research communications
Synthesis and structure of push–pull merocyanines based on barbituric and thiobarbituric acid
aDepartment of Chemistry, New Mexico Highlands University, Las Vegas, New Mexico, 87701, USA, and bSchool of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA
*Correspondence e-mail: bogdgv@gmail.com
Two compounds, 1,3-diethyl-5-{(2E,4E)-6-[(E)-1,3,3-trimethylindolin-2-ylidene]hexa-2,4-dien-1-ylidene}pyrimidine-2,4,6(1H,3H,5H)-trione or TMI, C25H29N3O3, and 1,3-diethyl-2-sulfanylidene-5-[2-(1,3,3-trimethylindolin-2-ylidene)ethylidene]dihydropyrimidine-4,6(1H,5H)-dione or DTB, C21H25N3O2S, have been crystallized and studied. These compounds contain the same indole derivative donor group and differ in their acceptor groups (in TMI it contains oxygen in the para position, and in DTB sulfur) and the length of the π-bridge. In both materials, molecules are packed in a herringbone manner with differences in the twist and fold angles. In both structures, the molecules are connected by weak C—H⋯O and/or C—H⋯S bonds.
1. Chemical context
The structures and properties of merocyanine dyes that lead to their potential use as non-linear optical materials have been studied widely over the past several decades (Del Zoppo et al., 1998; Bublitz & Boxer, 1998; Kulinich et al., 2007; Liess et al., 2015). For so-called push–pull systems with donor and acceptor groups connected by a π-conjugated bridge, non-linear optical applications are possible as a result of the charge-transfer phenomenon within one molecule. As previously reported (Klikar et al., 2013; Bideau et al., 1976, 1977; Bublitz, Ortiz, Marder et al., 1997; Bourhill et al., 1994), studies of molecules with barbituric or thiobarbituric acid as acceptor (Adamson et al., 1999; Padgett et al., 2007) show high values of first hyperpolarizability. Recently, more applications in the biological field have also been reported for such compounds (Collot et al.; 2018, Golovnev et al., 2018; Molokeev et al., 2015) related to their ability of bright fluorescence. Both structures reported here have the same 1,3,3-trimethyl-2-methyleneindoline moiety as a donor group. Studies of molecules with different lengths of the π-bridge between the donor and acceptor groups (Ortiz et al., 1994, Vázquez-Vuelvas et al., 2011) have demonstrated their different properties. Some non-linear optical studies were made on compounds with very similar structures to those presented here (Ikeda et al., 1991; Chamberlain et al., 1980; Kulinich et al., 2008), which vary by substitutions attached to the donor or acceptor groups (Song et al., 2005; Naik et al., 2017; Hirshberg et al., 1955). Almost all those studies were carried out in solution. Here we report the single-crystal X-ray structural analysis of two merocyanines, 1,3-diethyl-5-{(2E,4E)-6-[(E)-1,3,3-trimethylindolin-2-ylidene]hexa-2,4-dien-1-ylidene}pyrimidine-2,4,6(1H,3H,5H)-trione or TMI, and 1,3-diethyl-2-sulfanylidene-5-[2-(1,3,3-trimethylindolin-2-ylidene)ethylidene]dihydropyrimidine-4,6(1H,5H)-dione or DTB.
2. Structural commentary
Both title compounds have the same donor 2,3-dihydro-1,3,3-trimethyl-1H-indole moiety with different acceptors: 1,3-diethyl-2-oxobarbituric acid in TMI (Fig. 1a) and 1,3-diethyl-2-thiobarbituric acid in DTB (Fig. 1b). The double and single bonds in the TMI π-bridge vary in length from 1.372 (2) to 1.410 (2) Å, the difference between the single and double bonds getting smaller closer to the acceptor, indicating a higher degree of conjugation in this region. The dihedral angles between donor group and the bridge and between the bridge and the acceptor group are 9.10 (12) and 7.44 (12)°, respectively. All three fragments of the TMI structure are slightly distorted from a planar configuration, as shown by the r.m.s. deviations of 0.022 and 0.039 Å, respectively, for atoms in the donor and acceptor groups.
Comparing DTB to TMI, it is observed that DTB possesses a more planar and rigid structure, consistent with previously reported results for studies of push–pull chromophores with different π-bridge lengths (Tillotson et al., 2019). The dihedral angles between the three fragments are smaller, 3.21 (14)° between the donor group and the bridge and 1.04 (14)° between the bridge and the acceptor group. The r.m.s. deviations of atoms in DTB are also smaller, being 0.014 and 0.020 Å for the donor and acceptor groups, respectively.
In both structures, the π-bridge has an almost planar structure with insignificant r.m.s. deviations of atoms from planarity of 0.007 and 0.009 Å for TMI and DTB, respectively. In DTB, the bond-length distribution in the central fragment does not correspond to that in the scheme. According to the observed bond lengths [C8—C12 1.403 (1), C12—C13 1.386 (1), C13—C14 1.404 (1) Å], the central fragment can be presented as C8—C12=C13—C14, which indicates that the contribution of the zwitterionic form in the molecular structure of DTB. It should be mentioned that measurements of the first molecular hyperpolarizability, β, have positive values for dyes with hexamethine bridges, such as TMI, while dyes with a dimethine bridge have negative β values (Ortiz et al., 1994). The authors connect this effect with the high polarization and zwitterionic form of molecule DTB, which has a short conjugated bridge.
3. Supramolecular features
In the crystals of both TMI and DTB molecules are packed in a herringbone manner with a twist angle of 38.57 (1)° and fold angle of 57.08 (1)° in TMI (Fig. 2a) and a twist angle of 54.90 (7)° and fold angle of 78.96 (3)° in DTB (Fig. 2b). In both compounds, molecules are hold together via three hydrogen bonds, of the C—H⋯O type in TMI and of the C—H⋯O and C—H⋯S types in DTB (Tables 1 and 2, Fig. 3).
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For push–pull molecules be applied in the form of non-linear crystalline materials, they should exhibit a non-centrosymmetric type of packing. TMI and DTB both crystallize in the centrosymmetric P21/c. According to the bond order alternation pattern in these structures (see the supporting information), we suggest that they have the potential to be used as non-linear optical materials, but for this application they should be either be embedded in a polymer matrix or recrystallized under different conditions to attain an acentric packing mode.
4. Database survey
The Cambridge Structural Database (CSD version 5.40, last update November 2018; Groom et al., 2016) was searched three times: for the donor group, which is the same for both studied structures, and separately for each acceptor group. A search for the full structures gave zero hits. The dependence of the first hyperpolarizability on polarization and the length of the π-bridge that comprises donor or acceptors of studied molecules is described in several publications [KIYTOC and KOFMAU, Kulinich et al., 2007; GUBDAK, Liess et al., 2015 (Fig. 4); POLZEV, Ortiz et al., 1994; WIMHAD and WIMHEH, Klikar et al., 2013; WEVMUF, Bourhill et al., 1994]. In addition, the acceptor group of the TMI structure has been studied separately and the results were published (DETBAR10; Bideau et al., 1976). The acceptor group of DTB was studied as an independent molecule (DETSBR10; Bideau et al., 1976), as a part of several chromophore molecules (GUDWEH, Adamson et al., 1999; GUDWEH01, Naik et al., 2017; WEVMUF, Bourhill et al., 1994) and also as an anion in complexes with different cations (HUKMAD, HUKMEH, HUKMIL and HUKMOR; Molokeev et al., 2015). We found several publications in which the molecules are similar to our donor and acceptors, for instance PAQYEM (Song et al., 2005) is similar to TMI, but with a methyl group instead of an oxygen atom in the ortho position of the acceptor ring, and a cyano group in the meta position instead of an ethyl group (Fig. 4). Two structures of the separately crystallized acceptor group (DETSBR01, Bideau et al., 1977; DETSBR11, Padgett et al., 2007) are very close to that of the acceptor of DTB, but with hydroxy groups in the ortho positions instead of carbonyl oxygen atoms (Fig. 5).
5. Synthesis and crystallization
The synthesis of TMI was described by Ortiz et al. (1994), and this material was kindly presented to our group for structural studies by Professor Marderr's group. A scheme for the synthesis of DTB is shown in Fig. 6.
Synthesis of 1,3-diethyl-2-sulfanylidene-5-[2-(1,3,3-trimethylindolin-2-ylidene)ethylidene]dihydropyrimidine-4,6(1H,5H)-dione (DTB):
2-(1,3,3-Trimethylindolin-2-ylidene)acetaldehyde (0.25 g, 1.2 mmol) and diethylthiobarbituric acid (0.25 g, 1.24 mmol) were dissolved in about 35 mL of absolute ethanol with stirring and sonication. After stirring for 1 h at room temperature, the product was precipitated by adding distilled water. The mixture was then filtered and the residue redissolved in EtOH and precipitated again. The precipitant was washed with hexane and dried in vacuo to give 1,3-diethyl-2-sulfanylidene-5-[2-(1,3,3-trimethylindolin-2-ylidene)ethylidene]dihydropyrimidine-4,6(1H,5H)-dione as transparent red crystals (0.41 g, 86% yield). 1H NMR 8.69 (d, J = 14.6 Hz, 1H), 7.70 (d, J = 14.6 Hz, 1H), 7.40 (m, 2H), 7.26 (t, J = 7.9 Hz, 1H), 7.12 (d, J = 8.6 Hz, 1H), 4.55 (q, J = 7.0 Hz, 2H), 4.54 (q, J = 7.0 Hz, 2H), 3.59 (s, 3H), 1.73 (s, 6H), 1.27 (t, J = 7.0 Hz, 3H), 1.26 (t, J = 7.0 Hz, 3H) ppm.
Single crystals of both DTB and TMI were grown by vapour diffusion using chloroform as the solvent and cyclohexane as the antisolvent. Crystallization took place over a three week period to give DTB crystals of suitable size and quality.
6. Refinement
Crystal data, data collection and structure . The hydrogen atoms on the aromatic ring of the donor group and the π-bridge in both structures were positioned geometrically, C—H = 0.95 Å. Other hydrogens were positioned with idealized geometries C—H = 0.98–0.99 Å. All H atoms were refined using a riding model with Uiso(H) = 1.2Ueq(C) or 1.5Ueq(C-methyl).
details are summarized in Table 3Supporting information
https://doi.org/10.1107/S2056989019011071/yk2125sup1.cif
contains datablocks TMI, DTB. DOI:Structure factors: contains datablock TMI. DOI: https://doi.org/10.1107/S2056989019011071/yk2125TMIsup2.hkl
Structure factors: contains datablock DTB. DOI: https://doi.org/10.1107/S2056989019011071/yk2125DTBsup3.hkl
Supporting information file. DOI: https://doi.org/10.1107/S2056989019011071/yk2125TMIsup4.cml
Supporting information file. DOI: https://doi.org/10.1107/S2056989019011071/yk2125DTBsup5.cml
For both structures, data collection: APEX3 (Bruker, 2016); cell
SAINT (Bruker, 2016); data reduction: SAINT (Bruker, 2016); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: OLEX2 (Dolomanov et al., 2009).C25H29N3O3 | F(000) = 896 |
Mr = 419.51 | Dx = 1.262 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
a = 11.7624 (9) Å | Cell parameters from 8868 reflections |
b = 22.9546 (19) Å | θ = 2.5–28.2° |
c = 8.1934 (7) Å | µ = 0.08 mm−1 |
β = 93.717 (2)° | T = 100 K |
V = 2207.6 (3) Å3 | Plate, metallic light blue |
Z = 4 | 0.3 × 0.25 × 0.11 mm |
Bruker APEXII CCD diffractometer | 4810 reflections with I > 2σ(I) |
φ and ω scans | Rint = 0.085 |
Absorption correction: multi-scan (SADABS; Bruker, 2016) | θmax = 31.1°, θmin = 1.7° |
Tmin = 0.601, Tmax = 0.746 | h = −16→17 |
69450 measured reflections | k = −33→33 |
7037 independent reflections | l = −11→11 |
Refinement on F2 | Primary atom site location: dual |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.048 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.117 | H-atom parameters constrained |
S = 1.02 | w = 1/[σ2(Fo2) + (0.0433P)2 + 0.7306P] where P = (Fo2 + 2Fc2)/3 |
7037 reflections | (Δ/σ)max < 0.001 |
285 parameters | Δρmax = 0.33 e Å−3 |
0 restraints | Δρmin = −0.28 e Å−3 |
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 | ||
O1 | 0.57141 (8) | 0.28544 (4) | 0.06369 (11) | 0.0250 (2) | |
C14 | 0.45141 (11) | 0.39420 (5) | 0.74941 (16) | 0.0210 (3) | |
H14 | 0.486034 | 0.431317 | 0.765679 | 0.025* | |
O3 | 0.84399 (9) | 0.40063 (4) | −0.13659 (12) | 0.0300 (2) | |
O2 | 0.68018 (9) | 0.46420 (4) | 0.31743 (12) | 0.0314 (2) | |
N1 | 0.28095 (9) | 0.42110 (4) | 1.26866 (12) | 0.0195 (2) | |
N2 | 0.70066 (9) | 0.34541 (5) | −0.04349 (13) | 0.0203 (2) | |
N3 | 0.75975 (9) | 0.43289 (4) | 0.08893 (13) | 0.0201 (2) | |
C7 | 0.29334 (10) | 0.38885 (5) | 1.13030 (15) | 0.0172 (2) | |
C8 | 0.21355 (10) | 0.33601 (5) | 1.13327 (15) | 0.0174 (2) | |
C5 | 0.15411 (11) | 0.34692 (5) | 1.28882 (15) | 0.0187 (2) | |
C12 | 0.36413 (11) | 0.40500 (5) | 1.01155 (15) | 0.0196 (2) | |
H12 | 0.404050 | 0.440701 | 1.028219 | 0.023* | |
C4 | 0.19733 (11) | 0.39734 (5) | 1.36456 (15) | 0.0195 (2) | |
C13 | 0.38377 (11) | 0.37410 (5) | 0.86730 (15) | 0.0201 (2) | |
H13 | 0.348086 | 0.337243 | 0.850912 | 0.024* | |
C20 | 0.62694 (11) | 0.33057 (5) | 0.07785 (15) | 0.0195 (2) | |
C17 | 0.55933 (10) | 0.35433 (5) | 0.34446 (15) | 0.0201 (2) | |
H17 | 0.523420 | 0.317338 | 0.333554 | 0.024* | |
C21 | 0.77321 (11) | 0.39312 (6) | −0.03588 (15) | 0.0212 (3) | |
C15 | 0.47303 (11) | 0.36355 (6) | 0.60582 (16) | 0.0209 (3) | |
H15 | 0.439083 | 0.326297 | 0.589055 | 0.025* | |
C18 | 0.62303 (10) | 0.37085 (5) | 0.21547 (15) | 0.0188 (2) | |
C19 | 0.68610 (11) | 0.42537 (5) | 0.21503 (15) | 0.0206 (3) | |
C16 | 0.54072 (11) | 0.38470 (6) | 0.48855 (16) | 0.0214 (3) | |
H16 | 0.576385 | 0.421508 | 0.506047 | 0.026* | |
C22 | 0.83708 (11) | 0.48360 (5) | 0.09856 (16) | 0.0225 (3) | |
H22A | 0.797739 | 0.517098 | 0.146023 | 0.027* | |
H22B | 0.856797 | 0.494552 | −0.013005 | 0.027* | |
C9 | 0.12617 (11) | 0.33600 (6) | 0.98519 (15) | 0.0218 (3) | |
H9A | 0.069422 | 0.305443 | 0.999149 | 0.033* | |
H9B | 0.165282 | 0.328573 | 0.885221 | 0.033* | |
H9C | 0.088140 | 0.373965 | 0.976858 | 0.033* | |
C6 | 0.06730 (11) | 0.31656 (6) | 1.35644 (16) | 0.0229 (3) | |
H6 | 0.037084 | 0.282200 | 1.305626 | 0.028* | |
C3 | 0.15744 (12) | 0.41847 (6) | 1.50894 (16) | 0.0243 (3) | |
H3 | 0.188713 | 0.452496 | 1.560313 | 0.029* | |
C10 | 0.28018 (11) | 0.27818 (5) | 1.14518 (17) | 0.0230 (3) | |
H10A | 0.226542 | 0.245599 | 1.148562 | 0.034* | |
H10B | 0.330873 | 0.278119 | 1.244935 | 0.034* | |
H10C | 0.325495 | 0.274050 | 1.049600 | 0.034* | |
C24 | 0.70962 (12) | 0.30531 (6) | −0.18308 (15) | 0.0235 (3) | |
H24A | 0.730561 | 0.327686 | −0.279980 | 0.028* | |
H24B | 0.634697 | 0.286813 | −0.209861 | 0.028* | |
C2 | 0.06930 (12) | 0.38748 (6) | 1.57531 (16) | 0.0267 (3) | |
H2 | 0.039178 | 0.400960 | 1.673280 | 0.032* | |
C1 | 0.02468 (12) | 0.33723 (6) | 1.50078 (17) | 0.0272 (3) | |
H1 | −0.035165 | 0.316835 | 1.548404 | 0.033* | |
C11 | 0.34104 (12) | 0.47513 (6) | 1.30867 (17) | 0.0255 (3) | |
H11A | 0.331476 | 0.485237 | 1.423182 | 0.038* | |
H11B | 0.309903 | 0.506406 | 1.237660 | 0.038* | |
H11C | 0.422246 | 0.470163 | 1.292140 | 0.038* | |
C25 | 0.79828 (12) | 0.25841 (6) | −0.14451 (18) | 0.0289 (3) | |
H25A | 0.805058 | 0.233709 | −0.240946 | 0.043* | |
H25B | 0.775041 | 0.234562 | −0.053227 | 0.043* | |
H25C | 0.871977 | 0.276688 | −0.114467 | 0.043* | |
C23 | 0.94519 (12) | 0.47040 (6) | 0.20246 (19) | 0.0297 (3) | |
H23A | 0.994861 | 0.504712 | 0.206046 | 0.045* | |
H23B | 0.984717 | 0.437534 | 0.154931 | 0.045* | |
H23C | 0.925955 | 0.460408 | 0.313647 | 0.045* |
U11 | U22 | U33 | U12 | U13 | U23 | |
O1 | 0.0246 (5) | 0.0215 (5) | 0.0289 (5) | −0.0026 (4) | 0.0012 (4) | −0.0021 (4) |
C14 | 0.0197 (6) | 0.0193 (6) | 0.0243 (6) | −0.0012 (5) | 0.0032 (5) | 0.0022 (5) |
O3 | 0.0326 (6) | 0.0326 (5) | 0.0261 (5) | −0.0046 (4) | 0.0110 (4) | −0.0023 (4) |
O2 | 0.0397 (6) | 0.0235 (5) | 0.0325 (5) | −0.0086 (4) | 0.0153 (5) | −0.0079 (4) |
N1 | 0.0213 (5) | 0.0172 (5) | 0.0200 (5) | −0.0035 (4) | 0.0015 (4) | −0.0014 (4) |
N2 | 0.0204 (5) | 0.0212 (5) | 0.0193 (5) | 0.0011 (4) | 0.0011 (4) | −0.0016 (4) |
N3 | 0.0208 (5) | 0.0184 (5) | 0.0214 (5) | −0.0011 (4) | 0.0047 (4) | 0.0003 (4) |
C7 | 0.0171 (6) | 0.0148 (5) | 0.0193 (5) | 0.0003 (4) | −0.0010 (4) | 0.0008 (4) |
C8 | 0.0171 (6) | 0.0151 (5) | 0.0200 (5) | −0.0011 (4) | 0.0018 (4) | −0.0005 (4) |
C5 | 0.0190 (6) | 0.0182 (5) | 0.0186 (5) | 0.0007 (5) | −0.0001 (4) | 0.0017 (4) |
C12 | 0.0184 (6) | 0.0169 (5) | 0.0234 (6) | −0.0015 (5) | 0.0014 (5) | 0.0013 (5) |
C4 | 0.0197 (6) | 0.0202 (6) | 0.0183 (5) | −0.0003 (5) | −0.0006 (5) | 0.0019 (4) |
C13 | 0.0170 (6) | 0.0184 (6) | 0.0248 (6) | 0.0005 (5) | 0.0014 (5) | 0.0023 (5) |
C20 | 0.0170 (6) | 0.0204 (6) | 0.0210 (6) | 0.0037 (5) | 0.0001 (5) | 0.0014 (5) |
C17 | 0.0155 (6) | 0.0197 (6) | 0.0250 (6) | 0.0000 (5) | 0.0009 (5) | 0.0006 (5) |
C21 | 0.0210 (6) | 0.0222 (6) | 0.0203 (6) | 0.0019 (5) | 0.0012 (5) | 0.0006 (5) |
C15 | 0.0174 (6) | 0.0199 (6) | 0.0256 (6) | −0.0002 (5) | 0.0025 (5) | 0.0021 (5) |
C18 | 0.0167 (6) | 0.0185 (6) | 0.0211 (6) | 0.0008 (4) | 0.0011 (4) | 0.0001 (5) |
C19 | 0.0202 (6) | 0.0202 (6) | 0.0217 (6) | 0.0014 (5) | 0.0033 (5) | 0.0009 (5) |
C16 | 0.0181 (6) | 0.0212 (6) | 0.0250 (6) | −0.0006 (5) | 0.0024 (5) | 0.0011 (5) |
C22 | 0.0247 (7) | 0.0182 (6) | 0.0253 (6) | −0.0026 (5) | 0.0060 (5) | 0.0020 (5) |
C9 | 0.0205 (6) | 0.0243 (6) | 0.0204 (6) | −0.0008 (5) | −0.0006 (5) | −0.0031 (5) |
C6 | 0.0234 (7) | 0.0216 (6) | 0.0239 (6) | −0.0028 (5) | 0.0025 (5) | 0.0013 (5) |
C3 | 0.0287 (7) | 0.0246 (6) | 0.0194 (6) | −0.0008 (5) | −0.0007 (5) | −0.0015 (5) |
C10 | 0.0223 (6) | 0.0166 (6) | 0.0302 (7) | 0.0004 (5) | 0.0036 (5) | 0.0015 (5) |
C24 | 0.0254 (7) | 0.0263 (6) | 0.0187 (6) | 0.0022 (5) | −0.0001 (5) | −0.0041 (5) |
C2 | 0.0313 (7) | 0.0303 (7) | 0.0190 (6) | 0.0013 (6) | 0.0044 (5) | 0.0014 (5) |
C1 | 0.0269 (7) | 0.0307 (7) | 0.0245 (6) | −0.0037 (6) | 0.0060 (5) | 0.0041 (5) |
C11 | 0.0294 (7) | 0.0184 (6) | 0.0283 (7) | −0.0063 (5) | −0.0013 (6) | −0.0032 (5) |
C25 | 0.0254 (7) | 0.0301 (7) | 0.0308 (7) | 0.0060 (6) | −0.0025 (6) | −0.0096 (6) |
C23 | 0.0219 (7) | 0.0270 (7) | 0.0402 (8) | −0.0001 (5) | 0.0020 (6) | −0.0045 (6) |
O1—C20 | 1.2261 (15) | C15—C16 | 1.3756 (18) |
C14—H14 | 0.9500 | C18—C19 | 1.4550 (17) |
C14—C13 | 1.3706 (18) | C16—H16 | 0.9500 |
C14—C15 | 1.4080 (18) | C22—H22A | 0.9900 |
O3—C21 | 1.2218 (16) | C22—H22B | 0.9900 |
O2—C19 | 1.2291 (15) | C22—C23 | 1.5144 (19) |
N1—C7 | 1.3696 (15) | C9—H9A | 0.9800 |
N1—C4 | 1.4080 (16) | C9—H9B | 0.9800 |
N1—C11 | 1.4544 (16) | C9—H9C | 0.9800 |
N2—C20 | 1.4029 (16) | C6—H6 | 0.9500 |
N2—C21 | 1.3873 (16) | C6—C1 | 1.3971 (19) |
N2—C24 | 1.4772 (16) | C3—H3 | 0.9500 |
N3—C21 | 1.3876 (16) | C3—C2 | 1.3964 (19) |
N3—C19 | 1.4014 (16) | C10—H10A | 0.9800 |
N3—C22 | 1.4760 (16) | C10—H10B | 0.9800 |
C7—C8 | 1.5347 (16) | C10—H10C | 0.9800 |
C7—C12 | 1.3721 (17) | C24—H24A | 0.9900 |
C8—C5 | 1.5137 (17) | C24—H24B | 0.9900 |
C8—C9 | 1.5385 (17) | C24—C25 | 1.5177 (19) |
C8—C10 | 1.5414 (17) | C2—H2 | 0.9500 |
C5—C4 | 1.3936 (17) | C2—C1 | 1.392 (2) |
C5—C6 | 1.3816 (18) | C1—H1 | 0.9500 |
C12—H12 | 0.9500 | C11—H11A | 0.9800 |
C12—C13 | 1.4102 (18) | C11—H11B | 0.9800 |
C4—C3 | 1.3881 (18) | C11—H11C | 0.9800 |
C13—H13 | 0.9500 | C25—H25A | 0.9800 |
C20—C18 | 1.4614 (17) | C25—H25B | 0.9800 |
C17—H17 | 0.9500 | C25—H25C | 0.9800 |
C17—C18 | 1.3874 (17) | C23—H23A | 0.9800 |
C17—C16 | 1.4004 (18) | C23—H23B | 0.9800 |
C15—H15 | 0.9500 | C23—H23C | 0.9800 |
C13—C14—H14 | 117.8 | N3—C22—H22A | 109.4 |
C13—C14—C15 | 124.41 (12) | N3—C22—H22B | 109.4 |
C15—C14—H14 | 117.8 | N3—C22—C23 | 111.37 (11) |
C7—N1—C4 | 111.60 (10) | H22A—C22—H22B | 108.0 |
C7—N1—C11 | 124.84 (11) | C23—C22—H22A | 109.4 |
C4—N1—C11 | 123.46 (11) | C23—C22—H22B | 109.4 |
C20—N2—C24 | 118.41 (10) | C8—C9—H9A | 109.5 |
C21—N2—C20 | 124.51 (11) | C8—C9—H9B | 109.5 |
C21—N2—C24 | 116.88 (11) | C8—C9—H9C | 109.5 |
C21—N3—C19 | 124.60 (11) | H9A—C9—H9B | 109.5 |
C21—N3—C22 | 117.31 (10) | H9A—C9—H9C | 109.5 |
C19—N3—C22 | 117.77 (10) | H9B—C9—H9C | 109.5 |
N1—C7—C8 | 108.43 (10) | C5—C6—H6 | 120.6 |
N1—C7—C12 | 122.88 (11) | C5—C6—C1 | 118.90 (12) |
C12—C7—C8 | 128.65 (11) | C1—C6—H6 | 120.6 |
C7—C8—C9 | 111.44 (10) | C4—C3—H3 | 121.5 |
C7—C8—C10 | 111.88 (10) | C4—C3—C2 | 117.03 (12) |
C5—C8—C7 | 101.47 (9) | C2—C3—H3 | 121.5 |
C5—C8—C9 | 110.04 (10) | C8—C10—H10A | 109.5 |
C5—C8—C10 | 110.48 (10) | C8—C10—H10B | 109.5 |
C9—C8—C10 | 111.14 (10) | C8—C10—H10C | 109.5 |
C4—C5—C8 | 109.71 (11) | H10A—C10—H10B | 109.5 |
C6—C5—C8 | 130.38 (11) | H10A—C10—H10C | 109.5 |
C6—C5—C4 | 119.88 (12) | H10B—C10—H10C | 109.5 |
C7—C12—H12 | 116.6 | N2—C24—H24A | 109.4 |
C7—C12—C13 | 126.75 (12) | N2—C24—H24B | 109.4 |
C13—C12—H12 | 116.6 | N2—C24—C25 | 111.31 (10) |
C5—C4—N1 | 108.73 (11) | H24A—C24—H24B | 108.0 |
C3—C4—N1 | 128.85 (12) | C25—C24—H24A | 109.4 |
C3—C4—C5 | 122.41 (12) | C25—C24—H24B | 109.4 |
C14—C13—C12 | 123.73 (12) | C3—C2—H2 | 119.3 |
C14—C13—H13 | 118.1 | C1—C2—C3 | 121.31 (13) |
C12—C13—H13 | 118.1 | C1—C2—H2 | 119.3 |
O1—C20—N2 | 119.21 (11) | C6—C1—H1 | 119.8 |
O1—C20—C18 | 124.36 (12) | C2—C1—C6 | 120.47 (13) |
N2—C20—C18 | 116.42 (11) | C2—C1—H1 | 119.8 |
C18—C17—H17 | 115.6 | N1—C11—H11A | 109.5 |
C18—C17—C16 | 128.88 (12) | N1—C11—H11B | 109.5 |
C16—C17—H17 | 115.6 | N1—C11—H11C | 109.5 |
O3—C21—N2 | 121.68 (12) | H11A—C11—H11B | 109.5 |
O3—C21—N3 | 121.35 (12) | H11A—C11—H11C | 109.5 |
N2—C21—N3 | 116.95 (11) | H11B—C11—H11C | 109.5 |
C14—C15—H15 | 118.3 | C24—C25—H25A | 109.5 |
C16—C15—C14 | 123.46 (12) | C24—C25—H25B | 109.5 |
C16—C15—H15 | 118.3 | C24—C25—H25C | 109.5 |
C17—C18—C20 | 117.41 (11) | H25A—C25—H25B | 109.5 |
C17—C18—C19 | 122.52 (11) | H25A—C25—H25C | 109.5 |
C19—C18—C20 | 120.05 (11) | H25B—C25—H25C | 109.5 |
O2—C19—N3 | 118.62 (12) | C22—C23—H23A | 109.5 |
O2—C19—C18 | 124.79 (12) | C22—C23—H23B | 109.5 |
N3—C19—C18 | 116.58 (11) | C22—C23—H23C | 109.5 |
C17—C16—H16 | 118.6 | H23A—C23—H23B | 109.5 |
C15—C16—C17 | 122.84 (12) | H23A—C23—H23C | 109.5 |
C15—C16—H16 | 118.6 | H23B—C23—H23C | 109.5 |
D—H···A | D—H | H···A | D···A | D—H···A |
C3—H3···O2i | 0.95 | 2.61 | 3.5458 (17) | 167 |
C24—H24B···O1ii | 0.99 | 2.56 | 3.2939 (16) | 131 |
C11—H11A···O2i | 0.98 | 2.43 | 3.3891 (17) | 165 |
Symmetry codes: (i) −x+1, −y+1, −z+2; (ii) x, −y+1/2, z−1/2. |
C21H25N3O2S | F(000) = 816 |
Mr = 383.50 | Dx = 1.311 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
a = 16.1504 (6) Å | Cell parameters from 9983 reflections |
b = 8.1264 (3) Å | θ = 2.6–37.3° |
c = 15.6487 (6) Å | µ = 0.19 mm−1 |
β = 108.849 (1)° | T = 100 K |
V = 1943.67 (13) Å3 | Block, clear light red |
Z = 4 | 0.3 × 0.26 × 0.24 mm |
Bruker APEXII CCD diffractometer | 8903 reflections with I > 2σ(I) |
φ and ω scans | Rint = 0.045 |
Absorption correction: multi-scan (SADABS; Bruker, 2016) | θmax = 40.4°, θmin = 1.3° |
Tmin = 0.678, Tmax = 0.748 | h = −29→29 |
92854 measured reflections | k = −14→14 |
12354 independent reflections | l = −28→28 |
Refinement on F2 | Primary atom site location: dual |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.046 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.141 | H-atom parameters constrained |
S = 1.04 | w = 1/[σ2(Fo2) + (0.0645P)2 + 0.5305P] where P = (Fo2 + 2Fc2)/3 |
12354 reflections | (Δ/σ)max = 0.002 |
249 parameters | Δρmax = 0.64 e Å−3 |
0 restraints | Δρmin = −0.46 e Å−3 |
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 | ||
S1 | 0.96141 (2) | 0.35712 (4) | 0.80259 (2) | 0.03286 (7) | |
O1 | 0.66676 (4) | 0.20400 (9) | 0.60288 (4) | 0.02461 (12) | |
N1 | 0.35986 (4) | 0.35270 (9) | 0.51788 (4) | 0.01788 (11) | |
O2 | 0.69412 (5) | 0.64835 (10) | 0.80519 (6) | 0.0389 (2) | |
N2 | 0.80016 (4) | 0.28754 (10) | 0.69633 (4) | 0.02129 (12) | |
N3 | 0.81446 (5) | 0.51652 (10) | 0.79244 (5) | 0.02353 (13) | |
C7 | 0.38323 (5) | 0.56295 (9) | 0.62627 (5) | 0.01636 (11) | |
C5 | 0.27705 (5) | 0.42249 (10) | 0.50767 (5) | 0.01701 (11) | |
C8 | 0.42390 (5) | 0.42923 (10) | 0.58292 (5) | 0.01659 (11) | |
C4 | 0.28730 (5) | 0.54688 (9) | 0.57129 (5) | 0.01715 (11) | |
C12 | 0.51201 (5) | 0.38347 (10) | 0.60429 (5) | 0.01905 (12) | |
H12 | 0.526462 | 0.294068 | 0.572630 | 0.023* | |
C14 | 0.66935 (5) | 0.43462 (10) | 0.69647 (5) | 0.01941 (12) | |
C13 | 0.57882 (5) | 0.46339 (10) | 0.66971 (5) | 0.01924 (12) | |
H13 | 0.560884 | 0.549633 | 0.700776 | 0.023* | |
C16 | 0.70815 (5) | 0.30405 (11) | 0.66025 (5) | 0.01949 (13) | |
C10 | 0.41564 (5) | 0.73819 (10) | 0.61661 (5) | 0.01950 (12) | |
H10A | 0.477565 | 0.747867 | 0.652692 | 0.029* | |
H10B | 0.381410 | 0.818280 | 0.637982 | 0.029* | |
H10C | 0.408539 | 0.759843 | 0.553031 | 0.029* | |
C3 | 0.21469 (5) | 0.63327 (11) | 0.57521 (6) | 0.02240 (14) | |
H3 | 0.220551 | 0.718222 | 0.618475 | 0.027* | |
C6 | 0.19664 (5) | 0.38216 (11) | 0.44549 (5) | 0.02134 (13) | |
H6 | 0.191296 | 0.298193 | 0.401796 | 0.026* | |
C11 | 0.39728 (5) | 0.52071 (11) | 0.72630 (5) | 0.02033 (13) | |
H11A | 0.377983 | 0.407614 | 0.730697 | 0.030* | |
H11B | 0.363251 | 0.596715 | 0.750444 | 0.030* | |
H11C | 0.459504 | 0.531035 | 0.761164 | 0.030* | |
C1 | 0.12383 (5) | 0.47033 (12) | 0.44987 (6) | 0.02465 (15) | |
H1 | 0.067688 | 0.446104 | 0.408353 | 0.030* | |
C15 | 0.72309 (5) | 0.54097 (11) | 0.76693 (6) | 0.02409 (15) | |
C9 | 0.37009 (6) | 0.20956 (12) | 0.46596 (6) | 0.02593 (16) | |
H9A | 0.345701 | 0.112329 | 0.486189 | 0.039* | |
H9B | 0.432365 | 0.191579 | 0.475090 | 0.039* | |
H9C | 0.339086 | 0.228611 | 0.401702 | 0.039* | |
C2 | 0.13236 (5) | 0.59308 (12) | 0.51416 (7) | 0.02590 (16) | |
H2 | 0.081895 | 0.650225 | 0.516706 | 0.031* | |
C17 | 0.85370 (5) | 0.38883 (12) | 0.76148 (5) | 0.02227 (14) | |
C18 | 0.83775 (5) | 0.14263 (14) | 0.66450 (6) | 0.02812 (18) | |
H18B | 0.898124 | 0.168077 | 0.665894 | 0.034* | |
H18A | 0.802474 | 0.117384 | 0.601326 | 0.034* | |
C19 | 0.83898 (6) | −0.00613 (13) | 0.72371 (7) | 0.02925 (18) | |
H19B | 0.865022 | −0.099926 | 0.702348 | 0.044* | |
H19C | 0.779012 | −0.033514 | 0.720698 | 0.044* | |
H19A | 0.873715 | 0.019095 | 0.786277 | 0.044* | |
C20 | 0.86824 (6) | 0.62716 (12) | 0.86467 (8) | 0.0319 (2) | |
H20A | 0.839194 | 0.735725 | 0.859387 | 0.038* | |
H20B | 0.926070 | 0.643783 | 0.856798 | 0.038* | |
C21 | 0.88084 (7) | 0.55668 (14) | 0.95736 (7) | 0.0341 (2) | |
H21A | 0.909420 | 0.449030 | 0.962662 | 0.051* | |
H21B | 0.823795 | 0.544084 | 0.966166 | 0.051* | |
H21C | 0.917496 | 0.631204 | 1.003387 | 0.051* |
U11 | U22 | U33 | U12 | U13 | U23 | |
S1 | 0.01270 (8) | 0.04879 (16) | 0.03404 (12) | −0.00224 (8) | 0.00332 (7) | −0.00092 (10) |
O1 | 0.0176 (2) | 0.0376 (4) | 0.0168 (2) | 0.0010 (2) | 0.00299 (18) | −0.0047 (2) |
N1 | 0.0150 (2) | 0.0200 (3) | 0.0174 (2) | −0.0009 (2) | 0.00355 (18) | −0.00432 (19) |
O2 | 0.0243 (3) | 0.0270 (3) | 0.0515 (5) | 0.0064 (3) | −0.0069 (3) | −0.0139 (3) |
N2 | 0.0135 (2) | 0.0331 (4) | 0.0167 (2) | −0.0002 (2) | 0.00410 (18) | 0.0020 (2) |
N3 | 0.0161 (3) | 0.0216 (3) | 0.0269 (3) | −0.0032 (2) | −0.0013 (2) | 0.0042 (2) |
C7 | 0.0150 (2) | 0.0183 (3) | 0.0143 (2) | −0.0008 (2) | 0.00274 (19) | −0.0018 (2) |
C5 | 0.0142 (2) | 0.0190 (3) | 0.0167 (2) | −0.0017 (2) | 0.00338 (19) | −0.0013 (2) |
C8 | 0.0144 (2) | 0.0196 (3) | 0.0145 (2) | −0.0008 (2) | 0.00288 (19) | −0.0009 (2) |
C4 | 0.0147 (2) | 0.0187 (3) | 0.0169 (3) | −0.0005 (2) | 0.00356 (19) | −0.0012 (2) |
C12 | 0.0141 (3) | 0.0240 (3) | 0.0176 (3) | 0.0006 (2) | 0.0031 (2) | 0.0000 (2) |
C14 | 0.0143 (3) | 0.0221 (3) | 0.0186 (3) | −0.0005 (2) | 0.0009 (2) | 0.0033 (2) |
C13 | 0.0152 (3) | 0.0216 (3) | 0.0185 (3) | 0.0005 (2) | 0.0020 (2) | 0.0021 (2) |
C16 | 0.0141 (2) | 0.0290 (4) | 0.0146 (2) | −0.0001 (2) | 0.00368 (19) | 0.0033 (2) |
C10 | 0.0197 (3) | 0.0189 (3) | 0.0181 (3) | −0.0024 (2) | 0.0035 (2) | −0.0010 (2) |
C3 | 0.0179 (3) | 0.0238 (3) | 0.0248 (3) | 0.0023 (3) | 0.0059 (2) | −0.0021 (3) |
C6 | 0.0165 (3) | 0.0234 (3) | 0.0209 (3) | −0.0043 (2) | 0.0016 (2) | −0.0020 (2) |
C11 | 0.0228 (3) | 0.0225 (3) | 0.0153 (3) | −0.0004 (3) | 0.0056 (2) | −0.0004 (2) |
C1 | 0.0149 (3) | 0.0276 (4) | 0.0277 (4) | −0.0029 (3) | 0.0016 (2) | 0.0017 (3) |
C15 | 0.0176 (3) | 0.0191 (3) | 0.0286 (4) | 0.0006 (2) | −0.0023 (2) | 0.0022 (3) |
C9 | 0.0231 (3) | 0.0254 (4) | 0.0280 (4) | −0.0003 (3) | 0.0065 (3) | −0.0112 (3) |
C2 | 0.0158 (3) | 0.0275 (4) | 0.0327 (4) | 0.0022 (3) | 0.0054 (3) | 0.0008 (3) |
C17 | 0.0144 (3) | 0.0302 (4) | 0.0207 (3) | −0.0028 (3) | 0.0037 (2) | 0.0056 (3) |
C18 | 0.0166 (3) | 0.0485 (6) | 0.0202 (3) | 0.0036 (3) | 0.0072 (2) | −0.0065 (3) |
C19 | 0.0206 (3) | 0.0327 (4) | 0.0337 (4) | 0.0031 (3) | 0.0078 (3) | −0.0107 (3) |
C20 | 0.0221 (4) | 0.0202 (4) | 0.0415 (5) | −0.0045 (3) | −0.0061 (3) | −0.0001 (3) |
C21 | 0.0306 (4) | 0.0283 (4) | 0.0324 (4) | 0.0041 (3) | −0.0048 (3) | −0.0082 (3) |
S1—C17 | 1.6683 (8) | C10—H10B | 0.9800 |
O1—C16 | 1.2354 (10) | C10—H10C | 0.9800 |
N1—C5 | 1.4135 (10) | C3—H3 | 0.9500 |
N1—C8 | 1.3462 (9) | C3—C2 | 1.4024 (12) |
N1—C9 | 1.4585 (11) | C6—H6 | 0.9500 |
O2—C15 | 1.2329 (12) | C6—C1 | 1.3974 (12) |
N2—C16 | 1.4152 (10) | C11—H11A | 0.9800 |
N2—C17 | 1.3766 (11) | C11—H11B | 0.9800 |
N2—C18 | 1.4829 (12) | C11—H11C | 0.9800 |
N3—C15 | 1.4128 (11) | C1—H1 | 0.9500 |
N3—C17 | 1.3825 (13) | C1—C2 | 1.3915 (14) |
N3—C20 | 1.4852 (12) | C9—H9A | 0.9800 |
C7—C8 | 1.5362 (10) | C9—H9B | 0.9800 |
C7—C4 | 1.5154 (10) | C9—H9C | 0.9800 |
C7—C10 | 1.5414 (11) | C2—H2 | 0.9500 |
C7—C11 | 1.5460 (10) | C18—H18B | 0.9900 |
C5—C4 | 1.3907 (10) | C18—H18A | 0.9900 |
C5—C6 | 1.3871 (10) | C18—C19 | 1.5194 (16) |
C8—C12 | 1.4027 (10) | C19—H19B | 0.9800 |
C4—C3 | 1.3850 (11) | C19—H19C | 0.9800 |
C12—H12 | 0.9500 | C19—H19A | 0.9800 |
C12—C13 | 1.3858 (11) | C20—H20A | 0.9900 |
C14—C13 | 1.4043 (10) | C20—H20B | 0.9900 |
C14—C16 | 1.4384 (12) | C20—C21 | 1.5109 (17) |
C14—C15 | 1.4483 (12) | C21—H21A | 0.9800 |
C13—H13 | 0.9500 | C21—H21B | 0.9800 |
C10—H10A | 0.9800 | C21—H21C | 0.9800 |
C5—N1—C9 | 122.03 (6) | C7—C11—H11A | 109.5 |
C8—N1—C5 | 111.58 (6) | C7—C11—H11B | 109.5 |
C8—N1—C9 | 126.30 (7) | C7—C11—H11C | 109.5 |
C16—N2—C18 | 115.62 (7) | H11A—C11—H11B | 109.5 |
C17—N2—C16 | 124.48 (7) | H11A—C11—H11C | 109.5 |
C17—N2—C18 | 119.75 (7) | H11B—C11—H11C | 109.5 |
C15—N3—C20 | 115.50 (8) | C6—C1—H1 | 119.5 |
C17—N3—C15 | 124.17 (7) | C2—C1—C6 | 120.98 (7) |
C17—N3—C20 | 119.97 (7) | C2—C1—H1 | 119.5 |
C8—C7—C10 | 113.77 (6) | O2—C15—N3 | 119.20 (8) |
C8—C7—C11 | 110.25 (6) | O2—C15—C14 | 124.33 (8) |
C4—C7—C8 | 101.13 (6) | N3—C15—C14 | 116.46 (8) |
C4—C7—C10 | 109.95 (6) | N1—C9—H9A | 109.5 |
C4—C7—C11 | 110.14 (6) | N1—C9—H9B | 109.5 |
C10—C7—C11 | 111.16 (6) | N1—C9—H9C | 109.5 |
C4—C5—N1 | 108.74 (6) | H9A—C9—H9B | 109.5 |
C6—C5—N1 | 128.44 (7) | H9A—C9—H9C | 109.5 |
C6—C5—C4 | 122.81 (7) | H9B—C9—H9C | 109.5 |
N1—C8—C7 | 109.09 (6) | C3—C2—H2 | 119.7 |
N1—C8—C12 | 122.01 (7) | C1—C2—C3 | 120.67 (8) |
C12—C8—C7 | 128.89 (6) | C1—C2—H2 | 119.7 |
C5—C4—C7 | 109.42 (6) | N2—C17—S1 | 121.36 (7) |
C3—C4—C7 | 131.01 (7) | N2—C17—N3 | 117.32 (7) |
C3—C4—C5 | 119.57 (7) | N3—C17—S1 | 121.31 (6) |
C8—C12—H12 | 118.7 | N2—C18—H18B | 109.5 |
C13—C12—C8 | 122.66 (7) | N2—C18—H18A | 109.5 |
C13—C12—H12 | 118.7 | N2—C18—C19 | 110.68 (7) |
C13—C14—C16 | 123.32 (7) | H18B—C18—H18A | 108.1 |
C13—C14—C15 | 115.97 (8) | C19—C18—H18B | 109.5 |
C16—C14—C15 | 120.66 (7) | C19—C18—H18A | 109.5 |
C12—C13—C14 | 129.01 (8) | C18—C19—H19B | 109.5 |
C12—C13—H13 | 115.5 | C18—C19—H19C | 109.5 |
C14—C13—H13 | 115.5 | C18—C19—H19A | 109.5 |
O1—C16—N2 | 118.64 (8) | H19B—C19—H19C | 109.5 |
O1—C16—C14 | 124.72 (7) | H19B—C19—H19A | 109.5 |
N2—C16—C14 | 116.59 (7) | H19C—C19—H19A | 109.5 |
C7—C10—H10A | 109.5 | N3—C20—H20A | 109.3 |
C7—C10—H10B | 109.5 | N3—C20—H20B | 109.3 |
C7—C10—H10C | 109.5 | N3—C20—C21 | 111.43 (8) |
H10A—C10—H10B | 109.5 | H20A—C20—H20B | 108.0 |
H10A—C10—H10C | 109.5 | C21—C20—H20A | 109.3 |
H10B—C10—H10C | 109.5 | C21—C20—H20B | 109.3 |
C4—C3—H3 | 120.6 | C20—C21—H21A | 109.5 |
C4—C3—C2 | 118.80 (8) | C20—C21—H21B | 109.5 |
C2—C3—H3 | 120.6 | C20—C21—H21C | 109.5 |
C5—C6—H6 | 121.4 | H21A—C21—H21B | 109.5 |
C5—C6—C1 | 117.15 (8) | H21A—C21—H21C | 109.5 |
C1—C6—H6 | 121.4 | H21B—C21—H21C | 109.5 |
D—H···A | D—H | H···A | D···A | D—H···A |
C12—H12···O1 | 0.95 | 2.28 | 2.9000 (10) | 122 |
C19—H19B···S1i | 0.98 | 2.85 | 3.5573 (9) | 130 |
C21—H21A···S1 | 0.98 | 2.98 | 3.4965 (12) | 114 |
Symmetry code: (i) −x+2, y−1/2, −z+3/2. |
Funding information
Funding for this research was provided by: National Science Foundation (grant No. DMR-1523611).
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