metal-organic compounds
Chloridobis[2-(pyridin-2-yl-κN)benzo[b][1,5]naphthyridine-κN1]copper(II) perchlorate acetonitrile disolvate
aGraduate School of Science and Engineering, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan, and bInstitute for Integrated Cell-Material Science (iCeMS), Kyoto University, Advanced Chemical Technology Center in Kyoto, 105 Jibu-cho, Fushimi-ku, Kyoto, 612-8374, Japan
*Correspondence e-mail: ohtsu@sci.u-toyama.ac.jp
The copper(II) ion in the title complex, [CuCl(C17H11N3)2]ClO4·2CH3CN, is coordinated by four N atoms from two pbn ligands and one Cl− ion in a distorted trigonal–bipyramidal geometry (τ = 0.84). The comprises half of the cationic complex molecule, and complete molecules are generated by twofold rotation symmetry with the corresponding axis running through the Cu atom and the coordinating Cl atom. The perchlorate anion is also located on a twofold rotation axis (passing through the Cl atom). In the crystal, there are π–π stacking interactions between the benzonaphthyridine rings of the pbn ligand of neighbouring cations.
CCDC reference: 1504744
Structure description
Understanding the relationship between coordination geometry and reactivity of complexes containing the NAD+/NADH-analogous ligand pbn [pbn = 2-(pyridin-2-yl)benzo[b][1,5]naphthyridine] is of great interest and importance in order to develop a photorenewable hydride reagent. In our previous studies, photocatalytic CO2 reduction using the pbn complex has proved to be successful (Ohtsu & Tanaka, 2012), and control over the reaction rate of the CO2 hydride reduction using a pbn complex has been accomplished by tuning of the basicity of the bases (Ohtsu et al., 2015). As part of our ongoing research on transition-metal complexes containing a pbn ligand, we have synthesized a new copper(II) pbn complex and its has been undertaken.
The molecular structure of the title complex is shown in Fig. 1. The copper(II) ion of the cation has a pentacoordinate structure formed by four N atoms from two pbn ligands and one Cl ligand. The complex cation exhibits symmetry 2, with the twofold rotation axis running through Cu1 and Cl1. The perchlorate anion is also located on a twofold rotation axis (passing through Cl2). The bond lengths from the copper to each of donor N atoms and chloride are Cu1—N1 2.0230 (18) Å, Cu1—N3 2.0778 (19) Å, and Cu1—Cl1 2.2795 (9) Å. The quantitative difference in five-coordinate geometry is indicated by the τ parameter, the value of which can range from τ = 1 for a perfect trigonal–bipyramidal geometry to τ = 0 for a perfect square-pyramidal geometry (Addison et al., 1984). The τ value for the copper(II) ion of the cation in the title complex is calculated to be 0.84 using the equation τ = (β − α)/60 (Addison et al., 1984), where α = N3—Cu1—Cl1 [125.66 (5)°] and β = N1—Cu1—N1i [175.78 (11)°; symmetry code: (i) x, − y, − z). Thus, the coordination environment of the copper(II) ion in [Cu(pbn)2Cl]+ is slightly distorted trigonal–bipyramidal.
The crystal packing of the title complex is shown in Fig. 2. The relatively short interplanar distances between the benzonaphthyridine rings of the pbn ligand of neighbouring cations indicate intermolecular π–π stacking interactions [distance between the centroids of the (C8/N2/C9–C12) and (C2/N1/C1/C9/C10/C3)ii rings = 3.6070 (3) Å; symmetry code: (ii) − + x, y, 1 − z].
Synthesis and crystallization
The NAD+/NADH-analogous ligand pbn [pbn = 2-(pyridin-2-yl)benzo[b][1,5]naphthyridine] was prepared according to the procedure of Koizumi & Tanaka (2005). To a dichloromethane solution (4 ml) of pbn (50.0 mg, 0.19 mmol) was added dropwise a mixture of CuCl2·2H2O (8.3 mg, 0.05 mmol) and Cu(ClO4)2·6H2O (19.9 mg, 0.05 mmol) in acetonitrile (4 ml). The resulting pale yellow–green precipitate was filtered and dissolved in hot acetonitrile for recrystallization. After the solution was left to stand for a few weeks at room temperature, pale yellow–green crystals of the title complex, [Cu(pbn)2Cl]ClO4·2CH3CN, were obtained (yield: 33.7 mg, 48.6%). Elemental analysis found: C 53.40, H 3.55, N 10.83%; calculated for C34H28Cl2CuN6O7: C 53.24, H 3.68, N 10.96%.
Refinement
Crystal data, data collection and structure .
details are summarized in Table 1Structural data
CCDC reference: 1504744
https://doi.org/10.1107/S2414314616015625/bt4028sup1.cif
contains datablocks global, I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314616015625/bt4028Isup2.hkl
Data collection: RAPID-AUTO (Rigaku, 2001); cell
RAPID-AUTO (Rigaku, 2001); data reduction: RAPID-AUTO (Rigaku, 2001); program(s) used to solve structure: SIR2011 (Burla et al., 2012); program(s) used to refine structure: SHELXL2016 (Sheldrick, 2015); molecular graphics: CrystalStructure (Rigaku, 2016), Mercury (Macrae et al., 2008) and CrystalMaker (Palmer, 2007); software used to prepare material for publication: CrystalStructure (Rigaku, 2016) and publCIF (Westrip, 2010).[CuCl(C17H11N3)2]ClO4·2C2H3N | Dx = 1.482 Mg m−3 |
Mr = 795.14 | Mo Kα radiation, λ = 0.71075 Å |
Orthorhombic, Pnna | Cell parameters from 21593 reflections |
a = 7.53614 (16) Å | θ = 3.0–27.5° |
b = 30.5246 (6) Å | µ = 0.82 mm−1 |
c = 15.4918 (4) Å | T = 173 K |
V = 3563.71 (13) Å3 | Platelet, yellowish green |
Z = 4 | 0.25 × 0.23 × 0.02 mm |
F(000) = 1628.00 |
Rigaku R-AXIS RAPID diffractometer | 3235 reflections with F2 > 2.0σ(F2) |
Detector resolution: 10.000 pixels mm-1 | Rint = 0.043 |
ω scans | θmax = 27.5°, θmin = 3.0° |
Absorption correction: multi-scan (ABSCOR; Higashi, 1995) | h = −8→9 |
Tmin = 0.751, Tmax = 0.984 | k = −39→39 |
32886 measured reflections | l = −20→20 |
4072 independent reflections |
Refinement on F2 | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.043 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.132 | H-atom parameters constrained |
S = 1.06 | w = 1/[σ2(Fo2) + (0.0731P)2 + 2.7626P] where P = (Fo2 + 2Fc2)/3 |
4072 reflections | (Δ/σ)max < 0.001 |
242 parameters | Δρmax = 0.81 e Å−3 |
0 restraints | Δρmin = −0.50 e Å−3 |
Primary atom site location: structure-invariant direct methods |
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. |
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 sigma(F2) is used only for calculating R-factor (gt). |
x | y | z | Uiso*/Ueq | ||
CU1 | 0.27555 (5) | 0.250000 | 0.250000 | 0.02241 (13) | |
CL1 | −0.02693 (11) | 0.250000 | 0.250000 | 0.0367 (2) | |
CL2 | 0.750000 | 0.000000 | 0.16427 (8) | 0.0533 (3) | |
O1 | 0.8062 (9) | 0.03461 (19) | 0.1220 (6) | 0.244 (4) | |
O2 | 0.6099 (6) | 0.01641 (18) | 0.2183 (3) | 0.1367 (17) | |
N1 | 0.2854 (2) | 0.23357 (6) | 0.37642 (12) | 0.0233 (4) | |
N2 | 0.1294 (3) | 0.15656 (7) | 0.54355 (13) | 0.0294 (4) | |
N3 | 0.4363 (3) | 0.30003 (6) | 0.29646 (12) | 0.0271 (4) | |
N4 | 0.1061 (4) | 0.13340 (10) | 0.12987 (17) | 0.0557 (7) | |
C1 | 0.3578 (3) | 0.26382 (7) | 0.42751 (14) | 0.0241 (5) | |
C2 | 0.3555 (3) | 0.26007 (8) | 0.51920 (15) | 0.0283 (5) | |
H2 | 0.407636 | 0.282244 | 0.553951 | 0.034* | |
C3 | 0.2785 (3) | 0.22473 (8) | 0.55655 (14) | 0.0282 (5) | |
H3 | 0.275313 | 0.222235 | 0.617656 | 0.034* | |
C4 | −0.0133 (3) | 0.08709 (8) | 0.53424 (18) | 0.0357 (6) | |
H4 | −0.017468 | 0.085455 | 0.595443 | 0.043* | |
C5 | −0.0791 (4) | 0.05395 (9) | 0.48647 (19) | 0.0403 (6) | |
H5 | −0.129111 | 0.029212 | 0.514602 | 0.048* | |
C6 | −0.0750 (4) | 0.05533 (8) | 0.3947 (2) | 0.0408 (6) | |
H6 | −0.120543 | 0.031392 | 0.362345 | 0.049* | |
C7 | −0.0063 (4) | 0.09064 (8) | 0.35284 (17) | 0.0353 (6) | |
H7 | −0.005778 | 0.091390 | 0.291536 | 0.042* | |
C8 | 0.1360 (3) | 0.16370 (7) | 0.36126 (15) | 0.0268 (5) | |
H8 | 0.135199 | 0.166429 | 0.300175 | 0.032* | |
C9 | 0.2028 (3) | 0.19150 (7) | 0.50445 (15) | 0.0250 (5) | |
C10 | 0.2084 (3) | 0.19688 (7) | 0.41263 (14) | 0.0232 (4) | |
C11 | 0.0629 (3) | 0.12479 (8) | 0.49334 (16) | 0.0287 (5) | |
C12 | 0.0652 (3) | 0.12666 (7) | 0.40064 (15) | 0.0280 (5) | |
C13 | 0.4470 (3) | 0.30072 (7) | 0.38324 (15) | 0.0266 (5) | |
C14 | 0.5399 (4) | 0.33320 (8) | 0.42694 (17) | 0.0347 (6) | |
H14 | 0.545306 | 0.333179 | 0.488203 | 0.042* | |
C15 | 0.6248 (4) | 0.36570 (9) | 0.37968 (19) | 0.0424 (7) | |
H15 | 0.688212 | 0.388422 | 0.408040 | 0.051* | |
C16 | 0.6153 (4) | 0.36437 (9) | 0.2907 (2) | 0.0414 (6) | |
H16 | 0.673472 | 0.386018 | 0.256982 | 0.050* | |
C17 | 0.5203 (3) | 0.33121 (9) | 0.25129 (16) | 0.0334 (5) | |
H17 | 0.514287 | 0.330496 | 0.190050 | 0.040* | |
C18 | 0.2394 (6) | 0.05650 (14) | 0.1102 (4) | 0.0886 (15) | |
H18A | 0.256040 | 0.050434 | 0.048564 | 0.106* | |
H18B | 0.158888 | 0.034679 | 0.135016 | 0.106* | |
H18C | 0.354269 | 0.055080 | 0.139691 | 0.106* | |
C19 | 0.1648 (5) | 0.09945 (11) | 0.1207 (2) | 0.0506 (7) |
U11 | U22 | U33 | U12 | U13 | U23 | |
CU1 | 0.0261 (2) | 0.0236 (2) | 0.0175 (2) | 0.000 | 0.000 | −0.00087 (14) |
CL1 | 0.0256 (4) | 0.0562 (6) | 0.0283 (4) | 0.000 | 0.000 | 0.0163 (4) |
CL2 | 0.0604 (7) | 0.0417 (5) | 0.0579 (7) | −0.0012 (5) | 0.000 | 0.000 |
O1 | 0.189 (6) | 0.131 (4) | 0.412 (11) | 0.034 (4) | 0.106 (6) | 0.162 (6) |
O2 | 0.118 (3) | 0.190 (4) | 0.102 (3) | 0.080 (3) | 0.014 (2) | 0.006 (3) |
N1 | 0.0255 (10) | 0.0250 (9) | 0.0192 (9) | 0.0038 (8) | −0.0017 (7) | −0.0003 (7) |
N2 | 0.0269 (10) | 0.0343 (11) | 0.0269 (10) | 0.0065 (8) | 0.0020 (8) | 0.0043 (8) |
N3 | 0.0275 (10) | 0.0282 (9) | 0.0257 (10) | −0.0009 (8) | 0.0001 (8) | −0.0038 (8) |
N4 | 0.0638 (18) | 0.0584 (17) | 0.0449 (15) | −0.0029 (14) | −0.0009 (13) | 0.0052 (13) |
C1 | 0.0235 (11) | 0.0258 (10) | 0.0230 (11) | 0.0055 (9) | −0.0033 (9) | −0.0024 (8) |
C2 | 0.0256 (12) | 0.0351 (12) | 0.0243 (11) | 0.0042 (9) | −0.0046 (9) | −0.0079 (9) |
C3 | 0.0271 (12) | 0.0388 (13) | 0.0187 (10) | 0.0069 (10) | −0.0013 (9) | −0.0014 (9) |
C4 | 0.0305 (13) | 0.0373 (13) | 0.0393 (13) | 0.0066 (11) | 0.0048 (11) | 0.0095 (11) |
C5 | 0.0330 (14) | 0.0333 (13) | 0.0545 (17) | 0.0014 (11) | 0.0074 (12) | 0.0125 (12) |
C6 | 0.0384 (14) | 0.0281 (12) | 0.0559 (17) | −0.0023 (11) | 0.0018 (13) | −0.0029 (12) |
C7 | 0.0365 (14) | 0.0319 (12) | 0.0375 (13) | −0.0006 (11) | 0.0021 (11) | −0.0029 (10) |
C8 | 0.0308 (12) | 0.0259 (11) | 0.0236 (10) | 0.0034 (9) | −0.0018 (9) | −0.0012 (9) |
C9 | 0.0243 (11) | 0.0290 (11) | 0.0219 (10) | 0.0073 (9) | −0.0001 (8) | −0.0001 (9) |
C10 | 0.0228 (11) | 0.0246 (10) | 0.0223 (10) | 0.0054 (9) | −0.0014 (8) | 0.0002 (8) |
C11 | 0.0253 (12) | 0.0302 (11) | 0.0305 (12) | 0.0072 (10) | 0.0029 (9) | 0.0047 (9) |
C12 | 0.0258 (11) | 0.0273 (11) | 0.0310 (12) | 0.0047 (9) | 0.0006 (10) | 0.0003 (9) |
C13 | 0.0249 (11) | 0.0273 (11) | 0.0276 (11) | 0.0046 (9) | −0.0034 (9) | −0.0040 (9) |
C14 | 0.0391 (14) | 0.0323 (12) | 0.0327 (13) | −0.0006 (11) | −0.0080 (11) | −0.0057 (10) |
C15 | 0.0439 (16) | 0.0360 (14) | 0.0472 (16) | −0.0102 (12) | −0.0105 (13) | −0.0064 (12) |
C16 | 0.0385 (15) | 0.0383 (14) | 0.0473 (16) | −0.0134 (12) | 0.0009 (12) | 0.0009 (12) |
C17 | 0.0326 (13) | 0.0359 (13) | 0.0316 (12) | −0.0066 (11) | 0.0025 (10) | 0.0000 (10) |
C18 | 0.075 (3) | 0.058 (2) | 0.132 (4) | 0.005 (2) | −0.007 (3) | 0.001 (3) |
C19 | 0.0528 (18) | 0.0517 (18) | 0.0473 (17) | −0.0038 (16) | −0.0015 (15) | 0.0086 (14) |
CU1—N1 | 2.0230 (18) | C4—H4 | 0.9500 |
CU1—N1i | 2.0230 (18) | C5—C6 | 1.423 (4) |
CU1—N3 | 2.0778 (19) | C5—H5 | 0.9500 |
CU1—N3i | 2.0779 (19) | C6—C7 | 1.360 (4) |
CU1—CL1 | 2.2795 (9) | C6—H6 | 0.9500 |
CL2—O1ii | 1.313 (5) | C7—C12 | 1.431 (3) |
CL2—O1 | 1.313 (5) | C7—H7 | 0.9500 |
CL2—O2 | 1.438 (4) | C8—C12 | 1.391 (3) |
CL2—O2ii | 1.438 (4) | C8—C10 | 1.399 (3) |
N1—C1 | 1.333 (3) | C8—H8 | 0.9500 |
N1—C10 | 1.381 (3) | C9—C10 | 1.433 (3) |
N2—C11 | 1.341 (3) | C11—C12 | 1.437 (3) |
N2—C9 | 1.345 (3) | C13—C14 | 1.390 (3) |
N3—C17 | 1.340 (3) | C14—C15 | 1.389 (4) |
N3—C13 | 1.347 (3) | C14—H14 | 0.9500 |
N4—C19 | 1.136 (4) | C15—C16 | 1.380 (4) |
C1—C2 | 1.425 (3) | C15—H15 | 0.9500 |
C1—C13 | 1.480 (3) | C16—C17 | 1.382 (4) |
C2—C3 | 1.355 (4) | C16—H16 | 0.9500 |
C2—H2 | 0.9500 | C17—H17 | 0.9500 |
C3—C9 | 1.416 (3) | C18—C19 | 1.436 (6) |
C3—H3 | 0.9500 | C18—H18A | 0.9800 |
C4—C5 | 1.348 (4) | C18—H18B | 0.9800 |
C4—C11 | 1.434 (3) | C18—H18C | 0.9800 |
N1—CU1—N1i | 175.78 (11) | C6—C7—C12 | 120.4 (2) |
N1—CU1—N3 | 79.95 (8) | C6—C7—H7 | 119.8 |
N1i—CU1—N3 | 97.56 (7) | C12—C7—H7 | 119.8 |
N1—CU1—N3i | 97.57 (7) | C12—C8—C10 | 119.3 (2) |
N1i—CU1—N3i | 79.95 (8) | C12—C8—H8 | 120.4 |
N3—CU1—N3i | 108.69 (11) | C10—C8—H8 | 120.4 |
N1—CU1—CL1 | 92.11 (5) | N2—C9—C3 | 118.5 (2) |
N1i—CU1—CL1 | 92.11 (5) | N2—C9—C10 | 123.4 (2) |
N3—CU1—CL1 | 125.66 (5) | C3—C9—C10 | 118.2 (2) |
N3i—CU1—CL1 | 125.65 (5) | N1—C10—C8 | 121.3 (2) |
O1ii—CL2—O1 | 120.2 (9) | N1—C10—C9 | 120.6 (2) |
O1ii—CL2—O2 | 109.5 (4) | C8—C10—C9 | 118.1 (2) |
O1—CL2—O2 | 104.3 (4) | N2—C11—C4 | 118.3 (2) |
O1ii—CL2—O2ii | 104.3 (4) | N2—C11—C12 | 123.1 (2) |
O1—CL2—O2ii | 109.5 (4) | C4—C11—C12 | 118.6 (2) |
O2—CL2—O2ii | 108.8 (4) | C8—C12—C7 | 122.8 (2) |
C1—N1—C10 | 119.52 (19) | C8—C12—C11 | 118.4 (2) |
C1—N1—CU1 | 114.72 (15) | C7—C12—C11 | 118.8 (2) |
C10—N1—CU1 | 125.38 (15) | N3—C13—C14 | 121.8 (2) |
C11—N2—C9 | 117.8 (2) | N3—C13—C1 | 115.0 (2) |
C17—N3—C13 | 118.8 (2) | C14—C13—C1 | 123.1 (2) |
C17—N3—CU1 | 128.05 (16) | C15—C14—C13 | 119.0 (2) |
C13—N3—CU1 | 113.10 (16) | C15—C14—H14 | 120.5 |
N1—C1—C2 | 122.1 (2) | C13—C14—H14 | 120.5 |
N1—C1—C13 | 116.0 (2) | C16—C15—C14 | 118.8 (2) |
C2—C1—C13 | 121.9 (2) | C16—C15—H15 | 120.6 |
C3—C2—C1 | 119.7 (2) | C14—C15—H15 | 120.6 |
C3—C2—H2 | 120.2 | C15—C16—C17 | 119.3 (3) |
C1—C2—H2 | 120.2 | C15—C16—H16 | 120.3 |
C2—C3—C9 | 120.0 (2) | C17—C16—H16 | 120.3 |
C2—C3—H3 | 120.0 | N3—C17—C16 | 122.3 (2) |
C9—C3—H3 | 120.0 | N3—C17—H17 | 118.9 |
C5—C4—C11 | 120.5 (2) | C16—C17—H17 | 118.9 |
C5—C4—H4 | 119.8 | C19—C18—H18A | 109.5 |
C11—C4—H4 | 119.8 | C19—C18—H18B | 109.5 |
C4—C5—C6 | 121.2 (2) | H18A—C18—H18B | 109.5 |
C4—C5—H5 | 119.4 | C19—C18—H18C | 109.5 |
C6—C5—H5 | 119.4 | H18A—C18—H18C | 109.5 |
C7—C6—C5 | 120.5 (3) | H18B—C18—H18C | 109.5 |
C7—C6—H6 | 119.7 | N4—C19—C18 | 179.3 (4) |
C5—C6—H6 | 119.7 | ||
C10—N1—C1—C2 | −1.3 (3) | C5—C4—C11—N2 | −178.8 (2) |
CU1—N1—C1—C2 | 172.05 (17) | C5—C4—C11—C12 | 0.9 (4) |
C10—N1—C1—C13 | 176.41 (19) | C10—C8—C12—C7 | −178.0 (2) |
CU1—N1—C1—C13 | −10.3 (2) | C10—C8—C12—C11 | 2.5 (3) |
N1—C1—C2—C3 | 0.3 (4) | C6—C7—C12—C8 | −179.6 (2) |
C13—C1—C2—C3 | −177.2 (2) | C6—C7—C12—C11 | 0.0 (4) |
C1—C2—C3—C9 | 0.8 (3) | N2—C11—C12—C8 | −1.6 (4) |
C11—C4—C5—C6 | 0.0 (4) | C4—C11—C12—C8 | 178.7 (2) |
C4—C5—C6—C7 | −0.9 (4) | N2—C11—C12—C7 | 178.8 (2) |
C5—C6—C7—C12 | 0.9 (4) | C4—C11—C12—C7 | −0.9 (3) |
C11—N2—C9—C3 | −178.1 (2) | C17—N3—C13—C14 | 1.1 (4) |
C11—N2—C9—C10 | 1.9 (3) | CU1—N3—C13—C14 | −176.30 (18) |
C2—C3—C9—N2 | 179.2 (2) | C17—N3—C13—C1 | −177.1 (2) |
C2—C3—C9—C10 | −0.9 (3) | CU1—N3—C13—C1 | 5.5 (2) |
C1—N1—C10—C8 | −177.9 (2) | N1—C1—C13—N3 | 3.0 (3) |
CU1—N1—C10—C8 | 9.5 (3) | C2—C1—C13—N3 | −179.3 (2) |
C1—N1—C10—C9 | 1.1 (3) | N1—C1—C13—C14 | −175.2 (2) |
CU1—N1—C10—C9 | −171.43 (15) | C2—C1—C13—C14 | 2.5 (4) |
C12—C8—C10—N1 | 177.8 (2) | N3—C13—C14—C15 | −0.4 (4) |
C12—C8—C10—C9 | −1.3 (3) | C1—C13—C14—C15 | 177.7 (2) |
N2—C9—C10—N1 | 179.9 (2) | C13—C14—C15—C16 | −0.6 (4) |
C3—C9—C10—N1 | −0.1 (3) | C14—C15—C16—C17 | 0.8 (4) |
N2—C9—C10—C8 | −1.0 (3) | C13—N3—C17—C16 | −1.0 (4) |
C3—C9—C10—C8 | 179.0 (2) | CU1—N3—C17—C16 | 176.0 (2) |
C9—N2—C11—C4 | 179.1 (2) | C15—C16—C17—N3 | 0.0 (4) |
C9—N2—C11—C12 | −0.6 (3) |
Symmetry codes: (i) x, −y+1/2, −z+1/2; (ii) −x+3/2, −y, z. |
Acknowledgements
This work was supported in part by Grant-in-Aids for Scientific Research B (No. 26288024, to KT) and for Scientific Research C (No. 25410067, to HO) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT).
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