Bis{2-[(E)-(4-fluoro-benz-yl)imino-meth-yl]-6-meth-oxy-phenolato}palladium(II).

In the title compound, [Pd(C(15)H(13)FNO(2))(2)], the Pd(II) atom is tetra-coordinated by two N atoms and two O atoms from the two 2-[(4-fluoro-benz-yl)imino-meth-yl]-6-meth-oxy-phen-oxy ligands, forming a square-planar geometry. The two N atoms and the two O atoms around the Pd(II) atom are trans to each other. The dihedral angle between the two fluoro-substituted benzene rings is 39.03 (6)°. The mol-ecular structure is stabilized by an intra-molecular C-H⋯O hydrogen bond. In the crystal, weak inter-molecular C-H⋯π inter-actions occur.

Related literature

For applications of palladium(II)–Schiff base complexes, see: Ali et al. (2002 ▶); Gupta & Sutar (2008 ▶). For related structures, see: Jiang et al. (2008 ▶); Tsai et al. (2009 ▶); Mohd Tajuddin et al. (2010 ▶); Lin et al. (2010 ▶). For the stability of the temperature controller used in the data collection, see: Cosier & Glazer (1986 ▶).

Experimental

Crystal data

[Pd(C15H13FNO2)2]

M = 622.93

Triclinic,

a = 10.0025 (4) Å

b = 11.0082 (4) Å

c = 12.3152 (4) Å

α = 109.550 (1)°

β = 98.368 (1)°

γ = 90.054 (1)°

V = 1262.45 (8) Å3

Z = 2

Mo Kα radiation

μ = 0.79 mm−1

T = 100 K

0.54 × 0.19 × 0.16 mm

Data collection

Bruker SMART APEXII CCD area-detector diffractometer

Absorption correction: multi-scan (SADABS; Bruker, 2009 ▶) T min = 0.677, T max = 0.885

39095 measured reflections

11056 independent reflections

9774 reflections with I > 2σ(I)

R int = 0.027

Refinement

R[F 2 > 2σ(F 2)] = 0.029

wR(F 2) = 0.081

S = 1.03

11056 reflections

354 parameters

H-atom parameters constrained

Δρmax = 1.95 e Å−3

Δρmin = −1.72 e Å−3

Data collection: APEX2 (Bruker, 2009 ▶); cell refinement: SAINT (Bruker, 2009 ▶); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2008 ▶); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL and PLATON (Spek, 2009 ▶).

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536811017739/is2710sup1.cif

Structure factors: contains datablocks I. DOI: 10.1107/S1600536811017739/is2710Isup2.hkl

Additional supplementary materials: crystallographic information; 3D view; checkCIF report

[Pd(C15H13FNO2)2]	Z = 2
Mr = 622.93	F(000) = 632
Triclinic, P1	Dx = 1.639 Mg m−3
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 10.0025 (4) Å	Cell parameters from 9774 reflections
b = 11.0082 (4) Å	θ = 2.5–35.1°
c = 12.3152 (4) Å	µ = 0.79 mm−1
α = 109.550 (1)°	T = 100 K
β = 98.368 (1)°	Block, yellow
γ = 90.054 (1)°	0.54 × 0.19 × 0.16 mm
V = 1262.45 (8) Å3

Bruker SMART APEXII CCD area-detector diffractometer	11056 independent reflections
Radiation source: fine-focus sealed tube	9774 reflections with I > 2σ(I)
graphite	Rint = 0.027
φ and ω scans	θmax = 35.2°, θmin = 1.8°
Absorption correction: multi-scan (SADABS; Bruker, 2009)	h = −15→16
Tmin = 0.677, Tmax = 0.885	k = −17→17
39095 measured reflections	l = −19→19

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)] = 0.029	Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.081	H-atom parameters constrained
S = 1.03	w = 1/[σ2(Fo2) + (0.0422P)2 + 0.7245P] where P = (Fo2 + 2Fc2)/3
11056 reflections	(Δ/σ)max = 0.001
354 parameters	Δρmax = 1.95 e Å−3
0 restraints	Δρmin = −1.72 e Å−3

Experimental. The crystal was placed in the cold stream of an Oxford Cryosystems Cobra open-flow nitrogen cryostat (Cosier & Glazer, 1986) operating at 100.0 (1) K.

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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.

	x	y	z	Uiso*/Ueq
Pd1	0.248588 (8)	−0.003817 (7)	−0.004344 (7)	0.01066 (3)
F1	0.27490 (11)	−0.29889 (9)	0.45715 (8)	0.02764 (19)
F2	0.20856 (10)	0.27200 (9)	−0.47652 (8)	0.02562 (18)
O1	0.36986 (10)	0.15058 (9)	0.03227 (8)	0.01505 (15)
O2	0.12766 (10)	−0.15832 (9)	−0.03987 (8)	0.01526 (16)
O3	0.54754 (10)	0.32234 (9)	0.03930 (9)	0.01810 (17)
O4	−0.04950 (10)	−0.33148 (9)	−0.04619 (9)	0.01818 (17)
N1	0.17806 (10)	0.06583 (10)	0.14915 (9)	0.01244 (16)
N2	0.31884 (10)	−0.07394 (10)	−0.15808 (9)	0.01247 (16)
C1	0.39256 (12)	0.24727 (11)	0.13077 (10)	0.01246 (18)
C2	0.49156 (12)	0.34497 (11)	0.13870 (10)	0.01365 (19)
C3	0.52321 (13)	0.45087 (12)	0.23893 (11)	0.0169 (2)
H3A	0.5896	0.5145	0.2426	0.020*
C4	0.45737 (14)	0.46504 (13)	0.33603 (12)	0.0196 (2)
H4A	0.4803	0.5375	0.4052	0.023*
C5	0.36016 (14)	0.37416 (12)	0.33048 (11)	0.0175 (2)
H5A	0.3150	0.3850	0.3956	0.021*
C6	0.32634 (12)	0.26388 (11)	0.22825 (10)	0.01328 (18)
C7	0.22130 (12)	0.17496 (11)	0.22910 (10)	0.01358 (18)
H7A	0.1783	0.1991	0.2966	0.016*
C8	0.07085 (12)	−0.00674 (11)	0.17704 (10)	0.01394 (19)
H8A	0.0179	−0.0646	0.1035	0.017*
H8B	0.0085	0.0549	0.2194	0.017*
C9	0.12744 (12)	−0.08626 (11)	0.25037 (10)	0.01400 (19)
C10	0.05718 (13)	−0.09792 (12)	0.33660 (11)	0.0178 (2)
H10A	−0.0246	−0.0551	0.3486	0.021*
C11	0.10491 (15)	−0.17143 (13)	0.40555 (12)	0.0207 (2)
H11A	0.0562	−0.1801	0.4635	0.025*
C12	0.22457 (15)	−0.23096 (12)	0.38736 (11)	0.0196 (2)
C13	0.29778 (15)	−0.22301 (12)	0.30226 (11)	0.0196 (2)
H13A	0.3797	−0.2658	0.2913	0.023*
C14	0.24736 (13)	−0.15024 (12)	0.23327 (11)	0.0171 (2)
H14A	0.2952	−0.1441	0.1739	0.021*
C15	0.64506 (14)	0.41740 (13)	0.04021 (12)	0.0192 (2)
H15A	0.6772	0.3917	−0.0354	0.029*
H15B	0.7216	0.4250	0.1021	0.029*
H15C	0.6034	0.5008	0.0546	0.029*
C16	0.10422 (12)	−0.25480 (11)	−0.13811 (10)	0.01267 (18)
C17	0.00590 (12)	−0.35324 (11)	−0.14546 (11)	0.01388 (19)
C18	−0.02515 (13)	−0.45995 (12)	−0.24528 (11)	0.0170 (2)
H18A	−0.0909	−0.5239	−0.2485	0.020*
C19	0.04061 (15)	−0.47427 (12)	−0.34260 (12)	0.0191 (2)
H19A	0.0184	−0.5473	−0.4114	0.023*
C20	0.13651 (14)	−0.38259 (12)	−0.33769 (11)	0.0175 (2)
H20A	0.1815	−0.3935	−0.4029	0.021*
C21	0.16949 (12)	−0.27135 (11)	−0.23629 (10)	0.01365 (19)
C22	0.27473 (12)	−0.18294 (11)	−0.23782 (10)	0.01387 (19)
H22A	0.3171	−0.2074	−0.3056	0.017*
C23	0.42827 (12)	−0.00312 (11)	−0.18626 (10)	0.01336 (18)
H23A	0.4913	−0.0655	−0.2266	0.016*
H23B	0.4799	0.0567	−0.1130	0.016*
C24	0.37152 (12)	0.07264 (11)	−0.26307 (10)	0.01318 (18)
C25	0.37981 (13)	0.02717 (12)	−0.38181 (10)	0.0167 (2)
H25A	0.4228	−0.0510	−0.4136	0.020*
C26	0.32631 (14)	0.09414 (13)	−0.45479 (11)	0.0190 (2)
H26A	0.3325	0.0630	−0.5356	0.023*
C27	0.26401 (14)	0.20716 (13)	−0.40591 (11)	0.0173 (2)
C28	0.25358 (14)	0.25643 (12)	−0.28829 (11)	0.0173 (2)
H28A	0.2099	0.3344	−0.2573	0.021*
C29	0.30892 (13)	0.18839 (11)	−0.21691 (10)	0.0158 (2)
H29A	0.3041	0.2210	−0.1358	0.019*
C30	−0.14487 (14)	−0.42819 (13)	−0.04730 (13)	0.0194 (2)
H30A	−0.1760	−0.4041	0.0286	0.029*
H30B	−0.1019	−0.5110	−0.0629	0.029*
H30C	−0.2223	−0.4360	−0.1084	0.029*

	U11	U22	U33	U12	U13	U23
Pd1	0.01183 (4)	0.00891 (4)	0.01172 (4)	−0.00181 (3)	0.00113 (3)	0.00440 (3)
F1	0.0435 (6)	0.0223 (4)	0.0244 (4)	0.0072 (4)	0.0073 (4)	0.0166 (3)
F2	0.0345 (5)	0.0268 (4)	0.0219 (4)	0.0067 (4)	0.0042 (3)	0.0165 (3)
O1	0.0188 (4)	0.0115 (3)	0.0142 (4)	−0.0055 (3)	0.0029 (3)	0.0033 (3)
O2	0.0182 (4)	0.0113 (3)	0.0152 (4)	−0.0052 (3)	0.0033 (3)	0.0028 (3)
O3	0.0202 (4)	0.0147 (4)	0.0195 (4)	−0.0066 (3)	0.0049 (3)	0.0052 (3)
O4	0.0190 (4)	0.0145 (4)	0.0217 (4)	−0.0050 (3)	0.0063 (3)	0.0058 (3)
N1	0.0132 (4)	0.0117 (4)	0.0136 (4)	−0.0011 (3)	0.0019 (3)	0.0059 (3)
N2	0.0137 (4)	0.0114 (4)	0.0137 (4)	−0.0011 (3)	0.0023 (3)	0.0059 (3)
C1	0.0134 (4)	0.0099 (4)	0.0144 (4)	−0.0013 (3)	0.0005 (3)	0.0052 (3)
C2	0.0144 (5)	0.0110 (4)	0.0158 (5)	−0.0023 (3)	0.0011 (4)	0.0055 (4)
C3	0.0175 (5)	0.0113 (4)	0.0200 (5)	−0.0038 (4)	0.0007 (4)	0.0035 (4)
C4	0.0223 (6)	0.0140 (5)	0.0191 (5)	−0.0034 (4)	0.0022 (4)	0.0018 (4)
C5	0.0211 (5)	0.0134 (5)	0.0163 (5)	−0.0024 (4)	0.0032 (4)	0.0028 (4)
C6	0.0147 (5)	0.0114 (4)	0.0138 (4)	−0.0014 (3)	0.0013 (3)	0.0047 (4)
C7	0.0155 (5)	0.0120 (4)	0.0143 (4)	−0.0002 (4)	0.0025 (4)	0.0057 (4)
C8	0.0133 (5)	0.0142 (4)	0.0156 (5)	−0.0016 (4)	0.0029 (4)	0.0064 (4)
C9	0.0161 (5)	0.0113 (4)	0.0148 (5)	−0.0022 (3)	0.0026 (4)	0.0047 (4)
C10	0.0202 (5)	0.0165 (5)	0.0189 (5)	−0.0015 (4)	0.0063 (4)	0.0075 (4)
C11	0.0266 (6)	0.0185 (5)	0.0206 (5)	−0.0024 (4)	0.0072 (5)	0.0096 (4)
C12	0.0301 (7)	0.0138 (5)	0.0174 (5)	−0.0005 (4)	0.0042 (4)	0.0085 (4)
C13	0.0256 (6)	0.0164 (5)	0.0196 (5)	0.0040 (4)	0.0053 (4)	0.0091 (4)
C14	0.0211 (5)	0.0150 (5)	0.0183 (5)	0.0018 (4)	0.0062 (4)	0.0084 (4)
C15	0.0179 (5)	0.0168 (5)	0.0245 (6)	−0.0048 (4)	0.0038 (4)	0.0090 (4)
C16	0.0130 (4)	0.0102 (4)	0.0153 (5)	−0.0014 (3)	0.0012 (3)	0.0053 (4)
C17	0.0141 (5)	0.0108 (4)	0.0169 (5)	−0.0020 (3)	0.0015 (4)	0.0053 (4)
C18	0.0180 (5)	0.0117 (4)	0.0196 (5)	−0.0042 (4)	−0.0001 (4)	0.0044 (4)
C19	0.0243 (6)	0.0126 (5)	0.0175 (5)	−0.0044 (4)	0.0013 (4)	0.0022 (4)
C20	0.0216 (5)	0.0131 (5)	0.0159 (5)	−0.0026 (4)	0.0022 (4)	0.0028 (4)
C21	0.0155 (5)	0.0114 (4)	0.0145 (5)	−0.0012 (3)	0.0018 (4)	0.0051 (4)
C22	0.0164 (5)	0.0121 (4)	0.0144 (5)	−0.0008 (4)	0.0033 (4)	0.0057 (4)
C23	0.0131 (4)	0.0121 (4)	0.0163 (5)	−0.0008 (3)	0.0034 (4)	0.0063 (4)
C24	0.0138 (4)	0.0121 (4)	0.0143 (4)	−0.0018 (3)	0.0027 (3)	0.0051 (4)
C25	0.0203 (5)	0.0149 (5)	0.0155 (5)	0.0013 (4)	0.0042 (4)	0.0052 (4)
C26	0.0235 (6)	0.0196 (5)	0.0146 (5)	0.0012 (4)	0.0039 (4)	0.0063 (4)
C27	0.0201 (5)	0.0180 (5)	0.0162 (5)	−0.0002 (4)	0.0015 (4)	0.0095 (4)
C28	0.0243 (6)	0.0125 (4)	0.0161 (5)	0.0001 (4)	0.0033 (4)	0.0059 (4)
C29	0.0219 (5)	0.0120 (4)	0.0141 (5)	0.0008 (4)	0.0037 (4)	0.0047 (4)
C30	0.0168 (5)	0.0165 (5)	0.0286 (6)	−0.0030 (4)	0.0051 (4)	0.0115 (5)

Pd1—O1	1.9717 (9)	C11—H11A	0.9500
Pd1—O2	1.9727 (9)	C12—C13	1.3882 (19)
Pd1—N1	2.0194 (10)	C13—C14	1.3962 (18)
Pd1—N2	2.0209 (10)	C13—H13A	0.9500
F1—C12	1.3624 (16)	C14—H14A	0.9500
F2—C27	1.3599 (15)	C15—H15A	0.9800
O1—C1	1.3081 (14)	C15—H15B	0.9800
O2—C16	1.3053 (14)	C15—H15C	0.9800
O3—C2	1.3674 (15)	C16—C21	1.4156 (16)
O3—C15	1.4261 (15)	C16—C17	1.4339 (16)
O4—C17	1.3639 (15)	C17—C18	1.3818 (17)
O4—C30	1.4241 (16)	C18—C19	1.4132 (19)
N1—C7	1.2974 (15)	C18—H18A	0.9500
N1—C8	1.4817 (15)	C19—C20	1.3721 (18)
N2—C22	1.2974 (15)	C19—H19A	0.9500
N2—C23	1.4888 (15)	C20—C21	1.4225 (17)
C1—C6	1.4136 (16)	C20—H20A	0.9500
C1—C2	1.4305 (16)	C21—C22	1.4394 (17)
C2—C3	1.3804 (17)	C22—H22A	0.9500
C3—C4	1.4117 (19)	C23—C24	1.5117 (17)
C3—H3A	0.9500	C23—H23A	0.9900
C4—C5	1.3725 (18)	C23—H23B	0.9900
C4—H4A	0.9500	C24—C25	1.3934 (16)
C5—C6	1.4232 (17)	C24—C29	1.3996 (17)
C5—H5A	0.9500	C25—C26	1.3934 (18)
C6—C7	1.4388 (17)	C25—H25A	0.9500
C7—H7A	0.9500	C26—C27	1.3813 (18)
C8—C9	1.5111 (18)	C26—H26A	0.9500
C8—H8A	0.9900	C27—C28	1.3862 (17)
C8—H8B	0.9900	C28—C29	1.3929 (18)
C9—C10	1.3951 (17)	C28—H28A	0.9500
C9—C14	1.3983 (17)	C29—H29A	0.9500
C10—C11	1.3951 (19)	C30—H30A	0.9800
C10—H10A	0.9500	C30—H30B	0.9800
C11—C12	1.376 (2)	C30—H30C	0.9800
O1—Pd1—O2	179.60 (3)	C13—C14—H14A	119.6
O1—Pd1—N1	92.57 (4)	C9—C14—H14A	119.6
O2—Pd1—N1	87.15 (4)	O3—C15—H15A	109.5
O1—Pd1—N2	87.59 (4)	O3—C15—H15B	109.5
O2—Pd1—N2	92.70 (4)	H15A—C15—H15B	109.5
N1—Pd1—N2	179.85 (4)	O3—C15—H15C	109.5
C1—O1—Pd1	126.95 (8)	H15A—C15—H15C	109.5
C16—O2—Pd1	126.89 (8)	H15B—C15—H15C	109.5
C2—O3—C15	116.63 (10)	O2—C16—C21	125.54 (10)
C17—O4—C30	116.34 (10)	O2—C16—C17	116.76 (10)
C7—N1—C8	115.47 (10)	C21—C16—C17	117.69 (10)
C7—N1—Pd1	123.53 (8)	O4—C17—C18	124.87 (11)
C8—N1—Pd1	121.00 (7)	O4—C17—C16	113.91 (10)
C22—N2—C23	115.28 (10)	C18—C17—C16	121.21 (11)
C22—N2—Pd1	123.34 (8)	C17—C18—C19	120.21 (11)
C23—N2—Pd1	121.36 (7)	C17—C18—H18A	119.9
O1—C1—C6	125.61 (10)	C19—C18—H18A	119.9
O1—C1—C2	116.59 (10)	C20—C19—C18	119.96 (11)
C6—C1—C2	117.80 (10)	C20—C19—H19A	120.0
O3—C2—C3	125.21 (11)	C18—C19—H19A	120.0
O3—C2—C1	113.62 (10)	C19—C20—C21	120.91 (12)
C3—C2—C1	121.16 (11)	C19—C20—H20A	119.5
C2—C3—C4	120.27 (11)	C21—C20—H20A	119.5
C2—C3—H3A	119.9	C16—C21—C20	120.01 (11)
C4—C3—H3A	119.9	C16—C21—C22	123.08 (10)
C5—C4—C3	120.00 (12)	C20—C21—C22	116.84 (11)
C5—C4—H4A	120.0	N2—C22—C21	128.03 (11)
C3—C4—H4A	120.0	N2—C22—H22A	116.0
C4—C5—C6	120.70 (12)	C21—C22—H22A	116.0
C4—C5—H5A	119.7	N2—C23—C24	111.43 (10)
C6—C5—H5A	119.7	N2—C23—H23A	109.3
C1—C6—C5	120.05 (11)	C24—C23—H23A	109.3
C1—C6—C7	122.95 (10)	N2—C23—H23B	109.3
C5—C6—C7	116.98 (11)	C24—C23—H23B	109.3
N1—C7—C6	128.04 (11)	H23A—C23—H23B	108.0
N1—C7—H7A	116.0	C25—C24—C29	118.91 (11)
C6—C7—H7A	116.0	C25—C24—C23	120.18 (10)
N1—C8—C9	112.50 (10)	C29—C24—C23	120.91 (10)
N1—C8—H8A	109.1	C24—C25—C26	121.27 (11)
C9—C8—H8A	109.1	C24—C25—H25A	119.4
N1—C8—H8B	109.1	C26—C25—H25A	119.4
C9—C8—H8B	109.1	C27—C26—C25	117.94 (11)
H8A—C8—H8B	107.8	C27—C26—H26A	121.0
C10—C9—C14	118.88 (12)	C25—C26—H26A	121.0
C10—C9—C8	119.18 (11)	F2—C27—C26	118.60 (11)
C14—C9—C8	121.93 (10)	F2—C27—C28	118.47 (12)
C9—C10—C11	121.15 (12)	C26—C27—C28	122.92 (12)
C9—C10—H10A	119.4	C27—C28—C29	118.09 (11)
C11—C10—H10A	119.4	C27—C28—H28A	121.0
C12—C11—C10	118.16 (12)	C29—C28—H28A	121.0
C12—C11—H11A	120.9	C28—C29—C24	120.88 (11)
C10—C11—H11A	120.9	C28—C29—H29A	119.6
F1—C12—C11	118.70 (12)	C24—C29—H29A	119.6
F1—C12—C13	118.39 (13)	O4—C30—H30A	109.5
C11—C12—C13	122.90 (13)	O4—C30—H30B	109.5
C12—C13—C14	118.01 (12)	H30A—C30—H30B	109.5
C12—C13—H13A	121.0	O4—C30—H30C	109.5
C14—C13—H13A	121.0	H30A—C30—H30C	109.5
C13—C14—C9	120.89 (11)	H30B—C30—H30C	109.5

Cg1, Cg2, Cg3 and Cg5 are the centroids of the Pd1/N1/O1/C1/C6/C7, Pd1/O2/N2/C16/C21/C22, C1–C6 and C16–C21 rings, respectively.

D—H···A	D—H	H···A	D···A	D—H···A
C29—H29A···O1	0.95	2.45	3.2051 (15)	136
C8—H8B···Cg2i	0.99	2.67	3.3882 (13)	130
C15—H15B···Cg5ii	0.98	2.71	3.6530 (15)	162
C23—H23A···Cg1ii	0.99	2.67	3.3612 (13)	127
C30—H30C···Cg3i	0.98	2.69	3.6146 (16)	158

Table 1

Hydrogen-bond geometry (Å, °)

Cg1, Cg2, Cg3 and Cg5 are the centroids of the Pd1/N1/O1/C1/C6/C7, Pd1/O2/N2/C16/C21/C22, C1–C6 and C16–C21 rings, respectively.

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C29—H29A⋯O1	0.95	2.45	3.2051 (15)	136
C8—H8B⋯Cg2i	0.99	2.67	3.3882 (13)	130
C15—H15B⋯Cg5ii	0.98	2.71	3.6530 (15)	162
C23—H23A⋯Cg1ii	0.99	2.67	3.3612 (13)	127
C30—H30C⋯Cg3i	0.98	2.69	3.6146 (16)	158

Symmetry codes: (i) ; (ii) .