Poly[[hexa-μ-cyanido-manganese(II)iron(III)] penta­hydrate]

Matsuda, T.; Tokoro, H.; Shiro, M.; Hashimoto, K.; Ohkoshi, S.

doi:10.1107/S1600536807068869

inorganic compounds

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ISSN: 2056-9890

Volume 64| Part 2| February 2008| Pages i11-i12

doi:10.1107/S1600536807068869

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Poly[[hexa-μ-cyanido-manganese(II)iron(III)] pentahydrate]

Tomoyuki Matsuda,^a,^b Hiroko Tokoro,^a,^c Motoo Shiro,^d Kazuhito Hashimoto ^b and Shin-ichi Ohkoshi ^a ^*

^aDepartment of Chemistry, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, ^bDepartment of Applied Chemistry, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, ^cPRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan, and ^dRigaku Corporation, 3-9-12 Matsubaracho, Akishima, Tokyo 196-8666, Japan
^*Correspondence e-mail: ohkoshi@chem.s.u-tokyo.ac.jp

(Received 16 November 2007; accepted 31 December 2007; online 9 January 2008)

The structure of the title compound, Mn^II[Fe^III(CN)₆]_2/3·5H₂O, features a face-centered cubic –Mn—NC—Fe– framework with both Mn and Fe having site symmetry m $[\overline{3}]$ m. Since one-third of the [Fe(CN)₆]³⁻ units are missing for a given formula in order to maintain charge neutrality, each Mn atom around such a vacancy is coordinated not only by the N atoms of the CN groups but also by the O atoms of the ligand water molecules. In addition to ligand water molecules, two types of non-coordinated water molecules, so-called zeolitic water molecules, exist in the interstitial sites of the –Mn—NC—Fe– framework. The positions of the O atoms of the zeolitic water molecules are fixed by the linkage via hydrogen bonds between ligand water and zeolitic water molecules. The structure is related to a recently reported rubidium manganese hexacyanoferrate. Site occupancy factors for Fe, C, N are 0.67; for two O atoms the value is 0.83 and for one O atom is 0.17.

Related literature

For structure and properties of the related rubidium manganese hexacyanoferrate, see: Kato et al. (2003 ); Tokoro et al. (2007 ). For general background on Prussian blue compounds, see: Ludi & Güdel (1973 ). For related literature, see: Egan et al. (2006 ); Ferlay et al. (1995 ); Güdel et al. (1973 ); Gadet et al. (1992 ); Hatlevik et al. (1999 ); Holmes & Girolami (1999 ); Ludi et al. (1970 ); Margadonna et al. (2004 ); Ohkoshi & Hashimoto (2001 ); Ohkoshi et al. (1997 , 2000 , 2004 , 2005 ); Sato et al. (1996 ); Tokoro et al. (2003 , 2004 ); Zeigler et al. (1999 ).

Experimental

Crystal data

Mn[Fe(CN)₆]_2/3·5H₂O
M_r = 286.50
Cubic, $[F m \overline 3m ]$
a = 10.3859 (13) Å
V = 1120.3 (2) Å³
Z = 4
Mo Kα radiation
μ = 2.02 mm⁻¹
T = 90 (1) K
0.25 × 0.20 × 0.15 mm

Data collection

Rigaku R-AXIS RAPID diffractometer
Absorption correction: multi-scan (ABSCOR; Higashi, 1995 ) T_min = 0.655, T_max = 0.739
15777 measured reflections
278 independent reflections
268 reflections with F² > 2σ(F²)
R_int = 0.032

Refinement

R[F² > 2σ(F²)] = 0.047
wR(F²) = 0.136
S = 1.37
278 reflections
21 parameters
H-atom parameters not defined
Δρ_max = 0.59 e Å⁻³
Δρ_min = −1.41 e Å⁻³

Table 1
Selected geometric parameters (Å, °)

Fe1—C1	1.918 (8)
Mn1—N1	2.105 (13)
N1—C1	1.169 (15)
Mn1—O1	2.247 (12)

O1—Mn1—O1ⁱ	87.8 (4)
O1—Mn1—O1ⁱⁱ	157.4 (3)
O1—Mn1—O1ⁱⁱⁱ	180
O1—Mn1—N1^iv	78.69 (14)
O1—Mn1—N1^v	163.90 (14)
Symmetry codes: (i) y, z, -x+1; (ii) -x+1, y, -z+1; (iii) -x+1, -y+1, -z+1; (iv) y, z, x; (v) x, y, -z+1.

Data collection: PROCESS-AUTO (Rigaku, 1998 ); cell refinement: PROCESS-AUTO; data reduction: CrystalStructure (Rigaku, 2007 ); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: VESTA (Momma & Izumi, 2006 ); software used to prepare material for publication: CrystalStructure.

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536807068869/sq2003sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536807068869/sq2003Isup2.hkl

checkCIF report

Comment top

In the last decade, various interesting magnetic functionalities have been reported with Prussian blue analogs, e.g., high Curie temperatures (T_C) (Ferlay et al., 1995; Holmes & Girolami, 1999; Hatlevik et al., 1999; Ohkoshi et al., 2000), humidity-response (Ohkoshi et al., 2004), photomagnetism (Ohkoshi & Hashimoto, 2001; Sato et al., 1996; Ohkoshi et al.,1997), and zero thermal expansion (Margadonna et al., 2004). Prussian blue analogs have two types of crystal structures, M_A[M_B(CN)₆]_2/3.zH₂O (Ludi et al., 1970; Ludi & Güdel, 1973; Güdel et al., 1973) and AM_A[M_B(CN)₆] (Gadet et al., 1992; Zeigler et al., 1999; Kato et al., 2003), where M_A and M_B are transition metal ions and A is an alkali metal ion. Recently, rubidium manganese hexacyanoferrate, Rb_xMn[Fe(CN)₆]₍_x_{+ 2)/3}.zH₂O, has received attention due to its various functionalities such as a charge-transfer phase transition (Tokoro et al., 2004; Ohkoshi et al., 2005), a pressure-induced magnetic pole inversion (Egan et al., 2006), and a photomagnetic effect (Tokoro et al., 2003). Although the crystal structure of rubidium manganese hexacyanoferrate was determined (Kato et al., 2003; Tokoro et al., 2007), the structure of manganese hexacyanoferrate of M_A[M_B(CN)₆]_2/3.zH₂O has not been determined yet. In this work, we successfully synthesized a single-crystal of Mn[Fe(CN)₆]_2/3.5H₂O and analyzed the crystal structure.

The crystal structure of the title compound consists of Mn^II and Fe^III with cyanide bridges to form a three-dimensional face-centered cubic structure (space group; Fm3m), containing ligand water and zeolitic water molecules (Fig. 1). Fe, Mn, C, and N atoms occupy the positions 4a (0, 0, 0), 4 b (1/2, 1/2, 1/2), 24 e (0.1847 (8), 0,0), and 24 e (0.2973 (12), 0, 0), respectively. The Fe atoms are coordinated to six C atoms with octahedral geometries. On the other hand, the Mn atoms are coordinated to four N atoms and two O1 atoms of ligand water, since there are vacancies of 1/3 × [Fe(CN)₆]^3- to maintain charge neutrality. The O1 atoms occupy the 96k (0.4576 (10), 0.4576 (10), 0.2922 (11)) positions with occupancy of 1/12. The coordination geometry in the MnN_xO_{6 -}_x (x = 0–5) moiety is octahedral with some potentially large distortions [O1—Mn—N bond angles of 78.19 (14)°, and 163.9 (2)°] due to the location of the disordered O1 water molecule. The oxygen atoms (O2 and O3) of zeolitic waters occupy 8c (1/4, 1/4, 1/4) positions with occupancy of 5/6 and 32f (0.1550 (16), 0.1550 (16), 0.1550 (16)) positions with occupancy of 1/6. The contact distances of 3.081 (11), 2.76 (2), 2.79 (2) Å between O1—O2ⁱ, O1—O3, and O3—O3ⁱⁱ [Symmetry codes: (i) 1 - x, y, z; (ii) 1 - z, 1 - x, y], respectively, suggest the existence of hydrogen bonds.

The structure of the title compound differs from that of the rubidium phase in the position of the O1 atom of the ligand water. This atom occupies the 96k position in Mn[Fe(CN)₆]_2/3.5H₂O and the 24 e position in Rb_0.61Mn[Fe(CN)₆]_0.87.1.7H₂O (Tokoro et al., 2007). This difference may be explained by the hydrogen bonding between ligand water and zeolitic water in the title compound. The O2 atom of the zeolitic water exists on the 8c (1/4, 1/4, 1/4) position in Mn[Fe(CN)₆]_2/3.5H₂O. The shortest length between the 8c and 24 e positions is 3.67 Å which is rather far to construct a hydrogen bond. In our refinement with the O1 atom in the 96k position, the distance of 3.081 (11) Å between O1 and O2ⁱ [Symmetry code: (i) 1 - x, y, z] is acceptable as a hydrogen bond. By contrast, in Rb_0.61Mn[Fe(CN)₆]_0.87.1.7H₂O, since the Rb cation is contained in the channels between the –Mn–NC–Fe– framework and the amount of vacant space is thus less than in Mn[Fe(CN)₆]_2/3.5H₂O, the O2 atom of zeolitic water does not exist on the 8c position in the Rb compound, so no similar O1···O2 interaction occurs.

Related literature top

For structure and properties of the related rubidium manganese hexacyanoferrate, see: Kato et al. (2003); Tokoro et al. (2007). For general background on Prussian blue compounds, see: Ludi & Güdel (1973). For related literature, see: Egan et al. (2006); Ferlay et al. (1995); Güdel et al. (1973); Gadet et al. (1992); Hatlevik et al. (1999); Holmes & Girolami (1999); Ludi et al. (1970); Margadonna et al. (2004); Ohkoshi & Hashimoto (2001); Ohkoshi et al. (1997, 2000, 2004, 2005); Sato et al. (1996); Tokoro et al. (2003, 2004); Zeigler et al. (1999).

Experimental top

Single crystals of Mn[Fe(CN)₆]_2/3.5H₂O were prepared by slow diffusion of aqueous solutions of MnCl₂.5H₂O (0.1 mmol) and K₃[Fe(CN)₆] (0.07 mmol) at 40 °C. After one month, dark brown block-shaped crystals were obtained. Elemental analysis of Mn and Fe was performed using inductively coupled plasma mass spectrometry (ICP-MS). The observed ratio of metal ions was Mn:Fe = 0.67:1.00. The density measured by the flotation method in toluene and tetrabromoethane was 1.64 (1) g cm^-3, which is consistent with the expected value of 1.63 g cm^-3 calculated considering the lattice constant of 10.480 Å at 293 K. The CN stretching vibrations are observed at 2151 cm^-1 in the IR spectrum.

Computing details top

Data collection: PROCESS-AUTO (Rigaku, 1998); cell refinement: PROCESS-AUTO (Rigaku, 1998); data reduction: CrystalStructure (Rigaku, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: VESTA (Momma & Izumi, 2006); software used to prepare material for publication: CrystalStructure (Rigaku, 2007).

Figures top

Fig. 1. (a) Three dimensional crystal structure of Mn[Fe(CN)₆]_2/3.5H₂O, showing the distribution of zeolitic water molecules (teal spheres). The –Mn–NC–Fe– framework is described in stick form for clarity. Blue, red, dark gray, light gray and teal represent Fe, Mn, C, N and O atoms, respectively. (b) Projection of the structure in the ab plane. The value g is the occupancy for each atom. [Symmetry codes: (i) 1/2 - z, 1/2 - x, 1 - y; (ii) z, -x, 1 - y; (iii) z, -y, x; (iv) z, 1/2 - x, 1/2 + y.]

Poly[[hexa-µ-cyanido-manganese(II)iron(III)] pentahydrate] top

Crystal data top

Mn[Fe(CN)₆]_0.6667·5H₂O	D_x = 1.699 Mg m⁻³ D_m = 1.64 (1) Mg m⁻³ D_m measured by flotation in toluene and tetrabromomethane
M_r = 286.50	Mo Kα radiation, λ = 0.71075 Å
Cubic, Fm3m	Cell parameters from 3216 reflections
Hall symbol: -F 4 2 3	θ = 5.6–45.1°
a = 10.3859 (13) Å	µ = 2.02 mm⁻¹
V = 1120.3 (2) Å³	T = 90 K
Z = 4	Block, brown
F(000) = 577.68	0.25 × 0.20 × 0.15 mm

Data collection top

Rigaku R-AXIS RAPID diffractometer	268 reflections with F² > 2σ(F²)
Detector resolution: 10.00 pixels mm^-1	R_int = 0.032
ω scans	θ_max = 45.1°
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	h = −20→20
T_min = 0.655, T_max = 0.739	k = −20→20
15777 measured reflections	l = −20→20
278 independent reflections

Refinement top

Refinement on F²	w = 1/[σ²(F_o²) + (0.0526P)² + 2.6431P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.047	(Δ/σ)_max < 0.001
wR(F²) = 0.136	Δρ_max = 0.59 e Å⁻³
S = 1.37	Δρ_min = −1.41 e Å⁻³
278 reflections	Extinction correction: SHELXL97 (Sheldrick, 1997)
21 parameters	Extinction coefficient: 0.002 (2)
H-atom parameters not defined

Crystal data top

Mn[Fe(CN)₆]_0.6667·5H₂O	Z = 4
M_r = 286.50	Mo Kα radiation
Cubic, Fm3m	µ = 2.02 mm⁻¹
a = 10.3859 (13) Å	T = 90 K
V = 1120.3 (2) Å³	0.25 × 0.20 × 0.15 mm

Data collection top

Rigaku R-AXIS RAPID diffractometer	278 independent reflections
Absorption correction: multi-scan (ABSCOR; Higashi, 1995)	268 reflections with F² > 2σ(F²)
T_min = 0.655, T_max = 0.739	R_int = 0.032
15777 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.047	21 parameters
wR(F²) = 0.136	H-atom parameters not defined
S = 1.37	Δρ_max = 0.59 e Å⁻³
278 reflections	Δρ_min = −1.41 e Å⁻³

Special details top

Refinement. Refinement was performed using all reflections. The weighted R-factor (wR) and goodness of fit (S) are based on F². R-factor (gt) are based on F. The threshold expression of F² > 2.0 σ(F²) is used only for calculating R-factor (gt).

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Fe1	0.5000	0.5000	0.0000	0.0176 (2)	0.6667
Mn1	0.5000	0.5000	0.5000	0.0183 (2)
O1	0.4576 (10)	0.4576 (10)	0.2922 (11)	0.036 (3)	0.0833
O2	0.7500	0.2500	0.2500	0.096 (6)	0.8333
O3	0.6550 (16)	0.3450 (16)	0.1550 (16)	0.054 (6)	0.1667
N1	0.5000	0.5000	0.2973 (12)	0.086 (3)	0.6667
C1	0.5000	0.5000	0.1847 (8)	0.064 (2)	0.6667

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Fe1	0.0176 (2)	0.0176 (2)	0.0176 (2)	0.0000	0.0000	0.0000
Mn1	0.0183 (2)	0.0183 (2)	0.0183 (2)	0.0000	0.0000	0.0000
O1	0.052 (5)	0.052 (5)	0.006 (3)	−0.026 (5)	−0.002 (2)	−0.002 (2)
O2	0.096 (6)	0.096 (6)	0.096 (6)	0.0000	0.0000	0.0000
O3	0.054 (6)	0.054 (6)	0.054 (6)	−0.018 (6)	0.018 (6)	−0.018 (6)
N1	0.114 (5)	0.114 (5)	0.030 (3)	0.0000	0.0000	0.0000
C1	0.085 (4)	0.085 (4)	0.023 (2)	0.0000	0.0000	0.0000

Geometric parameters (Å, º) top

Fe1—C1	1.918 (8)	Mn1—O1^ix	2.247 (12)
Fe1—C1ⁱ	1.918 (8)	Mn1—O1^xiii	2.247 (12)
Fe1—C1ⁱⁱ	1.918 (8)	Mn1—O1^x	2.247 (12)
Fe1—C1ⁱⁱⁱ	1.918 (8)	Mn1—O1^xiv	2.247 (12)
Fe1—C1^iv	1.918 (8)	Mn1—O1^xv	2.247 (12)
Fe1—C1^v	1.918 (8)	Mn1—O1^xvi	2.247 (12)
Mn1—N1	2.105 (13)	Mn1—O1^xvii	2.247 (12)
Mn1—N1^vi	2.105 (13)	Mn1—O1^xviii	2.247 (12)
Mn1—N1^vii	2.105 (13)	Mn1—O1^xix	2.247 (12)
Mn1—N1^viii	2.105 (13)	Mn1—O1^xx	2.247 (12)
Mn1—N1^ix	2.105 (13)	Mn1—O1^xxi	2.247 (12)
Mn1—N1^x	2.105 (13)	Mn1—O1^xxii	2.247 (12)
N1—C1	1.169 (15)	Mn1—O1^xxiii	2.247 (12)
Mn1—O1	2.247 (12)	Mn1—O1^xxiv	2.247 (12)
Mn1—O1^vi	2.247 (12)	Mn1—O1^xxv	2.247 (12)
Mn1—O1^vii	2.247 (12)	Mn1—O1^xxvi	2.247 (12)
Mn1—O1^viii	2.247 (12)	Mn1—O1^xxvii	2.247 (12)
Mn1—O1^xi	2.247 (12)	Mn1—O1^xxviii	2.247 (12)
Mn1—O1^xii	2.247 (12)

C1—Fe1—C1ⁱ	180.0000	N1^ix—Mn1—N1^x	90.0000
C1—Fe1—C1ⁱⁱ	90.0000	Mn1—N1—C1	180.0000
C1—Fe1—C1ⁱⁱⁱ	90.0000	Fe1—C1—N1	180.0000
C1—Fe1—C1^iv	90.0000	O1—Mn1—O1^vi	65.5 (4)
C1—Fe1—C1^v	90.0000	O1—Mn1—O1^vii	65.5 (4)
C1ⁱ—Fe1—C1ⁱⁱ	90.0000	O1—Mn1—O1^viii	147.8 (3)
C1ⁱ—Fe1—C1ⁱⁱⁱ	90.0000	O1—Mn1—O1^xi	87.8 (4)
C1ⁱ—Fe1—C1^iv	90.0000	O1—Mn1—O1^xii	87.8 (4)
C1ⁱ—Fe1—C1^v	90.0000	O1—Mn1—O1^ix	109.8 (4)
C1ⁱⁱ—Fe1—C1ⁱⁱⁱ	180.0000	O1—Mn1—O1^xiii	92.2 (4)
C1ⁱⁱ—Fe1—C1^iv	90.0000	O1—Mn1—O1^x	109.8 (4)
C1ⁱⁱ—Fe1—C1^v	90.0000	O1—Mn1—O1^xiv	157.4 (3)
C1ⁱⁱⁱ—Fe1—C1^iv	90.0000	O1—Mn1—O1^xv	92.2 (4)
C1ⁱⁱⁱ—Fe1—C1^v	90.0000	O1—Mn1—O1^xvi	157.4 (3)
C1^iv—Fe1—C1^v	180.0000	O1—Mn1—O1^xvii	180.0 (5)
N1—Mn1—N1^vi	90.0000	O1—Mn1—O1^xviii	114.5 (4)
N1—Mn1—N1^vii	90.0000	O1—Mn1—O1^xix	114.5 (4)
N1—Mn1—N1^viii	180.0000	O1—Mn1—O1^xxi	92.2 (4)
N1—Mn1—N1^ix	90.0000	O1—Mn1—O1^xxii	92.2 (4)
N1—Mn1—N1^x	90.0000	O1—Mn1—O1^xxiii	70.2 (4)
N1^vi—Mn1—N1^vii	90.0000	O1—Mn1—O1^xxiv	87.8 (4)
N1^vi—Mn1—N1^viii	90.0000	O1—Mn1—O1^xxv	70.2 (4)
N1^vi—Mn1—N1^ix	180.0000	O1—Mn1—O1^xxvii	87.8 (4)
N1^vi—Mn1—N1^x	90.0000	O1—Mn1—N1^vi	78.69 (14)
N1^vii—Mn1—N1^viii	90.0000	O1—Mn1—N1^vii	78.19 (14)
N1^vii—Mn1—N1^ix	90.0000	O1—Mn1—N1^viii	163.90 (14)
N1^vii—Mn1—N1^x	180.0000	O1—Mn1—N1^ix	101.31 (14)
N1^viii—Mn1—N1^ix	90.0000	O1—Mn1—N1^x	101.31 (14)
N1^viii—Mn1—N1^x	90.0000

Symmetry codes: (i) x, y, −z; (ii) y, z+1/2, x−1/2; (iii) y, −z+1/2, −x+1/2; (iv) z+1/2, x, y−1/2; (v) −z+1/2, x, −y+1/2; (vi) y, z, x; (vii) z, x, y; (viii) x, y, −z+1; (ix) y, −z+1, −x+1; (x) −z+1, x, −y+1; (xi) y, z, −x+1; (xii) z, x, −y+1; (xiii) z, −x+1, −y+1; (xiv) −x+1, y, −z+1; (xv) −y+1, z, −x+1; (xvi) x, −y+1, −z+1; (xvii) −x+1, −y+1, −z+1; (xviii) −y+1, −z+1, −x+1; (xix) −z+1, −x+1, −y+1; (xx) −x+1, −y+1, z; (xxi) −y+1, −z+1, x; (xxii) −z+1, −x+1, y; (xxiii) −y+1, z, x; (xxiv) −z+1, x, y; (xxv) z, −x+1, y; (xxvi) x, −y+1, z; (xxvii) y, −z+1, x; (xxviii) −x+1, y, z.

Experimental details

Crystal data
Chemical formula	Mn[Fe(CN)₆]_0.6667·5H₂O
M_r	286.50
Crystal system, space group	Cubic, Fm3m
Temperature (K)	90
a (Å)	10.3859 (13)
V (Å³)	1120.3 (2)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	2.02
Crystal size (mm)	0.25 × 0.20 × 0.15

Data collection
Diffractometer	Rigaku R-AXIS RAPID diffractometer
Absorption correction	Multi-scan (ABSCOR; Higashi, 1995)
T_min, T_max	0.655, 0.739
No. of measured, independent and observed [F² > 2σ(F²)] reflections	15777, 278, 268
R_int	0.032
(sin θ/λ)_max (Å⁻¹)	0.996

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.047, 0.136, 1.37
No. of reflections	278
No. of parameters	21
No. of restraints	?
H-atom treatment	H-atom parameters not defined
Δρ_max, Δρ_min (e Å⁻³)	0.59, −1.41

Computer programs: PROCESS-AUTO (Rigaku, 1998), CrystalStructure (Rigaku, 2007), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), VESTA (Momma & Izumi, 2006).

Selected geometric parameters (Å, º) top

Fe1—C1	1.918 (8)	N1—C1	1.169 (15)
Mn1—N1	2.105 (13)	Mn1—O1	2.247 (12)

O1—Mn1—O1ⁱ	87.8 (4)	O1—Mn1—N1^iv	78.69 (14)
O1—Mn1—O1ⁱⁱ	157.4 (3)	O1—Mn1—N1^v	163.90 (14)
O1—Mn1—O1ⁱⁱⁱ	180.0 (5)

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

Acknowledgements

This research was supported in part by a Grant for the Global COE Program for Chemistry Innovation, a Grant-in-Aid for Scientific Research in Priority Area `Chemistry of Coordination Space', a Grant-in-Aid for Scientific Research (B), and a Grant-in-Aid for Exploratory Research from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, the Asahi Glass Foundation, Iketani Science and Technology Foundation, Inamori Foundation, the Kurata Memorial Hitachi Science and Technology Foundation, the Murata Science Foundation and the Yamada Science Foundation.

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