Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807018806/at2272sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536807018806/at2272Isup2.hkl |
CCDC reference: 647682
16α-Brornoandrost-5-en-3β-ol-l7-one (5.04 g, 17.6 mmol) was dissolved in 100 ml of dimethylacetamide, and 7.38 g of lithium bromide and 6.38 g of lithium carbonate were added. The mixture was refluxed for 4 hrs under nitrogen. To the cooled mixture 20% acetic acid was added until no bubble emerged and the mixture was extracted with a 1: 1 mixture of toluene-ether. The organic layer was washed with a 5% NaHCO3 solution and with H2O. After evaporation of the solvent, the dried solution was recrystallized from acetone to give colorless crystals suitable for X-ray diffraction (yield 23%). Analytical data: m.p. 216.1—216.7°; [α]D= (+)307° (c=2.3, CHCl3); 1HNMR (500 MHz, CDCl3): 0.99 (s, 3H, CH3-19), 1.09 (s, 3H, CH3-18), 3.46–3.52(m, 1H, H-3), 5.41–5.42 (m, 1H, H-6), 6.26–6.28(m, 1H, H-16), 7.80(dd, J=2.6 Hz, 1H, H-15); 13C-NMR (126 MHz, CDCl3): 17.71, 19.11, 22.84, 29.75, 30.27, 31.18, 33.52, 36.43, 38.54, 41.94, 42.38, 47.63, 53.69, 71.64, 120.87, 134.59, 141.36, 165.43, 216.49.
All the H atoms were placed in geometrically idealized positions and constrained to ride their parent atoms, with C—H = 0.93 Å and Uiso(H) = 1.2Ueq(C).
The title compound, (I) (Fig 1), a steroid derivative used as an intermediate in the synthesis of steroid hormones, was prepared from dehydroepiandrosterone (Sondheimer et al., 1960, Pataki & Siade, 1972). A Cotton effect positive for the title compound was reported to identify it as 14β isomer. It is a C14 epimer of 3-hydroxyandrosta-5, 15-dien-17- one. The only difference between them lies in that the former is C14β-H, while the latter is C14α-H.
In the solid state of (I), ring A has a chair conformation (Fig. 1), ring C has a boat conformation. The C5?C6 bond length of 1.330 (3)Å confirms the presence of the double bond in this position and imposes an 8β, 9α-half-chair conformation on ring B. Differing from the normal steroid compounds, its C/D ring junction shows cis fusion. The five-membered ring D is essentially planar, mainly due to conjugation of the C15? C16 and C17? O2 bonds. The C16—C17 bond length of 1.446 (3) Å suggests partial double-bond character.
In (I), the hydroxyl group forms an intermolecular (Bernstein et al., 1995) O—H···O hydrogen bond with the carbonyl atom O2 of an adjacent molecule (Table 2), forming infinite chains along the body diagonal of the unit cell.
The corresponding steroid without double bond on the C15?C16 (Quader et al., 2006), with layers of molecules linked by O—H···O hydrogen bonds.
For related literature, see: Bernstein et al. (1995); Pataki & Siade (1972); Sondheimer et al. (1960).
Data collection: SMART (Bruker, 2000); cell refinement: SMART; data reduction: SAINT (Bruker, 2000); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Sheldrick, 2000); software used to prepare material for publication: SHELXTL.
C19H26O2 | F(000) = 312 |
Mr = 286.40 | Dx = 1.209 Mg m−3 |
Monoclinic, P21 | Mo Kα radiation, λ = 0.71073 Å |
a = 5.9984 (8) Å | Cell parameters from 2564 reflections |
b = 11.4923 (14) Å | θ = 2.5–27.5° |
c = 11.5350 (14) Å | µ = 0.08 mm−1 |
β = 98.413 (1)° | T = 273 K |
V = 786.61 (17) Å3 | Block, colorless |
Z = 2 | 0.30 × 0.30 × 0.25 mm |
Bruker SMART CCD area-detector diffractometer | 1460 independent reflections |
Radiation source: fine-focus sealed tube | 1384 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.015 |
φ and ω scans | θmax = 25.0°, θmin = 2.5° |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | h = −7→6 |
Tmin = 0.978, Tmax = 0.981 | k = −9→13 |
4092 measured reflections | l = −13→13 |
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)] = 0.028 | H-atom parameters constrained |
wR(F2) = 0.067 | w = 1/[σ2(Fo2) + (0.028P)2 + 0.0991P] where P = (Fo2 + 2Fc2)/3 |
S = 1.12 | (Δ/σ)max < 0.001 |
1460 reflections | Δρmax = 0.16 e Å−3 |
194 parameters | Δρmin = −0.11 e Å−3 |
1 restraint | Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.026 (3) |
C19H26O2 | V = 786.61 (17) Å3 |
Mr = 286.40 | Z = 2 |
Monoclinic, P21 | Mo Kα radiation |
a = 5.9984 (8) Å | µ = 0.08 mm−1 |
b = 11.4923 (14) Å | T = 273 K |
c = 11.5350 (14) Å | 0.30 × 0.30 × 0.25 mm |
β = 98.413 (1)° |
Bruker SMART CCD area-detector diffractometer | 1460 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | 1384 reflections with I > 2σ(I) |
Tmin = 0.978, Tmax = 0.981 | Rint = 0.015 |
4092 measured reflections |
R[F2 > 2σ(F2)] = 0.028 | 1 restraint |
wR(F2) = 0.067 | H-atom parameters constrained |
S = 1.12 | Δρmax = 0.16 e Å−3 |
1460 reflections | Δρmin = −0.11 e Å−3 |
194 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 | ||
O2 | 0.0766 (3) | 0.92718 (15) | 0.65893 (15) | 0.0641 (5) | |
O1 | 0.0741 (4) | 0.05263 (15) | 0.88264 (17) | 0.0693 (5) | |
H1 | 0.0881 | 0.0018 | 0.8343 | 0.104* | |
C8 | 0.4141 (3) | 0.54983 (17) | 0.69129 (16) | 0.0332 (4) | |
H8 | 0.5373 | 0.5563 | 0.7569 | 0.040* | |
C9 | 0.1990 (3) | 0.52163 (16) | 0.74278 (15) | 0.0310 (4) | |
H9 | 0.0854 | 0.4996 | 0.6765 | 0.037* | |
C14 | 0.3967 (3) | 0.66663 (18) | 0.62660 (16) | 0.0373 (5) | |
H14 | 0.5392 | 0.6802 | 0.5967 | 0.045* | |
C5 | 0.3398 (3) | 0.31637 (17) | 0.76381 (16) | 0.0345 (4) | |
C7 | 0.4703 (3) | 0.44943 (19) | 0.61473 (17) | 0.0418 (5) | |
H7A | 0.3727 | 0.4529 | 0.5399 | 0.050* | |
H7B | 0.6247 | 0.4573 | 0.6000 | 0.050* | |
C3 | 0.0842 (4) | 0.16448 (19) | 0.82944 (19) | 0.0466 (5) | |
H3 | −0.0094 | 0.1632 | 0.7523 | 0.056* | |
C10 | 0.2314 (3) | 0.41454 (16) | 0.82460 (15) | 0.0313 (4) | |
C19 | 0.3807 (4) | 0.4429 (2) | 0.94150 (16) | 0.0434 (5) | |
H19A | 0.4125 | 0.3726 | 0.9858 | 0.065* | |
H19B | 0.3032 | 0.4965 | 0.9854 | 0.065* | |
H19C | 0.5193 | 0.4772 | 0.9261 | 0.065* | |
C2 | −0.0080 (4) | 0.2544 (2) | 0.90441 (19) | 0.0470 (5) | |
H2B | 0.0813 | 0.2553 | 0.9816 | 0.056* | |
H2A | −0.1618 | 0.2346 | 0.9133 | 0.056* | |
C6 | 0.4423 (3) | 0.33427 (18) | 0.67060 (17) | 0.0382 (5) | |
H6 | 0.5015 | 0.2696 | 0.6375 | 0.046* | |
C1 | −0.0033 (3) | 0.37422 (19) | 0.84925 (19) | 0.0412 (5) | |
H1A | −0.0591 | 0.4304 | 0.9008 | 0.049* | |
H1B | −0.1059 | 0.3743 | 0.7760 | 0.049* | |
C11 | 0.1058 (4) | 0.63047 (17) | 0.79864 (19) | 0.0400 (5) | |
H11A | −0.0271 | 0.6578 | 0.7478 | 0.048* | |
H11B | 0.0604 | 0.6087 | 0.8730 | 0.048* | |
C17 | 0.1567 (4) | 0.8350 (2) | 0.63157 (19) | 0.0453 (5) | |
C13 | 0.3531 (3) | 0.77164 (18) | 0.70425 (17) | 0.0381 (5) | |
C4 | 0.3239 (4) | 0.1954 (2) | 0.8138 (2) | 0.0473 (5) | |
H4A | 0.4198 | 0.1908 | 0.8890 | 0.057* | |
H4B | 0.3785 | 0.1393 | 0.7618 | 0.057* | |
C15 | 0.2089 (4) | 0.6739 (2) | 0.52509 (17) | 0.0473 (5) | |
H15 | 0.1843 | 0.6178 | 0.4665 | 0.057* | |
C12 | 0.2756 (4) | 0.72926 (18) | 0.81897 (17) | 0.0422 (5) | |
H12A | 0.4059 | 0.7032 | 0.8725 | 0.051* | |
H12B | 0.2085 | 0.7939 | 0.8555 | 0.051* | |
C16 | 0.0822 (4) | 0.7676 (2) | 0.52722 (19) | 0.0515 (6) | |
H16 | −0.0374 | 0.7874 | 0.4699 | 0.062* | |
C18 | 0.5541 (4) | 0.8536 (2) | 0.7317 (2) | 0.0513 (6) | |
H18A | 0.6015 | 0.8790 | 0.6599 | 0.077* | |
H18B | 0.6759 | 0.8134 | 0.7784 | 0.077* | |
H18C | 0.5114 | 0.9198 | 0.7741 | 0.077* |
U11 | U22 | U33 | U12 | U13 | U23 | |
O2 | 0.0709 (11) | 0.0462 (11) | 0.0742 (11) | 0.0139 (9) | 0.0077 (9) | 0.0010 (9) |
O1 | 0.0964 (14) | 0.0402 (10) | 0.0754 (12) | −0.0073 (10) | 0.0256 (11) | 0.0106 (9) |
C8 | 0.0339 (10) | 0.0377 (11) | 0.0284 (9) | 0.0004 (8) | 0.0059 (8) | −0.0005 (8) |
C9 | 0.0313 (9) | 0.0341 (10) | 0.0277 (9) | 0.0008 (8) | 0.0049 (7) | −0.0004 (8) |
C14 | 0.0401 (11) | 0.0419 (12) | 0.0316 (9) | −0.0037 (9) | 0.0105 (8) | 0.0034 (9) |
C5 | 0.0327 (10) | 0.0338 (11) | 0.0362 (10) | 0.0015 (8) | 0.0019 (8) | −0.0008 (9) |
C7 | 0.0440 (11) | 0.0475 (12) | 0.0363 (10) | 0.0032 (10) | 0.0140 (9) | −0.0024 (10) |
C3 | 0.0601 (14) | 0.0348 (12) | 0.0446 (12) | −0.0052 (10) | 0.0069 (10) | 0.0056 (10) |
C10 | 0.0311 (9) | 0.0332 (10) | 0.0298 (9) | 0.0003 (8) | 0.0054 (7) | −0.0001 (8) |
C19 | 0.0517 (12) | 0.0470 (13) | 0.0303 (9) | −0.0013 (11) | 0.0019 (9) | 0.0018 (10) |
C2 | 0.0457 (12) | 0.0468 (13) | 0.0507 (12) | −0.0056 (11) | 0.0148 (10) | 0.0074 (11) |
C6 | 0.0390 (11) | 0.0366 (12) | 0.0401 (10) | 0.0048 (9) | 0.0094 (8) | −0.0067 (9) |
C1 | 0.0375 (11) | 0.0406 (12) | 0.0478 (12) | 0.0012 (9) | 0.0140 (9) | 0.0057 (10) |
C11 | 0.0470 (12) | 0.0347 (11) | 0.0419 (11) | 0.0050 (9) | 0.0190 (9) | 0.0027 (9) |
C17 | 0.0482 (12) | 0.0405 (13) | 0.0482 (12) | −0.0002 (11) | 0.0109 (10) | 0.0079 (10) |
C13 | 0.0437 (11) | 0.0351 (11) | 0.0357 (10) | −0.0017 (9) | 0.0070 (9) | 0.0023 (9) |
C4 | 0.0552 (13) | 0.0372 (12) | 0.0503 (12) | 0.0078 (10) | 0.0110 (10) | 0.0019 (10) |
C15 | 0.0640 (14) | 0.0477 (13) | 0.0289 (10) | −0.0011 (11) | 0.0023 (9) | 0.0016 (10) |
C12 | 0.0589 (13) | 0.0342 (11) | 0.0353 (10) | 0.0027 (10) | 0.0133 (9) | −0.0030 (9) |
C16 | 0.0543 (13) | 0.0542 (14) | 0.0429 (12) | 0.0028 (12) | −0.0031 (10) | 0.0090 (11) |
C18 | 0.0554 (13) | 0.0476 (13) | 0.0502 (12) | −0.0094 (11) | 0.0056 (10) | −0.0001 (11) |
O2—C17 | 1.223 (3) | C19—H19B | 0.9600 |
O1—C3 | 1.429 (3) | C19—H19C | 0.9600 |
O1—H1 | 0.8200 | C2—C1 | 1.518 (3) |
C8—C7 | 1.520 (3) | C2—H2B | 0.9700 |
C8—C14 | 1.532 (3) | C2—H2A | 0.9700 |
C8—C9 | 1.532 (3) | C6—H6 | 0.9300 |
C8—H8 | 0.9800 | C1—H1A | 0.9700 |
C9—C10 | 1.546 (2) | C1—H1B | 0.9700 |
C9—C11 | 1.549 (3) | C11—C12 | 1.520 (3) |
C9—H9 | 0.9800 | C11—H11A | 0.9700 |
C14—C15 | 1.504 (3) | C11—H11B | 0.9700 |
C14—C13 | 1.548 (3) | C17—C16 | 1.446 (3) |
C14—H14 | 0.9800 | C17—C13 | 1.527 (3) |
C5—C6 | 1.330 (3) | C13—C18 | 1.526 (3) |
C5—C4 | 1.513 (3) | C13—C12 | 1.544 (3) |
C5—C10 | 1.523 (3) | C4—H4A | 0.9700 |
C7—C6 | 1.492 (3) | C4—H4B | 0.9700 |
C7—H7A | 0.9700 | C15—C16 | 1.320 (3) |
C7—H7B | 0.9700 | C15—H15 | 0.9300 |
C3—C2 | 1.504 (3) | C12—H12A | 0.9700 |
C3—C4 | 1.518 (3) | C12—H12B | 0.9700 |
C3—H3 | 0.9800 | C16—H16 | 0.9300 |
C10—C19 | 1.540 (3) | C18—H18A | 0.9600 |
C10—C1 | 1.547 (3) | C18—H18B | 0.9600 |
C19—H19A | 0.9600 | C18—H18C | 0.9600 |
C3—O1—H1 | 109.5 | C1—C2—H2A | 109.5 |
C7—C8—C14 | 112.78 (15) | H2B—C2—H2A | 108.1 |
C7—C8—C9 | 109.60 (16) | C5—C6—C7 | 125.50 (19) |
C14—C8—C9 | 111.88 (16) | C5—C6—H6 | 117.3 |
C7—C8—H8 | 107.4 | C7—C6—H6 | 117.3 |
C14—C8—H8 | 107.4 | C2—C1—C10 | 114.95 (17) |
C9—C8—H8 | 107.4 | C2—C1—H1A | 108.5 |
C8—C9—C10 | 111.56 (15) | C10—C1—H1A | 108.5 |
C8—C9—C11 | 111.49 (15) | C2—C1—H1B | 108.5 |
C10—C9—C11 | 114.19 (14) | C10—C1—H1B | 108.5 |
C8—C9—H9 | 106.3 | H1A—C1—H1B | 107.5 |
C10—C9—H9 | 106.3 | C12—C11—C9 | 113.13 (16) |
C11—C9—H9 | 106.3 | C12—C11—H11A | 109.0 |
C15—C14—C8 | 114.72 (17) | C9—C11—H11A | 109.0 |
C15—C14—C13 | 103.69 (17) | C12—C11—H11B | 109.0 |
C8—C14—C13 | 113.99 (15) | C9—C11—H11B | 109.0 |
C15—C14—H14 | 108.0 | H11A—C11—H11B | 107.8 |
C8—C14—H14 | 108.0 | O2—C17—C16 | 126.4 (2) |
C13—C14—H14 | 108.0 | O2—C17—C13 | 124.9 (2) |
C6—C5—C4 | 120.82 (18) | C16—C17—C13 | 108.71 (19) |
C6—C5—C10 | 122.44 (18) | C18—C13—C17 | 110.03 (18) |
C4—C5—C10 | 116.74 (16) | C18—C13—C12 | 110.16 (17) |
C6—C7—C8 | 111.94 (15) | C17—C13—C12 | 108.41 (17) |
C6—C7—H7A | 109.2 | C18—C13—C14 | 113.96 (17) |
C8—C7—H7A | 109.2 | C17—C13—C14 | 103.66 (16) |
C6—C7—H7B | 109.2 | C12—C13—C14 | 110.33 (16) |
C8—C7—H7B | 109.2 | C5—C4—C3 | 111.97 (18) |
H7A—C7—H7B | 107.9 | C5—C4—H4A | 109.2 |
O1—C3—C2 | 109.22 (18) | C3—C4—H4A | 109.2 |
O1—C3—C4 | 111.22 (19) | C5—C4—H4B | 109.2 |
C2—C3—C4 | 109.98 (18) | C3—C4—H4B | 109.2 |
O1—C3—H3 | 108.8 | H4A—C4—H4B | 107.9 |
C2—C3—H3 | 108.8 | C16—C15—C14 | 113.5 (2) |
C4—C3—H3 | 108.8 | C16—C15—H15 | 123.3 |
C5—C10—C19 | 109.08 (16) | C14—C15—H15 | 123.3 |
C5—C10—C9 | 109.42 (14) | C11—C12—C13 | 112.48 (17) |
C19—C10—C9 | 111.79 (15) | C11—C12—H12A | 109.1 |
C5—C10—C1 | 108.90 (16) | C13—C12—H12A | 109.1 |
C19—C10—C1 | 109.29 (16) | C11—C12—H12B | 109.1 |
C9—C10—C1 | 108.31 (15) | C13—C12—H12B | 109.1 |
C10—C19—H19A | 109.5 | H12A—C12—H12B | 107.8 |
C10—C19—H19B | 109.5 | C15—C16—C17 | 110.1 (2) |
H19A—C19—H19B | 109.5 | C15—C16—H16 | 124.9 |
C10—C19—H19C | 109.5 | C17—C16—H16 | 124.9 |
H19A—C19—H19C | 109.5 | C13—C18—H18A | 109.5 |
H19B—C19—H19C | 109.5 | C13—C18—H18B | 109.5 |
C3—C2—C1 | 110.56 (17) | H18A—C18—H18B | 109.5 |
C3—C2—H2B | 109.5 | C13—C18—H18C | 109.5 |
C1—C2—H2B | 109.5 | H18A—C18—H18C | 109.5 |
C3—C2—H2A | 109.5 | H18B—C18—H18C | 109.5 |
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···O2i | 0.82 | 2.19 | 2.958 (3) | 156 |
Symmetry code: (i) x, y−1, z. |
Experimental details
Crystal data | |
Chemical formula | C19H26O2 |
Mr | 286.40 |
Crystal system, space group | Monoclinic, P21 |
Temperature (K) | 273 |
a, b, c (Å) | 5.9984 (8), 11.4923 (14), 11.5350 (14) |
β (°) | 98.413 (1) |
V (Å3) | 786.61 (17) |
Z | 2 |
Radiation type | Mo Kα |
µ (mm−1) | 0.08 |
Crystal size (mm) | 0.30 × 0.30 × 0.25 |
Data collection | |
Diffractometer | Bruker SMART CCD area-detector |
Absorption correction | Multi-scan (SADABS; Sheldrick, 1996) |
Tmin, Tmax | 0.978, 0.981 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 4092, 1460, 1384 |
Rint | 0.015 |
(sin θ/λ)max (Å−1) | 0.595 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.028, 0.067, 1.12 |
No. of reflections | 1460 |
No. of parameters | 194 |
No. of restraints | 1 |
H-atom treatment | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.16, −0.11 |
Computer programs: SMART (Bruker, 2000), SMART, SAINT (Bruker, 2000), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), SHELXTL (Sheldrick, 2000), SHELXTL.
O2—C17 | 1.223 (3) | C17—C16 | 1.446 (3) |
O1—C3 | 1.429 (3) | C15—C16 | 1.320 (3) |
C5—C6 | 1.330 (3) | ||
C15—C14—C8 | 114.72 (17) | C6—C5—C10 | 122.44 (18) |
C15—C14—C13 | 103.69 (17) | O1—C3—C4 | 111.22 (19) |
C8—C14—C13 | 113.99 (15) | O2—C17—C16 | 126.4 (2) |
C6—C5—C4 | 120.82 (18) | C15—C16—C17 | 110.1 (2) |
D—H···A | D—H | H···A | D···A | D—H···A |
O1—H1···O2i | 0.82 | 2.19 | 2.958 (3) | 156.2 |
Symmetry code: (i) x, y−1, z. |
The title compound, (I) (Fig 1), a steroid derivative used as an intermediate in the synthesis of steroid hormones, was prepared from dehydroepiandrosterone (Sondheimer et al., 1960, Pataki & Siade, 1972). A Cotton effect positive for the title compound was reported to identify it as 14β isomer. It is a C14 epimer of 3-hydroxyandrosta-5, 15-dien-17- one. The only difference between them lies in that the former is C14β-H, while the latter is C14α-H.
In the solid state of (I), ring A has a chair conformation (Fig. 1), ring C has a boat conformation. The C5?C6 bond length of 1.330 (3)Å confirms the presence of the double bond in this position and imposes an 8β, 9α-half-chair conformation on ring B. Differing from the normal steroid compounds, its C/D ring junction shows cis fusion. The five-membered ring D is essentially planar, mainly due to conjugation of the C15? C16 and C17? O2 bonds. The C16—C17 bond length of 1.446 (3) Å suggests partial double-bond character.
In (I), the hydroxyl group forms an intermolecular (Bernstein et al., 1995) O—H···O hydrogen bond with the carbonyl atom O2 of an adjacent molecule (Table 2), forming infinite chains along the body diagonal of the unit cell.