research communications
Byproduct identification: crystal structure of potassium 2-ethoxy-2-oxoacetate
aUS Naval Research Laboratory, Center for Biomolecular Science and Engineering, 4555 Overlook Ave., SW Washington, DC 20375, USA, bUS Naval Research Laboratory, Materials Chemistry and Dynamics Branch, 4555 Overlook Ave., SW Washington, DC 20375, USA, and cDepartment of Chemistry, Washington College, 300 Washington Ave., Chestertown, MD 21620, USA
*Correspondence e-mail: [email protected]
Potassium 2-ethoxy-2-oxoacetate, K+·C4H5O4−, was identified as a byproduct in the first step of synthesizing the shelf-stable salt potassium nitroacetonitrile (KNAN). A single crystal of the title salt was obtained by recrystallization of the ethanol filtrate resulting from the purification of the intended product salt, potassium ethyl nitrocyanoacetate. The asymmetric unit of K+·C4H5O4−, contains a single potassium cation and a 2-ethoxy-2-oxoacetate anion, the ethyl group of which is disordered over two sets of sites in a 0.792 (13):0.208 (13) ratio. The packing is dictated primarily by K—O electrostatic interactions and comprises eight bonded oxygen atoms per cation, with distances ranging from 2.706 (2) to 3.053 (4) Å.
CCDC reference: 2584812
1. Chemical context
Voinkov et al. (2016
) reported an alternative synthesis method for the α-nitronitrile compound, nitroacetonitrile, C2H2N2O2 (NAN). This synthesis was developed to bypass the greatest hazard of NAN synthesis, spontaneous explosion (Thomas, 2009
), while improving the yield and purity of the NAN produced. The final product of the reaction detailed by Voinkov et al. (2016
) is the potassium salt of nitroacetonitrile (KNAN). Two key features of KNAN are its shelf-stability and that, as a salt, it is ready for immediate use in contrast to neutral NAN, which is unstable, requires careful storage, and needs to be deprotonated prior to use. The shelf-stable KNAN is produced in a two-step synthesis from ethyl (hydroxyimino)cyanoacetate. During the first step of this process, ethyl (hydroxyimino)cyanoacetate is oxidized with potassium permanganate in the presence of potassium hydroxide to form the salt potassium ethyl nitrocyanoacetate in 63% yield (Fig. 1
). It was in executing this first step that we identified the salt potassium 2-ethoxy-2-oxoacetate, the crystal structure of which is reported here.
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Figure 1
Synthesis scheme for the potassium salt of ethyl nitrocyanoacetate. |
2. Structural commentary
The asymmetric unit of the title compound contains a single potassium cation and an anion, the ethyl fragment of which is disordered in a 0.792 (13):0.208 (13) ratio (Fig. 2
). All bond lengths are in expected ranges when compared to similar potassium oxalate salt structures. The dihedral angle between the carboxy groups was determined to be 15.2 (6)°. The observed packing interactions (Fig. 3
) of this polymeric salt structure are primarily electrostatic interactions between the potassium ion and the oxygen atoms of the 2-ethoxy-2-oxoacetate anion. These distances between potassium and oxygen range from 2.706 (2) to 3.053 (4) Å in length (see Table 1
for all K—O bonds).
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Figure 2
The asymmetric unit showing the potassium cation and the disordered 2-ethoxy-2-oxoacetate anion. Displacement ellipsoids are drawn at the 50% probability level; bonds lengths are detailed in green. |
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Figure 3
Ball-and-stick representation of the packing of 2-ethoxy-2-oxoacetate molecules and potassium cations viewed down [010]. Several K—O distances are noted with black dotted lines. |
Taking into account K—O distances of less than 3.0 Å, the oxygen atoms arrange in form of a distorted square pyramid around K+, as represented by a purple polyhedron in Fig. 4
. The extended structure reveals the formation of potassium-oxygen chains propagating parallel to [001] (Figs. 4
, 5
). Within a distance of 3.05 Å, atom O1 binds in a μ3-mode to three potassium ions while O2 interacts with two cations (Fig. 6
). In contrast, both O3 and O4 only interact with one potassium ion each, and at longer distances (Table 1
).
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Figure 4
Ball-and-stick representation showing the distorted square-pyramidal coordination environment around the potassium cation as a purple polyhedron. |
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Figure 5
Ball and stick model of the extended structure of the title salt, showing the formation of potassium–oxygen chains propagating along [001] in polyhedral representation. |
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Figure 6
Interactions of O1 and O2 with potassium cations. |
3. Database survey
A search of the Cambridge Structural Database (CSD, Version 5.46; Groom et al., 2016
) yielded entries containing either 2-ethoxy-2-oxoacetate bound to a metal or containing oxalate moieties bound to potassium as either a backbone structure or a metal coordinating ligand (Fig. 7
). The most similar structures found were K0.53(NH4)0.47(H2C2O4)((HC2O4)H2O)2 (refcode ZAXLOB; Hamdouni et al., 2011
) and [Cu(EtOOC–COO)2(Hpz)4] (MUVFIT; Garau et al., 2010
). The ZAXLOB structure contains both oxalic acid and the hydrogenoxalate anion bound to potassium ions with K—O interaction distances from 2.900 to 2.920 Å. MUVFIT contains two 2-ethoxy-2-oxoacetate units bound to copper(II) through a single oxygen per unit at 2.359 Å, a closer distance than any found in either the title structure or ZAXLOB structure to the potassium ion. An additional five CSD entries were found containing any metal bound to an oxalate group where a single oxygen atom is bonded to a methyl or tert-butyl group with another two entries having metal bound to oxalate where two oxygen atoms are bonded to methyl groups. The bound metals include titanium (PUTRUV, Okumura et al., 2025
), lithium (OXATIT and OXATOZ; Sun et al., 2021
), iridium (IKUJII, Padilla et al., 2010
; ILEZEE and ILEZII, Paneque et al., 2003
), and osmium (UKEZUI, Lin et al., 2020
).
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Figure 7
Chemical structures of the compounds referenced in the database survey. |
4. Synthesis and crystallization
A solution of KMnO4 (11.85 g, 75 mmol) in water (200 ml) was added dropwise over 1 h to a warm solution of KOH (0.9 g, 16 mmol) and ethyl (hydroxyimino)cyanoacetate (7.15 g, 50.3 mmol) in water (140 ml). The solution was stirred overnight, until the KMnO4 was fully consumed as shown by the depletion of the dark purple coloring in favor of black. The solution was filtered, removing the black colored solids, and the filtrate concentrated on a rotary evaporator, producing pale-yellow crystalline material. The solids were washed with ethanol and isolated by filtration. The yellow filtrate was stored overnight in a refrigerator and additional material precipitated. From this precipitate, a crystal of the salt potassium 2-ethoxy-2-oxoacetate was isolated for single-crystal X-ray diffraction. Comparison of the calculated pattern to the experimental powder pattern of bulk material collected showed both the byproduct potassium 2-ethoxy-2-oxoacetate and potassium ethyl nitrocyanoacetate present, next to some unassigned reflections (Fig. 8
).
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Figure 8
XRD pattern of isolated bulk material with comparison to the calculated pattern of the byproduct potassium 2-ethoxy-2-oxoacetate (red) and the intended product potassium ethyl nitrocyanoacetate (blue). XRD pattern plotted with DIFFRAC·EVA with X-offset of 0.09° to correct for sample height. |
5. Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2
. A PART command in SHELXL (Sheldrick, 2015b
), accompanied by SIMU and RIGU restraints set to 0.01, were used to model the positional disorder within the ethyl group and resulted in a refined ratio of 0.792 (13):0.208 (2). Corresponding H atoms were included using a riding model for the methyl and methylene groups.
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Supporting information
CCDC reference: 2584812
Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S205698902600914X/wm5809sup1.cif
Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S205698902600914X/wm5809Isup2.hkl
Supporting information file. DOI: https://doi.org/10.1107/S205698902600914X/wm5809Isup3.cml
| K+·C4H5O4− | F(000) = 320 |
| Mr = 156.18 | Dx = 1.548 Mg m−3 |
| Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
| a = 14.052 (2) Å | Cell parameters from 1931 reflections |
| b = 5.9280 (8) Å | θ = 2.9–27.2° |
| c = 8.0579 (10) Å | µ = 0.73 mm−1 |
| β = 93.242 (5)° | T = 296 K |
| V = 670.15 (16) Å3 | Plate, yellow |
| Z = 4 | 0.12 × 0.09 × 0.02 mm |
| Photon II CCD diffractometer | 1593 independent reflections |
| Radiation source: 1uS 3.0 microfocus | 1192 reflections with I > 2σ(I) |
| Helios multilayer optics monochromator | Rint = 0.059 |
| φ and ω scans | θmax = 27.9°, θmin = 2.9° |
| Absorption correction: multi-scan (SADABS; Krause et al., 2015) | h = −17→18 |
| Tmin = 0.660, Tmax = 0.746 | k = −7→7 |
| 10487 measured reflections | l = −10→10 |
| Refinement on F2 | Primary atom site location: intrinsic phasing |
| Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
| R[F2 > 2σ(F2)] = 0.064 | H-atom parameters constrained |
| wR(F2) = 0.150 | w = 1/[σ2(Fo2) + (0.0533P)2 + 0.7606P] where P = (Fo2 + 2Fc2)/3 |
| S = 1.10 | (Δ/σ)max = 0.003 |
| 1593 reflections | Δρmax = 0.42 e Å−3 |
| 103 parameters | Δρmin = −0.30 e Å−3 |
| 43 restraints |
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 | Occ. (<1) | |
| K1 | 0.09360 (6) | 0.26080 (10) | 0.61193 (8) | 0.0455 (3) | |
| O1 | 0.0930 (2) | 0.5589 (4) | 0.3575 (3) | 0.0552 (7) | |
| O2 | 0.1067 (2) | 0.9317 (4) | 0.3806 (3) | 0.0650 (8) | |
| O3 | 0.2563 (3) | 0.9045 (6) | 0.1792 (5) | 0.0985 (12) | |
| O4 | 0.2588 (2) | 0.5356 (5) | 0.2237 (4) | 0.0761 (9) | |
| C1 | 0.1325 (3) | 0.7420 (5) | 0.3364 (4) | 0.0436 (8) | |
| C2 | 0.2238 (3) | 0.7407 (6) | 0.2392 (5) | 0.0552 (9) | |
| C3 | 0.3425 (7) | 0.521 (2) | 0.1236 (14) | 0.114 (3) | 0.792 (13) |
| H3A | 0.325405 | 0.450607 | 0.017359 | 0.137* | 0.792 (13) |
| H3B | 0.367178 | 0.670628 | 0.103228 | 0.137* | 0.792 (13) |
| C4 | 0.4131 (6) | 0.388 (2) | 0.2152 (16) | 0.144 (4) | 0.792 (13) |
| H4A | 0.467205 | 0.366411 | 0.149261 | 0.216* | 0.792 (13) |
| H4B | 0.386482 | 0.243678 | 0.241020 | 0.216* | 0.792 (13) |
| H4C | 0.432783 | 0.464288 | 0.316375 | 0.216* | 0.792 (13) |
| C3A | 0.376 (3) | 0.547 (8) | 0.198 (6) | 0.122 (5) | 0.208 (13) |
| H3AA | 0.395966 | 0.686855 | 0.149019 | 0.147* | 0.208 (13) |
| H3AB | 0.414355 | 0.513027 | 0.298734 | 0.147* | 0.208 (13) |
| C4A | 0.369 (3) | 0.362 (7) | 0.083 (5) | 0.125 (6) | 0.208 (13) |
| H4AA | 0.345767 | 0.416681 | −0.024271 | 0.187* | 0.208 (13) |
| H4AB | 0.325420 | 0.251309 | 0.121351 | 0.187* | 0.208 (13) |
| H4AC | 0.430521 | 0.295372 | 0.074146 | 0.187* | 0.208 (13) |
| U11 | U22 | U33 | U12 | U13 | U23 | |
| K1 | 0.0772 (6) | 0.0234 (3) | 0.0364 (4) | 0.0041 (3) | 0.0082 (3) | 0.0011 (3) |
| O1 | 0.0809 (19) | 0.0348 (12) | 0.0516 (14) | −0.0030 (12) | 0.0190 (13) | 0.0021 (10) |
| O2 | 0.103 (2) | 0.0317 (13) | 0.0605 (17) | 0.0068 (13) | 0.0097 (16) | −0.0088 (11) |
| O3 | 0.103 (3) | 0.068 (2) | 0.128 (3) | −0.0207 (19) | 0.040 (2) | 0.016 (2) |
| O4 | 0.078 (2) | 0.0634 (18) | 0.089 (2) | 0.0200 (15) | 0.0244 (17) | 0.0030 (16) |
| C1 | 0.069 (2) | 0.0284 (14) | 0.0332 (14) | 0.0018 (15) | 0.0006 (14) | −0.0003 (12) |
| C2 | 0.066 (2) | 0.0461 (19) | 0.053 (2) | −0.0061 (18) | 0.0035 (18) | −0.0002 (16) |
| C3 | 0.074 (6) | 0.145 (7) | 0.125 (8) | 0.045 (5) | 0.029 (5) | 0.008 (6) |
| C4 | 0.082 (6) | 0.163 (8) | 0.188 (10) | 0.035 (6) | 0.021 (6) | 0.045 (8) |
| C3A | 0.080 (10) | 0.147 (10) | 0.144 (12) | 0.047 (9) | 0.035 (9) | 0.015 (10) |
| C4A | 0.081 (12) | 0.151 (12) | 0.146 (13) | 0.033 (11) | 0.032 (11) | 0.018 (12) |
| K1—O1 | 2.706 (2) | O4—C3 | 1.465 (9) |
| K1—O2i | 2.712 (2) | O4—C3A | 1.67 (4) |
| K1—O1ii | 2.741 (2) | C1—C2 | 1.540 (5) |
| K1—O2iii | 2.828 (3) | C3—C4 | 1.439 (12) |
| K1—O1iv | 2.855 (3) | C3—H3A | 0.9700 |
| K1—O4ii | 3.008 (3) | C3—H3B | 0.9700 |
| K1—O2iv | 3.041 (3) | C4—H4A | 0.9600 |
| K1—O3iii | 3.053 (4) | C4—H4B | 0.9600 |
| K1—C1iv | 3.228 (4) | C4—H4C | 0.9600 |
| K1—C1iii | 3.485 (3) | C3A—C4A | 1.44 (2) |
| K1—C1ii | 3.513 (3) | C3A—H3AA | 0.9700 |
| K1—K1ii | 4.0310 (5) | C3A—H3AB | 0.9700 |
| O1—C1 | 1.235 (4) | C4A—H4AA | 0.9600 |
| O2—C1 | 1.240 (4) | C4A—H4AB | 0.9600 |
| O3—C2 | 1.187 (5) | C4A—H4AC | 0.9600 |
| O4—C2 | 1.320 (4) | ||
| O1—K1—O2i | 86.93 (8) | C1iv—K1—K1ii | 79.35 (6) |
| O1—K1—O1ii | 176.99 (7) | C1iii—K1—K1ii | 61.12 (5) |
| O2i—K1—O1ii | 90.11 (8) | C1ii—K1—K1ii | 57.81 (5) |
| O1—K1—O2iii | 98.99 (7) | C1—O1—K1 | 134.1 (2) |
| O2i—K1—O2iii | 170.36 (12) | C1—O1—K1v | 119.2 (2) |
| O1ii—K1—O2iii | 84.01 (7) | K1—O1—K1v | 95.47 (7) |
| O1—K1—O1iv | 81.80 (8) | C1—O1—K1iv | 96.1 (2) |
| O2i—K1—O1iv | 115.28 (9) | K1—O1—K1iv | 98.20 (8) |
| O1ii—K1—O1iv | 98.99 (6) | K1v—O1—K1iv | 111.19 (10) |
| O2iii—K1—O1iv | 73.33 (8) | C1—O2—K1vi | 151.9 (2) |
| O1—K1—O4ii | 125.26 (8) | C1—O2—K1vii | 111.8 (2) |
| O2i—K1—O4ii | 72.80 (9) | K1vi—O2—K1vii | 93.36 (7) |
| O1ii—K1—O4ii | 54.12 (8) | C1—O2—K1iv | 87.2 (2) |
| O2iii—K1—O4ii | 97.56 (9) | K1vi—O2—K1iv | 99.06 (9) |
| O1iv—K1—O4ii | 152.84 (8) | K1vii—O2—K1iv | 103.70 (9) |
| O1—K1—O2iv | 107.27 (8) | C2—O3—K1vii | 107.6 (3) |
| O2i—K1—O2iv | 80.94 (9) | C2—O4—C3 | 114.9 (6) |
| O1ii—K1—O2iv | 71.67 (8) | C2—O4—C3A | 110.5 (16) |
| O2iii—K1—O2iv | 104.30 (6) | C2—O4—K1v | 106.3 (3) |
| O1iv—K1—O2iv | 44.20 (7) | C3—O4—K1v | 115.5 (6) |
| O4ii—K1—O2iv | 118.32 (8) | O1—C1—O2 | 128.0 (4) |
| O1—K1—O3iii | 71.36 (10) | O1—C1—C2 | 117.4 (3) |
| O2i—K1—O3iii | 120.69 (9) | O2—C1—C2 | 114.6 (3) |
| O1ii—K1—O3iii | 110.74 (10) | O1—C1—K1iv | 61.6 (2) |
| O2iii—K1—O3iii | 55.21 (9) | O2—C1—K1iv | 70.2 (2) |
| O1iv—K1—O3iii | 115.07 (8) | C2—C1—K1iv | 156.9 (2) |
| O4ii—K1—O3iii | 76.63 (9) | O1—C1—K1vii | 139.1 (3) |
| O2iv—K1—O3iii | 157.70 (8) | O2—C1—K1vii | 48.87 (17) |
| O1—K1—C1iv | 98.06 (8) | C2—C1—K1vii | 81.45 (18) |
| O2i—K1—C1iv | 100.99 (9) | K1iv—C1—K1vii | 86.81 (8) |
| O1ii—K1—C1iv | 81.96 (8) | O1—C1—K1v | 42.90 (15) |
| O2iii—K1—C1iv | 85.78 (8) | O2—C1—K1v | 151.4 (3) |
| O1iv—K1—C1iv | 22.36 (7) | C2—C1—K1v | 81.02 (18) |
| O4ii—K1—C1iv | 134.99 (8) | K1iv—C1—K1v | 86.35 (8) |
| O2iv—K1—C1iv | 22.57 (6) | K1vii—C1—K1v | 115.78 (9) |
| O3iii—K1—C1iv | 135.50 (8) | O3—C2—O4 | 124.1 (4) |
| O1—K1—C1iii | 80.47 (7) | O3—C2—C1 | 123.6 (4) |
| O2i—K1—C1iii | 161.88 (9) | O4—C2—C1 | 112.2 (3) |
| O1ii—K1—C1iii | 102.53 (7) | C4—C3—O4 | 107.6 (8) |
| O2iii—K1—C1iii | 19.29 (7) | C4—C3—H3A | 110.2 |
| O1iv—K1—C1iii | 75.92 (8) | O4—C3—H3A | 110.2 |
| O4ii—K1—C1iii | 104.05 (9) | C4—C3—H3B | 110.2 |
| O2iv—K1—C1iii | 115.18 (8) | O4—C3—H3B | 110.2 |
| O3iii—K1—C1iii | 42.61 (9) | H3A—C3—H3B | 108.5 |
| C1iv—K1—C1iii | 93.68 (9) | C3—C4—H4A | 109.5 |
| O1—K1—C1ii | 159.67 (7) | C3—C4—H4B | 109.5 |
| O2i—K1—C1ii | 74.27 (8) | H4A—C4—H4B | 109.5 |
| O1ii—K1—C1ii | 17.87 (7) | C3—C4—H4C | 109.5 |
| O2iii—K1—C1ii | 98.69 (7) | H4A—C4—H4C | 109.5 |
| O1iv—K1—C1ii | 112.97 (8) | H4B—C4—H4C | 109.5 |
| O4ii—K1—C1ii | 41.87 (8) | C4A—C3A—O4 | 91 (3) |
| O2iv—K1—C1ii | 77.81 (8) | C4A—C3A—H3AA | 113.5 |
| O3iii—K1—C1ii | 111.51 (10) | O4—C3A—H3AA | 113.5 |
| C1iv—K1—C1ii | 93.16 (8) | C4A—C3A—H3AB | 113.5 |
| C1iii—K1—C1ii | 115.79 (9) | O4—C3A—H3AB | 113.5 |
| O1—K1—K1ii | 141.05 (6) | H3AA—C3A—H3AB | 110.8 |
| O2i—K1—K1ii | 131.92 (6) | C3A—C4A—H4AA | 109.5 |
| O1ii—K1—K1ii | 41.94 (5) | C3A—C4A—H4AB | 109.5 |
| O2iii—K1—K1ii | 42.18 (5) | H4AA—C4A—H4AB | 109.5 |
| O1iv—K1—K1ii | 82.75 (5) | C3A—C4A—H4AC | 109.5 |
| O4ii—K1—K1ii | 74.10 (6) | H4AA—C4A—H4AC | 109.5 |
| O2iv—K1—K1ii | 85.18 (5) | H4AB—C4A—H4AC | 109.5 |
| O3iii—K1—K1ii | 83.42 (8) | ||
| K1—O1—C1—O2 | −83.4 (5) | K1vii—O2—C1—K1v | −66.8 (5) |
| K1v—O1—C1—O2 | 142.7 (3) | K1iv—O2—C1—K1v | 36.9 (5) |
| K1iv—O1—C1—O2 | 24.2 (4) | K1vii—O3—C2—O4 | 151.2 (4) |
| K1—O1—C1—C2 | 98.6 (3) | K1vii—O3—C2—C1 | −25.4 (5) |
| K1v—O1—C1—C2 | −35.4 (4) | C3—O4—C2—O3 | −0.5 (8) |
| K1iv—O1—C1—C2 | −153.8 (3) | C3A—O4—C2—O3 | 28.4 (19) |
| K1—O1—C1—K1iv | −107.6 (3) | K1v—O4—C2—O3 | −129.6 (4) |
| K1v—O1—C1—K1iv | 118.4 (2) | C3—O4—C2—C1 | 176.4 (6) |
| K1—O1—C1—K1vii | −151.46 (18) | C3A—O4—C2—C1 | −154.7 (18) |
| K1v—O1—C1—K1vii | 74.6 (4) | K1v—O4—C2—C1 | 47.4 (3) |
| K1iv—O1—C1—K1vii | −43.8 (3) | O1—C1—C2—O3 | 162.8 (4) |
| K1—O1—C1—K1v | 134.0 (4) | O2—C1—C2—O3 | −15.6 (6) |
| K1iv—O1—C1—K1v | −118.4 (2) | K1iv—C1—C2—O3 | 81.5 (7) |
| K1vi—O2—C1—O1 | 81.6 (7) | K1vii—C1—C2—O3 | 21.2 (4) |
| K1vii—O2—C1—O1 | −126.2 (3) | K1v—C1—C2—O3 | 139.2 (4) |
| K1iv—O2—C1—O1 | −22.6 (4) | O1—C1—C2—O4 | −14.2 (5) |
| K1vi—O2—C1—C2 | −100.3 (5) | O2—C1—C2—O4 | 167.5 (3) |
| K1vii—O2—C1—C2 | 51.9 (4) | K1iv—C1—C2—O4 | −95.4 (6) |
| K1iv—O2—C1—C2 | 155.5 (3) | K1vii—C1—C2—O4 | −155.7 (3) |
| K1vi—O2—C1—K1iv | 104.1 (5) | K1v—C1—C2—O4 | −37.7 (3) |
| K1vii—O2—C1—K1iv | −103.65 (16) | C2—O4—C3—C4 | 132.1 (10) |
| K1vi—O2—C1—K1vii | −152.2 (6) | K1v—O4—C3—C4 | −103.5 (11) |
| K1iv—O2—C1—K1vii | 103.65 (16) | C2—O4—C3A—C4A | −143 (3) |
| K1vi—O2—C1—K1v | 141.0 (4) | K1v—O4—C3A—C4A | 5 (5) |
| Symmetry codes: (i) x, y−1, z; (ii) x, −y+1/2, z+1/2; (iii) x, −y+3/2, z+1/2; (iv) −x, −y+1, −z+1; (v) x, −y+1/2, z−1/2; (vi) x, y+1, z; (vii) x, −y+3/2, z−1/2. |
Funding information
We would like to thank the Office of Naval Research (ONR) and the U·S. Naval Research Laboratory (NRL) for their generous support of this base 6.1 program.
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