1. Introduction

Dianin's compound (DIN) is a well established cage-forming host that gives clathrate compounds with a wide range of guest molecules. The structural characteristics of the series were first established by Flippen et al. (1970) and Flippen & Karle (1971). Their crystallographic investigations indicated a -quinol type cage system in space group with cavities that are bounded by six host molecules, where each host molecule is shared by two cavities. These cavities were described as hour-glass shaped with the axis aligned along the trigonal c axis. The length of the cavity is 11.0 Å, with a waist diameter of 4.2 Å at z = 0.5 and a greatest diameter of 6.2 Å at z = 0.3 and 0.7. The ends of the cavity are closed by a ring of six O-HOⁱ (i: x - y, x, z) hydrogen bonds. The cage so formed is larger than the more familiar -quinol structure, which differs by having molecules hydrogen bonded at both ends. In Dianin's compound (DIN) the six larger molecules are hydrogen bonded (three up and three down) at only one end, the lower ends being simply enmeshed. In the structures reported by the earlier workers the host network was able to enclose such diverse guests as heptanol (one molecule per cavity), ethanol (two molecules per cavity) or chloroform (two molecules per cavity). The trigonal spacegroup requires that the cavity has symmetry, which implies that a single unsymmetrical guest molecule be statistically sixfold disordered.

An extensive spectroscopic investigation of the clathrates formed by Dianin's compound and a series of carboxylic acids (formic to octanoic) has already been reported (Davies & Tabner, 1997). The investigation described here is concerned with the crystallographic aspects of this series of clathrates.

2. The scope of the investigation

The preparation of Dianin's compound was described by Davies & Tabner (1997). The complexes were readily obtained by simple recrystallization from the appropriate guest acids, all of which were liquids at or near 293 K.

In addition to crystals containing the straight-chain acids (formic to octanoic), it was possible to prepare crystals containing the branched-chain isobutyric acid (dimethylacetic acid). Attempts were then made, unsuccessfully, to prepare the complex with pivalic (trimethylacetic) acid, which is a solid at room temperature (melting point 308.3 K), by using a solution of Dianin's compound in the molten acid. A further attempt, which used stoichiometric amounts of the host and guest in carbon tetrachloride solution, yielded only the carbon tetrachloride clathrate. It was concluded that the breadth of the pivalic acid molecule was incompatible with the shape of the Dianin cavity.

In view of the interest in this laboratory in the trifluoroacetate group (Gleghorn & Small, 1995) small crystals of the clathrate from trifluoroacetic acid solution were grown and included in the investigation.

In all, ten such complexes were crystallized. We will refer to them by code names according to the scheme below.

3. Experimental

The colourless crystals of all of the clathrate complexes were small (0.4-0.8 mm long) and all possessed the same thin acicular hexagonal prismatic habit. The largest available crystal of each complex was selected for intensity data collection.¹ A Stoë Stadi-2 two-circle diffractometer was used with the c direction of each crystal aligned with the diffractometer axis. An identical counting procedure, which involved variable scans with 2 fixed, was followed for each crystal, and the same set of layer-line standard reflections and counting times was used for each compound. A useful estimate of the relative sizes of the crystals used was provided by comparison of the intensities of the zero-layer standard reflection, (330). These values are recorded in Table 1 and show a factor of five in size between the largest and smallest crystals used (Small, 1977). Intensity data for the complex with pentanoic (valeric) acid, DIV, was collected first. The structure of the host network was confirmed with the direct-methods program MULTAN87 (Debaerdemaeker et al., 1987), which gave DIN coordinates equivalent to those reported by the original workers (Flippen et al., 1970). At the same time, using the experimental data for DIV and a theoretical structure containing only DIN, a difference map showed a distinct region of ordered electron density, presumably the result of the valeric acid solvent interacting with the host molecules or neighbouring guests.

In view of the wide range of sizes and shapes of the possible entrapped acid species, a fuller investigation that used a more extended system appeared justified. For convenience of comparison and in the interest of consistency, the atomic DIN coordinates of Flippen et al. (1970) were adopted as the starting point for each structure refinement, thereby implying the selection of the same set of unit-cell directions; in particular, the positive direction of c is defined. When a crystal is being mounted on the two-circle diffractometer there are no means of identifying whether the positive or negative direction of c is aligned with the axis. The ambiguity was resolved for each crystal after it had been mounted by comparison of the relative magnitudes of the intensities of the reflections -17 13 0 and -13 17 0, which are related by symmetry in position but are quite different in intensity. The matrix transformation

was then applied to the indices where appropriate to make the data sets consistent with the selected axial set.

4. Interpretation

SHELX76, which is most suited to deal with experimental data from a Weissenberg diffractometer, was used for the refinement. In order to check that no advantage would result from using the more recent routines of SHELXL97 (Sheldrick, 1997), three of the data sets (for DIA, DIH and DIO) were reformatted and data-reduction routines were written to make them compatible with the requirements of SHELXL97. The two methods gave very similar results to the rigid-body refinement of the symmetrical disorder, and the results reported here are those of SHELX76.

For each compound the parameters of the DIN molecule alone were refined. The refinement started with the values of Flippen et al. (1970) and used the collected F data. The initial R values, which at this stage were large, are included in Table 1. F maps in the form of sections parallel to (100) and (001) were calculated using SHELX76 (Sheldrick, 1976). These sections were suitable for producing contour maps with a routine CONTOUR provided by Glazer (1988). A selection of the difference maps are shown in Figs. 1(a)-10(a). These contour maps vary considerably in appearance and contain definite features that are attributable to the particular guest molecules included. A discussion of the individual maps will follow later, but note that the symmetry of the difference electron density will be that implied by the space group, i.e. symmetry. It follows that if the cavity holds one complete molecule it will appear in six orientations, each with one-sixth occupation. Inevitably there will be considerable overlap of the guest-atom positions, and the consequent disorder renders normal refinement of the atom coordinates impossible. When a possible interpretation of the electron density had been proposed a rigid-body model of the included guest molecule was set up by defining a sufficient number of interatomic distances using a set of DFIX instructions in SHELX76 (Sheldrick, 1976). Alternate refinement of the DIN host molecule and the rigid guest molecule then gave a significant improvement in the residual R. The DIN parameters usually converged rapidly, while the rigid guest parameters tended to drift as would be expected from the shallow nature of the residual electron-density maxima. Usually two or three refinement cycles of the rigid-body parameters gave an initial improvement of R and a perceptible reduction of the difference electron density.

This improvement in the R values was accompanied by a decrease in the level of the residual electron density; the electron-density distribution in the cavities eventually becomes low and featureless. This behaviour is illustrated by Figs. 1(b)-10(b), which are juxtaposed with the original difference maps and give an indication of the success in explaining the electron density.

Treatment of the site occupation factors of the guest atoms posed a difficult problem. Ideally, knowledge of the stoichiometric composition of the crystal actually used is required, and this composition is not necessarily identical to the overall composition of a batch measured by a method such as density determination. Furthermore, densities are difficult to determine for these compounds because of continual interchange of guest solvent and flotation liquid. On account of the large correlation of temperature and site occupation factors, refinement of both simultaneously was inadvisable. Accordingly the problem was circumvented by fixing site occupation factors at the ideal value, i.e. 1/3 or 1/6, and allowing the temperature factors to account for site occupation and positional disorder in addition to thermal effects. It should be stressed that the main evidence for the structures proposed lies in the general appearance of the electron-density difference maps together with the improved agreement achieved after the inclusion of the scattering that is attributed to the included guest molecule. Least-squares refinement of the atomic parameters of the included acids is not feasible because of overlap of the disordered positions.

5. Interpretation of the difference maps

It is impractical to show all the contour maps for reasons of space: some are shown as Figs. 1-10, and Table 1 includes the greatest residual electron density when the guest molecules are omitted and included. Depending on the size and shape of the guest molecules the structures can be interpreted in terms of a limited number of possibilities.

6. General effects on the Dianin framework

Intramolecular distances within the Dianin moiety are not significantly affected by the nature or size of the included guest molecules: the mean values of the interatomic distances over the series conform with the expected values. A significant increase in the intermolecular O1O1ⁱ (i: y, -x + y, -z) hydrogen-bond distances can be noted as strain develops from the inclusion of larger included species. The unstrained O1O1ⁱ distance appears to be 2.82-2.85 Å; increasingly larger values can be explained in terms of greater stress from larger guest molecules (Table 1). It is clear that hydrogen-bonding effects, which arise from the carboxyl groups, combined with the elongated shape of the clathrate cavity can produce partial ordering of guest molecules within these compounds.