research communications
trans-bis[2-(1H-benzotriazol-1-yl)acetato-κO]bis(ethanolamine-κ2N,O)copper(II)
ofaInstitute of General and Inorganic Chemistry of Uzbekistan Academy of Sciences, M.Ulugbek Str, 77a, Tashkent, bInstitute of Bioorganic Chemistry, Academy of Sciences of Uzbekistan, M. Ulugbek Str 83, Tashkent, cChemistry Department, National University of Uzbekistan, Tashkent, and dSamarkand State University 140104, University blv. 15, Samarkand, Samarkand region, Uzbekistan
*Correspondence e-mail: x-ray.uz@mail.ru
The reaction of 2-(1H-benzotriazol-1-yl)acetic acid (HBTA; C8H7N3O2) and monoethanolamine (MEA; C2H7NO) with CuCl2·2H2O resulted in the formation of the title complex, [Cu(C8H6N3O2)2(C2H7NO)2] or [Cu(BTA)2(MEA)2]. Its comprises one BTA anion coordinating to the Cu2+ cation (site symmetry ) through the carboxyl O atom, and one MEA ligand chelating the metal cation by two heteroatoms (O and N). The equatorial Cu—O and Cu—N bond lengths are similar at 2.029 (1) and 1.980 (2) Å, respectively, while the length of the axial Cu—O bond is considerably greater [2.492 (2) Å], as is typical for Jahn–Teller-distorted systems. An intramolecular hydrogen bond is present between the hydroxy group of the MEA ligand and the non-coordinating O atom of the carboxylate group. Intermolecular hydrogen bonding involving the amino function of the MEA ligand and the carboxylate group results in eight-membered rings with an R22(8) graph-set motif. The molecules are further linked by C—H⋯π interactions involving the triazole rings and methylene groups of MEA, thus generating an overall three-dimensional supramolecular framework.
Keywords: copper(II); crystal structure; benzotriazol; monoethanolamine; hydrogen bonding.
CCDC reference: 1891272
1. Chemical context
Recently, systematic studies of the structures and metal complex formation features of benzoic acid (Ibragimov et al., 2016a,b) and benzotriazole derivatives have been carried out by our group. Benzotriazoles consist of nitrogen-containing bicyclic ring systems and demonstrate many types of biological activities, such as antibacterial (Wan et al., 2010; Suma et al., 2012), antimicrobial (Nanjunda Swamy et al., 2006; Singh et al., 2009; Patel et al., 2012; Ramachandran et al., 2011), antifungal (Khabnadideh et al., 2012; Rezaei et al., 2009; Gaikwad et al., 2012; Rakesh et al., 2010), anticancer, anti-inflammatory, analgesic, antimalarial and antitubercular (Kopańska (née Zastąpiło) et al., 2004; Jamkhandi et al., 2015). Functional groups such as carboxylate, hydroxyl and pyridyl can be introduced to benzotriazole, increasing the coordination possibilities (Stoumpos et al., 2008; Wang et al., 2008a,b). The interaction of metal ions with HBTA results in the formation of complexes in which it demonstrates monodentate (Ma et al., 2015; Zeng et al., 2012; Wang et al., 2014a) coordination. HBTA also can show bridging (Li et al., 2016; Wang et al., 2014b) and catena-type (Wang et al., 2011, 2014b; Liu et al., 2012) coordination modes. The interaction of metal cations with MEA results in the formation of complexes in which MEA demonstrates monodentate (Hajji & Guerfel, 2016; Luo et al., 2012; Ren et al., 2014; Heinrich et al., 2012; Guzei et al., 2010a) and bidentate (Ibragimov et al., 2017; Seppälä et al., 2013; Yeşilel et al., 2012; Xue et al., 2016; Ashurov et al., 2015) coordination modes. In some complexes, MEA has bridging properties (Shahid et al., 2015; Tudor et al., 2013; Schwarz et al., 2010; Maclaren et al., 2012; Seppälä et al., 2012). In addition, there are metal complexes in which MEA molecules show non-coordinating behaviour (Wang et al., 2013; Lemmerer & Billing, 2010; Calderone et al., 2011; Yadav et al., 2015; Sutradhar et al., 2012; Liu et al., 2011).
We have reported the synthesis of mixed-ligand complexes of Cu and Zn with MEA and α-naphthylacetic acid (NAA) and determined the structures of [Cu (NAA)2(MEA)2] and [Zn(NAA)2(MEA)2] (Ashurov et al., 2015). A search in the Cambridge Structural Database (CSD Version 5.39, last update August 2018; Groom et al., 2016) revealed that crystal structures have been reported for complexes of HBTA and MEA with many metal ions. However, no mixed-ligand metal complex including HBTA and MEA is documented in the CSD. Here, the synthesis and structure of the title compound, [Cu(BTA)2(MEA)2], (I), is described.
2. Structural commentary
The molecular structure of trans-bis(ethanolamine-κ2N,O)bis[2-(1H-benzotriazol-1-yl)acetato-κO]copper(II), (I), is shown in Fig. 1 and consists of isolated [Cu(MEA)2(BTA)2] units. The Cu2+ cation is located on a center of inversion. Its is a distorted N2O4 octahedron formed by two oxygen atoms (O2) of the carboxy groups of symmetry-related BTA anions, by two nitrogen atoms (N4) of two symmetry-related MEA ligands in the equatorial plane and by two O atoms (O3) of the same set of MEA ligands in the axial positions. The Cu—O2 and Cu—N4 bond lengths are 2.029 (1) and 1.980 (2) Å, respectively, whereas the length of the axial Cu—O3 bond is 2.492 (2) Å, typical for Jahn–Teller distortions. The MEA ligand is neutral and acts as a bidentate N- and O-donor ligand and forms CuNC2O five-membered chelate rings which have a twist conformation; the O3—C10—C9—N4 torsion angle is −60.3 (3)°. The planar benzotriazole ring system (N1–N3/C1–C6: r.m.s. deviation = 0.0064 Å) is co-planar with the methyl carbon atom C7 [deviation from the plane of 0.158 (2) Å], whereas the carboxylate group is nearly normal to this plane [88.0 (2)°]. The difference of the C8—O(1,2) distances of the carboxylate group (Δ = 0.036 Å) is due to the monodentate coordination, with the longer C—O distance involving the coordinating O2 atom.
The molecular structure is stabilized by an intramolecular O3—H3⋯O1 hydrogen bond between the OH group of the MEA ligand and the non-coordinating carboxylate O atom (Fig. 1, Table 1).
3. Supramolecular features
In the , molecules are linked by C7—H7A⋯O1iii, N4—H4A⋯O2ii and N4—H4B⋯O3ii hydrogen bonds between the amino function and carboxylate/hydroxy O-atom acceptors (Table 1, Fig. 2), forming chains propagating parallel to [010]. Adjacent chains are linked by C9—H9A⋯N3iv hydrogen bonds into a layered arrangement parallel to (10) (Fig. 3). Additional C—H⋯π interactions between the triazole rings and methylene groups of MEA (H⋯Cg = 2.88, C—H⋯Cg = 140°, − x, + y, − z) generate a three-dimensional supramolecular framework.
of (I)4. Database survey
There are thirty-one structures of coordination compounds that are derived from 2-(1H-benzotriazol-1-yl)acetic acid and different metal cations in the CSD (Version 5.39, last update August 2018; Groom et al., 2016). The interaction of metal ions with BTA results in the formation of complexes in which metals demonstrate monodentate [CUYGAG (Ma et al., 2015), DUWQES (Zheng et al., 2010), LAMYUV (Zeng et al., 2012), TIVWOM (Wang et al., 2014b), TOBDUK (Hang & Ye, 2008)] and bridging [COHFOW (Ren et al., 2013), DEZHIB (Zeng, 2013), GADVEP (Li et al., 2016), TIVXAZ (Wang et al., 2014b)] coordination modes. BTA also can show catena-type structures [DEZHOH (Zeng, 2013), DUWQAO (Zheng et al., 2010), DUWQIW (Zheng et al., 2010), GUTZAX (Wang et al., 2009), IPAGIQ (Wang et al., 2011), TIVXED (Wang et al., 2014b), TIVXON (Wang et al., 2014b), UFETEF (Hu et al., 2008), YATPAM (Liu, 2012), ZIPLOB (Chen et al., 2010) etc]. In most cases, MEA behaves as a chelating ligand; however, there are metal complexes in which non-coordinating MEA molecules are situated in the outer coordination sphere [AXUQAN (Ibragimov et al., 2016c), FAFTOV (Spitsin et al., 1986), TIRQEQ (Halvorson et al., 1995), WUZZOH (Guzei et al., 2010b) etc]. Mixed-ligand metal complexes including BTA and MEA have not been reported in the CSD up to date.
5. Synthesis and crystallization
To an aqueous solution (2.5 ml) of CuCl2·2H2O (0.048 g, 0.282 mmol) was slowly added an ethanol solution (5 ml) containing MEA (0.034 g, 0.565 mmol) and HBTA (0.1 g, 0.565 mmol) under constant stirring. Blue crystals of the product were obtained by solvent evaporation at room temperature after one week. Yield: 70%. Elemental analysis: Calc. for C20H26CuN8O6 (538.04): C, 44.65; H, 4.87 N, 20.83%. Found: C, 44.73; H, 4.93; N, 20.88%.
6. Refinement
Crystal data, data collection and structure . The C-bound hydrogen atoms were placed in calculated positions and refined as riding atoms with C—H = 0.93 and 0.97 Å for aromatic and methylene hydrogen atoms, respectively, and with Uiso(H) = 1.2Ueq(C). The positions of the O- and N bound H atoms were located from a difference-Fourier map and were refined with soft distance restraints, 0.82 Å for the hydroxyl group and 0.95 Å for the primary amine group.
details are summarized in Table 2
|
Supporting information
CCDC reference: 1891272
https://doi.org/10.1107/S2056989019000744/wm5481sup1.cif
contains datablock I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989019000744/wm5481Isup2.hkl
Data collection: CrysAlis PRO (Rigaku OD, 2015); cell
CrysAlis PRO (Rigaku OD, 2015); data reduction: CrysAlis PRO (Rigaku OD, 2015); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015b); molecular graphics: Mercury (Macrae et al., 2006; software used to prepare material for publication: publCIF (Westrip, 2010).[Cu(C8H6N3O2)2(C2H7NO)2] | F(000) = 558 |
Mr = 538.03 | Dx = 1.489 Mg m−3 |
Monoclinic, P21/n | Cu Kα radiation, λ = 1.54184 Å |
a = 12.4283 (4) Å | Cell parameters from 3723 reflections |
b = 4.84866 (9) Å | θ = 3.7–75.7° |
c = 20.6944 (5) Å | µ = 1.75 mm−1 |
β = 105.823 (3)° | T = 293 K |
V = 1199.80 (5) Å3 | Block, blue |
Z = 2 | 0.36 × 0.22 × 0.12 mm |
Rigaku Xcalibur Ruby diffractometer | 2444 independent reflections |
Radiation source: fine-focus sealed X-ray tube | 2152 reflections with I > 2σ(I) |
Detector resolution: 10.2576 pixels mm-1 | Rint = 0.031 |
ω scans | θmax = 75.9°, θmin = 3.8° |
Absorption correction: multi-scan (CrysAlis PRO; Rigaku OD, 2015) | h = −15→15 |
Tmin = 0.558, Tmax = 1.000 | k = −5→5 |
8833 measured reflections | l = −20→25 |
Refinement on F2 | Hydrogen site location: mixed |
Least-squares matrix: full | H atoms treated by a mixture of independent and constrained refinement |
R[F2 > 2σ(F2)] = 0.033 | w = 1/[σ2(Fo2) + (0.048P)2 + 0.364P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.096 | (Δ/σ)max < 0.001 |
S = 1.06 | Δρmax = 0.24 e Å−3 |
2444 reflections | Δρmin = −0.31 e Å−3 |
173 parameters | Extinction correction: SHELXL2014 (Sheldrick, 2015b), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
3 restraints | Extinction coefficient: 0.0009 (2) |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Cu | 0.5000 | 0.5000 | 0.5000 | 0.03515 (14) | |
O2 | 0.53163 (12) | 0.2852 (3) | 0.58733 (6) | 0.0434 (3) | |
O3 | 0.66203 (12) | 0.2720 (3) | 0.47288 (7) | 0.0449 (3) | |
O1 | 0.46322 (14) | 0.5886 (3) | 0.64711 (7) | 0.0535 (4) | |
N1 | 0.56782 (14) | 0.3490 (4) | 0.76528 (8) | 0.0420 (4) | |
N4 | 0.62260 (16) | 0.7586 (3) | 0.54159 (8) | 0.0432 (4) | |
N3 | 0.60695 (19) | 0.6560 (5) | 0.84410 (10) | 0.0659 (6) | |
C7 | 0.57879 (18) | 0.2195 (5) | 0.70430 (9) | 0.0458 (5) | |
H7A | 0.5484 | 0.0342 | 0.7013 | 0.055* | |
H7B | 0.6574 | 0.2054 | 0.7061 | 0.055* | |
N2 | 0.64071 (17) | 0.5465 (5) | 0.79544 (10) | 0.0582 (5) | |
C8 | 0.51797 (16) | 0.3819 (4) | 0.64159 (9) | 0.0383 (4) | |
C3 | 0.50966 (19) | 0.5287 (5) | 0.84514 (11) | 0.0494 (5) | |
C2 | 0.48288 (17) | 0.3334 (4) | 0.79457 (10) | 0.0430 (4) | |
C10 | 0.74518 (19) | 0.4794 (5) | 0.49439 (13) | 0.0568 (6) | |
H10A | 0.7391 | 0.6123 | 0.4585 | 0.068* | |
H10B | 0.8187 | 0.3956 | 0.5041 | 0.068* | |
C9 | 0.73262 (19) | 0.6246 (5) | 0.55560 (12) | 0.0557 (5) | |
H9A | 0.7405 | 0.4930 | 0.5919 | 0.067* | |
H9B | 0.7910 | 0.7621 | 0.5696 | 0.067* | |
C1 | 0.3878 (2) | 0.1733 (5) | 0.78222 (14) | 0.0628 (6) | |
H1 | 0.3704 | 0.0434 | 0.7479 | 0.075* | |
C4 | 0.4385 (3) | 0.5704 (7) | 0.88710 (14) | 0.0763 (8) | |
H4 | 0.4549 | 0.7005 | 0.9214 | 0.092* | |
C6 | 0.3200 (3) | 0.2185 (7) | 0.82423 (19) | 0.0817 (9) | |
H6 | 0.2551 | 0.1146 | 0.8180 | 0.098* | |
C5 | 0.3452 (3) | 0.4120 (7) | 0.87504 (19) | 0.0849 (10) | |
H5 | 0.2967 | 0.4345 | 0.9018 | 0.102* | |
H4A | 0.609 (2) | 0.836 (6) | 0.5773 (10) | 0.078 (9)* | |
H4B | 0.623 (2) | 0.895 (4) | 0.5130 (11) | 0.063 (7)* | |
H3 | 0.6329 (19) | 0.295 (5) | 0.4336 (6) | 0.055 (7)* |
U11 | U22 | U33 | U12 | U13 | U23 | |
Cu | 0.0477 (2) | 0.0285 (2) | 0.0312 (2) | 0.00425 (15) | 0.01401 (15) | 0.00123 (13) |
O2 | 0.0614 (9) | 0.0372 (7) | 0.0338 (6) | 0.0079 (6) | 0.0165 (6) | 0.0036 (5) |
O3 | 0.0546 (8) | 0.0376 (7) | 0.0420 (7) | 0.0017 (6) | 0.0123 (6) | 0.0019 (6) |
O1 | 0.0741 (10) | 0.0485 (8) | 0.0375 (7) | 0.0204 (8) | 0.0144 (7) | 0.0023 (6) |
N1 | 0.0441 (9) | 0.0473 (10) | 0.0336 (8) | −0.0002 (7) | 0.0088 (6) | 0.0049 (7) |
N4 | 0.0584 (10) | 0.0309 (9) | 0.0406 (9) | 0.0015 (7) | 0.0143 (8) | −0.0008 (7) |
N3 | 0.0681 (13) | 0.0681 (14) | 0.0559 (11) | −0.0137 (11) | 0.0077 (10) | −0.0147 (10) |
C7 | 0.0558 (12) | 0.0469 (11) | 0.0350 (9) | 0.0103 (9) | 0.0130 (8) | 0.0053 (8) |
N2 | 0.0507 (11) | 0.0671 (13) | 0.0535 (11) | −0.0122 (9) | 0.0085 (8) | −0.0018 (9) |
C8 | 0.0472 (10) | 0.0361 (10) | 0.0322 (8) | 0.0001 (8) | 0.0119 (7) | 0.0025 (7) |
C3 | 0.0562 (12) | 0.0505 (13) | 0.0401 (10) | 0.0043 (10) | 0.0109 (9) | 0.0045 (9) |
C2 | 0.0446 (10) | 0.0441 (11) | 0.0385 (9) | 0.0040 (8) | 0.0082 (8) | 0.0103 (8) |
C10 | 0.0449 (11) | 0.0573 (14) | 0.0721 (15) | −0.0031 (10) | 0.0227 (11) | −0.0066 (11) |
C9 | 0.0502 (12) | 0.0472 (13) | 0.0611 (13) | −0.0009 (10) | 0.0009 (10) | −0.0049 (10) |
C1 | 0.0580 (14) | 0.0556 (15) | 0.0722 (15) | −0.0095 (11) | 0.0133 (12) | 0.0092 (12) |
C4 | 0.105 (2) | 0.0715 (18) | 0.0614 (15) | 0.0215 (17) | 0.0369 (16) | 0.0050 (13) |
C6 | 0.0641 (16) | 0.0718 (19) | 0.121 (3) | 0.0015 (14) | 0.0447 (17) | 0.0307 (19) |
C5 | 0.087 (2) | 0.082 (2) | 0.105 (2) | 0.0210 (18) | 0.060 (2) | 0.0341 (19) |
Cu—N4i | 1.9798 (18) | C7—H7A | 0.9700 |
Cu—N4 | 1.9798 (18) | C7—H7B | 0.9700 |
Cu—O2 | 2.0292 (12) | C3—C2 | 1.383 (3) |
Cu—O2i | 2.0293 (12) | C3—C4 | 1.413 (4) |
Cu—O3i | 2.4917 (15) | C2—C1 | 1.378 (3) |
O2—C8 | 1.270 (2) | C10—C9 | 1.494 (3) |
O3—C10 | 1.424 (3) | C10—H10A | 0.9700 |
O3—H3 | 0.802 (10) | C10—H10B | 0.9700 |
O1—C8 | 1.234 (2) | C9—H9A | 0.9700 |
N1—N2 | 1.349 (3) | C9—H9B | 0.9700 |
N1—C2 | 1.355 (3) | C1—C6 | 1.383 (4) |
N1—C7 | 1.449 (2) | C1—H1 | 0.9300 |
N4—C9 | 1.470 (3) | C4—C5 | 1.356 (5) |
N4—H4A | 0.885 (10) | C4—H4 | 0.9300 |
N4—H4B | 0.887 (10) | C6—C5 | 1.380 (5) |
N3—N2 | 1.305 (3) | C6—H6 | 0.9300 |
N3—C3 | 1.363 (3) | C5—H5 | 0.9300 |
C7—C8 | 1.530 (3) | ||
N4i—Cu—N4 | 180.0 | N3—C3—C4 | 130.7 (3) |
N4i—Cu—O2 | 90.08 (6) | C2—C3—C4 | 120.1 (2) |
N4—Cu—O2 | 89.92 (6) | N1—C2—C3 | 104.13 (18) |
N4i—Cu—O2i | 89.92 (6) | N1—C2—C1 | 132.9 (2) |
N4—Cu—O2i | 90.08 (6) | C3—C2—C1 | 122.9 (2) |
O2—Cu—O2i | 180.0 | O3—C10—C9 | 111.30 (18) |
C8—O2—Cu | 123.91 (12) | O3—C10—H10A | 109.4 |
C10—O3—H3 | 107.8 (19) | C9—C10—H10A | 109.4 |
N2—N1—C2 | 109.84 (17) | O3—C10—H10B | 109.4 |
N2—N1—C7 | 120.00 (17) | C9—C10—H10B | 109.4 |
C2—N1—C7 | 129.44 (18) | H10A—C10—H10B | 108.0 |
C9—N4—Cu | 111.72 (13) | N4—C9—C10 | 110.35 (18) |
C9—N4—H4A | 113.6 (19) | N4—C9—H9A | 109.6 |
Cu—N4—H4A | 110 (2) | C10—C9—H9A | 109.6 |
C9—N4—H4B | 106.4 (17) | N4—C9—H9B | 109.6 |
Cu—N4—H4B | 109.1 (18) | C10—C9—H9B | 109.6 |
H4A—N4—H4B | 106 (3) | H9A—C9—H9B | 108.1 |
N2—N3—C3 | 107.5 (2) | C2—C1—C6 | 115.6 (3) |
N1—C7—C8 | 111.94 (16) | C2—C1—H1 | 122.2 |
N1—C7—H7A | 109.2 | C6—C1—H1 | 122.2 |
C8—C7—H7A | 109.2 | C5—C4—C3 | 116.9 (3) |
N1—C7—H7B | 109.2 | C5—C4—H4 | 121.5 |
C8—C7—H7B | 109.2 | C3—C4—H4 | 121.5 |
H7A—C7—H7B | 107.9 | C5—C6—C1 | 122.4 (3) |
N3—N2—N1 | 109.23 (18) | C5—C6—H6 | 118.8 |
O1—C8—O2 | 126.26 (17) | C1—C6—H6 | 118.8 |
O1—C8—C7 | 119.79 (16) | C4—C5—C6 | 122.0 (3) |
O2—C8—C7 | 113.94 (17) | C4—C5—H5 | 119.0 |
N3—C3—C2 | 109.3 (2) | C6—C5—H5 | 119.0 |
N2—N1—C7—C8 | −86.8 (2) | C7—N1—C2—C1 | 8.5 (4) |
C2—N1—C7—C8 | 82.4 (3) | N3—C3—C2—N1 | 0.9 (2) |
C3—N3—N2—N1 | −0.6 (3) | C4—C3—C2—N1 | −179.9 (2) |
C2—N1—N2—N3 | 1.2 (2) | N3—C3—C2—C1 | −178.9 (2) |
C7—N1—N2—N3 | 172.31 (19) | C4—C3—C2—C1 | 0.3 (3) |
Cu—O2—C8—O1 | 16.3 (3) | Cu—N4—C9—C10 | 50.9 (2) |
Cu—O2—C8—C7 | −162.68 (14) | O3—C10—C9—N4 | −60.3 (3) |
N1—C7—C8—O1 | −3.5 (3) | N1—C2—C1—C6 | 179.8 (2) |
N1—C7—C8—O2 | 175.61 (17) | C3—C2—C1—C6 | −0.4 (3) |
N2—N3—C3—C2 | −0.2 (3) | N3—C3—C4—C5 | 179.0 (3) |
N2—N3—C3—C4 | −179.3 (3) | C2—C3—C4—C5 | −0.1 (4) |
N2—N1—C2—C3 | −1.2 (2) | C2—C1—C6—C5 | 0.4 (4) |
C7—N1—C2—C3 | −171.29 (19) | C3—C4—C5—C6 | 0.0 (5) |
N2—N1—C2—C1 | 178.6 (2) | C1—C6—C5—C4 | −0.1 (5) |
Symmetry code: (i) −x+1, −y+1, −z+1. |
D—H···A | D—H | H···A | D···A | D—H···A |
O3—H3···O1i | 0.80 (1) | 1.86 (1) | 2.634 (2) | 163 (3) |
N4—H4A···O2ii | 0.89 (1) | 2.41 (2) | 3.046 (2) | 129 (2) |
N4—H4B···O3ii | 0.89 (1) | 2.12 (1) | 2.973 (2) | 161 (2) |
C7—H7A···O1iii | 0.97 | 2.53 | 3.449 (3) | 158 |
C9—H9A···N3iv | 0.97 | 2.58 | 3.345 (3) | 136 |
Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x, y+1, z; (iii) x, y−1, z; (iv) −x+3/2, y−1/2, −z+3/2. |
Funding information
This work was supported by a Grant for Fundamental Research of the Center of Science and Technology, Uzbekistan (No. BA-FA– F7–004).
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