1-Nitronaphthalene, a non-OD, non-MDO polytype

2.1 Crystallization

Needles of 1-nitronaphthalene were grown by dissolving 100 mg of commercial material (Fluka, purum) in 10 ml methanol followed by evaporation of the solvent at room temperature over night.

2.2 Data collection and refinement

Multiple crystals were selected under a polarizing microscope and checked for diffraction quality using CuKα radiation on an STOE StadiVari diffractometer system equipped with a Dectris Eiger CdTe hybrid photon counting detector. Crystals were systematically twinned with a high degree of reflection overlap and featured pronounced mosaicity. Generally, small crystals were of better diffraction quality. Intensity data of the crystal with the least mosaicity were then collected at 200 K in a dry stream of nitrogen up to 2θ = 140° using fine-sliced (0.3°) ω-scans.

Data were processed with X-Area. ³ Two domains were identified and integrated concurrently using overlap information (HKLF5 format). Periodic refinement of the orientation matrix from reflection positions had to be turned off for reliable results. This proved to be a non-issue owing to the stability of the goniometer. A correction for absorption and beam inhomogeneity was applied using the multi-scan approach implemented in LANA. ³

The structure was solved using the dual-space approach implemented in SHELXT ⁴ and refined against F² using SHELXL. ⁵ C, N and O atoms were refined using anisotropic atomic displacement parameters (ADPs). H atoms were placed at calculated positions and refined as riding on the parent C atom. More data collection and refinement details are collected in Table 1.

3.1 Crystal and molecular structure

1-Nitronaphthalene crystallizes in a space group of type P2₁/c with Z′ = 2 molecules in the asymmetric unit. The crystallographically independent molecules are indicated by different shading in Figure 1. The atoms in both molecules are labeled equivalently up to an added A or B letter. The molecules are accordingly called the A and B molecule, respectively.

Figure 1:

The crystal structure of 1-nitronaphthalene viewed along [010]. C (gray), N (blue) and O (red) atoms are represented by ellipsoids drawn at the 75 % probability levels, H atoms by white spheres of arbitrary radius (0.2 Å). The crystallographically distinct A (light) and B (dark) molecules are differentiated by brightness. Symmetry elements of the P2₁/c space group are indicated using the usual graphical symbols. ⁶

The molecules are arranged in layers extending parallel to (001), which are called L _n , where n is a sequential number (Figure 1). Adjacent layers L _n and L_n+1 are alternately related by the 1‾ and [−2₁−] operations of the P2₁/c space group. Note: For symmetry operations with a directional element, we use a notation with places to indicate the direction (e.g. [− − 2₁] is a screw rotation in the [001] direction, etc.). ⁷ Layers L _n and L_n+2 are mapped by c-glides reflections, which arise from a combination of the [−2₁−] and 1‾ operations. Four layers form a translation period in the [001] direction.

The two distinct molecules are geometrically practically equivalent (see below for quantification). The nitro group is tilted with respect to the naphthalene ring system (Figure 2), owing to steric interaction with C9’s hydrogen atom. The torsion angle between the respective least squares planes is 40.1(6)° and 38.1(6)° for the A and B molecule, respectively.

Figure 2:

The A molecule (a) projected on the plane of the naphthalene system and (b) viewed along the bond connecting the nitro group the naphthalene moiety. Atoms as in Figure 1. The B molecule is geometrically practically equivalent and therefore not shown.

3.2 Pseudo-symmetry of layers

Our argument that the crystal structure of 1-nitronaphthalene possesses polytype character is based on the pseudo-symmetry of the L _n layers. In fact, the layers can be considered as having (pseudo) p2₁11 symmetry (see Figure 3). According to the International Tables of Crystallography, the lower case Bravais symbol indicates the two-dimensionality of the translation lattice and it is implicitly assumed that the layer extends in the (001) plane. ⁸ The A and B molecules, which are distinct according to the space group symmetry, are related by pseudo-[2₁ − −] screw rotations.

Figure 3:

L _n layer in 1-nitronaphthalene projected on the layer plane (001). Atoms as in Figure 1. The locations of the pseudo [2₁ − −] axes are represented by the usual symbols.

To prove the validity of our interpretation, it is crucial to quantify the deviation from this idealized symmetry. Thereto, the atom coordinates were transformed into a Cartesian coordinate system and the location of the screw axis determined by averaging the y and z coordinates of the C, N and O atoms. The intrinsic translation of the screw rotation was derived by halving the a basis vector. This, now well defined, screw rotation was then applied to the A molecule, to map it onto the B molecule. An overlay of the molecules is shown in Figure 2 and the distance between atoms is given in Table 2. A maximum distance of 0.233 Å for the C7A/C7B pair confirms the pseudo-symmetry and henceforth we will consider (slightly) idealized L _n layers with p2₁11 symmetry. ⁸ The slight deviation is mostly due to a rotation about an axis parallel to [100], as seen in Figure 4(a).

Figure 4:

Overlay of the image of the A-molecule by the pseudo-[2₁ − −] screw rotation (red) and the B-molecule (blue), viewed along (a) [100] and (b) [010].

3.3 Polytypism

According to the p2₁11 symmetry, ⁸ the L _n layers are non-polar, which means that both sides are related by symmetry. However, in the crystal structure of 1-nitronaphthalene, both sides connect in non-equivalent ways to adjacent layers: by 1‾, resulting in (L _n , L_n+1) pairs of layers with p1‾ layer symmetry, and by [−2₁−] resulting in pairs with p12₁1 symmetry. Since these pairs feature distinct symmetry, notably the orientation relation of the adjacent layers are different, they are geometrically different. The two distinct layer contacts will be designated according to the operations relating the adjacent layers as 1‾- and [−2₁−]-contact, respectively.

This proves the polytype character of 1-nitronaphthalene, since a layer can contact in different ways to adjacent layers. Moreover, it violates the vicinity condition of OD theory, ⁹ which states that equivalent sides of equivalent layers connect in such a way to adjacent layers that the resulting pairs are equivalent. 1-Nitronaphthalene is therefore a non-OD polytype. Note that the non-OD character stems from different sets of operations that relate layers of the same kind. An alternative way of achieving non-OD polytypes is a layer that can contact to two (or more) layers of different kind. If this leads to structures composed of distinct sets of layers, one also speaks of merotypes instead of polytypes. ⁷

In OD polytypes, layer contacts are equivalent and therefore it is reasonable to associate a ‘width’ or ‘thickness’ to layers. The vector perpendicular to the layer plane and of the length of one layer width is typically called c₀ (for stacking direction [001]). In contrast, in non-OD polytypes, the distinct layer contacts may lead to structures with different density and there may therefore be a distinct c₀ for each layer contact.

Interestingly, for 1-nitronaphthalene, the [2₁ − −] axis (see above for determination) of the layer symmetry is located a negligible 0.003 Å away from the z = 1 8 (with respect to the basis of the P2₁/c structure) plane. That is, it is equidistant to the 1‾ and [−2₁−] symmetry elements of the P2₁/c space group. Thus, in both kinds of layer contacts, the layer planes are equidistant, which means that we can define a common c₀ vector, with the length c sin(β)/4 = 7.961 Å. It is indicated in Figure 1.

3.4 Comparison of layer contacts

Even if adjacent layers do not form equivalent pairs, it is sometimes possible to construe an OD interpretation by (formally) ‘cutting’ the molecules and considering the layer contact as a distinct OD layer with higher symmetry (see for example Ref 10).

To rule out such an interpretation and to show that the layer contacts are indeed chemically different, we performed a Hirshfeld surface analysis ¹¹ using Crystal Explorer. ¹² Figure 5 shows the Hirshfeld surface of both sides of an L _n layer decorated with d_norm values. For the 1‾-contact, large d_norm values (red spots in Figure 5(a)) show that the most prominent inter-layer interactions are O3B–H8A contacts. In contrast, there are no such prominent interactions for the [−2₁−]-contact (Figure 5(b)).

Figure 5:

Hirshfeld surfaces of an L _n layer decorated with d_norm values for the (a) 1‾- and the (b) [−2₁−]-contact.

While these results shouldn’t be over-interpreted, since Hirshfeld surfaces analyses are sensitive to small distortions, it shows that the contacts are chemically different and that the crucial contact is from the O atom of the nitro-group to an H atom in the adjacent layer.

To get a clearer picture of the different layer contacts, we applied the [−2₁−] screw rotation of the L _n layer to a (L_n−1, L _n ) pair of layers and overlaid it with the (L _n , L_n+1) pair. The result is shown in Figure 6(a). As described above, the L _n layer and its image overlap nearly perfectly. The overlay of the image of L_n−1 and L_n+1 quantifies the difference of the two contacts.

Figure 6:

Comparison of the two kinds of layer contacts. (a) Overlay of an (L _n , L_n+1) pair (red) and the image of the (L_n−1, L _n ) pair (blue) by the [2₁ − −] operation of the L _n layer viewed along [010]. A dotted line represents the interface between the layers, short O1–H contacts are indicated by solid lines. (b) Overlay of the L_n+1 layer (red) and the image of the L_n−1 layer (blue) by the [2₁ − −] operation of the L _n layer. H atoms are omitted for clarity.

First observe that, as noted above, the [001] components of the layer origins are virtually identical, which justifies the choice of a single c₀ vector connecting the planes of adjacent layers. However, in the [100] direction, there is a small, but distinct difference in the origin shift. Apart from that, both layer contacts look very similar in the [010] projection. However, a projection along [001] (Figure 6(b)) reveals that their orientation is reflected with respect to [010], which follows from the fact that [−2₁−] retains, but 1‾ inverses the orientation with respect to [010].

This results in entirely different inter-layer O–H contacts. As noted above, at the 1‾-contact, two molecules ‘touch’ via short O1A–H3B contacts (2.55 Å, red lines in Figure 6(a)). The two connected molecules feature the same orientation with respect to [001] (the nitro group points in the same direction).

In the [−2₁−]-contact, on the other hand, the shortest inter-layer O–H contact is significantly longer (O1A–H8A, 2.70 Å, blue lines in Figure 6(a)). Here, the connected molecules are related by 1‾ and thus feature different orientation with respect to [001].

Ultimately, we note that the layer interfaces are chemically distinct and there are two ways of placing the L_n+1 layer into the mold of the L _n layer’s interface. We see no reasonable way of forcing an OD interpretation in this case.

3.5 Application of the OD formalism

In the context of OD theory a rich formalism for analyzing OD polytypes has been developed, which can however also be applied to non-OD polytypes with small adaptations, as we will do in the upcoming sections.

3.6 Twinning

The twin laws (i.e. the symmetry relationships between the orientations of the twin individuals ²¹ ) are derived by coset decomposition of the point group of a polytype in the point group of the polytype family (mmm, see above). For the P2₁/c polytype (point group 2/m), we obtain, besides the point group itself, a second coset {[2 − −], [m − −], [− − 2], [− − m]}. This corresponds precisely to the observed two-domain twinning (see Table 1) and thus shows the predictive power of the polytype theory. At the twin interface is probably located either a fragment of the MDO₁ polytype or the MDO₂ polytype, since in both cases their point groups (222 and 2/m11, respectively) contain operations of the twin law. However, theoretically between the twin individuals could also be located a different polytype or a disordered region of layers. In any case, the twin interface is at least one, though possibly more, layers wide. One therefore should speak of an composition region or slab instead of a composition plane. The precise nature of this region cannot be derived from routine diffraction experiments.

The slight deviation from orthorhombic metrics (β = 91.173°) makes this twinning a problematic case for structure elucidation, as most reflections overlap, yet the twin obliquity is too large to integrate data using a single domain (Figure 7). Faint streaking along c^∗ (exemplarily indicated by red arrows in Figure 7) suggests either disordered domains or small twin domains.

Figure 7:

(h2l)* section of reciprocal space of the 1-nitronaphthalene twin under investigation. Multiples of reciprocal lattice basis vectors of the major domain are indicated in black, the 4a* vector of the minor domain in red.