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ISSN: 2056-9890

L-Leucylglycylglycine

aInstitute of Radioisotope Research, St. Marianna University Graduate School of Medicine, 2-16-1 Sugao, Miyamae-ku, Kawasaki, Kanagawa 216-8511, Japan, bDepartment of Molecular and Behavioral Neuroscience, St. Marianna University Graduate School of Medicine, 2-16-1 Sugao, Miyamae-ku, Kawasaki, Kanagawa 216-8511, Japan, and cSchool of Science, Kitasato University, 1-15-1 Kitasato, Minami-ku, Sagamihara, Kanagawa 252-0373, Japan
*Correspondence e-mail: m_ootaki@marianna-u.ac.jp

(Received 12 March 2013; accepted 27 March 2013; online 5 April 2013)

In the title compound, C10H19N3O4, the N- and C-termini are protonated and ionized, respectively, and the mol­ecule forms a zwitterion. The main chain is in a folded form. In the crystal, the N-terminal –NH3+ group hydrogen bonds to three C-terminal –COO groups and one carbonyl O atom, forming a three-dimensional network. In addition, an N—H⋯O hydrogen bond between the amide groups of the middle glycine residue and a C—H⋯O inter­action continue along the a-axis direction. The side chains of the leucyl residues form a hydro­phobic region along the a axis.

Related literature

For related structures of L-leucylglycylglycine, see: Goswami et al. (1977[Goswami, K. N., Yadava, V. S. & Padmanabhan, V. M. (1977). Acta Cryst. B33, 1280-1283.]); Srikrishnan & Parthasarathy (1987[Srikrishnan, T. & Parthasarathy, R. (1987). Int. J. Pept. Protein Res. 30, 557-563.]); Kiyotani & Sugawara (2012[Kiyotani, T. & Sugawara, Y. (2012). Acta Cryst. C68, o498-o501.]).

[Scheme 1]

Experimental

Crystal data
  • C10H19N3O4

  • Mr = 245.28

  • Orthorhombic, P 21 21 21

  • a = 5.391 (5) Å

  • b = 11.742 (10) Å

  • c = 19.975 (16) Å

  • V = 1264.4 (19) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.10 mm−1

  • T = 173 K

  • 0.48 × 0.18 × 0.08 mm

Data collection
  • Rigaku Mercury CCD area-detecter diffractometer

  • 9374 measured reflections

  • 2887 independent reflections

  • 2200 reflections with I > 2σ(I)

  • Rint = 0.070

Refinement
  • R[F2 > 2σ(F2)] = 0.038

  • wR(F2) = 0.087

  • S = 0.96

  • 2887 reflections

  • 176 parameters

  • 3 restraints

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 0.14 e Å−3

  • Δρmin = −0.17 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1⋯O3i 0.97 (3) 1.78 (3) 2.743 (2) 168 (2)
N1—H2⋯O4ii 0.92 (2) 1.94 (2) 2.822 (2) 160 (2)
N1—H2⋯O3ii 0.92 (2) 2.52 (2) 3.260 (2) 138 (2)
N1—H3⋯O1iii 0.89 (2) 2.45 (2) 3.031 (2) 123 (2)
N1—H3⋯O3iv 0.89 (2) 2.05 (2) 2.870 (2) 151 (2)
N2—H5⋯O2v 0.83 (2) 2.05 (2) 2.832 (2) 155 (2)
C1—H4⋯O1v 1.00 2.33 3.269 (2) 155
Symmetry codes: (i) [-x+{\script{1\over 2}}, -y+1, z-{\script{1\over 2}}]; (ii) [-x-{\script{1\over 2}}, -y+1, z-{\script{1\over 2}}]; (iii) [x-{\script{1\over 2}}, -y+{\script{3\over 2}}, -z+1]; (iv) [-x, y+{\script{1\over 2}}, -z+{\script{3\over 2}}]; (v) x-1, y, z.

Data collection: CrystalClear (Rigaku, 2006[Rigaku (2006). CrystalClear. Rigaku Corporation, Tokyo, Japan.]); cell refinement: CrystalClear; data reduction: CrystalClear; 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: Mercury (Macrae et al., 2006[Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G. P., Taylor, R., Towler, M. & van de Streek, J. (2006). J. Appl. Cryst. 39, 453-457.]); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]) and Yadokari-XG 2009 (Kabuto et al., 2009[Kabuto, C., Akine, S., Nemoto, T. & Kwon, E. (2009). J. Cryst. Soc. Jpn, 51, 218-224.]).

Supporting information


Comment top

A moderately large number of oligopeptides are biologically active, and their structures are investigated to facilitate the determination of the possible conformations of oligopeptide and polypeptide chains. The N-terminus and C-terminus of L-leucylglycylglycine (L-LGG) are protonated and ionized, respectively, and the molecule is a zwitterion (Fig. 1). The main chain is in a folded form. The torsion angles of C2—N2—C3—C4 and N2—C3—C4—N3 are -87.54 (18)° and -52.78 (19)°, respectively. The N-terminal –NH3+ groups and the C-terminal –COO- groups form hydrogen bond networks (Fig. 2 & Fig. 3). One of the hydrogen atoms of the –NH3 group forms a three-centered hydrogen bond with the carboxyl and carboxyl oxygen atoms. In addition, intermolecular hydrogen bonds among amide groups (NH···OC) are formed along the a axis. The hydrophobic region composed of leucyl side chains is surrounded by hydrophilic parts, and forms a column along the a axis.

In the case of the L-leucylglycylglycylglycine (Srikrishnan & Parthasarathy, 1987), the main chain is a folded form, and hydrophobic columns are formed along the a axis as in the case of L-LGG. On the other hand, the main chain of D,L-leucylglycylglycine (D,L-LGG) (Goswami et al., 1977) is in a nearly all-trans form expect the N-terminus. The main chains align parallel to the b axis in a head-to-tail manner and a β-sheetlike structure is formed parallel to the bc plane. The hydrophobic regions of the leucyl side chains and the hydrophilic regions are aligned alternately along the a axis. As in the case of D,L-LGG, the main chain in L-leucylglycine 0.67 hydrate (Kiyotani & Sugawara, 2012) is in a extended form, and hydrophobic and hydrophilic regions are aligned alternately along the c axis.

Related literature top

For related structures of L-leucylglycylglycine, see: Goswami et al. (1977); Srikrishnan & Parthasarathy (1987); Kiyotani & Sugawara (2012).

Experimental top

L-Leucylglycylglycine was purchased from Bachem Inc. Single crystals were obtained from an aqueous solution.

Refinement top

H atoms were placed in calculated positions with C—H = 0.98 Å (CH3), 0.99 Å (CH2) or 1.00 Å (CH) and refined in a riding mode with Uiso(H) = 1.2Ueq(C). The other H atoms were placed in a difference Fourier map. The N-terminal H atoms were restrained to N—H = 0.87 (4) Å during refinements. The absolute configuration was known for the purchased material.

Structure description top

A moderately large number of oligopeptides are biologically active, and their structures are investigated to facilitate the determination of the possible conformations of oligopeptide and polypeptide chains. The N-terminus and C-terminus of L-leucylglycylglycine (L-LGG) are protonated and ionized, respectively, and the molecule is a zwitterion (Fig. 1). The main chain is in a folded form. The torsion angles of C2—N2—C3—C4 and N2—C3—C4—N3 are -87.54 (18)° and -52.78 (19)°, respectively. The N-terminal –NH3+ groups and the C-terminal –COO- groups form hydrogen bond networks (Fig. 2 & Fig. 3). One of the hydrogen atoms of the –NH3 group forms a three-centered hydrogen bond with the carboxyl and carboxyl oxygen atoms. In addition, intermolecular hydrogen bonds among amide groups (NH···OC) are formed along the a axis. The hydrophobic region composed of leucyl side chains is surrounded by hydrophilic parts, and forms a column along the a axis.

In the case of the L-leucylglycylglycylglycine (Srikrishnan & Parthasarathy, 1987), the main chain is a folded form, and hydrophobic columns are formed along the a axis as in the case of L-LGG. On the other hand, the main chain of D,L-leucylglycylglycine (D,L-LGG) (Goswami et al., 1977) is in a nearly all-trans form expect the N-terminus. The main chains align parallel to the b axis in a head-to-tail manner and a β-sheetlike structure is formed parallel to the bc plane. The hydrophobic regions of the leucyl side chains and the hydrophilic regions are aligned alternately along the a axis. As in the case of D,L-LGG, the main chain in L-leucylglycine 0.67 hydrate (Kiyotani & Sugawara, 2012) is in a extended form, and hydrophobic and hydrophilic regions are aligned alternately along the c axis.

For related structures of L-leucylglycylglycine, see: Goswami et al. (1977); Srikrishnan & Parthasarathy (1987); Kiyotani & Sugawara (2012).

Computing details top

Data collection: CrystalClear (Rigaku, 2006); cell refinement: CrystalClear (Rigaku, 2006); data reduction: CrystalClear (Rigaku, 2006); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: Mercury (Macrae et al., 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and Yadokari-XG 2009 (Kabuto et al., 2009).

Figures top
[Figure 1] Fig. 1. View of the title compound with the atomic numbering scheme. Displacement ellipsoids are drawn at 50% probability level and H atoms are shown as small spheres of arbitrary radii.
[Figure 2] Fig. 2. Packing diagram of the title compound viewed along the a axis. Hydrophobic columns are indicated by green circles.
[Figure 3] Fig. 3. Hydrogen bonding scheme around the molecule, whose carbon atoms are colored with black. Hydrogen bonds are indicated by dotted lines. Side-chain atoms of the leucyl residues have been omitted for clarity.
L-Leucylglycylglycine top
Crystal data top
C10H19N3O4F(000) = 528
Mr = 245.28Dx = 1.288 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71070 Å
Hall symbol: P 2ac 2abCell parameters from 949 reflections
a = 5.391 (5) Åθ = 7.6–17.5°
b = 11.742 (10) ŵ = 0.10 mm1
c = 19.975 (16) ÅT = 173 K
V = 1264.4 (19) Å3Block Rod, colorless
Z = 40.48 × 0.18 × 0.08 mm
Data collection top
Rigaku Mercury CCD area-detecter
diffractometer
2200 reflections with I > 2σ(I)
Radiation source: rotating anodeRint = 0.070
Graphite monochromatorθmax = 27.5°, θmin = 3.5°
ω scansh = 66
9374 measured reflectionsk = 1515
2887 independent reflectionsl = 2125
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)] = 0.038Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.087H atoms treated by a mixture of independent and constrained refinement
S = 0.96 w = 1/[σ2(Fo2) + (0.0374P)2]
where P = (Fo2 + 2Fc2)/3
2887 reflections(Δ/σ)max = 0.012
176 parametersΔρmax = 0.14 e Å3
3 restraintsΔρmin = 0.17 e Å3
Crystal data top
C10H19N3O4V = 1264.4 (19) Å3
Mr = 245.28Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 5.391 (5) ŵ = 0.10 mm1
b = 11.742 (10) ÅT = 173 K
c = 19.975 (16) Å0.48 × 0.18 × 0.08 mm
Data collection top
Rigaku Mercury CCD area-detecter
diffractometer
2200 reflections with I > 2σ(I)
9374 measured reflectionsRint = 0.070
2887 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0383 restraints
wR(F2) = 0.087H atoms treated by a mixture of independent and constrained refinement
S = 0.96Δρmax = 0.14 e Å3
2887 reflectionsΔρmin = 0.17 e Å3
176 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
N10.1744 (3)0.64554 (12)0.49670 (7)0.0348 (3)
N20.0484 (3)0.64749 (12)0.67001 (6)0.0315 (3)
H50.195 (4)0.6402 (15)0.6825 (9)0.036 (5)*
N30.1814 (3)0.52895 (12)0.78349 (7)0.0362 (3)
H80.022 (4)0.5354 (16)0.7880 (9)0.048 (6)*
O10.2239 (2)0.64148 (11)0.58454 (5)0.0415 (3)
O20.5246 (2)0.62376 (11)0.75146 (6)0.0485 (3)
C10.1911 (3)0.58011 (12)0.56075 (8)0.0290 (3)
H40.35700.59210.58200.035*
C20.0137 (3)0.62595 (12)0.60611 (7)0.0273 (3)
C30.1320 (3)0.69772 (14)0.71523 (8)0.0368 (4)
H60.04220.74310.74930.044*
H70.23810.75070.68940.044*
C40.2975 (3)0.61277 (13)0.75092 (7)0.0314 (4)
C50.3059 (3)0.45098 (16)0.82883 (9)0.0406 (4)
H90.45500.48830.84770.049*
H100.36040.38260.80380.049*
C60.1333 (4)0.41541 (13)0.88559 (8)0.0354 (4)
O30.2277 (3)0.35522 (11)0.93090 (6)0.0536 (4)
O40.0855 (3)0.44525 (12)0.88306 (7)0.0545 (4)
C70.1526 (3)0.45349 (13)0.54488 (8)0.0374 (4)
H110.27110.43120.50940.045*
H120.01680.44340.52670.045*
C80.1855 (4)0.37232 (14)0.60441 (9)0.0413 (4)
H130.06790.39590.64060.050*
C90.1199 (5)0.25116 (15)0.58278 (10)0.0636 (7)
H140.13790.19950.62100.076*
H150.05180.24920.56670.076*
H160.23160.22720.54670.095*
C100.4475 (5)0.3769 (2)0.63228 (13)0.0715 (7)
H170.56640.36090.59640.086*
H180.47960.45290.65070.086*
H190.46560.31990.66780.086*
H10.011 (5)0.636 (2)0.4768 (12)0.089 (9)*
H20.284 (5)0.6147 (19)0.4666 (12)0.076 (7)*
H30.202 (4)0.7193 (16)0.5047 (11)0.058 (6)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
N10.0420 (9)0.0301 (7)0.0322 (7)0.0012 (7)0.0133 (7)0.0028 (6)
N20.0312 (8)0.0404 (8)0.0228 (6)0.0052 (7)0.0020 (6)0.0025 (6)
N30.0288 (8)0.0458 (8)0.0341 (7)0.0020 (7)0.0000 (6)0.0152 (6)
O10.0248 (6)0.0666 (8)0.0332 (6)0.0019 (6)0.0030 (5)0.0004 (6)
O20.0387 (8)0.0668 (9)0.0399 (7)0.0099 (7)0.0061 (5)0.0128 (6)
C10.0284 (8)0.0304 (7)0.0282 (8)0.0006 (7)0.0021 (7)0.0001 (6)
C20.0272 (8)0.0294 (8)0.0253 (7)0.0018 (7)0.0018 (6)0.0038 (6)
C30.0496 (12)0.0340 (8)0.0268 (8)0.0083 (8)0.0054 (8)0.0034 (7)
C40.0375 (10)0.0396 (9)0.0172 (7)0.0051 (8)0.0031 (7)0.0006 (6)
C50.0365 (10)0.0480 (10)0.0373 (9)0.0046 (9)0.0010 (8)0.0148 (8)
C60.0498 (11)0.0301 (8)0.0264 (8)0.0120 (8)0.0017 (8)0.0028 (7)
O30.0698 (9)0.0532 (7)0.0379 (7)0.0196 (7)0.0195 (7)0.0220 (6)
O40.0427 (8)0.0644 (9)0.0562 (8)0.0010 (7)0.0156 (7)0.0178 (7)
C70.0482 (11)0.0303 (8)0.0338 (9)0.0007 (8)0.0012 (8)0.0004 (7)
C80.0532 (11)0.0325 (8)0.0381 (9)0.0025 (9)0.0036 (8)0.0037 (8)
C90.096 (2)0.0342 (10)0.0602 (14)0.0078 (10)0.0029 (13)0.0088 (9)
C100.0713 (16)0.0552 (13)0.0882 (17)0.0017 (12)0.0223 (13)0.0234 (12)
Geometric parameters (Å, º) top
N1—C11.495 (2)C5—C61.525 (3)
N1—H10.97 (2)C5—H90.9900
N1—H20.92 (2)C5—H100.9900
N1—H30.894 (19)C6—O41.232 (3)
N2—C21.344 (2)C6—O31.256 (2)
N2—C31.452 (2)C7—C81.534 (2)
N2—H50.83 (2)C7—H110.9900
N3—C41.336 (2)C7—H120.9900
N3—C51.452 (2)C8—C101.519 (3)
N3—H80.87 (2)C8—C91.528 (3)
O1—C21.226 (2)C8—H131.0000
O2—C41.231 (2)C9—H140.9800
C1—C21.526 (2)C9—H150.9800
C1—C71.534 (2)C9—H160.9800
C1—H41.0000C10—H170.9800
C3—C41.516 (2)C10—H180.9800
C3—H60.9900C10—H190.9800
C3—H70.9900
C1—N1—H1110.2 (15)C6—C5—H9109.5
C1—N1—H2108.6 (14)N3—C5—H10109.5
H1—N1—H2105 (2)C6—C5—H10109.5
C1—N1—H3109.6 (14)H9—C5—H10108.1
H1—N1—H3110 (2)O4—C6—O3125.31 (17)
H2—N1—H3113 (2)O4—C6—C5118.43 (16)
C2—N2—C3120.03 (15)O3—C6—C5116.25 (18)
C2—N2—H5120.0 (13)C8—C7—C1115.23 (14)
C3—N2—H5119.4 (13)C8—C7—H11108.5
C4—N3—C5123.47 (17)C1—C7—H11108.5
C4—N3—H8116.8 (13)C8—C7—H12108.5
C5—N3—H8116.7 (13)C1—C7—H12108.5
N1—C1—C2106.45 (13)H11—C7—H12107.5
N1—C1—C7108.24 (13)C10—C8—C9110.59 (17)
C2—C1—C7111.49 (13)C10—C8—C7111.68 (16)
N1—C1—H4110.2C9—C8—C7109.41 (15)
C2—C1—H4110.2C10—C8—H13108.4
C7—C1—H4110.2C9—C8—H13108.4
O1—C2—N2122.41 (14)C7—C8—H13108.4
O1—C2—C1120.84 (14)C8—C9—H14109.5
N2—C2—C1116.75 (14)C8—C9—H15109.5
N2—C3—C4114.79 (14)H14—C9—H15109.5
N2—C3—H6108.6C8—C9—H16109.5
C4—C3—H6108.6H14—C9—H16109.5
N2—C3—H7108.6H15—C9—H16109.5
C4—C3—H7108.6C8—C10—H17109.5
H6—C3—H7107.5C8—C10—H18109.5
O2—C4—N3122.62 (16)H17—C10—H18109.5
O2—C4—C3121.36 (15)C8—C10—H19109.5
N3—C4—C3115.97 (17)H17—C10—H19109.5
N3—C5—C6110.74 (16)H18—C10—H19109.5
N3—C5—H9109.5
C3—N2—C2—O14.0 (2)N2—C3—C4—O2129.75 (17)
C3—N2—C2—C1176.27 (13)N2—C3—C4—N352.78 (19)
N1—C1—C2—O145.43 (19)C4—N3—C5—C6147.06 (16)
C7—C1—C2—O172.41 (19)N3—C5—C6—O47.0 (2)
N1—C1—C2—N2134.83 (14)N3—C5—C6—O3174.41 (14)
C7—C1—C2—N2107.33 (16)N1—C1—C7—C8175.12 (14)
C2—N2—C3—C487.54 (18)C2—C1—C7—C868.14 (19)
C5—N3—C4—O27.5 (2)C1—C7—C8—C1062.1 (2)
C5—N3—C4—C3169.93 (15)C1—C7—C8—C9175.13 (17)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O3i0.97 (3)1.78 (3)2.743 (2)168 (2)
N1—H2···O4ii0.92 (2)1.94 (2)2.822 (2)160 (2)
N1—H2···O3ii0.92 (2)2.52 (2)3.260 (2)138 (2)
N1—H3···O1iii0.89 (2)2.45 (2)3.031 (2)123 (2)
N1—H3···O3iv0.89 (2)2.05 (2)2.870 (2)151 (2)
N2—H5···O2v0.83 (2)2.05 (2)2.832 (2)155 (2)
C1—H4···O1v1.002.333.269 (2)155
Symmetry codes: (i) x+1/2, y+1, z1/2; (ii) x1/2, y+1, z1/2; (iii) x1/2, y+3/2, z+1; (iv) x, y+1/2, z+3/2; (v) x1, y, z.

Experimental details

Crystal data
Chemical formulaC10H19N3O4
Mr245.28
Crystal system, space groupOrthorhombic, P212121
Temperature (K)173
a, b, c (Å)5.391 (5), 11.742 (10), 19.975 (16)
V3)1264.4 (19)
Z4
Radiation typeMo Kα
µ (mm1)0.10
Crystal size (mm)0.48 × 0.18 × 0.08
Data collection
DiffractometerRigaku Mercury CCD area-detecter
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
9374, 2887, 2200
Rint0.070
(sin θ/λ)max1)0.649
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.038, 0.087, 0.96
No. of reflections2887
No. of parameters176
No. of restraints3
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.14, 0.17

Computer programs: CrystalClear (Rigaku, 2006), SHELXS97 (Sheldrick, 2008), Mercury (Macrae et al., 2006), SHELXL97 (Sheldrick, 2008) and Yadokari-XG 2009 (Kabuto et al., 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1···O3i0.97 (3)1.78 (3)2.743 (2)168 (2)
N1—H2···O4ii0.92 (2)1.94 (2)2.822 (2)160 (2)
N1—H2···O3ii0.92 (2)2.52 (2)3.260 (2)138 (2)
N1—H3···O1iii0.89 (2)2.45 (2)3.031 (2)123 (2)
N1—H3···O3iv0.89 (2)2.05 (2)2.870 (2)151 (2)
N2—H5···O2v0.83 (2)2.05 (2)2.832 (2)155 (2)
C1—H4···O1v1.002.333.269 (2)155
Symmetry codes: (i) x+1/2, y+1, z1/2; (ii) x1/2, y+1, z1/2; (iii) x1/2, y+3/2, z+1; (iv) x, y+1/2, z+3/2; (v) x1, y, z.
 

Acknowledgements

This work was partially supported by the JSPS KAKENHI (grant Nos. 24659548 and 23540478) and MEXT KAKENHI (grant No. 23108003).

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