trans-Di-fluorido-tetra-kis-(pyridine-κN)chromium(III) perchlorate from synchrotron radiation.

The are two independent complex cations in the title salt, [CrF2(C5H5N)4]ClO4, each located on a centre of inversion, as well as an independent perchlorate counter-ion. The complex cations adopt slightly distorted octa-hedral coordination environments around the Cr(III) ion, defined by four pyridine (py) N atoms in the equatorial plane and two F(-) ligands in the axial positions; intra-molecular C-H⋯F contacts are noted. The mean Cr-N(py) and Cr-F bond lengths are 2.088 (6) and 1.8559 (10) Å, respectively. The three-dimensional architecture is sustained by hydrogen bonds involving the pyridine C-H groups as donors, and F and O atoms as acceptors.

Related literature

For background to geometric isomerism in transition metal comlexes, see: Knight & Scott (2003 ▶); Ronconi & Sadler (2007 ▶). For the synthesis, see: Glerup et al. (1970 ▶). For the structure of trans-[Cr(py)4F2]PF6, see: Fochi et al. (1991 ▶).

Experimental

Crystal data

[CrF2(C5H5N)4]ClO4

M = 505.85

Triclinic,

a = 9.5690 (19) Å

b = 10.615 (2) Å

c = 12.663 (3) Å

α = 68.46 (3)°

β = 68.31 (3)°

γ = 79.38 (3)°

V = 1109.9 (5) Å3

Z = 2

Synchrotron radiation

λ = 0.63001 Å

μ = 0.49 mm−1

T = 99 K

0.03 × 0.03 × 0.02 mm

Data collection

ADSC Q210 CCD area-detector

Absorption correction: empirical (HKL3000sm; Otwinowski & Minor, 1997 ▶) T min = 0.985, T max = 0.993

11523 measured reflections

5842 independent reflections

4912 reflections with I > 2σ(I)

R int = 0.020

Refinement

R[F 2 > 2σ(F 2)] = 0.036

wR(F 2) = 0.099

S = 1.05

5842 reflections

293 parameters

H-atom parameters constrained

Δρmax = 0.51 e Å−3

Δρmin = −0.61 e Å−3

Data collection: PAL ADSC Quantum-210 ADX Software (Arvai & Nielsen, 1983 ▶); cell refinement: HKL3000sm (Otwinowski & Minor, 1997 ▶); data reduction: HKL3000sm; program(s) used to solve structure: SHELX-2013-XS (Sheldrick, 2008 ▶); program(s) used to refine structure: SHELX-2013-XL (Sheldrick, 2008 ▶); molecular graphics: DIAMOND (Brandenburg, 2007 ▶); software used to prepare material for publication: WinGX (Farrugia, 2012 ▶).

Crystal structure: contains datablock(s) I. DOI: 10.1107/S1600536813023052/tk5248sup1.cif

Structure factors: contains datablock(s) I. DOI: 10.1107/S1600536813023052/tk5248Isup2.hkl

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

[CrF2(C5H5N)4]ClO4	Z = 2
Mr = 505.85	F(000) = 518
Triclinic, P1	Dx = 1.514 Mg m−3
Hall symbol: -P 1	Synchrotron radiation, λ = 0.63001 Å
a = 9.5690 (19) Å	Cell parameters from 33119 reflections
b = 10.615 (2) Å	θ = 0.4–33.6°
c = 12.663 (3) Å	µ = 0.49 mm−1
α = 68.46 (3)°	T = 99 K
β = 68.31 (3)°	Pink, plate
γ = 79.38 (3)°	0.03 × 0.03 × 0.02 mm
V = 1109.9 (5) Å3

ADSC Q210 CCD area-detector diffractometer	4912 reflections with I > 2σ(I)
Radiation source: PLSII 2D bending magnet	Rint = 0.020
ω scan	θmax = 26.0°, θmin = 1.6°
Absorption correction: empirical (using intensity measurements) (HKL3000sm; Otwinowski & Minor, 1997)	h = −13→13
Tmin = 0.985, Tmax = 0.993	k = −14→14
11523 measured reflections	l = −17→17
5842 independent reflections

Refinement on F2	Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: full	H-atom parameters constrained
R[F2 > 2σ(F2)] = 0.036	w = 1/[σ2(Fo2) + (0.0543P)2 + 0.5188P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.099	(Δ/σ)max = 0.001
S = 1.05	Δρmax = 0.51 e Å−3
5842 reflections	Δρmin = −0.61 e Å−3
293 parameters	Extinction correction: SHELXL, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraints	Extinction coefficient: 0.062 (4)

Experimental. Since the Pohang Accelerator Laboratory goniostat has only one omega-axis, diffrn_measured_fraction_theta_full is not fully covered as 0.944, especially for the low symmetry such as a triclinic system. As this is an inherent problem, other command and option (such as OMIT) were not helpful to improve the completeness.

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.

	x	y	z	Uiso*/Ueq
Cr1	0.0000	1.0000	0.0000	0.01263 (9)
F1	0.01103 (10)	1.14193 (9)	0.04859 (8)	0.01655 (19)
N1	−0.16449 (15)	0.91455 (13)	0.16450 (12)	0.0144 (2)
C1	−0.24067 (17)	0.99130 (16)	0.23459 (14)	0.0160 (3)
H1	−0.2177	1.0836	0.2077	0.019*
C2	−0.35141 (18)	0.94021 (17)	0.34453 (15)	0.0184 (3)
H2	−0.4036	0.9969	0.3918	0.022*
C3	−0.38521 (19)	0.80573 (18)	0.38478 (15)	0.0206 (3)
H3	−0.4594	0.7682	0.4605	0.025*
C4	−0.30797 (19)	0.72648 (17)	0.31164 (16)	0.0213 (3)
H4	−0.3294	0.6341	0.3366	0.026*
C5	−0.19964 (18)	0.78444 (16)	0.20218 (15)	0.0177 (3)
H5	−0.1484	0.7307	0.1520	0.021*
N2	0.17550 (15)	0.89172 (13)	0.06286 (12)	0.0150 (3)
C6	0.24772 (18)	0.94873 (16)	0.10540 (14)	0.0182 (3)
H6	0.2131	1.0362	0.1120	0.022*
C7	0.37130 (19)	0.88404 (18)	0.14009 (16)	0.0212 (3)
H7	0.4210	0.9271	0.1691	0.025*
C8	0.42122 (19)	0.75607 (18)	0.13180 (15)	0.0214 (3)
H8	0.5052	0.7097	0.1556	0.026*
C9	0.34678 (19)	0.69668 (17)	0.08827 (16)	0.0210 (3)
H9	0.3789	0.6089	0.0817	0.025*
C10	0.22513 (18)	0.76705 (16)	0.05457 (15)	0.0181 (3)
H10	0.1746	0.7262	0.0245	0.022*
Cr2	0.0000	1.0000	0.5000	0.01280 (9)
F2	−0.15818 (10)	1.01373 (10)	0.44431 (8)	0.01706 (19)
N3	0.08874 (14)	0.82597 (13)	0.45187 (11)	0.0148 (3)
C11	0.02042 (18)	0.77691 (17)	0.40054 (15)	0.0179 (3)
H11	−0.0646	0.8267	0.3805	0.022*
C12	0.06960 (19)	0.65643 (17)	0.37590 (15)	0.0204 (3)
H12	0.0185	0.6242	0.3400	0.024*
C13	0.19391 (19)	0.58355 (17)	0.40415 (15)	0.0209 (3)
H13	0.2300	0.5010	0.3875	0.025*
C14	0.26469 (19)	0.63353 (17)	0.45721 (15)	0.0205 (3)
H14	0.3502	0.5855	0.4776	0.025*
C15	0.20934 (18)	0.75428 (17)	0.48022 (14)	0.0179 (3)
H15	0.2578	0.7877	0.5171	0.022*
N4	0.12228 (15)	1.12831 (14)	0.33344 (12)	0.0157 (3)
C16	0.05298 (18)	1.21171 (16)	0.25660 (14)	0.0177 (3)
H16	−0.0518	1.2052	0.2758	0.021*
C17	0.1294 (2)	1.30722 (17)	0.14993 (15)	0.0215 (3)
H17	0.0773	1.3660	0.0976	0.026*
C18	0.2822 (2)	1.31577 (18)	0.12077 (16)	0.0246 (4)
H18	0.3368	1.3805	0.0483	0.030*
C19	0.3546 (2)	1.2278 (2)	0.19953 (17)	0.0263 (4)
H19	0.4600	1.2304	0.1809	0.032*
C20	0.27139 (18)	1.13681 (18)	0.30494 (15)	0.0211 (3)
H20	0.3208	1.0781	0.3593	0.025*
Cl1P	0.64390 (4)	0.40483 (4)	0.24420 (3)	0.01718 (10)
O1P	0.53210 (15)	0.45637 (14)	0.33397 (13)	0.0305 (3)
O2P	0.5964 (2)	0.44001 (15)	0.14139 (13)	0.0374 (4)
O3P	0.66002 (17)	0.26002 (13)	0.29401 (13)	0.0304 (3)
O4P	0.78435 (15)	0.46338 (17)	0.20959 (16)	0.0387 (4)

	U11	U22	U33	U12	U13	U23
Cr1	0.01311 (16)	0.01227 (16)	0.01356 (16)	0.00203 (12)	−0.00396 (13)	−0.00714 (12)
F1	0.0183 (4)	0.0153 (4)	0.0190 (4)	0.0016 (3)	−0.0062 (4)	−0.0100 (3)
N1	0.0146 (6)	0.0150 (6)	0.0150 (6)	0.0008 (5)	−0.0050 (5)	−0.0071 (5)
C1	0.0153 (7)	0.0167 (7)	0.0178 (7)	0.0020 (5)	−0.0060 (6)	−0.0086 (6)
C2	0.0142 (7)	0.0245 (8)	0.0184 (7)	0.0011 (6)	−0.0046 (6)	−0.0110 (6)
C3	0.0161 (7)	0.0263 (8)	0.0183 (7)	−0.0041 (6)	−0.0036 (6)	−0.0067 (6)
C4	0.0225 (8)	0.0195 (8)	0.0223 (8)	−0.0046 (6)	−0.0066 (7)	−0.0063 (6)
C5	0.0197 (7)	0.0157 (7)	0.0195 (7)	0.0000 (6)	−0.0065 (6)	−0.0081 (6)
N2	0.0149 (6)	0.0152 (6)	0.0149 (6)	0.0021 (5)	−0.0042 (5)	−0.0069 (5)
C6	0.0188 (7)	0.0180 (7)	0.0182 (7)	0.0018 (6)	−0.0054 (6)	−0.0085 (6)
C7	0.0196 (7)	0.0241 (8)	0.0227 (8)	0.0014 (6)	−0.0089 (7)	−0.0101 (6)
C8	0.0176 (7)	0.0234 (8)	0.0212 (8)	0.0047 (6)	−0.0068 (6)	−0.0075 (6)
C9	0.0198 (7)	0.0193 (7)	0.0230 (8)	0.0061 (6)	−0.0067 (7)	−0.0098 (6)
C10	0.0185 (7)	0.0170 (7)	0.0188 (7)	0.0022 (6)	−0.0053 (6)	−0.0083 (6)
Cr2	0.00999 (15)	0.01573 (17)	0.01295 (16)	0.00214 (12)	−0.00418 (12)	−0.00595 (12)
F2	0.0138 (4)	0.0204 (5)	0.0191 (4)	0.0021 (3)	−0.0077 (4)	−0.0080 (4)
N3	0.0133 (6)	0.0163 (6)	0.0135 (6)	0.0011 (5)	−0.0033 (5)	−0.0057 (5)
C11	0.0153 (7)	0.0199 (7)	0.0187 (7)	0.0013 (6)	−0.0056 (6)	−0.0076 (6)
C12	0.0190 (7)	0.0213 (8)	0.0225 (8)	0.0003 (6)	−0.0065 (6)	−0.0101 (6)
C13	0.0200 (7)	0.0180 (7)	0.0218 (8)	0.0023 (6)	−0.0035 (6)	−0.0084 (6)
C14	0.0172 (7)	0.0214 (8)	0.0198 (7)	0.0056 (6)	−0.0053 (6)	−0.0072 (6)
C15	0.0146 (7)	0.0220 (8)	0.0176 (7)	0.0033 (6)	−0.0055 (6)	−0.0087 (6)
N4	0.0140 (6)	0.0183 (6)	0.0149 (6)	0.0007 (5)	−0.0035 (5)	−0.0076 (5)
C16	0.0175 (7)	0.0193 (7)	0.0165 (7)	0.0023 (6)	−0.0056 (6)	−0.0077 (6)
C17	0.0266 (8)	0.0191 (7)	0.0178 (7)	0.0018 (6)	−0.0068 (7)	−0.0068 (6)
C18	0.0272 (9)	0.0224 (8)	0.0196 (8)	−0.0054 (7)	−0.0003 (7)	−0.0073 (6)
C19	0.0183 (8)	0.0327 (10)	0.0242 (8)	−0.0051 (7)	−0.0013 (7)	−0.0090 (7)
C20	0.0149 (7)	0.0275 (8)	0.0194 (7)	−0.0010 (6)	−0.0046 (6)	−0.0073 (6)
Cl1P	0.01680 (17)	0.01445 (17)	0.02051 (18)	0.00369 (12)	−0.00615 (14)	−0.00815 (13)
O1P	0.0234 (6)	0.0276 (7)	0.0369 (8)	0.0019 (5)	0.0019 (6)	−0.0201 (6)
O2P	0.0580 (10)	0.0308 (8)	0.0269 (7)	−0.0049 (7)	−0.0253 (7)	−0.0007 (6)
O3P	0.0427 (8)	0.0139 (6)	0.0382 (8)	0.0093 (5)	−0.0219 (7)	−0.0092 (5)
O4P	0.0178 (6)	0.0411 (8)	0.0597 (10)	−0.0049 (6)	−0.0017 (7)	−0.0291 (8)

Cr1—F1i	1.8566 (10)	Cr2—N4	2.0799 (17)
Cr1—F1	1.8566 (10)	Cr2—N4ii	2.0800 (17)
Cr1—N1i	2.0867 (16)	Cr2—N3ii	2.0908 (14)
Cr1—N1	2.0867 (16)	Cr2—N3	2.0908 (14)
Cr1—N2i	2.0929 (15)	N3—C11	1.345 (2)
Cr1—N2	2.0929 (15)	N3—C15	1.350 (2)
N1—C1	1.3478 (19)	C11—C12	1.385 (2)
N1—C5	1.348 (2)	C11—H11	0.9500
C1—C2	1.386 (2)	C12—C13	1.383 (2)
C1—H1	0.9500	C12—H12	0.9500
C2—C3	1.384 (2)	C13—C14	1.386 (3)
C2—H2	0.9500	C13—H13	0.9500
C3—C4	1.396 (2)	C14—C15	1.385 (2)
C3—H3	0.9500	C14—H14	0.9500
C4—C5	1.386 (2)	C15—H15	0.9500
C4—H4	0.9500	N4—C16	1.341 (2)
C5—H5	0.9500	N4—C20	1.348 (2)
N2—C6	1.343 (2)	C16—C17	1.387 (2)
N2—C10	1.350 (2)	C16—H16	0.9500
C6—C7	1.388 (2)	C17—C18	1.382 (3)
C6—H6	0.9500	C17—H17	0.9500
C7—C8	1.383 (2)	C18—C19	1.391 (3)
C7—H7	0.9500	C18—H18	0.9500
C8—C9	1.386 (3)	C19—C20	1.378 (3)
C8—H8	0.9500	C19—H19	0.9500
C9—C10	1.381 (2)	C20—H20	0.9500
C9—H9	0.9500	Cl1P—O4P	1.4342 (15)
C10—H10	0.9500	Cl1P—O3P	1.4342 (14)
Cr2—F2ii	1.8552 (10)	Cl1P—O2P	1.4351 (15)
Cr2—F2	1.8552 (10)	Cl1P—O1P	1.4416 (14)
F1i—Cr1—F1	180.0	F2ii—Cr2—N4ii	90.36 (6)
F1i—Cr1—N1i	90.52 (5)	F2—Cr2—N4ii	89.64 (6)
F1—Cr1—N1i	89.48 (5)	N4—Cr2—N4ii	180.0
F1i—Cr1—N1	89.48 (5)	F2ii—Cr2—N3ii	90.31 (5)
F1—Cr1—N1	90.52 (5)	F2—Cr2—N3ii	89.69 (5)
N1i—Cr1—N1	180.00 (7)	N4—Cr2—N3ii	87.08 (6)
F1i—Cr1—N2i	90.40 (5)	N4ii—Cr2—N3ii	92.92 (6)
F1—Cr1—N2i	89.60 (5)	F2ii—Cr2—N3	89.68 (5)
N1i—Cr1—N2i	92.68 (6)	F2—Cr2—N3	90.32 (5)
N1—Cr1—N2i	87.32 (6)	N4—Cr2—N3	92.92 (6)
F1i—Cr1—N2	89.60 (5)	N4ii—Cr2—N3	87.08 (6)
F1—Cr1—N2	90.40 (5)	N3ii—Cr2—N3	180.0
N1i—Cr1—N2	87.32 (6)	C11—N3—C15	118.33 (14)
N1—Cr1—N2	92.68 (6)	C11—N3—Cr2	120.91 (11)
N2i—Cr1—N2	180.0	C15—N3—Cr2	120.55 (11)
C1—N1—C5	118.53 (14)	N3—C11—C12	122.38 (15)
C1—N1—Cr1	119.68 (11)	N3—C11—H11	118.8
C5—N1—Cr1	121.77 (11)	C12—C11—H11	118.8
N1—C1—C2	122.25 (15)	C13—C12—C11	119.25 (16)
N1—C1—H1	118.9	C13—C12—H12	120.4
C2—C1—H1	118.9	C11—C12—H12	120.4
C3—C2—C1	119.33 (15)	C12—C13—C14	118.63 (15)
C3—C2—H2	120.3	C12—C13—H13	120.7
C1—C2—H2	120.3	C14—C13—H13	120.7
C2—C3—C4	118.55 (15)	C15—C14—C13	119.30 (15)
C2—C3—H3	120.7	C15—C14—H14	120.4
C4—C3—H3	120.7	C13—C14—H14	120.4
C5—C4—C3	119.09 (16)	N3—C15—C14	122.11 (15)
C5—C4—H4	120.5	N3—C15—H15	118.9
C3—C4—H4	120.5	C14—C15—H15	118.9
N1—C5—C4	122.22 (15)	C16—N4—C20	118.68 (15)
N1—C5—H5	118.9	C16—N4—Cr2	120.86 (11)
C4—C5—H5	118.9	C20—N4—Cr2	120.25 (12)
C6—N2—C10	118.41 (14)	N4—C16—C17	122.13 (16)
C6—N2—Cr1	120.40 (10)	N4—C16—H16	118.9
C10—N2—Cr1	121.05 (11)	C17—C16—H16	118.9
N2—C6—C7	122.17 (15)	C18—C17—C16	119.13 (17)
N2—C6—H6	118.9	C18—C17—H17	120.4
C7—C6—H6	118.9	C16—C17—H17	120.4
C8—C7—C6	119.12 (16)	C17—C18—C19	118.76 (17)
C8—C7—H7	120.4	C17—C18—H18	120.6
C6—C7—H7	120.4	C19—C18—H18	120.6
C7—C8—C9	118.91 (16)	C20—C19—C18	119.08 (17)
C7—C8—H8	120.5	C20—C19—H19	120.5
C9—C8—H8	120.5	C18—C19—H19	120.5
C10—C9—C8	119.00 (15)	N4—C20—C19	122.20 (17)
C10—C9—H9	120.5	N4—C20—H20	118.9
C8—C9—H9	120.5	C19—C20—H20	118.9
N2—C10—C9	122.39 (16)	O4P—Cl1P—O3P	110.13 (10)
N2—C10—H10	118.8	O4P—Cl1P—O2P	109.84 (11)
C9—C10—H10	118.8	O3P—Cl1P—O2P	109.44 (9)
F2ii—Cr2—F2	180.0	O4P—Cl1P—O1P	109.02 (9)
F2ii—Cr2—N4	89.64 (6)	O3P—Cl1P—O1P	108.90 (9)
F2—Cr2—N4	90.36 (6)	O2P—Cl1P—O1P	109.50 (10)
C5—N1—C1—C2	1.2 (2)	C15—N3—C11—C12	−0.1 (2)
Cr1—N1—C1—C2	179.81 (12)	Cr2—N3—C11—C12	−175.00 (12)
N1—C1—C2—C3	0.3 (2)	N3—C11—C12—C13	−0.4 (3)
C1—C2—C3—C4	−1.2 (2)	C11—C12—C13—C14	0.4 (3)
C2—C3—C4—C5	0.5 (3)	C12—C13—C14—C15	0.0 (2)
C1—N1—C5—C4	−1.9 (2)	C11—N3—C15—C14	0.5 (2)
Cr1—N1—C5—C4	179.55 (13)	Cr2—N3—C15—C14	175.44 (12)
C3—C4—C5—N1	1.0 (3)	C13—C14—C15—N3	−0.5 (2)
C10—N2—C6—C7	0.4 (2)	C20—N4—C16—C17	−0.9 (2)
Cr1—N2—C6—C7	−175.43 (12)	Cr2—N4—C16—C17	173.85 (12)
N2—C6—C7—C8	−0.6 (3)	N4—C16—C17—C18	0.9 (2)
C6—C7—C8—C9	0.4 (3)	C16—C17—C18—C19	0.1 (2)
C7—C8—C9—C10	0.0 (3)	C17—C18—C19—C20	−1.2 (3)
C6—N2—C10—C9	0.1 (2)	C16—N4—C20—C19	−0.3 (2)
Cr1—N2—C10—C9	175.84 (12)	Cr2—N4—C20—C19	−175.00 (14)
C8—C9—C10—N2	−0.2 (3)	C18—C19—C20—N4	1.3 (3)

D—H···A	D—H	H···A	D···A	D—H···A
C1—H1···F1	0.95	2.36	2.892 (2)	115
C6—H6···F1	0.95	2.31	2.874 (2)	118
C11—H11···F2	0.95	2.32	2.879 (2)	117
C16—H16···F2	0.95	2.39	2.915 (2)	115
C14—H14···O1P	0.95	2.61	3.154 (2)	117
C9—H9···O2P	0.95	2.63	3.320 (3)	130
C1—H1···O3Piii	0.95	2.41	3.107 (2)	130
C4—H4···O1Piv	0.95	2.51	3.368 (2)	150
C5—H5···F1i	0.95	2.38	2.900 (2)	114
C10—H10···F1i	0.95	2.31	2.863 (2)	117
C15—H15···F2ii	0.95	2.29	2.856 (2)	117
C20—H20···F2ii	0.95	2.34	2.860 (2)	114
C15—H15···O3Pv	0.95	2.64	3.466 (2)	146
C19—H19···O2Pvi	0.95	2.58	3.227 (3)	125

Table 1

Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
C1—H1⋯F1	0.95	2.36	2.892 (2)	115
C6—H6⋯F1	0.95	2.31	2.874 (2)	118
C11—H11⋯F2	0.95	2.32	2.879 (2)	117
C16—H16⋯F2	0.95	2.39	2.915 (2)	115
C14—H14⋯O1P	0.95	2.61	3.154 (2)	117
C9—H9⋯O2P	0.95	2.63	3.320 (3)	130
C1—H1⋯O3P i	0.95	2.41	3.107 (2)	130
C4—H4⋯O1P ii	0.95	2.51	3.368 (2)	150
C5—H5⋯F1iii	0.95	2.38	2.900 (2)	114
C10—H10⋯F1iii	0.95	2.31	2.863 (2)	117
C15—H15⋯F2iv	0.95	2.29	2.856 (2)	117
C20—H20⋯F2iv	0.95	2.34	2.860 (2)	114
C15—H15⋯O3P v	0.95	2.64	3.466 (2)	146
C19—H19⋯O2P vi	0.95	2.58	3.227 (3)	125

Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) ; (vi) .