	113.63 (9)	C5—C6—H6	123.7 (9)
Cl1—Fe1—N1—C1	−7.58 (8)	C3—N2—C1—N1	1.16 (12)
Cl1—Fe1—N1—C2	163.34 (8)	C1—N2—C3—C2	−1.28 (11)
Cl2—Fe1—N1—C1	82.07 (8)	C1—N2—C3—C4	177.73 (11)
Cl2—Fe1—N1—C2	−107.02 (8)	C6—N3—C2—N1	178.75 (10)
Cl1^i—Fe1—N1—C1	172.42 (8)	C6—N3—C2—C3	−0.74 (14)
Cl1^i—Fe1—N1—C2	−16.66 (8)	C2—N3—C6—C5	−0.45 (15)
Cl2^i—Fe1—N1—C1	−97.93 (8)	N1—C2—C3—N2	1.06 (11)
Cl2^i—Fe1—N1—C2	72.98 (8)	N1—C2—C3—C4	−178.12 (9)
Fe1—N1—C1—N2	172.38 (7)	N3—C2—C3—N2	−179.38 (9)
C2—N1—C1—N2	−0.47 (11)	N3—C2—C3—C4	1.45 (15)
Fe1—N1—C2—N3	7.58 (15)	N2—C3—C4—C5	−179.78 (11)
Fe1—N1—C2—C3	−172.89 (7)	C2—C3—C4—C5	−0.90 (15)
C1—N1—C2—N3	−179.92 (10)	C3—C4—C5—C6	−0.28 (15)
C1—N1—C2—C3	−0.39 (11)	C4—C5—C6—N3	0.98 (16)

Symmetry code: (i) −x, −y, −z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N2—H2···Cl2^ii	0.86 (2)	2.66 (2)	3.3061 (10)	133.0 (17)
N2—H2···Cl2^iii	0.86 (2)	2.56 (2)	3.1862 (9)	130.4 (17)
N3—H3···Cl1^i	0.89 (2)	2.15 (2)	2.9944 (10)	160.7 (19)
C1—H1···Cl1	0.942 (15)	2.702 (15)	3.2841 (10)	120.7 (11)
C5—H5···Cl2^iv	0.958 (15)	2.725 (15)	3.6357 (10)	159.1 (12)
C6—H6···Cl1^v	0.954 (15)	2.641 (15)	3.5932 (11)	176.2 (13)

Symmetry codes: (i) −x, −y, −z; (ii) x+1, y+1, z; (iii) −x+1, −y, −z; (iv) −x+1, −y+1, −z+1; (v) x, y+1, z+1.

Geometric parameters of π··· π stacking (Å,°)

Cg ⋯ Cg (Ring)	Cg ⋯ Cg (Å)	α(°)	β(°)	γ(°)
Cg(5) ⋯ Cg(5)i	3.459 (1)	0.00	23.13	23.13
Cg(6) ⋯ Cg(6)ii	3.591 (1)	0.00	21.67	21.67

Symmetry codes: (i) 1-x,1-y,-z, (ii) 1-x,1-y,1-z Cg(5): center of gravity of imidazole ring. Cg(6): center of gravity of pyridine ring. α: dihedral angle between ring planes. β, γ: Slipping angles defined by centroid–centroid vector and the normal to the plane of the ring.