organic compounds
2-[1-(1-Oxoindan-2-yl)ethyl]indan-1-one
aCenter of Excellence for Advanced Materials Research (CEAMR), King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia, bChemistry Department, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia, and cDepartment of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia
*Correspondence e-mail: edward.tiekink@gmail.com
In the title compound, C20H18O2, the fused-ring systems are essentially planar (r.m.s. deviations of the nine fitted atoms = 0.009 and 0.027 Å) and exhibit an orthogonal relationship [dihedral angle = 79.83 (5)°]. To a first approximation, the ketone-O atoms are directed to opposite sides of the molecule. A three-dimensional architecture arises in the crystal packing owing to C—H⋯O, C—H⋯π and π–π interactions [between centrosymmetrically related benzene rings with centroid–centroid distance = 3.7647 (10) Å].
Related literature
For the biological activity of related indan-1-one derivatives, see: Vera-DiVaio et al. (2009). For a related structure see: Asiri et al. (2012).
Experimental
Crystal data
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Refinement
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Data collection: CrysAlis PRO (Agilent, 2012); cell CrysAlis PRO; data reduction: CrysAlis PRO; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).
Supporting information
https://doi.org/10.1107/S1600536812029315/mw2075sup1.cif
contains datablocks global, I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600536812029315/mw2075Isup2.hkl
Supporting information file. DOI: https://doi.org/10.1107/S1600536812029315/mw2075Isup3.cml
A solution of acetaldehyde (0.44 g, 0.01 M) in ethanol (20 mL) was added to a stirred solution of 1-indanone (1.3 g,0.01 M) in (20%) ethanolic KOH (20 mL) and stirring was maintained at room temperature for 6 h. The reaction mixture was then poured onto water (200 mL) and set aside overnight. The precipitated solid product was collected by filtration, washed with water, dried and recrystallized from ethanol. M.P.: 413–414 K. Yield: 86%.
Carbon-bound H-atoms were placed in calculated positions [C—H = 0.95–0.99 Å, Uiso(H) = 1.2–1.5Ueq(C)] and were included in the
in the riding model approximation. Owing to poor agreement, the (-8 1 5) reflection was omitted from the final cycles of refinement.The motivation for the synthesis of the title compound, 2-[1-(1-oxo-2,3-dihydro-1H-inden-2-yl)ethyl]-2,3-dihydro-1H-inden-1-one (I), rests with its relationship to biologically active compounds (Vera-DiVaio et al., 2009). Herein, the crystal and molecular structure of (I) is described in continuation of on-going structural studies of indan-1-one derivatives (Asiri et al., 2012).
In (I), Fig. 1, each fused ring system is planar [C1-containing system: r.m.s. deviation of the nine fitted atoms = 0.009 Å with maximum deviation of 0.012 (2) Å for atom C7; C19-containing system: 0.027 Å and 0.044 (2) Å for atom C13]. The dihedral angle between the indan-1-one residues = 79.83 (5)°, indicating an almost orthogonal relationship. To a first approximation the ketone-O atoms are directed to opposite sides of the molecule.
In the crystal packing, molecules are arranged in a three-dimensional architecture by C—H···O and C—H···π interactions, Table 1, as well as π—π contacts between centrosymmetrically related C2–C6 benzene rings [inter-centroid distance = 3.7647 (10) Å for -x, -y, -z], Fig. 2.
For the biological activity of related indan-1-one derivatives, see: Vera-DiVaio et al. (2009). For a related structure see: Asiri et al. (2012).
Data collection: CrysAlis PRO (Agilent, 2012); cell
CrysAlis PRO (Agilent, 2012); data reduction: CrysAlis PRO (Agilent, 2012); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).C20H18O2 | Z = 2 |
Mr = 290.34 | F(000) = 308 |
Triclinic, P1 | Dx = 1.337 Mg m−3 |
Hall symbol: -P 1 | Mo Kα radiation, λ = 0.71073 Å |
a = 7.9225 (6) Å | Cell parameters from 2265 reflections |
b = 10.1226 (8) Å | θ = 2.3–27.5° |
c = 10.3927 (7) Å | µ = 0.09 mm−1 |
α = 103.200 (6)° | T = 100 K |
β = 103.304 (6)° | Prism, colourless |
γ = 109.462 (7)° | 0.40 × 0.20 × 0.10 mm |
V = 721.25 (9) Å3 |
Agilent SuperNova Dual diffractometer with an Atlas detector | 3299 independent reflections |
Radiation source: SuperNova (Mo) X-ray Source | 2663 reflections with I > 2σ(I) |
Mirror monochromator | Rint = 0.021 |
Detector resolution: 10.4041 pixels mm-1 | θmax = 27.6°, θmin = 2.3° |
ω scan | h = −10→8 |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2012) | k = −13→13 |
Tmin = 0.748, Tmax = 1.000 | l = −13→13 |
4961 measured reflections |
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
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) = 0.130 | H-atom parameters constrained |
S = 1.05 | w = 1/[σ2(Fo2) + (0.0616P)2 + 0.1751P] where P = (Fo2 + 2Fc2)/3 |
3299 reflections | (Δ/σ)max < 0.001 |
199 parameters | Δρmax = 0.29 e Å−3 |
0 restraints | Δρmin = −0.23 e Å−3 |
C20H18O2 | γ = 109.462 (7)° |
Mr = 290.34 | V = 721.25 (9) Å3 |
Triclinic, P1 | Z = 2 |
a = 7.9225 (6) Å | Mo Kα radiation |
b = 10.1226 (8) Å | µ = 0.09 mm−1 |
c = 10.3927 (7) Å | T = 100 K |
α = 103.200 (6)° | 0.40 × 0.20 × 0.10 mm |
β = 103.304 (6)° |
Agilent SuperNova Dual diffractometer with an Atlas detector | 3299 independent reflections |
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2012) | 2663 reflections with I > 2σ(I) |
Tmin = 0.748, Tmax = 1.000 | Rint = 0.021 |
4961 measured reflections |
R[F2 > 2σ(F2)] = 0.048 | 0 restraints |
wR(F2) = 0.130 | H-atom parameters constrained |
S = 1.05 | Δρmax = 0.29 e Å−3 |
3299 reflections | Δρmin = −0.23 e Å−3 |
199 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. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. |
x | y | z | Uiso*/Ueq | ||
O1 | 0.33484 (17) | 0.32248 (12) | 0.00936 (11) | 0.0238 (3) | |
O2 | 0.79274 (16) | 0.78862 (12) | 0.39844 (11) | 0.0198 (3) | |
C1 | 0.3010 (2) | 0.27906 (16) | 0.10437 (15) | 0.0163 (3) | |
C2 | 0.1106 (2) | 0.20108 (16) | 0.11050 (15) | 0.0155 (3) | |
C3 | −0.0656 (2) | 0.16295 (17) | 0.01190 (16) | 0.0187 (3) | |
H3 | −0.0744 | 0.1886 | −0.0711 | 0.022* | |
C4 | −0.2270 (2) | 0.08665 (17) | 0.03875 (17) | 0.0210 (4) | |
H4 | −0.3488 | 0.0593 | −0.0265 | 0.025* | |
C5 | −0.2120 (2) | 0.04949 (18) | 0.16127 (17) | 0.0214 (4) | |
H5 | −0.3244 | −0.0030 | 0.1779 | 0.026* | |
C6 | −0.0367 (2) | 0.08758 (17) | 0.25916 (17) | 0.0195 (3) | |
H6 | −0.0280 | 0.0619 | 0.3421 | 0.023* | |
C7 | 0.1266 (2) | 0.16466 (16) | 0.23241 (16) | 0.0160 (3) | |
C8 | 0.3313 (2) | 0.21549 (18) | 0.31939 (16) | 0.0187 (3) | |
H8A | 0.3590 | 0.1297 | 0.3313 | 0.022* | |
H8B | 0.3606 | 0.2859 | 0.4132 | 0.022* | |
C9 | 0.4496 (2) | 0.29281 (16) | 0.23705 (15) | 0.0159 (3) | |
H9 | 0.5224 | 0.2343 | 0.2081 | 0.019* | |
C10 | 0.5928 (2) | 0.45371 (16) | 0.32567 (15) | 0.0144 (3) | |
H10 | 0.5205 | 0.5090 | 0.3618 | 0.017* | |
C11 | 0.7368 (2) | 0.45252 (18) | 0.45280 (16) | 0.0200 (3) | |
H11A | 0.8267 | 0.5547 | 0.5091 | 0.030* | |
H11B | 0.8060 | 0.3952 | 0.4201 | 0.030* | |
H11C | 0.6694 | 0.4070 | 0.5101 | 0.030* | |
C12 | 0.6953 (2) | 0.53610 (16) | 0.23973 (15) | 0.0161 (3) | |
H12 | 0.5969 | 0.5394 | 0.1621 | 0.019* | |
C13 | 0.8140 (2) | 0.46661 (17) | 0.17407 (16) | 0.0190 (3) | |
H13A | 0.8209 | 0.3838 | 0.2074 | 0.023* | |
H13B | 0.7582 | 0.4284 | 0.0705 | 0.023* | |
C14 | 1.0084 (2) | 0.59087 (16) | 0.22124 (15) | 0.0155 (3) | |
C15 | 1.1668 (2) | 0.58854 (17) | 0.18552 (16) | 0.0183 (3) | |
H15 | 1.1600 | 0.5013 | 0.1221 | 0.022* | |
C16 | 1.3348 (2) | 0.71586 (18) | 0.24424 (16) | 0.0197 (3) | |
H16 | 1.4434 | 0.7157 | 0.2201 | 0.024* | |
C17 | 1.3462 (2) | 0.84420 (18) | 0.33833 (16) | 0.0191 (3) | |
H17 | 1.4630 | 0.9296 | 0.3789 | 0.023* | |
C18 | 1.1889 (2) | 0.84811 (17) | 0.37301 (16) | 0.0169 (3) | |
H18 | 1.1957 | 0.9353 | 0.4363 | 0.020* | |
C19 | 1.0201 (2) | 0.72010 (16) | 0.31216 (15) | 0.0149 (3) | |
C20 | 0.8326 (2) | 0.69643 (16) | 0.32874 (15) | 0.0153 (3) |
U11 | U22 | U33 | U12 | U13 | U23 | |
O1 | 0.0241 (6) | 0.0235 (6) | 0.0171 (5) | 0.0014 (5) | 0.0050 (5) | 0.0092 (5) |
O2 | 0.0198 (6) | 0.0187 (6) | 0.0208 (6) | 0.0077 (5) | 0.0085 (5) | 0.0046 (5) |
C1 | 0.0184 (8) | 0.0119 (7) | 0.0156 (7) | 0.0037 (6) | 0.0052 (6) | 0.0038 (6) |
C2 | 0.0155 (8) | 0.0116 (7) | 0.0170 (7) | 0.0044 (6) | 0.0046 (6) | 0.0031 (6) |
C3 | 0.0201 (8) | 0.0154 (7) | 0.0175 (7) | 0.0062 (6) | 0.0028 (6) | 0.0047 (6) |
C4 | 0.0155 (8) | 0.0192 (8) | 0.0226 (8) | 0.0054 (7) | 0.0016 (6) | 0.0040 (7) |
C5 | 0.0154 (8) | 0.0204 (8) | 0.0257 (8) | 0.0041 (6) | 0.0086 (7) | 0.0059 (7) |
C6 | 0.0188 (8) | 0.0198 (8) | 0.0203 (7) | 0.0062 (7) | 0.0083 (6) | 0.0081 (7) |
C7 | 0.0160 (8) | 0.0133 (7) | 0.0175 (7) | 0.0055 (6) | 0.0053 (6) | 0.0038 (6) |
C8 | 0.0152 (8) | 0.0199 (8) | 0.0206 (7) | 0.0043 (6) | 0.0056 (6) | 0.0103 (7) |
C9 | 0.0141 (7) | 0.0155 (7) | 0.0183 (7) | 0.0047 (6) | 0.0064 (6) | 0.0070 (6) |
C10 | 0.0136 (7) | 0.0151 (7) | 0.0139 (7) | 0.0045 (6) | 0.0050 (6) | 0.0052 (6) |
C11 | 0.0167 (8) | 0.0238 (8) | 0.0193 (7) | 0.0064 (7) | 0.0050 (6) | 0.0104 (7) |
C12 | 0.0145 (8) | 0.0159 (7) | 0.0151 (7) | 0.0029 (6) | 0.0051 (6) | 0.0050 (6) |
C13 | 0.0200 (8) | 0.0156 (7) | 0.0198 (7) | 0.0038 (6) | 0.0107 (6) | 0.0038 (6) |
C14 | 0.0175 (8) | 0.0152 (7) | 0.0147 (7) | 0.0054 (6) | 0.0063 (6) | 0.0073 (6) |
C15 | 0.0224 (8) | 0.0186 (8) | 0.0201 (7) | 0.0108 (7) | 0.0106 (7) | 0.0102 (7) |
C16 | 0.0165 (8) | 0.0267 (8) | 0.0213 (7) | 0.0116 (7) | 0.0080 (6) | 0.0120 (7) |
C17 | 0.0134 (8) | 0.0205 (8) | 0.0191 (7) | 0.0040 (6) | 0.0020 (6) | 0.0069 (7) |
C18 | 0.0161 (8) | 0.0167 (7) | 0.0160 (7) | 0.0054 (6) | 0.0039 (6) | 0.0054 (6) |
C19 | 0.0143 (8) | 0.0164 (7) | 0.0144 (7) | 0.0053 (6) | 0.0042 (6) | 0.0076 (6) |
C20 | 0.0156 (8) | 0.0164 (7) | 0.0130 (7) | 0.0046 (6) | 0.0040 (6) | 0.0070 (6) |
O1—C1 | 1.2172 (18) | C10—H10 | 1.0000 |
O2—C20 | 1.2200 (18) | C11—H11A | 0.9800 |
C1—C2 | 1.475 (2) | C11—H11B | 0.9800 |
C1—C9 | 1.537 (2) | C11—H11C | 0.9800 |
C2—C7 | 1.388 (2) | C12—C20 | 1.532 (2) |
C2—C3 | 1.397 (2) | C12—C13 | 1.537 (2) |
C3—C4 | 1.383 (2) | C12—H12 | 1.0000 |
C3—H3 | 0.9500 | C13—C14 | 1.508 (2) |
C4—C5 | 1.399 (2) | C13—H13A | 0.9900 |
C4—H4 | 0.9500 | C13—H13B | 0.9900 |
C5—C6 | 1.388 (2) | C14—C19 | 1.388 (2) |
C5—H5 | 0.9500 | C14—C15 | 1.394 (2) |
C6—C7 | 1.397 (2) | C15—C16 | 1.389 (2) |
C6—H6 | 0.9500 | C15—H15 | 0.9500 |
C7—C8 | 1.506 (2) | C16—C17 | 1.398 (2) |
C8—C9 | 1.552 (2) | C16—H16 | 0.9500 |
C8—H8A | 0.9900 | C17—C18 | 1.384 (2) |
C8—H8B | 0.9900 | C17—H17 | 0.9500 |
C9—C10 | 1.546 (2) | C18—C19 | 1.396 (2) |
C9—H9 | 1.0000 | C18—H18 | 0.9500 |
C10—C11 | 1.539 (2) | C19—C20 | 1.481 (2) |
C10—C12 | 1.541 (2) | ||
O1—C1—C2 | 125.93 (14) | C10—C11—H11A | 109.5 |
O1—C1—C9 | 125.80 (14) | C10—C11—H11B | 109.5 |
C2—C1—C9 | 108.26 (12) | H11A—C11—H11B | 109.5 |
C7—C2—C3 | 121.93 (15) | C10—C11—H11C | 109.5 |
C7—C2—C1 | 109.99 (13) | H11A—C11—H11C | 109.5 |
C3—C2—C1 | 128.07 (14) | H11B—C11—H11C | 109.5 |
C4—C3—C2 | 117.95 (14) | C20—C12—C13 | 105.56 (12) |
C4—C3—H3 | 121.0 | C20—C12—C10 | 111.74 (12) |
C2—C3—H3 | 121.0 | C13—C12—C10 | 115.59 (12) |
C3—C4—C5 | 120.44 (15) | C20—C12—H12 | 107.9 |
C3—C4—H4 | 119.8 | C13—C12—H12 | 107.9 |
C5—C4—H4 | 119.8 | C10—C12—H12 | 107.9 |
C6—C5—C4 | 121.51 (15) | C14—C13—C12 | 105.17 (12) |
C6—C5—H5 | 119.2 | C14—C13—H13A | 110.7 |
C4—C5—H5 | 119.2 | C12—C13—H13A | 110.7 |
C5—C6—C7 | 118.21 (14) | C14—C13—H13B | 110.7 |
C5—C6—H6 | 120.9 | C12—C13—H13B | 110.7 |
C7—C6—H6 | 120.9 | H13A—C13—H13B | 108.8 |
C2—C7—C6 | 119.95 (14) | C19—C14—C15 | 119.78 (14) |
C2—C7—C8 | 111.50 (14) | C19—C14—C13 | 111.79 (14) |
C6—C7—C8 | 128.54 (14) | C15—C14—C13 | 128.43 (14) |
C7—C8—C9 | 105.61 (12) | C16—C15—C14 | 118.87 (15) |
C7—C8—H8A | 110.6 | C16—C15—H15 | 120.6 |
C9—C8—H8A | 110.6 | C14—C15—H15 | 120.6 |
C7—C8—H8B | 110.6 | C15—C16—C17 | 120.85 (15) |
C9—C8—H8B | 110.6 | C15—C16—H16 | 119.6 |
H8A—C8—H8B | 108.8 | C17—C16—H16 | 119.6 |
C1—C9—C10 | 114.59 (12) | C18—C17—C16 | 120.66 (15) |
C1—C9—C8 | 104.64 (12) | C18—C17—H17 | 119.7 |
C10—C9—C8 | 112.64 (13) | C16—C17—H17 | 119.7 |
C1—C9—H9 | 108.2 | C17—C18—C19 | 118.06 (14) |
C10—C9—H9 | 108.2 | C17—C18—H18 | 121.0 |
C8—C9—H9 | 108.2 | C19—C18—H18 | 121.0 |
C11—C10—C12 | 110.83 (12) | C14—C19—C18 | 121.75 (15) |
C11—C10—C9 | 109.67 (12) | C14—C19—C20 | 109.52 (13) |
C12—C10—C9 | 112.68 (12) | C18—C19—C20 | 128.74 (14) |
C11—C10—H10 | 107.8 | O2—C20—C19 | 126.32 (14) |
C12—C10—H10 | 107.8 | O2—C20—C12 | 125.82 (14) |
C9—C10—H10 | 107.8 | C19—C20—C12 | 107.85 (12) |
Cg1 is the centroid of the C14–C19 benzene ring. |
D—H···A | D—H | H···A | D···A | D—H···A |
C12—H12···O1i | 1.00 | 2.55 | 3.2317 (19) | 125 |
C3—H3···Cg1i | 0.95 | 2.62 | 3.5395 (17) | 163 |
C11—H11C···Cg1ii | 0.98 | 2.99 | 3.6481 (18) | 126 |
Symmetry codes: (i) −x+1, −y+1, −z; (ii) −x+2, −y+1, −z+1. |
Experimental details
Crystal data | |
Chemical formula | C20H18O2 |
Mr | 290.34 |
Crystal system, space group | Triclinic, P1 |
Temperature (K) | 100 |
a, b, c (Å) | 7.9225 (6), 10.1226 (8), 10.3927 (7) |
α, β, γ (°) | 103.200 (6), 103.304 (6), 109.462 (7) |
V (Å3) | 721.25 (9) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm−1) | 0.09 |
Crystal size (mm) | 0.40 × 0.20 × 0.10 |
Data collection | |
Diffractometer | Agilent SuperNova Dual diffractometer with an Atlas detector |
Absorption correction | Multi-scan (CrysAlis PRO; Agilent, 2012) |
Tmin, Tmax | 0.748, 1.000 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 4961, 3299, 2663 |
Rint | 0.021 |
(sin θ/λ)max (Å−1) | 0.651 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.048, 0.130, 1.05 |
No. of reflections | 3299 |
No. of parameters | 199 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.29, −0.23 |
Computer programs: CrysAlis PRO (Agilent, 2012), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2006), publCIF (Westrip, 2010).
Cg1 is the centroid of the C14–C19 benzene ring. |
D—H···A | D—H | H···A | D···A | D—H···A |
C12—H12···O1i | 1.00 | 2.55 | 3.2317 (19) | 125 |
C3—H3···Cg1i | 0.95 | 2.62 | 3.5395 (17) | 163 |
C11—H11C···Cg1ii | 0.98 | 2.99 | 3.6481 (18) | 126 |
Symmetry codes: (i) −x+1, −y+1, −z; (ii) −x+2, −y+1, −z+1. |
Footnotes
‡Additional correspondence author, e-mail: aasiri2@kau.edu.sa.
Acknowledgements
The authors are grateful to King Abdulaziz University for providing research facilities. We also thank the Ministry of Higher Education (Malaysia) for funding structural studies through the High-Impact Research scheme (UM.C/HIR/MOHE/SC/12).
References
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The motivation for the synthesis of the title compound, 2-[1-(1-oxo-2,3-dihydro-1H-inden-2-yl)ethyl]-2,3-dihydro-1H-inden-1-one (I), rests with its relationship to biologically active compounds (Vera-DiVaio et al., 2009). Herein, the crystal and molecular structure of (I) is described in continuation of on-going structural studies of indan-1-one derivatives (Asiri et al., 2012).
In (I), Fig. 1, each fused ring system is planar [C1-containing system: r.m.s. deviation of the nine fitted atoms = 0.009 Å with maximum deviation of 0.012 (2) Å for atom C7; C19-containing system: 0.027 Å and 0.044 (2) Å for atom C13]. The dihedral angle between the indan-1-one residues = 79.83 (5)°, indicating an almost orthogonal relationship. To a first approximation the ketone-O atoms are directed to opposite sides of the molecule.
In the crystal packing, molecules are arranged in a three-dimensional architecture by C—H···O and C—H···π interactions, Table 1, as well as π—π contacts between centrosymmetrically related C2–C6 benzene rings [inter-centroid distance = 3.7647 (10) Å for symmetry operation -x, -y, -z], Fig. 2.