Pseudomerohedrally twinned crystal structure of 2,3-diphenyl­buta-1,3-diene

The title compound, C₁₆H₁₄, is twinned by reticular pseudomerohedry of twin index 2. The primitive monoclinic cell of the single crystal can be transformed into a B-centred pseudo-orthorhombic supercell with a fourfold volume. The twofold twin operation about the reciprocal a* axis of the primitive monoclinic cell is co-directional with the approximate C₂ axis of the mol­ecule and a symmetry element of the orthorhombic supercell. A tentative twin domain model is proposed.

S1. Comment

In the course of our studies about electronic interactions in branched π-conjugated systems (van der Wiel et al., 2004), the crystal structure of 2,3-diphenylbutadiene, (I), was determined in order to obtain more insight into the electronic spectra.

In the crystal structure, 2,3-diphenylbutadiene has an approximate, non-crystallographic C₂ symmetry (Fig. 1). The maximum (r.m.s.?) deviation of corresponding atoms from an exact C₂ symmetry is 0.0245 Å (Pilati & Forni, 1998). This approximate molecular C₂ axis is perpendicular to the monoclinic b axis. The two perpendicular twofold rotations imply a third C₂ axis. In fact, this third C₂ axis is here parallel to the crystallographic c axis. In other words, the approximate molecular C₂ axis is parallel to the a^* axis. It appears that the molecular C₂ symmetry and the orientation of the C₂ axis in the unit cell results in a twinned crystal with this rotation as the twin operation. The twin relationship was taken into account during the intensity evaluation with EVALCCD (Duisenberg et al., 2003) and the HKLF5 refinement with SHELXL97 (Herbst-Irmer & Sheldrick, 1998). The twin fraction refined to a value of 0.319 (2).

Because this light-atom structure does not reveal sufficient anomalous dispersion, a distinction between proper and improper rotations as twin operations is not possible here. We chose the proper rotation based on the approximate molecular symmetry in the discussion below.

The twofold twin axis about c is a symmetry element of a pseudo-orthorhombic B-centered supercell (Fig. 2) with a fourfold volume and a = 31.8982 Å, b = 5.7966 Å, c = 12.3414 Å, α = γ = 90° and β = 90.568°. The corresponding transformation matrix from subcell to supercell is (4 0 1 / 0 1 0 / 0 0 1). The twin index, derived from the primitive lattices, is consequently 2, and we can describe the twinning as reticular pseudomerohedral. The primitive supercell in direct space is obtained by a doubling of the a axis or, correspondingly, the primitive subcell in reciprocal space by halving of the a^* axis (Fig. 3). We were able to find the supercell with the indexing program DIRAX (Duisenberg, 1992) or, independently, by applying the Le Page algorithm for finding twin laws (Le Page, 2002) as implemented in PLATON (Spek, 2003). With an exact orthorhombic cell, we would expect a perfect overlap of the two twin domains for all reflections with hkl, l = 2n (n is an integer?). In an exact orthorhombic cell we also would expect additional (non-space-group) extinctions due to the twinning; all reflections with l = 2n, h + l = 4n + 2 are absent. However, because of the non-zero obliquity of 0.568°, the overlap is not perfect and the supercell is not really suitable for the intensity evaluation. An exact description of the diffraction experiment for the prediction of reflection size, shape and position on the CCD detector was used instead, as implemented in EVALCCD (Duisenberg et al., 2003).

The intermolecular interactions are determined by weak C—H···π interactions (Table 2 and Fig. 4), leading to a two-dimensional arrangement in the crystallographic bc plane. Stacking faults of these two-dimensional layers due to local twofold axial symmetry are a plausible structural explanation for the twinned crystallization (Fig. 4). The changes in the local environments of the molecules are very minor and the energetic differences at the interface between the twin domains are small. Similar effects on boundary layers of twinned crystals have been described before (see e.g. Cannas et al., 1972).

The butadiene subsystem is in a gauche conformation, with a C11—C12—C22—C21 torsion angle of −55.6 (2)°. There is only one comparable crystal structure of a diene in the literature, 2,3-di-tert-butyl-1,3-butadiene, which has a torsion angle of 96.62 (14)° (Roth et al., 1991). Interestingly enough, a similar torsion angle for this compound is found by electron diffraction in the gas phase (reference in Roth et al., 1991), so that crystal packing effects can be excluded. In fact, quantum chemical calculations indicate that 2,3-diphenylbutadiene also has the same conformation in the crystal and in the free molecule (van Walree et al., 2005). Thus, in both cases the central torsion angle is a molecular rather than a crystal property.

The C11—C12—C13—C18 and C21—C22—C23—C28 torsion angles are −17.0 (3) and −19.3 (3)°, respectively. This picture supports the idea of two relatively planar styrene units linked at their α atoms. The C12—C22 bond length of 1.492 (2) Å supports this assumption because it is rather long for a C(sp²)-C(sp²) bond, even in a gauche conformation. On the other hand the C12—C13 and C22—C23 bond lengths of 1.491 (2) and 1.486 (2) Å, respectively, are quite long for C(sp²)—C(aryl) bonds in styrene-type systems. We assume that this slight bond elongation is caused by steric effects.

Atoms H11A/H18 and H21A/H28 are in close proximity, with intramolecular distances of 2.08 and 2.13 Å, respectively, thus prohibiting perfect planarity of the styrene entities.

S2. Experimental

2,3-Diphenylbutadiene was synthesized by a double Wittig reaction of benzil with triphenylmethylphosphonium bromide. Details of the synthesis will be published elsewhere (van Walree et al., 2005). Crystals were grown by sublimation at 20 mm H g pressure with gentle heating. During sublimation, the cold finger was cooled with an ice–salt mixture.

S3. Refinement

728 frames were collected with a ϕ scan and 893 frames with ω scans. The crystal-to-detector distance was 40 mm, the rotation angle 0.5° per frame and the exposure time 20 s per frame. The refinement was performed in a non-reduced setting of space group P2₁ in order to align the twin axis parallel to the crystallographic a^* axis. In the reduced setting, the twin axis would be parallel to a face diagonal. The cell parameters of the reduced setting are a = 8.5791 (12) Å, b = 5.7966 (3) Å, c = 12.1575 (14) Å and β = 109.344 (9)° and the transformation matrix from the present setting to the reduced setting is (1 0 0 / 0 − 1 0 / −1 0 − 1). The absolute structure could not be determined reliably. Therefore, an arbitrary absolute structure was chosen and Friedel pairs were merged prior to the refinement using the program MERGEHKLF5 (Schreurs, 2003), which also merged the redundant data taking the twin relationship into account. All H atoms were located in a difference Fourier map and were constrained to ride on their parent atoms with U_iso(H) = 1.2U_eq(C).

Computing details

Data collection: COLLECT (Nonius, 1999); cell refinement: DIRAX (Duisenberg, 1992); data reduction: EVALCCD (Duisenberg et al., 2003); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 2003); software used to prepare material for publication: program (reference)?.

Figures

	Fig. 1. A displacement ellipsoid plot of (I), showing the gauche conformation. Displacement ellipsoids are drawn at the 50% probability level; H atoms are shown with arbitrary radii. The view is along the approximate molecular C2 axis.
	Fig. 2. A view of the unit cell along the crystallographic b axis. The approximate molecular C2 axis is oriented perpendicular to the direct b and c axes and parallel to the reciprocal a^* axis. The twin cell, marked in dashed lines and labeled with a prime, is generated by a twofold rotation about a^*. A primitive supercell containing both unit cells (shaded in grey) is obtained by a doubling of the a axis. This primitive supercell is monoclinic and can be transformed into a B-centered pseudo-orthorhombic cell (drawn in thick lines and labeled with double primes), where the original twin axes along a^* and c are now part of the lattice.
	Fig. 3. A simulated precession photo of the h0l plane showing the twin relationship in reciprocal space as a twofold rotation about a^*. The radii of the circles indicate the intensities of the reflections. The main twin domain is drawn in open circles; the minor twin domain, with a twin fraction of 0.319 (2), is drawn in filled circles. The approximate primitive subcell in reciprocal space, covering both twin domains, is obtained by halving a^* and is shaded in grey in the drawing.
	Fig. 4. The proposed stacking fault at the domain interfaces of the two-dimensional layers in the bc plane leading to a twinned structure as a result of the local twofold axial symmetry. In one of the layers, the C—H···π interactions are marked with dashed lines.

2,3-diphenylbuta-1,3-diene

Crystal data

C16H14	F(000) = 220
Mr = 206.27	Dx = 1.201 Mg m^−3
Monoclinic, P21	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2yb	Cell parameters from 290 reflections
a = 8.5791 (12) Å	θ = 4.0–27.1°
b = 5.7966 (3) Å	µ = 0.07 mm^−1
c = 12.3414 (17) Å	T = 150 K
β = 111.645 (10)°	Needle, colourless
V = 570.46 (12) Å^3	0.48 × 0.24 × 0.24 mm
Z = 2

Data collection

Nonius KappaCCD diffractometer	1355 reflections with I > 2σ(I)
Radiation source: rotating anode	Rint = 0.041
Graphite monochromator	θmax = 27.7°, θmin = 1.8°
ϕ and ω scans	h = −11→11
14083 measured reflections	k = −7→7
1444 independent reflections	l = −16→16

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.031	Hydrogen site location: difference Fourier map
wR(F^2) = 0.080	H-atom parameters constrained
S = 1.08	w = 1/[σ^2(Fo^2) + (0.042P)^2 + 0.0638P] where P = (Fo^2 + 2Fc^2)/3
1444 reflections	(Δ/σ)max < 0.001
146 parameters	Δρmax = 0.17 e Å^−3
1 restraint	Δρmin = −0.16 e Å^−3

Special details

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
C11	−0.1268 (2)	0.3546 (4)	0.17587 (18)	0.0412 (5)
H11A	−0.1344	0.2498	0.1149	0.049*
H11B	−0.2115	0.3561	0.2083	0.049*
C12	0.00212 (19)	0.4990 (3)	0.21569 (13)	0.0271 (4)
C13	0.1377 (2)	0.5024 (3)	0.16722 (12)	0.0251 (3)
C14	0.2457 (2)	0.6904 (3)	0.18584 (14)	0.0277 (4)
H14	0.2325	0.8183	0.2299	0.033*
C15	0.3724 (2)	0.6936 (4)	0.14090 (15)	0.0336 (4)
H15	0.4457	0.8225	0.1548	0.040*
C16	0.3918 (2)	0.5087 (4)	0.07578 (15)	0.0388 (5)
H16	0.4786	0.5100	0.0453	0.047*
C17	0.2846 (3)	0.3231 (4)	0.05546 (15)	0.0396 (5)
H17	0.2965	0.1973	0.0098	0.048*
C18	0.1596 (2)	0.3185 (4)	0.10110 (14)	0.0330 (4)
H18	0.0875	0.1883	0.0873	0.040*
C21	−0.1190 (2)	0.8116 (4)	0.29134 (17)	0.0368 (4)
H21A	−0.1177	0.9160	0.3510	0.044*
H21B	−0.2118	0.8096	0.2193	0.044*
C22	0.00939 (19)	0.6676 (3)	0.30879 (14)	0.0259 (3)
C23	0.15706 (19)	0.6647 (3)	0.42014 (14)	0.0234 (3)
C24	0.26332 (19)	0.4731 (3)	0.45078 (13)	0.0249 (3)
H24	0.2405	0.3441	0.3998	0.030*
C25	0.4019 (2)	0.4684 (4)	0.55461 (14)	0.0285 (4)
H25	0.4733	0.3372	0.5741	0.034*
C26	0.4356 (2)	0.6549 (4)	0.62942 (14)	0.0310 (4)
H26	0.5301	0.6520	0.7005	0.037*
C27	0.3317 (2)	0.8455 (4)	0.60075 (15)	0.0323 (4)
H27	0.3550	0.9736	0.6524	0.039*
C28	0.1944 (2)	0.8510 (3)	0.49760 (15)	0.0296 (4)
H28	0.1241	0.9833	0.4789	0.036*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C11	0.0348 (9)	0.0458 (12)	0.0398 (10)	−0.0102 (10)	0.0100 (8)	−0.0076 (10)
C12	0.0248 (7)	0.0292 (9)	0.0227 (7)	−0.0002 (8)	0.0032 (6)	0.0020 (8)
C13	0.0259 (7)	0.0266 (9)	0.0179 (7)	0.0035 (8)	0.0024 (6)	0.0021 (7)
C14	0.0309 (8)	0.0289 (9)	0.0219 (7)	0.0021 (8)	0.0080 (6)	−0.0001 (8)
C15	0.0330 (9)	0.0412 (11)	0.0266 (8)	−0.0002 (9)	0.0112 (7)	0.0049 (9)
C16	0.0406 (10)	0.0530 (14)	0.0260 (8)	0.0134 (11)	0.0162 (7)	0.0079 (10)
C17	0.0524 (11)	0.0402 (11)	0.0261 (9)	0.0146 (10)	0.0143 (8)	−0.0028 (9)
C18	0.0377 (9)	0.0288 (9)	0.0262 (8)	0.0043 (9)	0.0045 (7)	−0.0016 (8)
C21	0.0303 (8)	0.0420 (11)	0.0372 (9)	0.0070 (9)	0.0114 (7)	0.0025 (9)
C22	0.0239 (7)	0.0268 (9)	0.0283 (8)	−0.0018 (7)	0.0112 (6)	0.0025 (8)
C23	0.0235 (7)	0.0251 (9)	0.0242 (7)	−0.0009 (7)	0.0118 (6)	0.0012 (7)
C24	0.0274 (8)	0.0252 (8)	0.0243 (7)	−0.0002 (8)	0.0120 (6)	−0.0015 (7)
C25	0.0281 (8)	0.0330 (10)	0.0256 (8)	0.0027 (8)	0.0114 (7)	0.0053 (8)
C26	0.0281 (8)	0.0419 (11)	0.0228 (8)	−0.0084 (9)	0.0091 (6)	−0.0007 (8)
C27	0.0386 (9)	0.0321 (10)	0.0296 (8)	−0.0099 (8)	0.0167 (7)	−0.0093 (8)
C28	0.0324 (8)	0.0260 (9)	0.0347 (9)	−0.0009 (8)	0.0174 (7)	−0.0044 (8)

Geometric parameters (Å, º)

C11—C12	1.329 (3)	C21—C22	1.335 (3)
C11—H11A	0.9500	C21—H21A	0.9500
C11—H11B	0.9500	C21—H21B	0.9500
C12—C13	1.491 (2)	C22—C23	1.486 (2)
C12—C22	1.492 (2)	C23—C24	1.397 (2)
C13—C14	1.393 (2)	C23—C28	1.399 (3)
C13—C18	1.397 (3)	C24—C25	1.390 (2)
C14—C15	1.391 (2)	C24—H24	0.9500
C14—H14	0.9500	C25—C26	1.381 (3)
C15—C16	1.386 (3)	C25—H25	0.9500
C15—H15	0.9500	C26—C27	1.381 (3)
C16—C17	1.377 (3)	C26—H26	0.9500
C16—H16	0.9500	C27—C28	1.380 (2)
C17—C18	1.383 (3)	C27—H27	0.9500
C17—H17	0.9500	C28—H28	0.9500
C18—H18	0.9500
C12—C11—H11A	120.0	C22—C21—H21A	120.0
C12—C11—H11B	120.0	C22—C21—H21B	120.0
H11A—C11—H11B	120.0	H21A—C21—H21B	120.0
C11—C12—C13	121.75 (17)	C21—C22—C23	121.85 (17)
C11—C12—C22	119.35 (17)	C21—C22—C12	119.19 (16)
C13—C12—C22	118.87 (15)	C23—C22—C12	118.92 (15)
C14—C13—C18	117.95 (15)	C24—C23—C28	117.81 (14)
C14—C13—C12	120.92 (16)	C24—C23—C22	120.52 (16)
C18—C13—C12	121.13 (17)	C28—C23—C22	121.67 (16)
C15—C14—C13	120.99 (18)	C25—C24—C23	121.07 (17)
C15—C14—H14	119.5	C25—C24—H24	119.5
C13—C14—H14	119.5	C23—C24—H24	119.5
C16—C15—C14	120.0 (2)	C26—C25—C24	119.84 (18)
C16—C15—H15	120.0	C26—C25—H25	120.1
C14—C15—H15	120.0	C24—C25—H25	120.1
C17—C16—C15	119.67 (18)	C25—C26—C27	119.93 (16)
C17—C16—H16	120.2	C25—C26—H26	120.0
C15—C16—H16	120.2	C27—C26—H26	120.0
C16—C17—C18	120.45 (19)	C28—C27—C26	120.36 (18)
C16—C17—H17	119.8	C28—C27—H27	119.8
C18—C17—H17	119.8	C26—C27—H27	119.8
C17—C18—C13	120.98 (19)	C27—C28—C23	120.99 (18)
C17—C18—H18	119.5	C27—C28—H28	119.5
C13—C18—H18	119.5	C23—C28—H28	119.5
C11—C12—C13—C14	162.49 (18)	C11—C12—C22—C23	122.3 (2)
C22—C12—C13—C14	−15.6 (2)	C13—C12—C22—C23	−59.6 (2)
C11—C12—C13—C18	−17.0 (3)	C21—C22—C23—C24	160.50 (18)
C22—C12—C13—C18	164.92 (15)	C12—C22—C23—C24	−17.3 (2)
C18—C13—C14—C15	−0.6 (2)	C21—C22—C23—C28	−19.3 (3)
C12—C13—C14—C15	179.84 (16)	C12—C22—C23—C28	162.89 (15)
C13—C14—C15—C16	0.5 (3)	C28—C23—C24—C25	−0.2 (2)
C14—C15—C16—C17	0.3 (3)	C22—C23—C24—C25	179.93 (15)
C15—C16—C17—C18	−1.0 (3)	C23—C24—C25—C26	0.3 (2)
C16—C17—C18—C13	0.9 (3)	C24—C25—C26—C27	−0.1 (2)
C14—C13—C18—C17	−0.1 (2)	C25—C26—C27—C28	−0.1 (3)
C12—C13—C18—C17	179.47 (16)	C26—C27—C28—C23	0.1 (3)
C11—C12—C22—C21	−55.6 (2)	C24—C23—C28—C27	0.0 (2)
C13—C12—C22—C21	122.5 (2)	C22—C23—C28—C27	179.86 (16)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
C11—H11A···Cg1^i	0.95	3.05	3.96	161
C21—H21A···Cg2^ii	0.95	2.90	3.75	149

Symmetry codes: (i) −x, y−1/2, −z; (ii) −x, y+1/2, −z+1.