organic compounds
Ethyl 3-oxo-2-(2-phenylhydrazinylidene)butanoate: a re-determination
aDepartment of Physics, Ranchi University, Ranchi 834 008, India, and bDepartment of Chemistry, Bihar University, Muzzafarpur 842 002, India
*Correspondence e-mail: prasadsm50@hotmail.com
The previous crystallographic studies [Wang et al. (2005). Huaxue Yanjiu 16, 29–32; Wang et al. (2007). Youji Huaxue, 27, 524] of the title compound, C12H14N2O3, gave only the unit-cell dimensions and an R factor with no other details available: the full structure is presented here. The ethoxy group is disordered over two orientations with refined occupancies of 0.642 (15):0.358 (15). The nine C atoms and two N atoms of the 1-phenyl-2-(propan-2-ylidene)hydrazine segment of the molecule are close to being coplanar, with a maximum deviation of 0.0779 (14) Å for the phenylamino N atom and an intramolecular N—H⋯O hydrogen bond generates an S(6) ring. In the crystal, pairs of C—H⋯O hydrogen bonds link molecules into inverson dimers, generating R22(16) loops.
Related literature
For previous reports of the structure of the title compound, see: Wang et al. (2005, 2007). For further synthetic details, see: Fernandes et al. (1975). For graph-set analysis of hydrogen bonding, see: Bernstein et al. (1995).
Experimental
Crystal data
|
Data collection
|
Refinement
|
Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell CAD-4 EXPRESS; data reduction: MolEN (Fair, 1990); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: SHELXL97.
Supporting information
10.1107/S1600536811002200/hb5790sup1.cif
contains datablocks I, global. DOI:Structure factors: contains datablock I. DOI: 10.1107/S1600536811002200/hb5790Isup2.hkl
The title compound was prepared by the coupling of diazonium salt of aniline with ethyl acetoacetate (Fernandes et al., 1975). It was recrystalized from methanol by slow evaporation at room temperature to yield colourless blocks of (I).
High values of isotropic thermal parameters for atoms O3 and C10 and unacceptable bond lengths for O3—C10 and C10—C11 of the ethoxy group indicated possible disorder. A difference elctron density map excluding the atoms O3, C10 and C11 showed that the ethoxy group to be disordered over two sites. The ratio of the occupancy factors of the two disorder components refined to 0.642 (15):0.358 (15). All H-atoms were positioned geometrically and refined using a riding model with d(C-H) = 0.93Å, Uiso=1.2Ueq (C) for aromatic 0.97Å, Uiso = 1.2Ueq (C) for CH2, 0.86Å, Uiso = 1.2Ueq (N) for NH, and 0.96Å, Uiso = 1.5Ueq (C) for CH3 atoms.
Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell
CAD-4 EXPRESS (Enraf–Nonius, 1994); data reduction: MolEN (Fair, 1990); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).Fig. 1. The structre of (I) with 30% probability displacement ellipsoids for non-hyrogen atoms showing the disordered ethoxy group O3—C10—C11. | |
Fig. 2. Crystal packing of (I) viewed down the a axis. |
C12H14N2O3 | F(000) = 496 |
Mr = 234.25 | Dx = 1.275 Mg m−3 |
Monoclinic, P21/c | Cu Kα radiation, λ = 1.5418 Å |
Hall symbol: -P 2ybc | Cell parameters from 25 reflections |
a = 8.4375 (9) Å | θ = 25.8–35.5° |
b = 17.551 (2) Å | µ = 0.77 mm−1 |
c = 8.242 (1) Å | T = 293 K |
β = 91.24 (1)° | Block, colourless |
V = 1220.2 (2) Å3 | 0.2 × 0.16 × 0.12 mm |
Z = 4 |
Enraf–Nonius CAD-4 diffractometer | Rint = 0.022 |
Radiation source: fine-focus sealed tube | θmax = 69.8°, θmin = 5.0° |
Graphite monochromator | h = −10→10 |
ω–2θ scans | k = 0→21 |
2393 measured reflections | l = 0→9 |
2243 independent reflections | 3 standard reflections every 60 min |
1715 reflections with I > 2σ(I) | intensity decay: 0.0% |
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
R[F2 > 2σ(F2)] = 0.052 | H-atom parameters constrained |
wR(F2) = 0.185 | w = 1/[σ2(Fo2) + (0.1173P)2 + 0.0072P] where P = (Fo2 + 2Fc2)/3 |
S = 1.07 | (Δ/σ)max < 0.001 |
2243 reflections | Δρmax = 0.19 e Å−3 |
186 parameters | Δρmin = −0.17 e Å−3 |
0 restraints | Extinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.072 (5) |
C12H14N2O3 | V = 1220.2 (2) Å3 |
Mr = 234.25 | Z = 4 |
Monoclinic, P21/c | Cu Kα radiation |
a = 8.4375 (9) Å | µ = 0.77 mm−1 |
b = 17.551 (2) Å | T = 293 K |
c = 8.242 (1) Å | 0.2 × 0.16 × 0.12 mm |
β = 91.24 (1)° |
Enraf–Nonius CAD-4 diffractometer | Rint = 0.022 |
2393 measured reflections | 3 standard reflections every 60 min |
2243 independent reflections | intensity decay: 0.0% |
1715 reflections with I > 2σ(I) |
R[F2 > 2σ(F2)] = 0.052 | 0 restraints |
wR(F2) = 0.185 | H-atom parameters constrained |
S = 1.07 | Δρmax = 0.19 e Å−3 |
2243 reflections | Δρmin = −0.17 e Å−3 |
186 parameters |
Geometry. All su's are estimated using the full covariance matrix. The cell su's are taken into account individually in the estimation of su's in distances, angles and torsion angles; correlations between su's in cell parameters are only used when they are defined by crystal symmetry. |
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 > 2σ(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. |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
O3A | 0.5943 (5) | 0.3242 (3) | 0.4120 (7) | 0.0880 (14) | 0.642 (15) |
C10A | 0.7449 (8) | 0.2909 (5) | 0.3648 (8) | 0.104 (2) | 0.642 (15) |
H10A | 0.7582 | 0.2984 | 0.2493 | 0.125* | 0.642 (15) |
H10B | 0.7425 | 0.2365 | 0.3851 | 0.125* | 0.642 (15) |
C11A | 0.8803 (11) | 0.3242 (4) | 0.4529 (7) | 0.117 (2) | 0.642 (15) |
H11A | 0.8555 | 0.3295 | 0.5655 | 0.176* | 0.642 (15) |
H11B | 0.9035 | 0.3734 | 0.4084 | 0.176* | 0.642 (15) |
H11C | 0.9709 | 0.2916 | 0.4426 | 0.176* | 0.642 (15) |
O3B | 0.6366 (10) | 0.3601 (9) | 0.4633 (10) | 0.095 (3) | 0.358 (15) |
C10B | 0.792 (2) | 0.3348 (9) | 0.416 (2) | 0.126 (4) | 0.358 (15) |
H10C | 0.8323 | 0.3678 | 0.3320 | 0.151* | 0.358 (15) |
H10D | 0.8649 | 0.3363 | 0.5084 | 0.151* | 0.358 (15) |
C11B | 0.7762 (19) | 0.2558 (11) | 0.354 (2) | 0.168 (7) | 0.358 (15) |
H11D | 0.7167 | 0.2560 | 0.2538 | 0.252* | 0.358 (15) |
H11E | 0.7222 | 0.2252 | 0.4324 | 0.252* | 0.358 (15) |
H11F | 0.8796 | 0.2349 | 0.3371 | 0.252* | 0.358 (15) |
O1 | 0.1739 (2) | 0.49615 (9) | 0.38454 (16) | 0.0898 (5) | |
O2 | 0.6193 (2) | 0.41989 (13) | 0.2324 (2) | 0.1178 (7) | |
N1 | 0.23998 (17) | 0.41137 (8) | 0.63121 (16) | 0.0619 (4) | |
H1 | 0.1711 | 0.4412 | 0.5862 | 0.074* | |
N2 | 0.36686 (18) | 0.39265 (8) | 0.55505 (17) | 0.0621 (4) | |
C1 | 0.2155 (2) | 0.38255 (9) | 0.78858 (19) | 0.0585 (5) | |
C2 | 0.0821 (2) | 0.40648 (12) | 0.8691 (2) | 0.0727 (5) | |
H2 | 0.0112 | 0.4404 | 0.8199 | 0.087* | |
C3 | 0.0557 (3) | 0.37944 (14) | 1.0233 (3) | 0.0833 (6) | |
H3 | −0.0327 | 0.3958 | 1.0790 | 0.100* | |
C4 | 0.1590 (3) | 0.32856 (12) | 1.0954 (2) | 0.0803 (6) | |
H4 | 0.1396 | 0.3101 | 1.1989 | 0.096* | |
C5 | 0.2912 (3) | 0.30493 (11) | 1.0145 (2) | 0.0742 (6) | |
H5 | 0.3613 | 0.2707 | 1.0638 | 0.089* | |
C6 | 0.3204 (2) | 0.33190 (10) | 0.8599 (2) | 0.0647 (5) | |
H6 | 0.4097 | 0.3160 | 0.8051 | 0.078* | |
C7 | 0.4007 (2) | 0.42190 (11) | 0.4118 (2) | 0.0647 (5) | |
C8 | 0.3017 (2) | 0.47900 (11) | 0.3269 (2) | 0.0700 (5) | |
C9 | 0.5507 (3) | 0.39304 (14) | 0.3460 (3) | 0.0820 (6) | |
C12 | 0.3544 (3) | 0.51477 (14) | 0.1731 (3) | 0.0881 (7) | |
H12A | 0.2856 | 0.5565 | 0.1454 | 0.132* | |
H12B | 0.3507 | 0.4777 | 0.0875 | 0.132* | |
H12C | 0.4610 | 0.5331 | 0.1873 | 0.132* |
U11 | U22 | U33 | U12 | U13 | U23 | |
O3A | 0.0801 (18) | 0.079 (2) | 0.106 (3) | 0.0054 (16) | 0.0292 (17) | 0.0026 (18) |
C10A | 0.107 (4) | 0.093 (4) | 0.115 (4) | 0.023 (3) | 0.040 (3) | −0.008 (3) |
C11A | 0.087 (4) | 0.142 (5) | 0.122 (4) | 0.029 (3) | 0.018 (3) | 0.003 (3) |
O3B | 0.081 (3) | 0.111 (7) | 0.095 (4) | 0.020 (4) | 0.020 (3) | 0.005 (4) |
C10B | 0.085 (9) | 0.139 (10) | 0.154 (10) | 0.025 (7) | 0.033 (7) | −0.010 (8) |
C11B | 0.137 (10) | 0.129 (12) | 0.241 (16) | 0.046 (9) | 0.066 (9) | −0.030 (10) |
O1 | 0.1019 (11) | 0.1033 (11) | 0.0645 (8) | 0.0229 (8) | 0.0097 (7) | 0.0206 (7) |
O2 | 0.1127 (14) | 0.1545 (18) | 0.0879 (12) | 0.0112 (11) | 0.0391 (10) | 0.0288 (11) |
N1 | 0.0694 (9) | 0.0669 (9) | 0.0495 (8) | 0.0048 (6) | 0.0022 (6) | 0.0060 (6) |
N2 | 0.0684 (9) | 0.0645 (8) | 0.0535 (8) | −0.0050 (6) | 0.0021 (6) | −0.0015 (6) |
C1 | 0.0697 (10) | 0.0578 (9) | 0.0479 (9) | −0.0059 (7) | −0.0021 (7) | 0.0010 (7) |
C2 | 0.0725 (11) | 0.0827 (12) | 0.0631 (10) | 0.0069 (9) | 0.0064 (8) | 0.0105 (9) |
C3 | 0.0880 (13) | 0.0957 (14) | 0.0669 (12) | 0.0012 (11) | 0.0180 (10) | 0.0088 (10) |
C4 | 0.1020 (15) | 0.0811 (13) | 0.0579 (10) | −0.0139 (10) | 0.0066 (10) | 0.0127 (9) |
C5 | 0.0991 (14) | 0.0629 (11) | 0.0601 (10) | −0.0009 (9) | −0.0064 (9) | 0.0089 (8) |
C6 | 0.0786 (11) | 0.0583 (9) | 0.0572 (10) | 0.0041 (7) | −0.0002 (8) | −0.0005 (7) |
C7 | 0.0736 (11) | 0.0695 (10) | 0.0511 (9) | −0.0098 (8) | 0.0023 (7) | −0.0005 (7) |
C8 | 0.0816 (12) | 0.0753 (11) | 0.0529 (9) | −0.0100 (9) | −0.0013 (8) | 0.0033 (8) |
C9 | 0.0801 (13) | 0.1015 (16) | 0.0648 (11) | −0.0064 (11) | 0.0107 (10) | −0.0009 (10) |
C12 | 0.0926 (15) | 0.1040 (16) | 0.0677 (12) | −0.0173 (12) | −0.0002 (10) | 0.0252 (11) |
O3A—C9 | 1.373 (4) | N1—H1 | 0.8600 |
O3A—C10A | 1.459 (8) | N2—C7 | 1.324 (2) |
C10A—C11A | 1.462 (12) | C1—C2 | 1.384 (3) |
C10A—H10A | 0.9700 | C1—C6 | 1.377 (2) |
C10A—H10B | 0.9700 | C2—C3 | 1.379 (3) |
C11A—H11A | 0.9600 | C2—H2 | 0.9300 |
C11A—H11B | 0.9600 | C3—C4 | 1.374 (3) |
C11A—H11C | 0.9600 | C3—H3 | 0.9300 |
O3B—C9 | 1.328 (7) | C4—C5 | 1.376 (3) |
O3B—C10B | 1.445 (15) | C4—H4 | 0.9300 |
C10B—C11B | 1.48 (2) | C5—C6 | 1.387 (3) |
C10B—H10C | 0.9700 | C5—H5 | 0.9300 |
C10B—H10D | 0.9700 | C6—H6 | 0.9300 |
C11B—H11D | 0.9600 | C7—C8 | 1.472 (3) |
C11B—H11E | 0.9600 | C7—C9 | 1.477 (3) |
C11B—H11F | 0.9600 | C8—C12 | 1.491 (3) |
O1—C8 | 1.225 (2) | C12—H12A | 0.9600 |
O2—C9 | 1.207 (3) | C12—H12B | 0.9600 |
N1—N2 | 1.295 (2) | C12—H12C | 0.9600 |
N1—C1 | 1.412 (2) | ||
C9—O3A—C10A | 118.3 (4) | C4—C3—C2 | 120.6 (2) |
O3A—C10A—C11A | 112.6 (9) | C4—C3—H3 | 119.7 |
O3A—C10A—H10A | 109.1 | C2—C3—H3 | 119.7 |
C11A—C10A—H10A | 109.1 | C5—C4—C3 | 119.96 (18) |
O3A—C10A—H10B | 109.1 | C5—C4—H4 | 120.0 |
C11A—C10A—H10B | 109.1 | C3—C4—H4 | 120.0 |
H10A—C10A—H10B | 107.8 | C4—C5—C6 | 120.32 (18) |
C9—O3B—C10B | 114.9 (9) | C4—C5—H5 | 119.8 |
C11B—C10B—O3B | 107.8 (17) | C6—C5—H5 | 119.8 |
C11B—C10B—H10C | 110.1 | C1—C6—C5 | 119.16 (18) |
O3B—C10B—H10C | 110.1 | C1—C6—H6 | 120.4 |
C11B—C10B—H10D | 110.1 | C5—C6—H6 | 120.4 |
O3B—C10B—H10D | 110.1 | N2—C7—C8 | 123.80 (17) |
H10C—C10B—H10D | 108.5 | N2—C7—C9 | 113.43 (17) |
C10B—C11B—H11D | 109.5 | C8—C7—C9 | 122.76 (17) |
C10B—C11B—H11E | 109.5 | O1—C8—C7 | 118.59 (16) |
H11D—C11B—H11E | 109.5 | O1—C8—C12 | 120.48 (19) |
C10B—C11B—H11F | 109.5 | C7—C8—C12 | 120.92 (19) |
H11D—C11B—H11F | 109.5 | O2—C9—O3B | 118.1 (4) |
H11E—C11B—H11F | 109.5 | O2—C9—O3A | 121.5 (3) |
N2—N1—C1 | 119.56 (14) | O3B—C9—O3A | 36.0 (5) |
N2—N1—H1 | 120.2 | O2—C9—C7 | 125.4 (2) |
C1—N1—H1 | 120.2 | O3B—C9—C7 | 109.9 (3) |
N1—N2—C7 | 122.04 (15) | O3A—C9—C7 | 112.4 (2) |
C2—C1—C6 | 120.85 (16) | C8—C12—H12A | 109.5 |
C2—C1—N1 | 117.94 (15) | C8—C12—H12B | 109.5 |
C6—C1—N1 | 121.21 (16) | H12A—C12—H12B | 109.5 |
C1—C2—C3 | 119.12 (18) | C8—C12—H12C | 109.5 |
C1—C2—H2 | 120.4 | H12A—C12—H12C | 109.5 |
C3—C2—H2 | 120.4 | H12B—C12—H12C | 109.5 |
C9—O3A—C10A—C11A | 80.3 (6) | C9—C7—C8—O1 | 175.22 (18) |
C9—O3B—C10B—C11B | −89.0 (12) | N2—C7—C8—C12 | 174.34 (17) |
C1—N1—N2—C7 | −175.53 (14) | C9—C7—C8—C12 | −4.1 (3) |
N2—N1—C1—C2 | 177.16 (15) | C10B—O3B—C9—O2 | −22.3 (18) |
N2—N1—C1—C6 | −3.1 (3) | C10B—O3B—C9—O3A | 83.5 (14) |
C6—C1—C2—C3 | 0.6 (3) | C10B—O3B—C9—C7 | −175.5 (12) |
N1—C1—C2—C3 | −179.73 (18) | C10A—O3A—C9—O2 | 12.4 (9) |
C1—C2—C3—C4 | −0.9 (4) | C10A—O3A—C9—O3B | −83.2 (8) |
C2—C3—C4—C5 | 0.8 (4) | C10A—O3A—C9—C7 | −176.6 (6) |
C3—C4—C5—C6 | −0.4 (3) | N2—C7—C9—O2 | −167.1 (2) |
C2—C1—C6—C5 | −0.1 (3) | C8—C7—C9—O2 | 11.5 (3) |
N1—C1—C6—C5 | −179.79 (16) | N2—C7—C9—O3B | −16.3 (8) |
C4—C5—C6—C1 | 0.0 (3) | C8—C7—C9—O3B | 162.3 (8) |
N1—N2—C7—C8 | 1.4 (3) | N2—C7—C9—O3A | 22.3 (4) |
N1—N2—C7—C9 | 179.99 (16) | C8—C7—C9—O3A | −159.1 (4) |
N2—C7—C8—O1 | −6.3 (3) |
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1···O1 | 0.86 | 1.92 | 2.571 (2) | 131 |
C2—H2···O1i | 0.93 | 2.53 | 3.430 (3) | 163 |
Symmetry code: (i) −x, −y+1, −z+1. |
Experimental details
Crystal data | |
Chemical formula | C12H14N2O3 |
Mr | 234.25 |
Crystal system, space group | Monoclinic, P21/c |
Temperature (K) | 293 |
a, b, c (Å) | 8.4375 (9), 17.551 (2), 8.242 (1) |
β (°) | 91.24 (1) |
V (Å3) | 1220.2 (2) |
Z | 4 |
Radiation type | Cu Kα |
µ (mm−1) | 0.77 |
Crystal size (mm) | 0.2 × 0.16 × 0.12 |
Data collection | |
Diffractometer | Enraf–Nonius CAD-4 diffractometer |
Absorption correction | – |
No. of measured, independent and observed [I > 2σ(I)] reflections | 2393, 2243, 1715 |
Rint | 0.022 |
(sin θ/λ)max (Å−1) | 0.609 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.052, 0.185, 1.07 |
No. of reflections | 2243 |
No. of parameters | 186 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.19, −0.17 |
Computer programs: CAD-4 EXPRESS (Enraf–Nonius, 1994), MolEN (Fair, 1990), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 (Farrugia, 1997).
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1···O1 | 0.86 | 1.92 | 2.571 (2) | 131 |
C2—H2···O1i | 0.93 | 2.53 | 3.430 (3) | 163 |
Symmetry code: (i) −x, −y+1, −z+1. |
Acknowledgements
The authors thank the late Dr N. Prasad and his co-workers in the Department of Chemistry, BRA Bihar University, Muzaffarpur, India, for the gift of crystals and the X-ray Diffraction Group, Indian Institute of Technology, Chennai, India, for the data collection.
References
Bernstein, J., Davis, R. E., Shimoni, L. & Chang, N.-L. (1995). Angew. Chem. Int. Ed. Engl. 34, 1555–1573. CrossRef CAS Web of Science Google Scholar
Enraf–Nonius (1994). CAD-4 EXPRESS. Enraf–Nonius, Delft, The Netherlands. Google Scholar
Fair, C. K. (1990). MolEN. Enraf–Nonius, Delft, The Netherlands. Google Scholar
Farrugia, L. J. (1997). J. Appl. Cryst. 30, 565. CrossRef IUCr Journals Google Scholar
Fernandes, P. S., Nadkarny, V. V., Jaber, G. A. & Jain, R. P. (1975). J. Indian Chem. Soc. 52, 546, 840–842. Google Scholar
Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wang, J.-P., Cheng, X.-X. & Zhang, Y.-Q. (2005). Huaxue Yanjiu, 16, 29–32. CAS Google Scholar
Wang, J.-P., Fu, Y.-J., Yin, W.-P., Wang, J.-G. & Qin, J.-H. (2007). Youji Huaxue, 27, 524. Google Scholar
This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
The unit cell of the title compound, (I), was reported by Wang et al. (2005, 2007). In the full structure reported here, the ethoxy group is disordered over two orientations with refined occupancies 0.642 (15):0.358 (15). The planes C9—O3A—C10A (plane A) and C9—O3B—C10B (plane B) of the two disordered ethoxy groups are inclined at an angle of 38.3 (17)°. The bonds C10A—C11A and C10B—C11B are bent in opposite directions with atom C11A and C11B deviating from planes A & B by 1.33 (1)Å and -1.41 (2)Å, respectively. The torsion angles C9—O3A—C10A—C11A and C9—O3B—C10B—C11B are 80.3 (6) and -89.0 (12)°, respectively. An intramolecular N—H···O hydrogen bond contributes to the planarity of the C1···C9, N1, N2, 1-phenyl-2-(propan-2-ylidene)hydrazine segment of the molecule. In the crystal structure C2—H2···O1 hydrogen bonds link pairs of molecules into centrosymmetric dimers generating R22(16) rings (Bernstein et al., 1995).