Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807029285/wk2063sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536807029285/wk2063Isup2.hkl |
CCDC reference: 654794
The ligand C22H32N4O2 (H2L) was prepared by the reported procedure (Mandal & Nag, 1986). A mixture of H2L (0.10 g, 0.26 mmol) and Zn(NO3)2. 6H2O (0.15 g, 0.52 mmol) in methanol (20 ml) was stirred for 10 min. The resulting solution was filtered. Colorless single crystals were obtained by slow evaporation of the filtrate at room temperature (yield 56%).
All H-atoms bound to carbon were refined using a riding model with d(C—H) = 0.93 Å, Uiso = 1.2Ueq (C) for aromatic and 0.96 Å, Uiso = 1.5Ueq (C) for CH3 atoms. The imino H atoms were located in a difference Fourier map and refined isotropically with Uiso(H) = 1.5 Ueq(N).
Dinuclear zinc(II) cores have attracted much interest as a result of their significance in biological systems (Dealwis et al., 1995; Burley et al., 1990; Roderick & Mathews, 1993). In addition, some synthetic dinuclear zinc(II) compounds are found to have functions in dephosphorylation (Bazzicalupi et al., 1997). To further widen the scope of application of such zinc compounds, there is a need to prepare new series of dinuclear zinc compounds. In this work, a new dinuclear zinc(II) compound has been synthesized, and its structure (I) is reported here.
As shown in Fig. 1, [Zn2L(NO3)2] is a centrosymmetric dinuclear zinc compound. The coordination environment around zinc is a square-pyramid with two N atoms and two O atoms from L ligand occupying the basal positions and one O atom from NO3- anion occupying the apical position. In the crystal structure two zinc atoms are bridged by two phenolate O atoms to generate a four-membered Zn2O2 ring. The Zn—O and Zn—N distances are normal (Dutta et al., 2005).
For related literature, see: Dealwis et al. (1995); Burley et al. (1990); Roderick & Mathews (1993); Dutta et al. (2005); Mandal & Nag (1986); Bazzicalupi et al. (1997).
Data collection: SMART (Bruker, 1997); cell refinement: SAINT (Bruker, 1999); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL-Plus (Sheldrick, 1990); software used to prepare material for publication: SHELXL97.
Fig. 1. A view of the molecule of (I). Displacement ellipsoids are drawn at the 30% probability level. H atoms have been omitted for clarity. |
[Zn2(NO3)2(C22H30N4O2)] | F(000) = 656 |
Mr = 637.26 | Dx = 1.695 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71069 Å |
Hall symbol: -P 2ybc | Cell parameters from 3000 reflections |
a = 8.2190 (5) Å | θ = 2.4–28.4° |
b = 14.1450 (8) Å | µ = 1.98 mm−1 |
c = 11.0550 (6) Å | T = 293 K |
β = 103.744 (9)° | Block, colorless |
V = 1248.43 (12) Å3 | 0.40 × 0.30 × 0.25 mm |
Z = 2 |
Bruker APEX CCD area-detector diffractometer | 3027 independent reflections |
Radiation source: fine-focus sealed tube | 2524 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.019 |
ω scans | θmax = 28.4°, θmin = 2.4° |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | h = −10→10 |
Tmin = 0.495, Tmax = 0.609 | k = −10→18 |
7558 measured reflections | l = −14→14 |
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)] = 0.028 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.080 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.07 | w = 1/[σ2(Fo2) + (0.0446P)2 + 0.1778P] where P = (Fo2 + 2Fc2)/3 |
3027 reflections | (Δ/σ)max = 0.001 |
178 parameters | Δρmax = 0.40 e Å−3 |
0 restraints | Δρmin = −0.29 e Å−3 |
[Zn2(NO3)2(C22H30N4O2)] | V = 1248.43 (12) Å3 |
Mr = 637.26 | Z = 2 |
Monoclinic, P21/c | Mo Kα radiation |
a = 8.2190 (5) Å | µ = 1.98 mm−1 |
b = 14.1450 (8) Å | T = 293 K |
c = 11.0550 (6) Å | 0.40 × 0.30 × 0.25 mm |
β = 103.744 (9)° |
Bruker APEX CCD area-detector diffractometer | 3027 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | 2524 reflections with I > 2σ(I) |
Tmin = 0.495, Tmax = 0.609 | Rint = 0.019 |
7558 measured reflections |
R[F2 > 2σ(F2)] = 0.028 | 0 restraints |
wR(F2) = 0.080 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.07 | Δρmax = 0.40 e Å−3 |
3027 reflections | Δρmin = −0.29 e Å−3 |
178 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 | ||
Zn1 | 0.52604 (3) | 0.398830 (14) | 0.56583 (2) | 0.03572 (9) | |
C1 | 1.0529 (3) | 0.3634 (2) | 0.1572 (3) | 0.0680 (7) | |
H1A | 1.1433 | 0.3280 | 0.2081 | 0.102* | |
H1B | 1.0967 | 0.4190 | 0.1262 | 0.102* | |
H1C | 0.9960 | 0.3251 | 0.0885 | 0.102* | |
C2 | 0.9306 (3) | 0.39238 (14) | 0.2345 (3) | 0.0509 (6) | |
C3 | 0.9619 (3) | 0.37071 (14) | 0.3605 (2) | 0.0478 (5) | |
H3 | 1.0562 | 0.3352 | 0.3964 | 0.057* | |
C4 | 0.8564 (3) | 0.40063 (12) | 0.4347 (2) | 0.0419 (5) | |
C5 | 0.9026 (3) | 0.38988 (14) | 0.5739 (2) | 0.0463 (5) | |
H5A | 1.0041 | 0.3525 | 0.5969 | 0.056* | |
H5B | 0.9277 | 0.4520 | 0.6108 | 0.056* | |
C6 | 0.8087 (3) | 0.36047 (16) | 0.7661 (2) | 0.0487 (5) | |
H6A | 0.8335 | 0.4267 | 0.7845 | 0.058* | |
H6B | 0.9060 | 0.3237 | 0.8069 | 0.058* | |
C7 | 0.6586 (3) | 0.33110 (16) | 0.8152 (2) | 0.0495 (5) | |
H7A | 0.6401 | 0.2637 | 0.8027 | 0.059* | |
H7B | 0.6816 | 0.3436 | 0.9039 | 0.059* | |
C8 | 0.7136 (2) | 0.45295 (13) | 0.3782 (2) | 0.0402 (4) | |
C9 | 0.7880 (3) | 0.44471 (16) | 0.1820 (2) | 0.0493 (5) | |
H9 | 0.7665 | 0.4604 | 0.0980 | 0.059* | |
C10 | 0.6769 (3) | 0.47418 (14) | 0.2512 (2) | 0.0437 (5) | |
C11 | 0.5148 (3) | 0.52395 (15) | 0.1905 (2) | 0.0483 (5) | |
H11A | 0.5111 | 0.5339 | 0.1031 | 0.058* | |
H11B | 0.4214 | 0.4835 | 0.1956 | 0.058* | |
N1 | 0.7725 (2) | 0.34492 (11) | 0.62923 (17) | 0.0400 (4) | |
N2 | 0.5050 (2) | 0.38322 (13) | 0.75088 (18) | 0.0435 (4) | |
N3 | 0.3579 (2) | 0.22836 (14) | 0.4825 (2) | 0.0524 (5) | |
O1 | 0.61249 (19) | 0.48312 (10) | 0.44910 (15) | 0.0504 (4) | |
O2 | 0.3842 (3) | 0.30868 (13) | 0.44489 (18) | 0.0728 (5) | |
O3 | 0.2602 (3) | 0.17463 (14) | 0.4146 (2) | 0.0801 (6) | |
O4 | 0.4378 (4) | 0.20400 (16) | 0.5846 (2) | 0.1122 (9) | |
H1N | 0.773 (7) | 0.290 (3) | 0.614 (5) | 0.168* | |
H2N | 0.414 (7) | 0.353 (4) | 0.749 (5) | 0.168* |
U11 | U22 | U33 | U12 | U13 | U23 | |
Zn1 | 0.03569 (14) | 0.03053 (13) | 0.04245 (15) | 0.00473 (8) | 0.01229 (10) | 0.00441 (8) |
C1 | 0.0588 (15) | 0.0631 (15) | 0.095 (2) | −0.0046 (12) | 0.0434 (15) | −0.0265 (15) |
C2 | 0.0465 (12) | 0.0400 (11) | 0.0748 (16) | −0.0088 (9) | 0.0316 (11) | −0.0194 (10) |
C3 | 0.0346 (10) | 0.0321 (9) | 0.0811 (16) | −0.0013 (8) | 0.0227 (10) | −0.0089 (10) |
C4 | 0.0371 (10) | 0.0275 (9) | 0.0650 (13) | −0.0025 (7) | 0.0199 (9) | −0.0024 (8) |
C5 | 0.0352 (10) | 0.0368 (10) | 0.0672 (14) | −0.0018 (8) | 0.0129 (10) | 0.0041 (9) |
C6 | 0.0458 (11) | 0.0436 (11) | 0.0527 (12) | 0.0066 (9) | 0.0035 (9) | 0.0043 (9) |
C7 | 0.0573 (13) | 0.0453 (11) | 0.0444 (11) | 0.0103 (9) | 0.0092 (10) | 0.0099 (9) |
C8 | 0.0410 (10) | 0.0279 (9) | 0.0583 (12) | 0.0013 (7) | 0.0247 (9) | −0.0004 (8) |
C9 | 0.0513 (12) | 0.0462 (12) | 0.0554 (13) | −0.0061 (9) | 0.0226 (10) | −0.0136 (9) |
C10 | 0.0442 (11) | 0.0341 (10) | 0.0565 (12) | −0.0024 (8) | 0.0193 (9) | −0.0071 (8) |
C11 | 0.0479 (12) | 0.0478 (12) | 0.0492 (12) | 0.0017 (9) | 0.0117 (9) | −0.0077 (9) |
N1 | 0.0371 (8) | 0.0299 (8) | 0.0531 (10) | 0.0014 (6) | 0.0107 (7) | 0.0034 (7) |
N2 | 0.0460 (10) | 0.0402 (9) | 0.0450 (9) | 0.0038 (7) | 0.0124 (8) | 0.0023 (7) |
N3 | 0.0438 (10) | 0.0504 (11) | 0.0658 (13) | −0.0012 (8) | 0.0185 (9) | −0.0124 (9) |
O1 | 0.0557 (9) | 0.0413 (8) | 0.0654 (10) | 0.0207 (6) | 0.0365 (8) | 0.0171 (7) |
O2 | 0.0836 (13) | 0.0563 (11) | 0.0666 (11) | −0.0142 (9) | −0.0057 (10) | 0.0032 (8) |
O3 | 0.0671 (12) | 0.0692 (12) | 0.1050 (16) | −0.0187 (9) | 0.0225 (11) | −0.0374 (11) |
O4 | 0.144 (2) | 0.0728 (14) | 0.0964 (17) | −0.0331 (15) | −0.0171 (17) | 0.0208 (13) |
Zn1—O1i | 2.0057 (13) | C6—H6A | 0.9700 |
Zn1—O1 | 2.0068 (14) | C6—H6B | 0.9700 |
Zn1—O2 | 2.0079 (18) | C7—N2 | 1.489 (3) |
Zn1—N2 | 2.1051 (19) | C7—H7A | 0.9700 |
Zn1—N1 | 2.1216 (16) | C7—H7B | 0.9700 |
C1—C2 | 1.523 (3) | C8—O1 | 1.340 (2) |
C1—H1A | 0.9600 | C8—C10 | 1.397 (3) |
C1—H1B | 0.9600 | C9—C10 | 1.388 (3) |
C1—H1C | 0.9600 | C9—H9 | 0.9300 |
C2—C3 | 1.389 (4) | C10—C11 | 1.515 (3) |
C2—C9 | 1.391 (3) | C11—N2i | 1.490 (3) |
C3—C4 | 1.394 (3) | C11—H11A | 0.9700 |
C3—H3 | 0.9300 | C11—H11B | 0.9700 |
C4—C8 | 1.402 (3) | N1—H1N | 0.80 (5) |
C4—C5 | 1.503 (3) | N2—C11i | 1.490 (3) |
C5—N1 | 1.494 (3) | N2—H2N | 0.86 (5) |
C5—H5A | 0.9700 | N3—O4 | 1.213 (3) |
C5—H5B | 0.9700 | N3—O3 | 1.224 (3) |
C6—N1 | 1.488 (3) | N3—O2 | 1.246 (3) |
C6—C7 | 1.519 (3) | O1—Zn1i | 2.0057 (13) |
O1i—Zn1—O1 | 74.53 (6) | C6—C7—H7A | 109.4 |
O1i—Zn1—O2 | 104.21 (8) | N2—C7—H7B | 109.4 |
O1—Zn1—O2 | 100.80 (8) | C6—C7—H7B | 109.4 |
O1i—Zn1—N2 | 89.50 (6) | H7A—C7—H7B | 108.0 |
O1—Zn1—N2 | 144.15 (7) | O1—C8—C10 | 120.25 (18) |
O2—Zn1—N2 | 114.32 (8) | O1—C8—C4 | 118.52 (19) |
O1i—Zn1—N1 | 143.63 (7) | C10—C8—C4 | 121.23 (18) |
O1—Zn1—N1 | 88.27 (6) | C10—C9—C2 | 121.9 (2) |
O2—Zn1—N1 | 110.44 (8) | C10—C9—H9 | 119.0 |
N2—Zn1—N1 | 86.19 (7) | C2—C9—H9 | 119.0 |
C2—C1—H1A | 109.5 | C9—C10—C8 | 118.5 (2) |
C2—C1—H1B | 109.5 | C9—C10—C11 | 121.3 (2) |
H1A—C1—H1B | 109.5 | C8—C10—C11 | 120.12 (18) |
C2—C1—H1C | 109.5 | N2i—C11—C10 | 113.11 (18) |
H1A—C1—H1C | 109.5 | N2i—C11—H11A | 109.0 |
H1B—C1—H1C | 109.5 | C10—C11—H11A | 109.0 |
C3—C2—C9 | 118.26 (19) | N2i—C11—H11B | 109.0 |
C3—C2—C1 | 120.9 (2) | C10—C11—H11B | 109.0 |
C9—C2—C1 | 120.8 (2) | H11A—C11—H11B | 107.8 |
C2—C3—C4 | 122.0 (2) | C6—N1—C5 | 111.31 (17) |
C2—C3—H3 | 119.0 | C6—N1—Zn1 | 103.15 (12) |
C4—C3—H3 | 119.0 | C5—N1—Zn1 | 115.58 (12) |
C3—C4—C8 | 118.1 (2) | C6—N1—H1N | 111 (4) |
C3—C4—C5 | 122.1 (2) | C5—N1—H1N | 107 (4) |
C8—C4—C5 | 119.36 (18) | Zn1—N1—H1N | 110 (4) |
N1—C5—C4 | 115.52 (18) | C7—N2—C11i | 113.39 (18) |
N1—C5—H5A | 108.4 | C7—N2—Zn1 | 105.06 (13) |
C4—C5—H5A | 108.4 | C11i—N2—Zn1 | 111.88 (14) |
N1—C5—H5B | 108.4 | C7—N2—H2N | 113 (4) |
C4—C5—H5B | 108.4 | C11i—N2—H2N | 105 (4) |
H5A—C5—H5B | 107.5 | Zn1—N2—H2N | 108 (3) |
N1—C6—C7 | 109.84 (18) | O4—N3—O3 | 121.7 (2) |
N1—C6—H6A | 109.7 | O4—N3—O2 | 118.1 (2) |
C7—C6—H6A | 109.7 | O3—N3—O2 | 120.1 (2) |
N1—C6—H6B | 109.7 | C8—O1—Zn1i | 129.47 (12) |
C7—C6—H6B | 109.7 | C8—O1—Zn1 | 123.38 (12) |
H6A—C6—H6B | 108.2 | Zn1i—O1—Zn1 | 105.47 (6) |
N2—C7—C6 | 111.27 (17) | N3—O2—Zn1 | 118.45 (15) |
N2—C7—H7A | 109.4 | ||
C9—C2—C3—C4 | −0.7 (3) | O2—Zn1—N1—C5 | 104.10 (15) |
C1—C2—C3—C4 | 176.62 (19) | N2—Zn1—N1—C5 | −141.34 (15) |
C2—C3—C4—C8 | 0.9 (3) | C6—C7—N2—C11i | −86.8 (2) |
C2—C3—C4—C5 | −170.78 (18) | C6—C7—N2—Zn1 | 35.7 (2) |
C3—C4—C5—N1 | −129.7 (2) | O1i—Zn1—N2—C7 | −152.22 (14) |
C8—C4—C5—N1 | 58.7 (2) | O1—Zn1—N2—C7 | −90.10 (16) |
N1—C6—C7—N2 | −57.0 (2) | O2—Zn1—N2—C7 | 102.38 (15) |
C3—C4—C8—O1 | −179.12 (17) | N1—Zn1—N2—C7 | −8.36 (14) |
C5—C4—C8—O1 | −7.2 (3) | O1i—Zn1—N2—C11i | −28.78 (14) |
C3—C4—C8—C10 | 0.4 (3) | O1—Zn1—N2—C11i | 33.3 (2) |
C5—C4—C8—C10 | 172.34 (17) | O2—Zn1—N2—C11i | −134.18 (14) |
C3—C2—C9—C10 | −0.9 (3) | N1—Zn1—N2—C11i | 115.08 (15) |
C1—C2—C9—C10 | −178.2 (2) | C10—C8—O1—Zn1i | −32.2 (3) |
C2—C9—C10—C8 | 2.1 (3) | C4—C8—O1—Zn1i | 147.37 (15) |
C2—C9—C10—C11 | −174.79 (19) | C10—C8—O1—Zn1 | 130.89 (16) |
O1—C8—C10—C9 | 177.62 (18) | C4—C8—O1—Zn1 | −49.6 (2) |
C4—C8—C10—C9 | −1.9 (3) | O1i—Zn1—O1—C8 | −166.5 (2) |
O1—C8—C10—C11 | −5.4 (3) | O2—Zn1—O1—C8 | −64.57 (18) |
C4—C8—C10—C11 | 175.08 (18) | N2—Zn1—O1—C8 | 126.99 (17) |
C9—C10—C11—N2i | −125.4 (2) | N1—Zn1—O1—C8 | 45.92 (17) |
C8—C10—C11—N2i | 57.7 (3) | O1i—Zn1—O1—Zn1i | 0.0 |
C7—C6—N1—C5 | 169.00 (16) | O2—Zn1—O1—Zn1i | 101.92 (9) |
C7—C6—N1—Zn1 | 44.46 (18) | N2—Zn1—O1—Zn1i | −66.52 (14) |
C4—C5—N1—C6 | −164.74 (17) | N1—Zn1—O1—Zn1i | −147.59 (8) |
C4—C5—N1—Zn1 | −47.5 (2) | O4—N3—O2—Zn1 | −10.1 (3) |
O1i—Zn1—N1—C6 | 64.33 (16) | O3—N3—O2—Zn1 | 173.52 (17) |
O1—Zn1—N1—C6 | 124.92 (13) | O1i—Zn1—O2—N3 | −128.41 (18) |
O2—Zn1—N1—C6 | −134.20 (13) | O1—Zn1—O2—N3 | 155.00 (18) |
N2—Zn1—N1—C6 | −19.64 (13) | N2—Zn1—O2—N3 | −32.4 (2) |
O1i—Zn1—N1—C5 | −57.37 (19) | N1—Zn1—O2—N3 | 62.8 (2) |
O1—Zn1—N1—C5 | 3.22 (14) |
Symmetry code: (i) −x+1, −y+1, −z+1. |
Experimental details
Crystal data | |
Chemical formula | [Zn2(NO3)2(C22H30N4O2)] |
Mr | 637.26 |
Crystal system, space group | Monoclinic, P21/c |
Temperature (K) | 293 |
a, b, c (Å) | 8.2190 (5), 14.1450 (8), 11.0550 (6) |
β (°) | 103.744 (9) |
V (Å3) | 1248.43 (12) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm−1) | 1.98 |
Crystal size (mm) | 0.40 × 0.30 × 0.25 |
Data collection | |
Diffractometer | Bruker APEX CCD area-detector |
Absorption correction | Multi-scan (SADABS; Sheldrick, 1996) |
Tmin, Tmax | 0.495, 0.609 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 7558, 3027, 2524 |
Rint | 0.019 |
(sin θ/λ)max (Å−1) | 0.669 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.028, 0.080, 1.07 |
No. of reflections | 3027 |
No. of parameters | 178 |
H-atom treatment | H atoms treated by a mixture of independent and constrained refinement |
Δρmax, Δρmin (e Å−3) | 0.40, −0.29 |
Computer programs: SMART (Bruker, 1997), SAINT (Bruker, 1999), SAINT, SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), SHELXTL-Plus (Sheldrick, 1990), SHELXL97.
Zn1—O1i | 2.0057 (13) | Zn1—N2 | 2.1051 (19) |
Zn1—O1 | 2.0068 (14) | Zn1—N1 | 2.1216 (16) |
Zn1—O2 | 2.0079 (18) | O1—Zn1i | 2.0057 (13) |
O1i—Zn1—O1 | 74.53 (6) | O2—Zn1—N2 | 114.32 (8) |
O1i—Zn1—O2 | 104.21 (8) | O1i—Zn1—N1 | 143.63 (7) |
O1—Zn1—O2 | 100.80 (8) | O1—Zn1—N1 | 88.27 (6) |
O1i—Zn1—N2 | 89.50 (6) | O2—Zn1—N1 | 110.44 (8) |
O1—Zn1—N2 | 144.15 (7) | N2—Zn1—N1 | 86.19 (7) |
Symmetry code: (i) −x+1, −y+1, −z+1. |
Dinuclear zinc(II) cores have attracted much interest as a result of their significance in biological systems (Dealwis et al., 1995; Burley et al., 1990; Roderick & Mathews, 1993). In addition, some synthetic dinuclear zinc(II) compounds are found to have functions in dephosphorylation (Bazzicalupi et al., 1997). To further widen the scope of application of such zinc compounds, there is a need to prepare new series of dinuclear zinc compounds. In this work, a new dinuclear zinc(II) compound has been synthesized, and its structure (I) is reported here.
As shown in Fig. 1, [Zn2L(NO3)2] is a centrosymmetric dinuclear zinc compound. The coordination environment around zinc is a square-pyramid with two N atoms and two O atoms from L ligand occupying the basal positions and one O atom from NO3- anion occupying the apical position. In the crystal structure two zinc atoms are bridged by two phenolate O atoms to generate a four-membered Zn2O2 ring. The Zn—O and Zn—N distances are normal (Dutta et al., 2005).