Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229615015946/uk3117sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S2053229615015946/uk3117Isup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2053229615015946/uk3117IIsup3.hkl | |
Chemical Markup Language (CML) file https://doi.org/10.1107/S2053229615015946/uk3117IIsup4.cml |
CCDC references: 1420601; 1420600
The stable aminoxyl radical TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl) and its derivatives have received much attention due to their usefulness in synthesis and a wide variety of practical applications (Crich, 2008). They have been employed extensively as mild oxidants for alcohols, often in catalytic quantities (Gheorghe et al., 2006; Tojo & Fernández, 2007; Tebben & Studer, 2011), and as radical traps in biological science, and in molecular and polymer synthesis (Conte et al., 2009; Pattison et al., 2012; Hyslop & Parent, 2012). The polymer sub-discipline of nitroxide-mediated polymerization (NMP) derives its name from this class of compounds (Tebben & Studer, 2011). Other applications include use as a paramagnetic probe for EPR studies (Ricci et al., 2011), as a spin label in NMR (Jahnke et al., 2000, 2001), as a photostabilizer (Beaton & Argyropoulos, 2001) and as a synergist with antineoplastic agents (Ba & Mathias, 2011). In addition, the Nishide group have successfully utilized aminoxyl radicals as the cathode in organic rechargeable batteries (Nishide et al., 2009; Koshika et al., 2010).
Our primary interest in TEMPO derivatives is as redox-active subunits in polymer gel actuators (Goswami et al., 2013). During the course of this work, we have reported the structures of TEMPO-type complexes and their respective precursors (see, for example, Goswami et al., 2011, 2014, 2015). Recently, we prepared crystalline samples of both TEMPO acrylamide, (I), and its piperidinyl analogue, (II) (see scheme). We report here their molecular structures and packing arrangements.
The TEMPO HC(CH2)2(CMe2)2NO radical skeleton appears in more than 200 structures recorded in the Cambridge Structural Database (CSD, [Version?]; Groom & Allen, 2014). Interest in the crystal packing of such species derives from the fact that they often display intermolecular ferromagnetic interactions at extremely low temperatures, and the packing features in such materials show considerable similarities (Kajiwara et al., 1995; Iwasaki, Yoshikawa, Yamamoto, Kan-nari et al., 1999; Iwasaki, Yoshikawa, Yamamoto, Takada et al., 1999). Structures of compounds with a secondary amide substituent at the TEMPO 4-position are somewhat less plentiful, with 30 discrete examples in the CSD, ranging from the simple 4-acetamide-2,2,6,6-tetramethyl-piperidine-1-oxyl (CSD refcode UDOMUW; Yonekuta et al., 2007) to more complex compounds, e.g. the TEMPO dimer [EQUKIK; trans-N,N'-bis(2,2,6,6-tetramethylpiperidin-4-yl N-oxide)oxamide; Sommer et al., 2003], the fluorenyl derivative {AHIBEZ; 4-[(9H-fluoren-9-yl)(9H-fluoren-9-ylidene)methyl]-N-(1-oxyl-2,2,6,6-tetramethylpiperidin-4-yl)benzamide capable of forming a biradical species; Dane et al., 2009}, and various organometallic examples (Qiu et al., 2009; Yi et al., 2011).
A CSD search for 2,2,6,6-tetramethylpiperidines turns up many protonated or metal-coordinated quaternary examples, but the neutral amine is not common, registering only 12 hits. Of these, 4-amido derivatives are represented by succinic diamide (MPLSCA; Ruben et al., 1974) and oxalamide (MEFGIO; McFarland et al., 2006) structures.
A search for structures with the acrylamide functional group reveals 44 unique molecules, 13 of which are found in metal complexes. These include acrylamide itself (Zhou et al., 2007; Udovenko & Kolzunova, 2008) and N-(1-acryloyl-2,2,6,6-tetramethylpiperidin-4-yl)acrylamide (Goswami et al., 2011), a close relative of the acrylamide derivatives reported here.
2,2,6,6-Tetramethyl-4-acrylamido-1-piperidine-1-oxyl, (I), was synthesized using modifications (Gheorghe et al., 2006) to the original procedure of Rozantsev & Suskina (1968) (Fig. 1). To a stirred suspension of NaH (2 equivalents) in dry dimethylformamide (DMF, 100 ml) at 273 K, 4-amino-2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO-NH2, 1 equivalent) was added in small portions. The reaction mixture was then stirred at room temperature for 30 min, with the visible evolution of hydrogen gas. Acryloyl chloride (2 equivalents) was added dropwise at 273 K. The resulting mixture was stirred for 3 h at room temperature, after which water (100 ml) was added and the solution extracted with EtOAc (2 × 50 ml). The organic phase was washed with water (2 × 50 ml), dried over anhydrous MgSO4, filtered, evaporated under reduced pressure and purified by column chromatography (silica gel, 10% EtOAc in hexane) to give (I) as a dark-orange solid. Recrystallization from EtOAc gave near-colourless plates of (I) (72% yield).
N-(2,2,6,6-Tetramethylpiperidin-4-yl)acrylamide, (II), was synthesized according to the procedure of Nishide and co-workers (Koshika et al., 2010), an updated version of the method of Karrer (1980) (Fig. 1). Recrystallization of the acrylamide monomer from methanol gave colourless blocks of (II).
For (I): m.p. 321–322 K; IR (ATR, ν, cm-1): 1657 (C═O), 1636 (C═C); microanalysis, calculated: C 63.97, H 9.39, N 12.43%; found: C 63.55, H 9.44, N 11.96%; HRMS (ESI+), calculated for C12H21NaNO2: 248.1491; found: 248.1495 [M]+.
For (II): m.p. 381–383 K; IR (ATR, ν, cm-1): 1659 (C═O), 1625 (C═ C); 1H NMR (400 MHz, CDCl3, δ, p.p.m.): 6.25 (1H, dd, J = 1 and 17 Hz, –CH═CHtrans), 6.07 (1H, dd, J = 11 and 17 Hz, –CH═CH2), 6.06 (1H, br, amide NH), 5.60 (1H, dd, J = 1 and 11 Hz, –CH═CHcis), 4.34 (1H, m, piperidine CH), 3.24 (1H, br, amine NH), 1.88 (2H, dd, J = 4 and 13 Hz, piperidine CH2), 1.32 (6H, s, 2 × CH3), 1.22 (6H, s, 2 × CH3); 13C NMR (400 MHz, CDCl3, δ, p.p.m.): 164.9 (C═ O), 131.0 (–CH═), 126.2 (═CH2), 51.3, 44.8, 42.4, [34.6 and 28.2 (CH3)]; HRMS (ESI+), calculated for C12H22NaN2O: 234.1464; found: 234.1476 [M]+.
Crystal data, data collection and structure refinement details are summarised in Table 1. The H atoms on N1 for (I), and on N1, N4 and O1W for (II), were located in difference Fourier maps and their coordinates were refined, with Uiso(H) = 1.2Ueq(N) and 1.5Ueq(O). All H atoms bound to C atoms were refined using a riding model, with C—H = 0.95 Å for vinyl H atoms, 1.00 Å for C—H and 0.99 Å for CH2 H atoms, all with Uiso(H) = 1.2Ueq(C), and with C—H = 0.98 Å and Uiso(H) = 1.5Ueq(C) for CH3 H atoms. For (II), ISOR [Please rephrase using non-software-specific terms] restraints were applied to atoms N1, N4, O7 and C2–C9 to prevent them appearing as nonpositive definite.
The molecular structures of (I) and (II) (Figs. 2a and 2b) are sufficiently similar to be discussed together. The piperidine rings each adopt chair conformations, with two methyl substituents on each of atoms C2 and C6. An oxyl substituent on atom N1 of (I) generates the classical TEMPO skeleton (Lebedev & Kazarnovskii, 1960) from the precursor piperidine (II). The C4 acrylamide substituents complete their structural units. The relative conformations of the acrylamide C═O and vinyl double bonds are the usual s-cis; O7—C7—C8—C9 torsion angles = 3.59 (17)° for (I) and 16.3 (2)° for (II). This compares with Vista (Groom & Allen, 2014) results for acrylamide O═C—C═C torsion angles; median value = 4.443° over 134 observations.
There is a noticeable similarity in the geometry of the acrylamide residues with respect to the piperidinyl rings for (I) and (II). Illustrating this, the C7—N—C4—C3 torsion angles (see Fig. 3) for (I) and (II) are 91.74 (11) and 89.16 (14)°, respectively. This trans spatial arrangement of the piperidinyl and amide H atoms appears common for TEMPO secondary amides, for example, 4-acetamide-2,2,6,6-tetramethylpiperidine-1-oxyl (torsion angle = 91.23°; CSD refcode UDOMUW; Yonekuta et al., 2007), 4-[(9H-fluoren-9-yl)(9H-fluoren-9-ylidene)methyl]- N-(1-oxyl-2,2,6,6-tetramethylpiperidin-4-yl)benzamide acetone solvate (torsion angle = 91.34°; CSD refcode AHIBEZ; Dane et al., 2009), and the two piperidinyl examples in the CSD, i.e. N-(4-bromophenyl)-N'-(2,2,6,6-tetramethyl-4-piperidinyl)oxalamide (torsion angle = 97.61°; CSD refcode MEFGIO; McFarland et al., 2006) and N,N'-bis(2,2,6,6-tetramethylpiperidyl-4)succinic acid diamide dehydrate (torsion angle = 99.14°; CSD refcode MPLSCA; Ruben et al., 1974). The similarity also extends to the closely related TEMPO acrylate, namely 4-acryloyloxy-2,2,6,6-tetramethylpiperidine-1-oxyl (refcode LUFQIO00), and methacrylate, namely 4-methacryloyloxy-2,2,6,6-tetramethylpiperidine-1-oxyl, (refcode LUFQOU00) (Goswami et al., 2015), with equivalent torsion angles of 84.78 (13) and 83.1 (3)°, respectively.
Bond lengths (Allen et al., 1987) and angles are normal in both molecules and compare well with those found in closely related structures (Goswami et al., 2011, 2014). Compound (II) crystallizes with a water solvent molecule in the asymmetric unit, linked to the organic molecule via an N—H···O hydrogen bond from the acrylamide substituent.
For (I), a C(4) chain (Bernstein et al., 1995) of classical N4—H4N···O7 hydrogen bonds, supported by C8—H8···O7 contacts, links adjacent acrylamide substituents (Table 2). These contacts, with atom O7 acting as a bifurcated acceptor, generate an R21(6) ring (Bernstein et al., 1995) repeat structure that stacks the molecules along c. Within this chain, the molecules flip-flop in an approximately head-to-tail fashion, with a dihedral angle of 146.51° between adjacent R21(6) ring planes (Fig. 4). Similar chain propagation with the formation of six-membered rings has been observed for other acrylamide structures [N-(2-hydroxymethyl)-1,3-dihydroxy-2-propyl)acrylamic acid (refcode YOXBAO; Oddon et al., 1995) and N-tert-butylacrylamide (refcode CEDXUE01; Kashino et al., 1994)]. However, in these examples, the rings form between near-orthogonal molecules (the dihedral angles between ring motifs are 104.35° for YOXBAO and 107.44° for CEDXUE01). In the bis(2-acrylamido-2-methylpropane-1-sulfonate) salt (refcode JAVQON; Ribot et al., 2005), by contrast, the R21(6) motif propagates through the structure in a helical fashion.
The former packing motif does not result in any close contacts between the nitroxide O1 atoms. Indeed the closest intermolecular contacts involving O1 are two very weak nonclassical C61—H61C···O1 and C22—H22A···O1 hydrogen bonds that compose R22(10) rings and bridge the chains formed by the R21(6) repeat. The overall effect is the formation of layers in the bc plane (Fig. 5). Close and almost orthogonal contacts between nitroxide groups [O1···O1 = 4.184 (3) Å] have been implicated as a possible cause of ferromagnetic exchange reactions in TEMPO systems (Griesar et al., 1997, 2000). In (I), the shortest O···O contact distances are significantly longer [O1···O1iii = 4.945 (2) Å; symmetry code: (iii) x, -y + 1/2, z - 1/2] and the NO functional groups are not orthogonal. Finally, additional weak C21—H21B···O7 contacts form zigzag C(8) chains along b (Fig. 6) and interconnect the layers of molecules to generate a three-dimensional network.
The crystal structure of (II) contrasts sharply with that of (I), with the water solvent molecule playing a seminal role in the overall packing framework. Each water molecule acts as an acceptor in a classical N2—H2N···O1W hydrogen bond, and as a donor in O1W—H1W···O7 and O1W—H2W···N1 hydrogen bonds (Table 3). These contacts bind adjacent trios of molecules into a two-dimensional layer in the bc plane (Fig. 7). Weak C21—H21C···O7 contacts form inversion dimers enclosing R22(16) loops. These weaker contacts also link parallel layers of molecules, resulting in a three-dimensional network of molecules stacked along the b axis.
For both compounds, data collection: CrysAlis PRO (Agilent, 2013); cell refinement: CrysAlis PRO (Agilent, 2013); data reduction: CrysAlis PRO (Agilent, 2013). Program(s) used to solve structure: SHELXS97 (Sheldrick, 2008) and TITAN (Hunter & Simpson, 1999) for (I); SIR2011 (Burla et al., 2012) for (II). For both compounds, program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015) and TITAN (Hunter & Simpson, 1999); molecular graphics: Mercury (Macrae et al., 2008); software used to prepare material for publication: SHELXL2014 (Sheldrick, 2015), enCIFer (Allen et al., 2004) and publCIF (Westrip, 2010).
C12H21N2O2 | F(000) = 492 |
Mr = 225.31 | Dx = 1.197 Mg m−3 |
Monoclinic, P21/c | Cu Kα radiation, λ = 1.54184 Å |
a = 11.5408 (2) Å | Cell parameters from 7507 reflections |
b = 11.7953 (2) Å | θ = 4.1–74.2° |
c = 9.7964 (2) Å | µ = 0.66 mm−1 |
β = 110.299 (2)° | T = 100 K |
V = 1250.74 (4) Å3 | Plate, colourless |
Z = 4 | 0.27 × 0.11 × 0.05 mm |
Agilent SuperNova Dual Source diffractometer with an Atlas detector | 2516 independent reflections |
Radiation source: SuperNova (Cu) X-ray Source | 2275 reflections with I > 2σ(I) |
Detector resolution: 5.1725 pixels mm-1 | Rint = 0.030 |
ω scans | θmax = 74.3°, θmin = 4.1° |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2013) | h = −14→14 |
Tmin = 0.752, Tmax = 1.000 | k = −14→14 |
12123 measured reflections | l = −12→11 |
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Hydrogen site location: mixed |
R[F2 > 2σ(F2)] = 0.034 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.087 | w = 1/[σ2(Fo2) + (0.0381P)2 + 0.5066P] where P = (Fo2 + 2Fc2)/3 |
S = 1.04 | (Δ/σ)max < 0.001 |
2516 reflections | Δρmax = 0.29 e Å−3 |
152 parameters | Δρmin = −0.20 e Å−3 |
C12H21N2O2 | V = 1250.74 (4) Å3 |
Mr = 225.31 | Z = 4 |
Monoclinic, P21/c | Cu Kα radiation |
a = 11.5408 (2) Å | µ = 0.66 mm−1 |
b = 11.7953 (2) Å | T = 100 K |
c = 9.7964 (2) Å | 0.27 × 0.11 × 0.05 mm |
β = 110.299 (2)° |
Agilent SuperNova Dual Source diffractometer with an Atlas detector | 2516 independent reflections |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2013) | 2275 reflections with I > 2σ(I) |
Tmin = 0.752, Tmax = 1.000 | Rint = 0.030 |
12123 measured reflections |
R[F2 > 2σ(F2)] = 0.034 | 0 restraints |
wR(F2) = 0.087 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.04 | Δρmax = 0.29 e Å−3 |
2516 reflections | Δρmin = −0.20 e Å−3 |
152 parameters |
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. |
x | y | z | Uiso*/Ueq | ||
O1 | 0.31052 (7) | 0.22108 (6) | 0.21433 (8) | 0.01809 (19) | |
N1 | 0.29372 (8) | 0.32826 (7) | 0.19092 (9) | 0.01345 (19) | |
C2 | 0.18232 (9) | 0.37682 (9) | 0.21515 (11) | 0.0141 (2) | |
C21 | 0.07153 (10) | 0.30350 (10) | 0.13045 (13) | 0.0205 (2) | |
H21A | 0.0643 | 0.3007 | 0.0278 | 0.031* | |
H21B | −0.0039 | 0.3362 | 0.1384 | 0.031* | |
H21C | 0.0832 | 0.2266 | 0.1707 | 0.031* | |
C22 | 0.20027 (10) | 0.37189 (10) | 0.37769 (12) | 0.0191 (2) | |
H22A | 0.2239 | 0.2948 | 0.4141 | 0.029* | |
H22B | 0.1229 | 0.3927 | 0.3916 | 0.029* | |
H22C | 0.2655 | 0.4250 | 0.4312 | 0.029* | |
C3 | 0.16081 (9) | 0.49824 (9) | 0.15770 (11) | 0.0142 (2) | |
H3A | 0.1262 | 0.4961 | 0.0501 | 0.017* | |
H3B | 0.0987 | 0.5344 | 0.1923 | 0.017* | |
C4 | 0.27737 (9) | 0.57099 (9) | 0.20451 (11) | 0.0139 (2) | |
H4 | 0.3128 | 0.5743 | 0.3132 | 0.017* | |
C5 | 0.37062 (9) | 0.51704 (9) | 0.14639 (11) | 0.0153 (2) | |
H5A | 0.4463 | 0.5642 | 0.1760 | 0.018* | |
H5B | 0.3359 | 0.5169 | 0.0387 | 0.018* | |
C6 | 0.40608 (9) | 0.39531 (9) | 0.19946 (11) | 0.0138 (2) | |
C61 | 0.46605 (10) | 0.33808 (10) | 0.10064 (12) | 0.0182 (2) | |
H61A | 0.4882 | 0.2599 | 0.1332 | 0.027* | |
H61B | 0.5406 | 0.3799 | 0.1051 | 0.027* | |
H61C | 0.4078 | 0.3377 | 0.0003 | 0.027* | |
C62 | 0.49624 (10) | 0.39249 (10) | 0.35735 (11) | 0.0174 (2) | |
H62A | 0.4563 | 0.4253 | 0.4216 | 0.026* | |
H62B | 0.5702 | 0.4365 | 0.3650 | 0.026* | |
H62C | 0.5197 | 0.3138 | 0.3862 | 0.026* | |
N4 | 0.24829 (8) | 0.68545 (8) | 0.14626 (10) | 0.0144 (2) | |
H4N | 0.2418 (12) | 0.6979 (11) | 0.0576 (15) | 0.017* | |
C7 | 0.21800 (9) | 0.76929 (9) | 0.22023 (11) | 0.0137 (2) | |
O7 | 0.21901 (7) | 0.75780 (7) | 0.34628 (8) | 0.01844 (19) | |
C8 | 0.18506 (10) | 0.87821 (9) | 0.13881 (12) | 0.0169 (2) | |
H8 | 0.1812 | 0.8809 | 0.0404 | 0.020* | |
C9 | 0.16111 (11) | 0.97081 (10) | 0.19932 (13) | 0.0235 (3) | |
H9A | 0.1646 | 0.9694 | 0.2976 | 0.028* | |
H9B | 0.1404 | 1.0390 | 0.1447 | 0.028* |
U11 | U22 | U33 | U12 | U13 | U23 | |
O1 | 0.0211 (4) | 0.0124 (4) | 0.0212 (4) | 0.0017 (3) | 0.0080 (3) | 0.0004 (3) |
N1 | 0.0145 (4) | 0.0120 (4) | 0.0143 (4) | 0.0003 (3) | 0.0057 (3) | −0.0005 (3) |
C2 | 0.0138 (5) | 0.0143 (5) | 0.0159 (5) | 0.0004 (4) | 0.0073 (4) | 0.0002 (4) |
C21 | 0.0160 (5) | 0.0168 (5) | 0.0287 (6) | −0.0014 (4) | 0.0076 (5) | −0.0016 (4) |
C22 | 0.0224 (5) | 0.0203 (6) | 0.0183 (5) | 0.0022 (4) | 0.0118 (4) | 0.0038 (4) |
C3 | 0.0142 (5) | 0.0140 (5) | 0.0148 (5) | 0.0007 (4) | 0.0058 (4) | 0.0008 (4) |
C4 | 0.0171 (5) | 0.0126 (5) | 0.0124 (5) | 0.0002 (4) | 0.0059 (4) | 0.0014 (4) |
C5 | 0.0160 (5) | 0.0159 (5) | 0.0158 (5) | −0.0008 (4) | 0.0076 (4) | 0.0008 (4) |
C6 | 0.0129 (5) | 0.0162 (5) | 0.0130 (5) | −0.0005 (4) | 0.0054 (4) | −0.0008 (4) |
C61 | 0.0183 (5) | 0.0211 (6) | 0.0174 (5) | 0.0018 (4) | 0.0090 (4) | −0.0020 (4) |
C62 | 0.0157 (5) | 0.0210 (6) | 0.0147 (5) | 0.0000 (4) | 0.0044 (4) | −0.0014 (4) |
N4 | 0.0196 (4) | 0.0136 (5) | 0.0112 (4) | −0.0002 (3) | 0.0069 (3) | 0.0015 (3) |
C7 | 0.0114 (5) | 0.0152 (5) | 0.0146 (5) | −0.0024 (4) | 0.0049 (4) | −0.0009 (4) |
O7 | 0.0235 (4) | 0.0203 (4) | 0.0140 (4) | 0.0015 (3) | 0.0097 (3) | 0.0008 (3) |
C8 | 0.0191 (5) | 0.0170 (5) | 0.0163 (5) | −0.0013 (4) | 0.0080 (4) | 0.0014 (4) |
C9 | 0.0324 (6) | 0.0182 (6) | 0.0233 (6) | 0.0033 (5) | 0.0137 (5) | 0.0027 (4) |
O1—N1 | 1.2875 (12) | C5—H5A | 0.9900 |
N1—C6 | 1.4962 (13) | C5—H5B | 0.9900 |
N1—C2 | 1.4996 (13) | C6—C61 | 1.5286 (14) |
C2—C3 | 1.5273 (14) | C6—C62 | 1.5361 (14) |
C2—C21 | 1.5281 (15) | C61—H61A | 0.9800 |
C2—C22 | 1.5339 (15) | C61—H61B | 0.9800 |
C21—H21A | 0.9800 | C61—H61C | 0.9800 |
C21—H21B | 0.9800 | C62—H62A | 0.9800 |
C21—H21C | 0.9800 | C62—H62B | 0.9800 |
C22—H22A | 0.9800 | C62—H62C | 0.9800 |
C22—H22B | 0.9800 | N4—C7 | 1.3419 (14) |
C22—H22C | 0.9800 | N4—H4N | 0.859 (14) |
C3—C4 | 1.5258 (14) | C7—O7 | 1.2383 (13) |
C3—H3A | 0.9900 | C7—C8 | 1.4903 (15) |
C3—H3B | 0.9900 | C8—C9 | 1.3170 (16) |
C4—N4 | 1.4588 (13) | C8—H8 | 0.9500 |
C4—C5 | 1.5207 (14) | C9—H9A | 0.9500 |
C4—H4 | 1.0000 | C9—H9B | 0.9500 |
C5—C6 | 1.5336 (14) | ||
O1—N1—C6 | 115.79 (8) | C6—C5—H5A | 108.8 |
O1—N1—C2 | 115.54 (8) | C4—C5—H5B | 108.8 |
C6—N1—C2 | 124.28 (8) | C6—C5—H5B | 108.8 |
N1—C2—C3 | 109.78 (8) | H5A—C5—H5B | 107.7 |
N1—C2—C21 | 107.44 (8) | N1—C6—C61 | 107.77 (8) |
C3—C2—C21 | 109.40 (9) | N1—C6—C5 | 110.59 (8) |
N1—C2—C22 | 109.60 (8) | C61—C6—C5 | 108.97 (8) |
C3—C2—C22 | 111.35 (9) | N1—C6—C62 | 108.42 (8) |
C21—C2—C22 | 109.17 (9) | C61—C6—C62 | 109.32 (8) |
C2—C21—H21A | 109.5 | C5—C6—C62 | 111.68 (9) |
C2—C21—H21B | 109.5 | C6—C61—H61A | 109.5 |
H21A—C21—H21B | 109.5 | C6—C61—H61B | 109.5 |
C2—C21—H21C | 109.5 | H61A—C61—H61B | 109.5 |
H21A—C21—H21C | 109.5 | C6—C61—H61C | 109.5 |
H21B—C21—H21C | 109.5 | H61A—C61—H61C | 109.5 |
C2—C22—H22A | 109.5 | H61B—C61—H61C | 109.5 |
C2—C22—H22B | 109.5 | C6—C62—H62A | 109.5 |
H22A—C22—H22B | 109.5 | C6—C62—H62B | 109.5 |
C2—C22—H22C | 109.5 | H62A—C62—H62B | 109.5 |
H22A—C22—H22C | 109.5 | C6—C62—H62C | 109.5 |
H22B—C22—H22C | 109.5 | H62A—C62—H62C | 109.5 |
C4—C3—C2 | 113.76 (8) | H62B—C62—H62C | 109.5 |
C4—C3—H3A | 108.8 | C7—N4—C4 | 122.58 (9) |
C2—C3—H3A | 108.8 | C7—N4—H4N | 118.2 (9) |
C4—C3—H3B | 108.8 | C4—N4—H4N | 118.8 (9) |
C2—C3—H3B | 108.8 | O7—C7—N4 | 122.94 (10) |
H3A—C3—H3B | 107.7 | O7—C7—C8 | 122.71 (10) |
N4—C4—C5 | 109.72 (8) | N4—C7—C8 | 114.34 (9) |
N4—C4—C3 | 110.10 (8) | C9—C8—C7 | 121.91 (10) |
C5—C4—C3 | 108.47 (8) | C9—C8—H8 | 119.0 |
N4—C4—H4 | 109.5 | C7—C8—H8 | 119.0 |
C5—C4—H4 | 109.5 | C8—C9—H9A | 120.0 |
C3—C4—H4 | 109.5 | C8—C9—H9B | 120.0 |
C4—C5—C6 | 113.90 (8) | H9A—C9—H9B | 120.0 |
C4—C5—H5A | 108.8 | ||
O1—N1—C2—C3 | −169.83 (8) | C2—N1—C6—C61 | −152.56 (9) |
C6—N1—C2—C3 | 34.76 (12) | O1—N1—C6—C5 | 171.10 (8) |
O1—N1—C2—C21 | −50.95 (11) | C2—N1—C6—C5 | −33.55 (12) |
C6—N1—C2—C21 | 153.64 (9) | O1—N1—C6—C62 | −66.14 (11) |
O1—N1—C2—C22 | 67.56 (11) | C2—N1—C6—C62 | 89.22 (11) |
C6—N1—C2—C22 | −87.85 (11) | C4—C5—C6—N1 | 44.29 (11) |
N1—C2—C3—C4 | −46.86 (11) | C4—C5—C6—C61 | 162.58 (9) |
C21—C2—C3—C4 | −164.53 (9) | C4—C5—C6—C62 | −76.55 (11) |
C22—C2—C3—C4 | 74.70 (11) | C5—C4—N4—C7 | −148.95 (9) |
C2—C3—C4—N4 | −179.45 (8) | C3—C4—N4—C7 | 91.74 (11) |
C2—C3—C4—C5 | 60.48 (11) | C4—N4—C7—O7 | 4.10 (15) |
N4—C4—C5—C6 | −179.11 (8) | C4—N4—C7—C8 | −176.89 (9) |
C3—C4—C5—C6 | −58.80 (11) | O7—C7—C8—C9 | 3.59 (17) |
O1—N1—C6—C61 | 52.08 (11) | N4—C7—C8—C9 | −175.42 (11) |
D—H···A | D—H | H···A | D···A | D—H···A |
N4—H4N···O7i | 0.859 (14) | 2.061 (14) | 2.9171 (11) | 174.7 (13) |
C8—H8···O7i | 0.95 | 2.66 | 3.4233 (13) | 138 |
C21—H21B···O7ii | 0.98 | 2.70 | 3.4808 (13) | 137 |
C61—H61C···O1iii | 0.98 | 2.72 | 3.6494 (13) | 158 |
C22—H22A···O1iv | 0.98 | 2.76 | 3.2842 (13) | 114 |
Symmetry codes: (i) x, −y+3/2, z−1/2; (ii) −x, y−1/2, −z+1/2; (iii) x, −y+1/2, z−1/2; (iv) x, −y+1/2, z+1/2. |
C12H22N2O·H2O | F(000) = 504 |
Mr = 228.33 | Dx = 1.138 Mg m−3 |
Monoclinic, P21/c | Cu Kα radiation, λ = 1.54184 Å |
a = 11.9763 (3) Å | Cell parameters from 6993 reflections |
b = 10.3132 (2) Å | θ = 5.9–76.7° |
c = 11.8550 (3) Å | µ = 0.62 mm−1 |
β = 114.527 (3)° | T = 100 K |
V = 1332.12 (6) Å3 | Block, colourless |
Z = 4 | 0.14 × 0.10 × 0.07 mm |
Agilent SuperNova Dual Source diffractometer with an Atlas detector | 2777 independent reflections |
Radiation source: SuperNova (Cu) X-ray Source | 2442 reflections with I > 2σ(I) |
Detector resolution: 5.1725 pixels mm-1 | Rint = 0.085 |
ω scans | θmax = 77.0°, θmin = 4.1° |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2013) | h = −15→15 |
Tmin = 0.262, Tmax = 1.000 | k = −12→10 |
14047 measured reflections | l = −14→14 |
Refinement on F2 | 90 restraints |
Least-squares matrix: full | Hydrogen site location: mixed |
R[F2 > 2σ(F2)] = 0.057 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.137 | w = 1/[σ2(Fo2) + (0.0758P)2 + 0.5327P] where P = (Fo2 + 2Fc2)/3 |
S = 1.05 | (Δ/σ)max < 0.001 |
2777 reflections | Δρmax = 0.40 e Å−3 |
161 parameters | Δρmin = −0.39 e Å−3 |
C12H22N2O·H2O | V = 1332.12 (6) Å3 |
Mr = 228.33 | Z = 4 |
Monoclinic, P21/c | Cu Kα radiation |
a = 11.9763 (3) Å | µ = 0.62 mm−1 |
b = 10.3132 (2) Å | T = 100 K |
c = 11.8550 (3) Å | 0.14 × 0.10 × 0.07 mm |
β = 114.527 (3)° |
Agilent SuperNova Dual Source diffractometer with an Atlas detector | 2777 independent reflections |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2013) | 2442 reflections with I > 2σ(I) |
Tmin = 0.262, Tmax = 1.000 | Rint = 0.085 |
14047 measured reflections |
R[F2 > 2σ(F2)] = 0.057 | 90 restraints |
wR(F2) = 0.137 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.05 | Δρmax = 0.40 e Å−3 |
2777 reflections | Δρmin = −0.39 e Å−3 |
161 parameters |
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. |
x | y | z | Uiso*/Ueq | ||
N1 | 0.23575 (10) | 0.81721 (11) | 0.31083 (10) | 0.0125 (3) | |
H1N | 0.2568 (16) | 0.8522 (19) | 0.2538 (17) | 0.015* | |
C2 | 0.34171 (11) | 0.73387 (14) | 0.38824 (12) | 0.0134 (3) | |
C21 | 0.45717 (12) | 0.81265 (15) | 0.41063 (13) | 0.0188 (3) | |
H21A | 0.4549 | 0.8944 | 0.4518 | 0.028* | |
H21B | 0.4607 | 0.8311 | 0.3311 | 0.028* | |
H21C | 0.5299 | 0.7629 | 0.4633 | 0.028* | |
C22 | 0.34041 (13) | 0.70649 (15) | 0.51496 (12) | 0.0192 (3) | |
H22A | 0.2756 | 0.6437 | 0.5050 | 0.029* | |
H22B | 0.3248 | 0.7873 | 0.5495 | 0.029* | |
H22C | 0.4200 | 0.6710 | 0.5713 | 0.029* | |
C3 | 0.34483 (11) | 0.60693 (13) | 0.32152 (11) | 0.0132 (3) | |
H3A | 0.3730 | 0.6262 | 0.2557 | 0.016* | |
H3B | 0.4054 | 0.5476 | 0.3817 | 0.016* | |
C4 | 0.22048 (11) | 0.53796 (13) | 0.26314 (11) | 0.0128 (3) | |
H4 | 0.1961 | 0.5091 | 0.3303 | 0.015* | |
C5 | 0.12308 (11) | 0.63024 (14) | 0.17619 (11) | 0.0138 (3) | |
H5A | 0.0425 | 0.5858 | 0.1423 | 0.017* | |
H5B | 0.1435 | 0.6527 | 0.1058 | 0.017* | |
C6 | 0.11321 (11) | 0.75585 (14) | 0.24203 (12) | 0.0133 (3) | |
C61 | 0.03636 (12) | 0.85551 (15) | 0.14536 (13) | 0.0193 (3) | |
H61A | 0.0755 | 0.8744 | 0.0892 | 0.029* | |
H61B | 0.0303 | 0.9354 | 0.1872 | 0.029* | |
H61C | −0.0461 | 0.8205 | 0.0977 | 0.029* | |
C62 | 0.04944 (12) | 0.72972 (15) | 0.32824 (13) | 0.0183 (3) | |
H62A | 0.0502 | 0.8089 | 0.3743 | 0.027* | |
H62B | 0.0929 | 0.6605 | 0.3866 | 0.027* | |
H62C | −0.0356 | 0.7031 | 0.2789 | 0.027* | |
N4 | 0.23031 (10) | 0.42488 (12) | 0.19380 (10) | 0.0138 (3) | |
H4N | 0.2294 (16) | 0.4362 (19) | 0.1236 (18) | 0.017* | |
C7 | 0.26296 (11) | 0.30766 (13) | 0.24637 (12) | 0.0128 (3) | |
O7 | 0.27586 (9) | 0.28280 (10) | 0.35350 (9) | 0.0165 (2) | |
C8 | 0.28484 (12) | 0.20925 (14) | 0.16549 (13) | 0.0165 (3) | |
H8 | 0.2542 | 0.2242 | 0.0788 | 0.020* | |
C9 | 0.34633 (14) | 0.10151 (15) | 0.21287 (15) | 0.0224 (3) | |
H9A | 0.3773 | 0.0859 | 0.2995 | 0.027* | |
H9B | 0.3596 | 0.0397 | 0.1603 | 0.027* | |
O1W | 0.21928 (10) | 0.45323 (11) | −0.05444 (10) | 0.0214 (3) | |
H1W | 0.240 (2) | 0.390 (2) | −0.088 (2) | 0.032* | |
H2W | 0.2273 (19) | 0.525 (2) | −0.097 (2) | 0.032* |
U11 | U22 | U33 | U12 | U13 | U23 | |
N1 | 0.0152 (5) | 0.0063 (5) | 0.0156 (5) | 0.0010 (4) | 0.0061 (4) | 0.0005 (4) |
C2 | 0.0147 (5) | 0.0088 (6) | 0.0154 (5) | 0.0011 (4) | 0.0050 (4) | −0.0002 (4) |
C21 | 0.0173 (6) | 0.0109 (7) | 0.0252 (6) | −0.0013 (5) | 0.0056 (5) | −0.0019 (5) |
C22 | 0.0258 (6) | 0.0148 (7) | 0.0162 (6) | 0.0026 (5) | 0.0080 (5) | 0.0003 (5) |
C3 | 0.0149 (5) | 0.0085 (6) | 0.0156 (5) | 0.0016 (4) | 0.0059 (4) | 0.0003 (4) |
C4 | 0.0173 (5) | 0.0065 (6) | 0.0153 (5) | 0.0002 (4) | 0.0076 (4) | −0.0004 (4) |
C5 | 0.0155 (5) | 0.0097 (6) | 0.0153 (5) | 0.0005 (4) | 0.0055 (4) | −0.0010 (4) |
C6 | 0.0141 (5) | 0.0088 (6) | 0.0162 (5) | 0.0007 (4) | 0.0057 (4) | −0.0009 (4) |
C61 | 0.0202 (6) | 0.0126 (7) | 0.0215 (6) | 0.0058 (5) | 0.0051 (5) | 0.0010 (5) |
C62 | 0.0199 (6) | 0.0150 (7) | 0.0227 (6) | 0.0007 (5) | 0.0116 (5) | −0.0018 (5) |
N4 | 0.0203 (5) | 0.0074 (5) | 0.0155 (5) | 0.0004 (4) | 0.0091 (4) | 0.0001 (4) |
C7 | 0.0135 (5) | 0.0075 (6) | 0.0172 (5) | −0.0017 (4) | 0.0062 (4) | −0.0003 (4) |
O7 | 0.0243 (5) | 0.0072 (5) | 0.0185 (5) | 0.0015 (4) | 0.0093 (4) | 0.0015 (3) |
C8 | 0.0205 (5) | 0.0103 (6) | 0.0199 (5) | −0.0025 (4) | 0.0094 (4) | −0.0022 (4) |
C9 | 0.0309 (7) | 0.0092 (7) | 0.0315 (7) | 0.0017 (5) | 0.0174 (6) | −0.0010 (5) |
O1W | 0.0394 (6) | 0.0074 (6) | 0.0240 (5) | 0.0024 (4) | 0.0199 (5) | 0.0014 (4) |
N1—C2 | 1.4914 (16) | C5—H5B | 0.9900 |
N1—C6 | 1.4918 (16) | C6—C61 | 1.5300 (18) |
N1—H1N | 0.891 (19) | C6—C62 | 1.5325 (18) |
C2—C21 | 1.5291 (18) | C61—H61A | 0.9800 |
C2—C22 | 1.5350 (18) | C61—H61B | 0.9800 |
C2—C3 | 1.5380 (19) | C61—H61C | 0.9800 |
C21—H21A | 0.9800 | C62—H62A | 0.9800 |
C21—H21B | 0.9800 | C62—H62B | 0.9800 |
C21—H21C | 0.9800 | C62—H62C | 0.9800 |
C22—H22A | 0.9800 | N4—C7 | 1.3418 (18) |
C22—H22B | 0.9800 | N4—H4N | 0.84 (2) |
C22—H22C | 0.9800 | C7—O7 | 1.2408 (17) |
C3—C4 | 1.5320 (17) | C7—C8 | 1.4921 (19) |
C3—H3A | 0.9900 | C8—C9 | 1.323 (2) |
C3—H3B | 0.9900 | C8—H8 | 0.9500 |
C4—N4 | 1.4595 (17) | C9—H9A | 0.9500 |
C4—C5 | 1.5267 (17) | C9—H9B | 0.9500 |
C4—H4 | 1.0000 | O1W—H1W | 0.85 (3) |
C5—C6 | 1.5421 (19) | O1W—H2W | 0.93 (2) |
C5—H5A | 0.9900 | ||
C2—N1—C6 | 118.99 (11) | C6—C5—H5A | 109.1 |
C2—N1—H1N | 105.3 (11) | C4—C5—H5B | 109.1 |
C6—N1—H1N | 106.3 (11) | C6—C5—H5B | 109.1 |
N1—C2—C21 | 106.13 (11) | H5A—C5—H5B | 107.9 |
N1—C2—C22 | 110.88 (11) | N1—C6—C61 | 105.90 (11) |
C21—C2—C22 | 107.68 (11) | N1—C6—C62 | 111.06 (11) |
N1—C2—C3 | 111.73 (10) | C61—C6—C62 | 107.83 (11) |
C21—C2—C3 | 109.16 (11) | N1—C6—C5 | 111.61 (10) |
C22—C2—C3 | 111.04 (11) | C61—C6—C5 | 109.51 (11) |
C2—C21—H21A | 109.5 | C62—C6—C5 | 110.73 (11) |
C2—C21—H21B | 109.5 | C6—C61—H61A | 109.5 |
H21A—C21—H21B | 109.5 | C6—C61—H61B | 109.5 |
C2—C21—H21C | 109.5 | H61A—C61—H61B | 109.5 |
H21A—C21—H21C | 109.5 | C6—C61—H61C | 109.5 |
H21B—C21—H21C | 109.5 | H61A—C61—H61C | 109.5 |
C2—C22—H22A | 109.5 | H61B—C61—H61C | 109.5 |
C2—C22—H22B | 109.5 | C6—C62—H62A | 109.5 |
H22A—C22—H22B | 109.5 | C6—C62—H62B | 109.5 |
C2—C22—H22C | 109.5 | H62A—C62—H62B | 109.5 |
H22A—C22—H22C | 109.5 | C6—C62—H62C | 109.5 |
H22B—C22—H22C | 109.5 | H62A—C62—H62C | 109.5 |
C4—C3—C2 | 113.64 (10) | H62B—C62—H62C | 109.5 |
C4—C3—H3A | 108.8 | C7—N4—C4 | 122.31 (11) |
C2—C3—H3A | 108.8 | C7—N4—H4N | 118.0 (13) |
C4—C3—H3B | 108.8 | C4—N4—H4N | 118.6 (14) |
C2—C3—H3B | 108.8 | O7—C7—N4 | 123.37 (13) |
H3A—C3—H3B | 107.7 | O7—C7—C8 | 122.46 (13) |
N4—C4—C5 | 109.61 (10) | N2—C7—C8 | 114.16 (12) |
N4—C4—C3 | 109.56 (10) | C9—C8—C7 | 120.92 (13) |
C5—C4—C3 | 110.04 (11) | C9—C8—H8 | 119.5 |
N4—C4—H4 | 109.2 | C7—C8—H8 | 119.5 |
C5—C4—H4 | 109.2 | C8—C9—H9A | 120.0 |
C3—C4—H4 | 109.2 | C8—C9—H9B | 120.0 |
C4—C5—C6 | 112.31 (10) | H9A—C9—H9B | 120.0 |
C4—C5—H5A | 109.1 | H1W—O1W—H2W | 104 (2) |
C6—N1—C2—C21 | 162.00 (11) | C2—N1—C6—C62 | 79.16 (14) |
C6—N1—C2—C22 | −81.34 (14) | C2—N1—C6—C5 | −44.94 (15) |
C6—N1—C2—C3 | 43.11 (15) | C4—C5—C6—N1 | 50.50 (15) |
N1—C2—C3—C4 | −47.21 (15) | C4—C5—C6—C61 | 167.44 (11) |
C21—C2—C3—C4 | −164.28 (11) | C4—C5—C6—C62 | −73.79 (13) |
C22—C2—C3—C4 | 77.16 (13) | C5—C4—N4—C7 | −150.00 (12) |
C2—C3—C4—N4 | 175.41 (10) | C3—C4—N4—C7 | 89.16 (14) |
C2—C3—C4—C5 | 54.84 (14) | C4—N4—C7—O7 | 7.1 (2) |
N4—C4—C5—C6 | −176.68 (10) | C4—N4—C7—C8 | −171.86 (11) |
C3—C4—C5—C6 | −56.13 (14) | O7—C7—C8—C9 | −16.3 (2) |
C2—N1—C6—C61 | −164.04 (11) | N4—C7—C8—C9 | 162.73 (13) |
D—H···A | D—H | H···A | D···A | D—H···A |
N4—H4N···O1W | 0.84 (2) | 2.07 (2) | 2.9052 (16) | 176.1 (18) |
O1W—H2W···N1i | 0.93 (2) | 1.98 (2) | 2.9081 (16) | 176.9 (19) |
O1W—H1W···O7ii | 0.85 (3) | 2.02 (3) | 2.8617 (15) | 168 (2) |
C21—H21C···O7iii | 0.98 | 2.48 | 3.4041 (17) | 157 |
Symmetry codes: (i) x, −y+3/2, z−1/2; (ii) x, −y+1/2, z−1/2; (iii) −x+1, −y+1, −z+1. |
Experimental details
(I) | (II) | |
Crystal data | ||
Chemical formula | C12H21N2O2 | C12H22N2O·H2O |
Mr | 225.31 | 228.33 |
Crystal system, space group | Monoclinic, P21/c | Monoclinic, P21/c |
Temperature (K) | 100 | 100 |
a, b, c (Å) | 11.5408 (2), 11.7953 (2), 9.7964 (2) | 11.9763 (3), 10.3132 (2), 11.8550 (3) |
β (°) | 110.299 (2) | 114.527 (3) |
V (Å3) | 1250.74 (4) | 1332.12 (6) |
Z | 4 | 4 |
Radiation type | Cu Kα | Cu Kα |
µ (mm−1) | 0.66 | 0.62 |
Crystal size (mm) | 0.27 × 0.11 × 0.05 | 0.14 × 0.10 × 0.07 |
Data collection | ||
Diffractometer | Agilent SuperNova Dual Source diffractometer with an Atlas detector | Agilent SuperNova Dual Source diffractometer with an Atlas detector |
Absorption correction | Multi-scan (CrysAlis PRO; Agilent, 2013) | Multi-scan (CrysAlis PRO; Agilent, 2013) |
Tmin, Tmax | 0.752, 1.000 | 0.262, 1.000 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 12123, 2516, 2275 | 14047, 2777, 2442 |
Rint | 0.030 | 0.085 |
(sin θ/λ)max (Å−1) | 0.624 | 0.632 |
Refinement | ||
R[F2 > 2σ(F2)], wR(F2), S | 0.034, 0.087, 1.04 | 0.057, 0.137, 1.05 |
No. of reflections | 2516 | 2777 |
No. of parameters | 152 | 161 |
No. of restraints | 0 | 90 |
H-atom treatment | H atoms treated by a mixture of independent and constrained refinement | H atoms treated by a mixture of independent and constrained refinement |
Δρmax, Δρmin (e Å−3) | 0.29, −0.20 | 0.40, −0.39 |
Computer programs: CrysAlis PRO (Agilent, 2013), SHELXS97 (Sheldrick, 2008) and TITAN (Hunter & Simpson, 1999), SIR2011 (Burla et al., 2012), SHELXL2014 (Sheldrick, 2015) and TITAN (Hunter & Simpson, 1999), Mercury (Macrae et al., 2008), SHELXL2014 (Sheldrick, 2015), enCIFer (Allen et al., 2004) and publCIF (Westrip, 2010).
D—H···A | D—H | H···A | D···A | D—H···A |
N4—H4N···O7i | 0.859 (14) | 2.061 (14) | 2.9171 (11) | 174.7 (13) |
C8—H8···O7i | 0.95 | 2.66 | 3.4233 (13) | 138.1 |
C21—H21B···O7ii | 0.98 | 2.70 | 3.4808 (13) | 136.8 |
C61—H61C···O1iii | 0.98 | 2.72 | 3.6494 (13) | 158.2 |
C22—H22A···O1iv | 0.98 | 2.76 | 3.2842 (13) | 113.7 |
Symmetry codes: (i) x, −y+3/2, z−1/2; (ii) −x, y−1/2, −z+1/2; (iii) x, −y+1/2, z−1/2; (iv) x, −y+1/2, z+1/2. |
D—H···A | D—H | H···A | D···A | D—H···A |
N4—H4N···O1W | 0.84 (2) | 2.07 (2) | 2.9052 (16) | 176.1 (18) |
O1W—H2W···N1i | 0.93 (2) | 1.98 (2) | 2.9081 (16) | 176.9 (19) |
O1W—H1W···O7ii | 0.85 (3) | 2.02 (3) | 2.8617 (15) | 168 (2) |
C21—H21C···O7iii | 0.98 | 2.48 | 3.4041 (17) | 156.9 |
Symmetry codes: (i) x, −y+3/2, z−1/2; (ii) x, −y+1/2, z−1/2; (iii) −x+1, −y+1, −z+1. |