inorganic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 2056-9890

Tetra­ammine-2κ4C-μ-cyanido-1:2κ2C:N-tricyanido-1κ3C-copper(II)palladium(II)

aDepartment of Inorganic Chemistry, Institute of Chemistry, P.J. Šafárik University in Košice, Moyzesova 11, 041 54 Košice, Slovakia, and bFachbereich Chemie der Philipps Universität, Hans-Meerwein-Strasse, D-35043 Marburg, Germany
*Correspondence e-mail: juraj.kuchar@upjs.sk

(Received 17 April 2013; accepted 23 April 2013; online 30 April 2013)

The title compound, [Cu(NH3)4-(μ2-NC)—Pd(CN)3], is a binuclear copper(II)palladium(II) complex, in which the CuII coordination is defined by four ammine ligands and one bridging cyanide ligand. The Cu—N bond lengths in the base of the resulting CuN5 pyramid are in the range 2.016 (3)–2.024 (3) Å and the apical Cu—N(≡C) distance is 2.385 (4) Å. Based on the τ parameter, the shape of the coordination polyhedron is tetra­gonal–pyramidal (τ = 0). All atoms of the square-planar tetracyanidopalladate(II) moiety and the CuII ion are located on a mirror plane. The electroneutral mol­ecules inter­act by N—H⋯N hydrogen bonds, resulting in the formation of a three-dimensional network.

Related literature

For related crystal structures of CuII complexes see: Escorihuela et al. (2001[Escorihuela, I., Falvello, L. R. & Tomás, M. (2001). Inorg. Chem. 40, 636-640.]); Seitz et al. (2001[Seitz, K., Peschel, S. & Babel, D. (2001). Z. Anorg. Allg. Chem. 627, 929-934.]); Kuchár et al. (2004[Kuchár, J., Černák, J. & Abboud, K. A. (2004). Acta Cryst. C60, m492-m494.]). For additional analysis of structural parameters, see: Addison et al. (1984[Addison, A. W., Rao, T. N., Reedijk, J., van Rijn, J. & Verschoor, G. C. (1984). J. Chem. Soc. Dalton Trans. pp. 349-1356.]).

[Scheme 1]

Experimental

Crystal data
  • [CuPd(CN)4(NH3)4]

  • Mr = 342.17

  • Orthorhombic, P n m a

  • a = 14.5204 (9) Å

  • b = 7.2358 (5) Å

  • c = 10.3955 (6) Å

  • V = 1092.22 (12) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 3.57 mm−1

  • T = 100 K

  • 0.3 × 0.1 × 0.1 mm

Data collection
  • Stoe IPDS-II diffractometer

  • Absorption correction: multi-scan (Blessing, 1995[Blessing, R. H. (1995). Acta Cryst. A51, 33-38.]) Tmin = 0.332, Tmax = 0.646

  • 4036 measured reflections

  • 1051 independent reflections

  • 958 reflections with I > 2σ(I)

  • Rint = 0.032

Refinement
  • R[F2 > 2σ(F2)] = 0.025

  • wR(F2) = 0.061

  • S = 1.00

  • 1051 reflections

  • 81 parameters

  • H-atom parameters constrained

  • Δρmax = 0.54 e Å−3

  • Δρmin = −1.26 e Å−3

Table 1
Selected bond lengths (Å)

Pd1—C4 1.985 (5)
Pd1—C2 1.992 (5)
Pd1—C3 1.994 (5)
Pd1—C1 2.005 (5)
Cu1—N6 2.016 (3)
Cu1—N5 2.024 (3)
Cu1—N4 2.385 (4)

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N5—H5A⋯N1 0.91 2.34 3.237 (4) 167
N5—H5C⋯N3i 0.91 2.39 3.267 (4) 162
N5—H5B⋯N3ii 0.91 2.65 3.180 (4) 118
N5—H5B⋯N4iii 0.91 2.52 3.297 (4) 144
N6—H6B⋯N1ii 0.91 2.53 3.131 (4) 124
N6—H6B⋯N2iii 0.91 2.58 3.348 (4) 142
N6—H6A⋯N3i 0.91 2.31 3.199 (4) 165
Symmetry codes: (i) -x+1, -y+1, -z; (ii) [x+{\script{1\over 2}}, y, -z-{\script{1\over 2}}]; (iii) [-x+{\script{3\over 2}}, -y+1, z-{\script{1\over 2}}].

Data collection: X-AREA (Stoe & Cie, 2002[Stoe & Cie (2002). X-AREA. Stoe & Cie, Darmstadt, Germany.]); cell refinement: X-AREA; data reduction: X-AREA; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: DIAMOND (Crystal Impact, 2009[Crystal Impact (2009). DIAMOND. Crystal Impact GbR, Bonn, Germany.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

The compound [Cu(NH3)4-(µ2-CN)—Pd(CN)3] (1) is formed by [Pd(CN)4]2- and [Cu(NH3)4]2+ units held together by a bridging CN group (Fig. 1). In the solid state, the [Pd(CN)4]2- anion is located on a mirror plane, while from cation only copper(II) atom lies on it and the [Cu(NH3)4]2+ group is bisected by this crystallographic symmetry plane. All of the atoms except those of the NH3 ligands reside on special positions. The Pd(II) atom is coordinated by four cyanido ligands and the Cu(II) atom is coordinated by four NH3 groups and one CN bridging ligand forming a square pyramid around copper(II) (τ = 0). The distance Cu—N4, from copper to the nitrogen atom of the bridging cyanido ligand, has a value of 2.385 (4) Å and is larger than bonds between copper(II) and nitrogen atoms from ammin ligand (2.016 (3) and 2.024 (3) Å). For example this distance can be compared to the Cu—N(apical) distance of 2.394 (7) Å found in [Cu(NH3)4Pt(CN)4] (Escorihuela et al., 2001). This bond is perpendicular to the CuN4 plane, as expected for square-based pyramidal coordination environment. The Pd—C(bridge) distance (1.985 (5) Å) is smaller than Pd—C(terminal) distances, but the difference is within experimental error (1.992 (5)–2.005 (5) Å). The molecules are packed in such a way that the [Pd(CN)4] groups are stacked, with the Pd atoms forming nearly linear chain with a Pd···Pd distance of 3.654 (1) Å and a Pd···Pd···Pd angle of 163.97 (1)°. It is noteworthy that Cu—NC angle, which has values of 122.5 (4)°, should be collinear with the triple bond, but based on our previous study of the similar compounds observed angle is not uncommon in such compounds. For example, the Cu—N C angle in [Cu(en)2Ni(CN)4]n is 123.1 (1)°, with a Cu—N distance of 2.492 (3) Å (Seitz et al., 2001) and [Cu(dmen)2Pd(CN)4]n has Cu—NC angle of 138.0 (1)°, with corresponding Cu—N distance of 2.537 (1) Å (Kuchár et al., 2004). An explanation for the bended structure of [Cu(NH3)4-(µ2-CN)—Pd(CN)3] is revealed by the extensive network of the intra- and intermolecular interactions in which the complex participates (see Table 1, Fig. 2). Each nitrogen atom of the terminal cyanide groups is involved in at least two crystallographically unique interactions, one with an N—H···N angle greater than 150° and the other corresponding to the bifurcated hydrogen. Moreover, since the CN groups reside on mirror planes and the donor atoms do not, the total number of interactions in which the CN ligand acts as an acceptor is at least 4 for each nonbridging cyanide. It is obvious that this three-dimensional electrostatic net plays an important role in establishing the deformation observed in the Cu—NC angle.

Related literature top

For related crystal structures of CuII complexes see: Escorihuela et al. (2001); Seitz et al. (2001); Kuchár et al. (2004). For additional structural analysis, see: Addison et al. (1984).

Experimental top

To 10 cm3 of 0.1 M CuSO4 solution (1 mmol) under continuous stirring 10 cm3 of 0.1 M butane-1,4-diamine solution (1 mmol) was added, followed by addition of 10 ml of 0.1 M K2[Pd(CN)4] solution (1 mmol). Created insoluble precipitate was dissolved by addition of ammonium hydroxide in excess amount. The formed clear blue solution was left for crystallization at room temperature. Single crystals of 1, in the form of blue needles suitable for X-ray studies, appeared after one day. As the crystals lost transparency and color upon being removed from solution in short time, the crystal used for X-ray was removed from solution without washing and drying and put on diffractometer. Attempt for direct preparation (without butane-1,4-diamine) does not produce any suitable product for X-ray. Elemental analysis was not performed because of the behavior of the product in the absence of ambient ammonia. The IR-spectrum in form of KBr pellets was recorded on a Avatar 330 F T—IR spectrophotometer (Thermo Nicolet) and following absorption bands were observed (4000–400 cm-1, s = strong, m = medium, w = weak, v = very): ν(NH): 3360(vs), 3273(vs), 3182(s); ν(CN): 2179(s), 2156(m), 2148(s), 2133(vs); δ(NH2): 1618(m); δ(NH3): 1280(m), 1263(s); δ(NH2): 696(s); δ(Pd—CN): 402(s).

Refinement top

The structure was solved by direct method. Anisotropic thermal parameters were refined for all non-H atoms. All H atoms positions were calculated using the appropriate riding model with isotropic temperature factors being 1.5 times larger then temperature factors of their parent nitrogen atoms and with N—H = 0.910 Å. Geometrical analysis was performed using SHELXL97 (Sheldrick, 2008).

Structure description top

The compound [Cu(NH3)4-(µ2-CN)—Pd(CN)3] (1) is formed by [Pd(CN)4]2- and [Cu(NH3)4]2+ units held together by a bridging CN group (Fig. 1). In the solid state, the [Pd(CN)4]2- anion is located on a mirror plane, while from cation only copper(II) atom lies on it and the [Cu(NH3)4]2+ group is bisected by this crystallographic symmetry plane. All of the atoms except those of the NH3 ligands reside on special positions. The Pd(II) atom is coordinated by four cyanido ligands and the Cu(II) atom is coordinated by four NH3 groups and one CN bridging ligand forming a square pyramid around copper(II) (τ = 0). The distance Cu—N4, from copper to the nitrogen atom of the bridging cyanido ligand, has a value of 2.385 (4) Å and is larger than bonds between copper(II) and nitrogen atoms from ammin ligand (2.016 (3) and 2.024 (3) Å). For example this distance can be compared to the Cu—N(apical) distance of 2.394 (7) Å found in [Cu(NH3)4Pt(CN)4] (Escorihuela et al., 2001). This bond is perpendicular to the CuN4 plane, as expected for square-based pyramidal coordination environment. The Pd—C(bridge) distance (1.985 (5) Å) is smaller than Pd—C(terminal) distances, but the difference is within experimental error (1.992 (5)–2.005 (5) Å). The molecules are packed in such a way that the [Pd(CN)4] groups are stacked, with the Pd atoms forming nearly linear chain with a Pd···Pd distance of 3.654 (1) Å and a Pd···Pd···Pd angle of 163.97 (1)°. It is noteworthy that Cu—NC angle, which has values of 122.5 (4)°, should be collinear with the triple bond, but based on our previous study of the similar compounds observed angle is not uncommon in such compounds. For example, the Cu—N C angle in [Cu(en)2Ni(CN)4]n is 123.1 (1)°, with a Cu—N distance of 2.492 (3) Å (Seitz et al., 2001) and [Cu(dmen)2Pd(CN)4]n has Cu—NC angle of 138.0 (1)°, with corresponding Cu—N distance of 2.537 (1) Å (Kuchár et al., 2004). An explanation for the bended structure of [Cu(NH3)4-(µ2-CN)—Pd(CN)3] is revealed by the extensive network of the intra- and intermolecular interactions in which the complex participates (see Table 1, Fig. 2). Each nitrogen atom of the terminal cyanide groups is involved in at least two crystallographically unique interactions, one with an N—H···N angle greater than 150° and the other corresponding to the bifurcated hydrogen. Moreover, since the CN groups reside on mirror planes and the donor atoms do not, the total number of interactions in which the CN ligand acts as an acceptor is at least 4 for each nonbridging cyanide. It is obvious that this three-dimensional electrostatic net plays an important role in establishing the deformation observed in the Cu—NC angle.

For related crystal structures of CuII complexes see: Escorihuela et al. (2001); Seitz et al. (2001); Kuchár et al. (2004). For additional structural analysis, see: Addison et al. (1984).

Computing details top

Data collection: X-AREA (Stoe & Cie, 2002); cell refinement: X-AREA (Stoe & Cie, 2002); data reduction: X-AREA (Stoe & Cie, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Crystal Impact, 2009); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. Molecular structure of the title molecule 1 with the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level. Symmetry codes: i: 1 - x, -y, -z
[Figure 2] Fig. 2. View on the intermolecular hydrogen bonds (dashed lines) of 1. Symmetry codes: i: 1 - x, 0.5 + y, 0.5 - z; ii: 0.5 + x, 0.5 - y, -0.5 - z; iii: 1.5 - x, 1- y, -0.5 + z
Tetraammine-2κ4C-µ-cyanido-1:2κ2C:N-tricyanido-1κ3C-copper(II)palladium(II) top
Crystal data top
[CuPd(CN)4(NH3)4]F(000) = 668
Mr = 342.17Dx = 2.081 Mg m3
Orthorhombic, PnmaMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2nCell parameters from 1245 reflections
a = 14.5204 (9) Åθ = 2.4–26.7°
b = 7.2358 (5) ŵ = 3.57 mm1
c = 10.3955 (6) ÅT = 100 K
V = 1092.22 (12) Å3Needle, blue
Z = 40.3 × 0.1 × 0.1 mm
Data collection top
Stoe IPDS-II
diffractometer
1051 independent reflections
Radiation source: fine-focus sealed tube958 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.032
Detector resolution: 150 pixels mm-1θmax = 25.0°, θmin = 2.4°
ω scansh = 1617
Absorption correction: multi-scan
(Blessing, 1995)
k = 88
Tmin = 0.332, Tmax = 0.646l = 1012
4036 measured reflections
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.025Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.061H-atom parameters constrained
S = 1.00 w = 1/[σ2(Fo2) + (0.0469P)2]
where P = (Fo2 + 2Fc2)/3
1051 reflections(Δ/σ)max = 0.001
81 parametersΔρmax = 0.54 e Å3
0 restraintsΔρmin = 1.26 e Å3
Crystal data top
[CuPd(CN)4(NH3)4]V = 1092.22 (12) Å3
Mr = 342.17Z = 4
Orthorhombic, PnmaMo Kα radiation
a = 14.5204 (9) ŵ = 3.57 mm1
b = 7.2358 (5) ÅT = 100 K
c = 10.3955 (6) Å0.3 × 0.1 × 0.1 mm
Data collection top
Stoe IPDS-II
diffractometer
1051 independent reflections
Absorption correction: multi-scan
(Blessing, 1995)
958 reflections with I > 2σ(I)
Tmin = 0.332, Tmax = 0.646Rint = 0.032
4036 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0250 restraints
wR(F2) = 0.061H-atom parameters constrained
S = 1.00Δρmax = 0.54 e Å3
1051 reflectionsΔρmin = 1.26 e Å3
81 parameters
Special details top

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
xyzUiso*/Ueq
Pd10.48951 (2)0.25000.01963 (3)0.01617 (14)
Cu10.80131 (4)0.25000.13557 (5)0.01636 (17)
N10.5331 (3)0.25000.2768 (4)0.0219 (8)
N20.4665 (3)0.25000.3197 (4)0.0245 (8)
N30.2732 (3)0.25000.0018 (4)0.0199 (8)
N40.7043 (3)0.25000.0495 (4)0.0204 (8)
C10.5119 (3)0.25000.1707 (5)0.0204 (10)
C20.4741 (3)0.25000.2100 (5)0.0198 (9)
C30.3529 (3)0.25000.0004 (4)0.0189 (9)
C40.6252 (3)0.25000.0423 (4)0.0193 (9)
N50.73048 (18)0.4477 (4)0.2315 (3)0.0201 (5)
H5A0.67490.40190.25630.030*
H5B0.76300.48310.30220.030*
H5C0.72170.54690.17910.030*
N60.88190 (18)0.4483 (3)0.0588 (3)0.0201 (5)
H6A0.84700.54920.04000.030*
H6B0.92650.48010.11620.030*
H6C0.90860.40500.01450.030*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pd10.0149 (2)0.01665 (19)0.0170 (2)0.0000.00032 (13)0.000
Cu10.0168 (3)0.0143 (2)0.0180 (3)0.0000.0003 (2)0.000
N10.022 (2)0.0249 (18)0.019 (2)0.0000.0015 (18)0.000
N20.026 (2)0.0241 (18)0.023 (2)0.0000.0010 (19)0.000
N30.020 (2)0.0185 (17)0.021 (2)0.0000.0030 (17)0.000
N40.018 (2)0.0222 (17)0.021 (2)0.0000.0015 (16)0.000
C10.014 (2)0.017 (2)0.029 (3)0.0000.005 (2)0.000
C20.015 (2)0.0184 (19)0.026 (3)0.0000.000 (2)0.000
C30.024 (3)0.0148 (18)0.018 (2)0.0000.002 (2)0.000
C40.028 (3)0.0125 (18)0.017 (2)0.0000.001 (2)0.000
N50.0212 (13)0.0188 (11)0.0201 (13)0.0018 (11)0.0011 (11)0.0012 (10)
N60.0178 (13)0.0198 (11)0.0227 (13)0.0003 (10)0.0023 (11)0.0009 (11)
Geometric parameters (Å, º) top
Pd1—C41.985 (5)N2—C21.145 (6)
Pd1—C21.992 (5)N3—C31.157 (6)
Pd1—C31.994 (5)N4—C41.150 (6)
Pd1—C12.005 (5)N5—H5A0.9100
Cu1—N62.016 (3)N5—H5B0.9100
Cu1—N6i2.016 (3)N5—H5C0.9100
Cu1—N5i2.024 (3)N6—H6A0.9100
Cu1—N52.024 (3)N6—H6B0.9100
Cu1—N42.385 (4)N6—H6C0.9100
N1—C11.146 (7)
C4—Pd1—C289.63 (18)N1—C1—Pd1173.7 (4)
C4—Pd1—C3178.93 (18)N2—C2—Pd1179.1 (4)
C2—Pd1—C389.31 (17)N3—C3—Pd1175.4 (4)
C4—Pd1—C187.49 (17)N4—C4—Pd1176.9 (4)
C2—Pd1—C1177.11 (17)Cu1—N5—H5A109.5
C3—Pd1—C193.58 (17)Cu1—N5—H5B109.5
N6—Cu1—N6i90.73 (15)H5A—N5—H5B109.5
N6—Cu1—N5i173.08 (11)Cu1—N5—H5C109.5
N6i—Cu1—N5i89.26 (11)H5A—N5—H5C109.5
N6—Cu1—N589.26 (11)H5B—N5—H5C109.5
N6i—Cu1—N5173.08 (11)Cu1—N6—H6A109.5
N5i—Cu1—N589.91 (15)Cu1—N6—H6B109.5
N6—Cu1—N491.35 (10)H6A—N6—H6B109.5
N6i—Cu1—N491.35 (10)Cu1—N6—H6C109.5
N5i—Cu1—N495.57 (10)H6A—N6—H6C109.5
N5—Cu1—N495.57 (10)H6B—N6—H6C109.5
C4—N4—Cu1122.5 (4)
N6—Cu1—N4—C4134.62 (7)N5i—Cu1—N4—C445.23 (8)
N6i—Cu1—N4—C4134.62 (7)N5—Cu1—N4—C445.23 (8)
Symmetry code: (i) x, y+1/2, z.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N5—H5A···N10.912.343.237 (4)167
N5—H5C···N3ii0.912.393.267 (4)162
N5—H5B···N3iii0.912.653.180 (4)118
N5—H5B···N4iv0.912.523.297 (4)144
N6—H6B···N1iii0.912.533.131 (4)124
N6—H6B···N2iv0.912.583.348 (4)142
N6—H6A···N3ii0.912.313.199 (4)165
Symmetry codes: (ii) x+1, y+1, z; (iii) x+1/2, y, z1/2; (iv) x+3/2, y+1, z1/2.

Experimental details

Crystal data
Chemical formula[CuPd(CN)4(NH3)4]
Mr342.17
Crystal system, space groupOrthorhombic, Pnma
Temperature (K)100
a, b, c (Å)14.5204 (9), 7.2358 (5), 10.3955 (6)
V3)1092.22 (12)
Z4
Radiation typeMo Kα
µ (mm1)3.57
Crystal size (mm)0.3 × 0.1 × 0.1
Data collection
DiffractometerStoe IPDS-II
Absorption correctionMulti-scan
(Blessing, 1995)
Tmin, Tmax0.332, 0.646
No. of measured, independent and
observed [I > 2σ(I)] reflections
4036, 1051, 958
Rint0.032
(sin θ/λ)max1)0.594
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.025, 0.061, 1.00
No. of reflections1051
No. of parameters81
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.54, 1.26

Computer programs: X-AREA (Stoe & Cie, 2002), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Crystal Impact, 2009).

Selected bond lengths (Å) top
Pd1—C41.985 (5)Cu1—N62.016 (3)
Pd1—C21.992 (5)Cu1—N52.024 (3)
Pd1—C31.994 (5)Cu1—N42.385 (4)
Pd1—C12.005 (5)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N5—H5A···N10.912.343.237 (4)167.4
N5—H5C···N3i0.912.393.267 (4)162.3
N5—H5B···N3ii0.912.653.180 (4)118.1
N5—H5B···N4iii0.912.523.297 (4)144.0
N6—H6B···N1ii0.912.533.131 (4)123.8
N6—H6B···N2iii0.912.583.348 (4)142.0
N6—H6A···N3i0.912.313.199 (4)164.7
Symmetry codes: (i) x+1, y+1, z; (ii) x+1/2, y, z1/2; (iii) x+3/2, y+1, z1/2.
 

Acknowledgements

Financial support by the Slovak Ministry of Education (VEGA project No. 1/0075/13) and APVV-0132–11 is gratefully acknowledged.

References

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