Guanidinum diphenyl­phosphinate monohydrate

Najafpour, M.M.; McKee, V.

doi:10.1107/S1600536806007860

organic compounds

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ISSN: 2056-9890

Volume 62| Part 4| April 2006| Pages o1365-o1368

https://doi.org/10.1107/S1600536806007860

Guanidinum diphenylphosphinate monohydrate

M. Mahdi Najafpour ^a and Vickie McKee ^b ^*

^aDorna Institute of Science, Ahwaz, Khozestan, Iran, and ^bChemistry Department, Loughborough University, Loughborough, Leicestershire LE11 3TU, England
^*Correspondence e-mail: v.mckee@lboro.ac.uk

(Received 24 February 2006; accepted 3 March 2006; online 15 March 2006)

Hydrogen bonding in the title structure, CH₆N₃⁺·C₁₂H₁₀O₂P⁻·H₂O or [C(NH₂)₃]⁺[Ph₂PO₂]⁻·H₂O, results in a bilayer architecture, which also involves π–π stacking interactions between pairs of guanidinium ions. All the cation H atoms are involved in hydrogen bonds, five to O atoms of the anion or solvent water and the sixth in an N—H⋯π interaction with a neighbouring phenyl ring.

Comment

Guanidinium ions have long been utilized in the modelling of Arg–Glu or Arg–Asp side-chain interactions in proteins (see, for example, Melo et al., 1999 ; Fülscher & Mehler, 1988 ; Singh et al., 1987 ). More recently, guanidinium sulfonate interactions have been utilized in supramolecular chemistry and crystal engineering. Hydrogen-bonded networks involving guanidinium salts of a range of sulfonated phosphanes and other organic sulfonates have been intensively investigated (Burrows et al., 2003 ; Horner et al., 2001 ; Kathó et al., 2002 ; Smith et al., 2004 ). In these compounds, the match between the trigonal geometry of the cation, having two hydrogen-bond donors on each edge of the triangle, and that of the sulfonate group favours the formation of infinite hydrogen-bonded arrays. These structures generally contain either bilayers or single layers, not always planar, and comprising the quasi-hexagonal GS (guanidinium sulfonate) hydrogen-bonding motif. The most important factor in determining whether a single layer or bilayer structure results appears to be the packing interactions of the organic superstructure (Horner et al., 2001).

A search of the Cambridge Structural Database (Version 5.27; Allen, 2002 ; Fletcher et al., 1996 ) shows no previously reported phosphinate salts of guanidinium. However, it might be expected that the mismatch between the numbers of hydrogen-bond donors and acceptors could disrupt the sheet structure observed for sulfonate analogues. We have crystallized guanidinium diphenylphosphinate as the title monohydrate, (I), which has a bilayer architecture and, perhaps surprisingly, all the hydrogen-bond donors are satisfied.

Fig. 1 shows the components of the asymmetric unit and the atom-labelling scheme for (I). The bond distances and angles are unremarkable. Hydrogen-bond data are given in Table 1. Hydrogen bonding involving the guanidinium ion, the diphenylphosphinate O atoms and the water solvent molecule results in a hydrogen-bonded sheet (Fig. 2) lying perpendicular to the a axis, in which R₇⁷(20) rings (Etter et al., 1990 ) are supported by smaller R₃³(8) and R₂¹(6) patterns. All the phenyl groups of the anion lie on the same side and the sheets are paired to form a bilayer. Further hydrogen bonds link the sheets together, the smallest ring being R₅⁵(12) (Fig. 3). In addition to the hydrogen-bonding interactions, the guanidinium ions are paired via π–π stacking with a symmetry-equivalent ion under operation (iv) (2 − x, 1 − y, 1 − z). The interplanar distance is 3.293 (2) Å and the intermolecular C1—N2^iv distance is 3.332 (2) Å (Fig. 4).

Only five of the guanidinium H atoms are involved in conventional hydrogen-bonds to the diphenylphosphinate anion or water molecule (Fig. 5, Table 1). The sixth H atom (H1A) lies 2.73 (2) Å above the plane of a phenyl ring [C11–C16 under symmetry operation (x, $[{1\over 2}]$ − y, $[{1\over 2}]$ + z)]; the distance from the ring centroid to atom H1A is 2.85 (2) Å. This unusual interaction is probably responsible for the sharp signal at 3473 cm⁻¹ in the IR spectrum; normal hydrogen-bonding will contribute to the broad signal observed at lower frequency.

The phenyl groups are also involved in several intermolecular interactions. The C12–C16 ring, which interacts with the cation as described above, also has a π–π interaction with the C21–C26 ring of a symmetry-related anion at (x, $[{3\over 2}]$ − y, − $[{1\over 2}]$ + z). The planes of the rings are inclined at 2.6 (1)°, and the mean distance of the C21–C26 ring from the mean plane of C11–C16 is 3.530 (2) Å. The centroid-to-centroid distance [4.059 (3) Å] is rather long but the interatomic distances C13—C23 and C14—C22 [3.548 (2) and 3.652 (2), respectively] suggest the π–π interaction is real, although more staggered than the norm. This may be due to constraints imposed by both phenyl rings being part of the superstructure of the same hydrogen-bonded layer. The second face of the C21–C26 ring shows a C—H⋯π interaction with atom H13 [under symmetry operation (vi), (1 − x, 1 − y, −z)]; atom H13^iv is 2.690 (2) Å from the mean plane of the phenyl ring and 2.695 (2) Å from the centroid of the ring. This appears to be the only significant interbilayer interaction.

In summary, all six guanidinium hydrogen-bond donors of (I) are involved in hydrogen bonding, although one is unconventional. The solvent water molecule makes four hydrogen bonds, two as donor and two as acceptor. One of the phosphinate O atoms acts as acceptor for two hydrogen bonds and the other accepts three [two as part of the R₂¹(6) ring]. All hydrogen-bond donors have acceptors.

Figure 1
A perspective view of the asymmetric unit of (I)

. Displacement ellipsoids are drawn at the 50% probability level.

Figure 2
One layer of the hydrogen-bonded sheet, showing R₇⁷(20), R₃³(8) and R₂¹(6) rings. Phenyl groups have been omitted for clarity. Dashed lines indicate hydrogen bonds.

Figure 3
A packing diagram, viewed along the b axis. H atoms have been omitted and the dashed lines indicate O⋯O and N⋯N non-bonded distances.

Figure 4
A perspective view of the bilayer interactions. The C1—N2^iv and C1^iv—N2 π–π interactions are shown as dashed red lines. Dashed turquoise lines indicate hydrogen bonds. [Symmetry code: (iv) 2 − x, 1 − y, 1 − z.]

Figure 5
A view of the hydrogen bonding (dashed lines) involving the guanidinium ion. Symmetry codes are as in Table 1

. H atoms not involved in hydrogen bonding have been omitted.

Experimental

Diphenylphosphinic acid (Merck; 1 mmol, 0.218 g) was added to an aqueous solution (10 ml) of guanidinum carbonate (Merck; 1 mmol, 0.180 g) with stirring. This solution yielded large colourless single crystals of (I) after 10 d.

Crystal data

CH₆N₃⁺·C₁₂H₁₀O₂P⁻·H₂O
M_r = 295.27
Monoclinic, P 2₁ /c
a = 11.2395 (10) Å
b = 10.0101 (9) Å
c = 12.9814 (12) Å
β = 98.653 (2)°
V = 1443.9 (2) Å³
Z = 4
D_x = 1.358 Mg m⁻³
Mo Kα radiation
Cell parameters from 5028 reflections
θ = 2.6–28.8°
μ = 0.20 mm⁻¹
T = 150 (2) K
Block, colourless
0.31 × 0.25 × 0.21 mm

Data collection

Bruker SMART CCD area-detector diffractometer
φ and ω scans
Absorption correction: multi-scan(SADABS; Sheldrick, 2003 )T_min = 0.85, T_max = 0.96
11089 measured reflections
2839 independent reflections
2376 reflections with I > 2σ(I)
R_int = 0.028
θ_max = 26.0°
h = −13 → 13
k = −12 → 12
l = −15 → 16

Refinement

Refinement on F²
R[F² > 2σ(F²)] = 0.036
wR(F²) = 0.094
S = 1.04
2839 reflections
205 parameters
H atoms treated by a mixture of independent and constrained refinement
w = 1/[σ²(F_o²) + (0.0468P)² + 0.6736P] where P = (F_o² + 2F_c²)/3
(Δ/σ)_max = 0.001
Δρ_max = 0.32 e Å⁻³
Δρ_min = −0.35 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1B⋯O1W	0.91 (2)	2.09 (2)	2.993 (2)	169.9 (19)
N2—H2B⋯O1	0.89 (2)	1.90 (2)	2.7914 (19)	177 (2)
N2—H2A⋯O2ⁱ	0.88 (2)	2.11 (2)	2.932 (2)	153.8 (19)
N3—H3B⋯O2ⁱ	0.90 (2)	2.04 (2)	2.892 (2)	156.1 (19)
N3—H3A⋯O1Wⁱⁱ	0.88 (2)	1.99 (2)	2.863 (2)	175 (2)
O1W—H1WA⋯O1	0.86 (2)	1.88 (2)	2.7157 (18)	164 (2)
O1W—H1WB⋯O2ⁱⁱⁱ	0.86 (2)	1.86 (2)	2.7061 (18)	168 (2)
Symmetry codes: (i) $[x, -y+{\script{3\over 2}}, z+{\script{1\over 2}}]$ ; (ii) $[x, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (iii) $[-x+2, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ .

H atoms bonded to aryl C atoms were included in calculated positions, with C—H distances of 0.95 Å, and refined using a riding model, with U_iso(H) = 1.2U_eq(C). The H atoms bonded to O and N atoms were located in difference maps and assigned a common fixed U_iso of 0.04 Å²; their coordinates were freely refined.

Data collection: SMART (Bruker, 1998 ); cell refinement: SAINT (Bruker, 1998); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2001 ); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL and MERCURY (Bruno et al., 2002 ); software used to prepare material for publication: SHELXTL.

Supporting information

Crystal structure: contains datablocks I, global. DOI: https://doi.org/10.1107/S1600536806007860/lh2012sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600536806007860/lh2012Isup2.hkl

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SAINT (Bruker, 1998); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2001); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL and Mercury (Bruno et al., 2002); software used to prepare material for publication: SHELXTL.

Guanidinum diphenylphosphinate monohydrate top

Crystal data top

CH₆N₃⁺·C₁₂H₁₀O₂P⁻·H₂O	F(000) = 624
M_r = 295.27	D_x = 1.358 Mg m⁻³
Monoclinic, P2₁/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P2ybc	Cell parameters from 5028 reflections
a = 11.2395 (10) Å	θ = 2.6–28.8°
b = 10.0101 (9) Å	µ = 0.20 mm⁻¹
c = 12.9814 (12) Å	T = 150 K
β = 98.653 (2)°	Block, colourless
V = 1443.9 (2) Å³	0.31 × 0.25 × 0.21 mm
Z = 4

Data collection top

Bruker SMART CCD area-detector diffractometer	2839 independent reflections
Radiation source: normal-focus sealed tube	2376 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.028
φ and ω scans	θ_max = 26.0°, θ_min = 1.8°
Absorption correction: multi-scan (SADABS; Sheldrick, 2003)	h = −13→13
T_min = 0.85, T_max = 0.96	k = −12→12
11089 measured reflections	l = −15→16

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.036	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.094	H atoms treated by a mixture of independent and constrained refinement
S = 1.04	w = 1/[σ²(F_o²) + (0.0468P)² + 0.6736P] where P = (F_o² + 2F_c²)/3
2839 reflections	(Δ/σ)_max = 0.001
205 parameters	Δρ_max = 0.32 e Å⁻³
0 restraints	Δρ_min = −0.35 e Å⁻³

Special details top

Experimental. Spectroscopic analysis: IR (KBr, ν, cm^-1) inter alia: 3473 (m, sharp), 3228 (s, br), 1662 (s), 1438 (m), 1152 (m), 1126 (m). Analysis calculated for (CH₆N)(C₁₂H₁₀O₂P)(H₂O): C 52.9, H 6.1, N 14.2%; found: C 51.5, H 6.1, N 14.2%.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
P1	0.79796 (4)	0.67583 (4)	0.17036 (3)	0.01833 (13)
O1	0.83595 (11)	0.57444 (11)	0.25453 (8)	0.0236 (3)
O2	0.88275 (10)	0.79023 (11)	0.15923 (9)	0.0227 (3)
C11	0.77115 (15)	0.59049 (16)	0.04612 (12)	0.0193 (3)
C12	0.66859 (15)	0.51252 (17)	0.01707 (13)	0.0230 (4)
H12	0.6107	0.5045	0.0631	0.028*
C13	0.64994 (16)	0.44662 (17)	−0.07783 (13)	0.0258 (4)
H13	0.5791	0.3951	−0.0970	0.031*
C14	0.73516 (16)	0.45604 (17)	−0.14498 (13)	0.0258 (4)
H14	0.7222	0.4117	−0.2104	0.031*
C15	0.83878 (16)	0.53014 (18)	−0.11620 (13)	0.0275 (4)
H15	0.8979	0.5349	−0.1612	0.033*
C16	0.85656 (16)	0.59763 (17)	−0.02159 (13)	0.0237 (4)
H16	0.9275	0.6491	−0.0027	0.028*
C21	0.65394 (14)	0.74541 (16)	0.18905 (12)	0.0204 (4)
C22	0.60393 (15)	0.71836 (17)	0.27863 (13)	0.0239 (4)
H22	0.6443	0.6595	0.3298	0.029*
C23	0.49556 (16)	0.77648 (19)	0.29409 (15)	0.0292 (4)
H23	0.4624	0.7574	0.3556	0.035*
C24	0.43604 (16)	0.86223 (19)	0.21980 (15)	0.0305 (4)
H24	0.3621	0.9021	0.2303	0.037*
C25	0.48457 (17)	0.88968 (19)	0.13031 (15)	0.0313 (4)
H25	0.4436	0.9482	0.0792	0.038*
C26	0.59263 (16)	0.83230 (17)	0.11475 (13)	0.0257 (4)
H26	0.6254	0.8521	0.0532	0.031*
C1	0.84951 (15)	0.42953 (17)	0.51824 (13)	0.0211 (4)
N1	0.84711 (15)	0.31513 (16)	0.46534 (13)	0.0287 (4)
N2	0.85314 (14)	0.54552 (15)	0.47013 (12)	0.0260 (3)
N3	0.84615 (15)	0.42724 (17)	0.61987 (12)	0.0285 (4)
O1W	0.88781 (12)	0.31041 (13)	0.24274 (11)	0.0299 (3)
H1A	0.8343 (19)	0.243 (2)	0.4964 (17)	0.040*
H1B	0.8498 (19)	0.317 (2)	0.3955 (18)	0.040*
H2A	0.8634 (19)	0.615 (2)	0.5120 (17)	0.040*
H2B	0.8496 (19)	0.552 (2)	0.4010 (18)	0.040*
H3A	0.8597 (19)	0.352 (2)	0.6541 (17)	0.040*
H3B	0.8528 (19)	0.509 (2)	0.6505 (17)	0.040*
H1WA	0.8740 (19)	0.394 (2)	0.2340 (17)	0.040*
H1WB	0.963 (2)	0.302 (2)	0.2650 (17)	0.040*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
P1	0.0214 (2)	0.0171 (2)	0.0164 (2)	0.00022 (16)	0.00256 (16)	0.00037 (16)
O1	0.0308 (7)	0.0209 (6)	0.0190 (6)	0.0036 (5)	0.0030 (5)	0.0017 (5)
O2	0.0237 (6)	0.0221 (6)	0.0219 (6)	−0.0034 (5)	0.0023 (5)	−0.0005 (5)
C11	0.0237 (9)	0.0162 (8)	0.0179 (8)	0.0015 (6)	0.0029 (6)	0.0022 (6)
C12	0.0238 (9)	0.0223 (9)	0.0236 (9)	−0.0008 (7)	0.0056 (7)	−0.0015 (7)
C13	0.0245 (9)	0.0220 (9)	0.0296 (9)	0.0007 (7)	−0.0001 (7)	−0.0044 (7)
C14	0.0343 (10)	0.0240 (9)	0.0187 (8)	0.0041 (7)	0.0028 (7)	−0.0025 (7)
C15	0.0332 (10)	0.0285 (10)	0.0227 (9)	0.0005 (8)	0.0103 (7)	−0.0006 (7)
C16	0.0240 (9)	0.0236 (9)	0.0237 (9)	−0.0016 (7)	0.0047 (7)	0.0009 (7)
C21	0.0225 (8)	0.0168 (8)	0.0216 (9)	−0.0013 (6)	0.0021 (7)	−0.0034 (6)
C22	0.0276 (9)	0.0221 (9)	0.0223 (9)	−0.0004 (7)	0.0045 (7)	−0.0009 (7)
C23	0.0301 (10)	0.0298 (10)	0.0295 (10)	−0.0051 (8)	0.0107 (8)	−0.0063 (8)
C24	0.0254 (9)	0.0283 (10)	0.0382 (11)	0.0018 (8)	0.0063 (8)	−0.0104 (8)
C25	0.0297 (10)	0.0277 (10)	0.0355 (10)	0.0061 (8)	0.0013 (8)	0.0022 (8)
C26	0.0286 (9)	0.0240 (9)	0.0252 (9)	0.0023 (7)	0.0060 (7)	0.0018 (7)
C1	0.0193 (8)	0.0236 (9)	0.0204 (8)	0.0013 (6)	0.0030 (6)	−0.0018 (7)
N1	0.0380 (9)	0.0235 (8)	0.0256 (8)	−0.0027 (7)	0.0078 (7)	−0.0039 (6)
N2	0.0376 (9)	0.0227 (8)	0.0176 (7)	0.0010 (6)	0.0038 (6)	−0.0003 (6)
N3	0.0438 (10)	0.0224 (8)	0.0200 (8)	0.0042 (7)	0.0070 (7)	0.0029 (6)
O1W	0.0263 (7)	0.0213 (7)	0.0398 (8)	0.0030 (5)	−0.0019 (6)	−0.0037 (6)

Geometric parameters (Å, º) top

P1—O1	1.5053 (12)	C23—C24	1.386 (3)
P1—O2	1.5105 (12)	C23—H23	0.9500
P1—C11	1.8099 (16)	C24—C25	1.383 (3)
P1—C21	1.8117 (17)	C24—H24	0.9500
C11—C12	1.396 (2)	C25—C26	1.385 (2)
C11—C16	1.397 (2)	C25—H25	0.9500
C12—C13	1.385 (2)	C26—H26	0.9500
C12—H12	0.9500	C1—N2	1.322 (2)
C13—C14	1.392 (2)	C1—N3	1.326 (2)
C13—H13	0.9500	C1—N1	1.333 (2)
C14—C15	1.384 (2)	C1—N2ⁱ	3.332 (2)
C14—H14	0.9500	N1—H1A	0.85 (2)
C15—C16	1.390 (2)	N1—H1B	0.91 (2)
C15—H15	0.9500	N2—H2A	0.88 (2)
C16—H16	0.9500	N2—H2B	0.89 (2)
C21—C22	1.392 (2)	N3—H3A	0.88 (2)
C21—C26	1.401 (2)	N3—H3B	0.90 (2)
C22—C23	1.391 (2)	O1W—H1WA	0.86 (2)
C22—H22	0.9500	O1W—H1WB	0.86 (2)

O1—P1—O2	117.80 (7)	C21—C22—H22	119.6
O1—P1—C11	108.64 (7)	C24—C23—C22	120.01 (17)
O2—P1—C11	107.18 (7)	C24—C23—H23	120.0
O1—P1—C21	108.88 (7)	C22—C23—H23	120.0
O2—P1—C21	108.10 (7)	C25—C24—C23	119.83 (17)
C11—P1—C21	105.57 (7)	C25—C24—H24	120.1
C12—C11—C16	118.43 (15)	C23—C24—H24	120.1
C12—C11—P1	121.64 (12)	C24—C25—C26	120.35 (17)
C16—C11—P1	119.89 (13)	C24—C25—H25	119.8
C13—C12—C11	120.98 (16)	C26—C25—H25	119.8
C13—C12—H12	119.5	C25—C26—C21	120.55 (16)
C11—C12—H12	119.5	C25—C26—H26	119.7
C12—C13—C14	119.89 (16)	C21—C26—H26	119.7
C12—C13—H13	120.1	N2—C1—N3	119.52 (16)
C14—C13—H13	120.1	N2—C1—N1	120.71 (16)
C15—C14—C13	119.85 (16)	N3—C1—N1	119.75 (17)
C15—C14—H14	120.1	N2—C1—N2ⁱ	81.58 (11)
C13—C14—H14	120.1	N3—C1—N2ⁱ	97.74 (11)
C14—C15—C16	120.16 (16)	N1—C1—N2ⁱ	91.73 (11)
C14—C15—H15	119.9	C1—N1—H1A	118.3 (15)
C16—C15—H15	119.9	C1—N1—H1B	119.8 (13)
C15—C16—C11	120.66 (16)	H1A—N1—H1B	121 (2)
C15—C16—H16	119.7	C1—N2—H2A	114.6 (14)
C11—C16—H16	119.7	C1—N2—H2B	122.6 (14)
C22—C21—C26	118.51 (16)	H2A—N2—H2B	123 (2)
C22—C21—P1	121.21 (13)	C1—N3—H3A	119.4 (14)
C26—C21—P1	120.23 (13)	C1—N3—H3B	114.1 (14)
C23—C22—C21	120.75 (17)	H3A—N3—H3B	124 (2)
C23—C22—H22	119.6	H1WA—O1W—H1WB	107 (2)

Symmetry code: (i) −x+2, −y+1, −z+1.

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1B···O1W	0.91 (2)	2.09 (2)	2.993 (2)	169.9 (19)
N2—H2B···O1	0.89 (2)	1.90 (2)	2.7914 (19)	177 (2)
N2—H2A···O2ⁱⁱ	0.88 (2)	2.11 (2)	2.932 (2)	153.8 (19)
N3—H3B···O2ⁱⁱ	0.90 (2)	2.04 (2)	2.892 (2)	156.1 (19)
N3—H3A···O1Wⁱⁱⁱ	0.88 (2)	1.99 (2)	2.863 (2)	175 (2)
O1W—H1WA···O1	0.86 (2)	1.88 (2)	2.7157 (18)	164 (2)
O1W—H1WB···O2^iv	0.86 (2)	1.86 (2)	2.7061 (18)	168 (2)

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

Acknowledgements

The authors thank Loughborough University and Dorna Institute of Science for providing facilities.

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