Edinburgh Research Explorer Structures of Piperazine, Piperidine and Morpholine Acta Crystallographica Section B-structural Science Structures of Piperazine, Piperidine and Morpholine

Structures of piperazine, piperidine and morpholine' Acta crystallographica section b-Structural science, vol 60, pp. 219-227. General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. The crystal structures of piperazine, piperidine and morpho-line have been determined at 150 K. All three structures are characterized by the formation of NHÁ Á ÁN hydrogen-bonded chains. In piperazine these are linked to form sheets, but the chains are shifted so that the molecules interleave. In morpholine there are in addition weak CHÁ Á ÁO interactions. Topological analyses show that these three structures are closely related to that of cyclohexane-II, which can be described in terms of a pseudo-cubic close-packed array of molecules in a familiar ABC layered arrangement. While the positions of the molecules within each layer are similar, hydrogen bonding occurs between the ABC layers and in order to accommodate this the molecules are rotated relative to those in cyclohexane-II. Piperidine and morpholine also adopt layered structures, with hydrogen-bonding or CHÁ Á ÁO interactions between the layers. In these cases, however, the layering more resembles a hexagonal close-packed arrangement .

The crystal structures of piperazine, piperidine and morpholine have been determined at 150 K. All three structures are characterized by the formation of NHÁ Á ÁN hydrogen-bonded chains. In piperazine these are linked to form sheets, but the chains are shifted so that the molecules interleave. In morpholine there are in addition weak CHÁ Á ÁO interactions. Topological analyses show that these three structures are closely related to that of cyclohexane-II, which can be described in terms of a pseudo-cubic close-packed array of molecules in a familiar ABC layered arrangement. While the positions of the molecules within each layer are similar, hydrogen bonding occurs between the ABC layers and in order to accommodate this the molecules are rotated relative to those in cyclohexane-II. Piperidine and morpholine also adopt layered structures, with hydrogen-bonding or CHÁ Á ÁO interactions between the layers. In these cases, however, the layering more resembles a hexagonal close-packed arrangement.

Introduction
Although cyclohexane is a liquid under ambient conditions, it has been studied extensively by crystallographic methods (Kahn et al., 1973;Wilding et al., 1991Wilding et al., , 1993. It exhibits a signi®cant degree of phase diversity, with crystal structures of four polymorphs having been elucidated. Tetrahydropyran and 1,4-dioxane (Buschmann et al., 1986), and 1,3,5-trioxane (Busetti et al., 1969) have also been studied and characterized in the solid state under varying temperature conditions, and these also exhibit several different phases. Little work has as yet been performed to characterize the phase behaviour of heterocyclic cyclohexane analogues possessing groups capable of hydrogen bonding, and structural studies of piperidine, piperazine and morpholine were undertaken with this in mind.

Differential scanning calorimetry (DSC)
DSC traces were recorded using a Perkin±Elmer Pyris DSC 1. Samples were contained in open aluminium pans and purged with helium during the temperature scans. The ramping rate was 20 K min À1 . The DSC trace for piperidine is shown in Fig. 1. The features in this trace are discussed in x3.2. Traces for morpholine and piperazine revealed no thermal events other than melting or freezing.

Crystal growth
Colourless block-like crystals of piperazine were grown at room temperature from a saturated solution in ethanol. Piperazine is strongly hygroscopic and prolonged exposure to the air leads to the formation of a hexahydrate (Schwarzenbach, 1968); crystals used for data collection were therefore picked quickly from beneath per¯uoropolyether oil. Crystals of both piperidine and morpholine, which are liquids at room temperature, were grown in situ on the diffractometer from neat liquids in hand-drawn Pyrex capillaries of approximately 0.3 mm diameter. A single crystal of piperidine suitable for diffraction was obtained by¯ash-freezing the liquid to form a polycrystalline powder. The sample was held at 250 K and partially melted to leave a small seed crystal by interrupting the cryogenic¯ow with a spatula. Crystallization was allowed to proceed over a period of 30 min at 250 K. A single crystal of morpholine was obtained in a similar manner, with the polycrystalline powder being held at 269.5 K and the seed crystal being cooled from 269.5 to 259.5 K over a period of 15 min. Samples were cooled to 150 K for data collection.

Crystallography
X-ray diffraction intensities were collected at 150 K with Mo K radiation on a Bruker SMART APEX CCD diffractometer equipped with an Oxford Cryosystems low-temperature device (Cosier & Glazer, 1986). Integrations were carried out using SAINT (Bruker-AXS, 2002). Absorption corrections were applied using the multiscan procedure SADABS (Sheldrick, 1997b, based on the procedure described by Blessing, 1995). All structures were solved by direct methods (SHELXTL, Sheldrick, 1997a) and re®ned by full-matrix least squares against F 2 using all data (CRYSTALS; Watkin et al., 2003). H atoms attached to carbon were placed in calculated positions and allowed to ride on their parent atoms with U iso (H) = 1.2U iso (C). H atoms involved in hydrogen bonding were located in difference maps and re®ned freely. All non-H atoms were modelled with anisotropic displacement parameters. Morpholine crystallized in the non-centrosymmetric space group P2 1 2 1 2 1 , but no attempt was made to re®ne the Flack parameter (Flack, 1983) because anomalous scattering effects were negligible under the experimental conditions used and thus, Friedel pairs have been merged.
In the case of piperidine, least-squares re®nement converged to a relatively high R factor (based on F and all data) of 0.057. Inspection of a plot of F 2 o against F 2 c (Fig. 2a) revealed that this was largely owed to a few very strong data. Crystals grown using in situ methods are often of very high quality and extinction is often a serious systematic error; although an isotropic extinction correction (Larson, 1970) had been included in the model, these poorly ®tting data still had     (Fig. 2a). A leverage analysis (Prince, 1994; carried out using a locally written program) suggested that these data also had very high leverages and their systematic error compromised the ®tting of other weaker re¯ections (Fig. 2b). Omission of these data (14 re¯ections in all) led R to drop to a more acceptable 0.047. The extinction parameter was subsequently removed from the model after assuming a physically unreasonable, negative, value.
A full listing of crystal, data collection and re®nement parameters is given in Table 1; a set of hydrogen-bonding parameters are given in Table 2; primary bond distances and angles are available in the supplementary data. 1 Crystal packing was investigated using the program Mercury (Bruno et al., 2002), and ®gures were produced using SHELXTL or CAMERON (Watkin et al., 1993). Other analyses utilized the p.c. version of the program PLATON (Spek, 2002;Farrugia, 1999). Puckering parameters were calculated using the program PUCKER (Gould et al., 1995).
A new facility in CRYSTALS interfaces with MOGUL, a library of information about molecular geometry taken from the Cambridge Database (Cambridge Crystallographic Data Centre, 2003;Cooper, 2001). This enables primary bond distances and angles to be quickly compared with those in 0.16, À0.14 0.19, À0.24 0.23, À0.13 Extinction method Larson (1970) similar moieties; a combined ®gure of merit is generated for the bond distances and angles about each atom based on values of Z = |X obs À X median |/' for each parameter involving that atom (X obs is the observed value for a distance or angle, X median is the median value for that type of distance or angle in the CSD and ' is the standard deviation of the MOGUL distribution). Values of Z greater than 3 may indicate unusual geometry. This facility is extremely useful for checking whether geometrical parameters have assumed unusual values (Cooper, 2001).

Topological calculations
Topological analyses were carried out using the TOPOS3.1 program suite . Adjacent matrices were calculated using the program AUTOCN using the method of spherical sectors; the minimum solid angle of a Voronoi± Dirichlet polyhedron (VDP) face corresponding to an intermolecular contact was set to zero. Analysis of both smoothed and lattice VDPs were carried out with the program ADS, with the geometrical centres of the molecules (as opposed to their centres of gravity) as reference points. Coordination sequences were calculated out to three coordination spheres. In each case two sets of calculations were carried out: one in which all VDP faces were taken into account, and another in which very small VDP faces were omitted. Results for piperazine, morpholine, piperidine and cyclohexane-II are presented in Table 3 and illustrated in Fig. 3. Full details of these procedures can be found in the TOPOS3.1 manual, and in papers by Blatov and co-workers (for example, Blatov, 2001;Peresypkina & Blatov, 1999, 2000a. Calculations of continuous symmetry measures were carried out using a locally written program using the method described by Pinsky & Avnir (1998). Molecular volumes (V mol ) for packing coef®cient calculations (see Table 3) were obtained using CERIUS 2 (Molecular Simulations Inc., 1999). The packing coef®cient is de®ned as ZV mol /V cell , where V cell is the volume of the unit cell and Z the number of molecules per cell (Kitaigorodski, 1973).

Piperazine
Piperazine crystallizes from ethanol under ambient conditions in the space group P2 1 /n. The molecule resides on a crystallographic inversion centre and has the ideal chair conformation with NÐH bonds in the equatorial positions (Fig. 4a). The maximum MOGUL combined ®gure-of-merit was 1.36, indicating that the bond distances and angles in piperazine are normal. NÐHÁ Á ÁN hydrogen-bonding interactions, measuring 2.319 (16) A Ê , are formed between molecules (Table 2, Fig. 4b); the primary graph-set descriptor is a C(2) chain which is built along the 2 1 axes (Bernstein et al., 1995). These chains are related to other C(2) chains by the crystallographic inversion centres located at the centres of the molecules. The overall effect is to build up layers of molecules which lie parallel to the ( " 101) planes (Fig. 4c). The distance between successive planes of molecular centroids is 5.53 A Ê .

Piperidine
Piperidine is structurally related to piperazine by the substitution of one NH group by CH 2 . It crystallizes in the space group P2 1 /c with one molecule per asymmetric unit occupying a general position. Like piperazine, it has a chair conformation (95% of the puckering can be described with an ideal cyclohexane chair) with the H atom in an equatorial position (Fig. 5a). Primary bond distances and angles are Table 2 Hydrogen bonding and other intermolecular contact parameters in piperazine, piperidine and morpholine (A Ê , ).
Standard uncertainties were calculated using the full variance±covariance matrix, but are only quoted if all atoms involved were re®ned freely. The sums of the van der Waals radii of N and H, and O and H are 2.75 and 2.72 A Ê , respectively. In each case the primary graph-set descriptor is C(2).
CS represents the coordination sequence, i.e. the number of molecules in the ®rst, second and third coordination shells. K cov and K pack are the covering and packing coef®cients, respectively. The superscript a indicates that all Voronoi±Dirichlet polyhedron faces were taken into account in the calculation, b indicates that two faces which were much smaller than the others were omitted. For example, in the case of cyclohexane-II, two contacts made lattice VDP faces with areas of 0.24% of the full solid angle (4%sr), while the next smallest faces had areas of 3.97% of the full solid angle. There were no small faces in the lattice VDP of piperazine. Notice that quite similar results are obtained for both the smoothed and lattice VDP analyses; this is to be expected for small molecules such as these and deviations become more signi®cant as molecules become less isometric. Coordination sequences for perfect body-centred cubic, cubic closepacked and hexagonal close-packed structures are 14±50±110, 12±42±92 and 12±44±96, respectively (Blatov, 2001;Peresypkina & Blatov, 2000b Fig. 5b). This similarity with piperazine also extends to the primary graph set, which is comprised by C(2) chains disposed about the crystallographic 2 1 axes. The substitution of NH by CH 2 in the 4-position disrupts the layer structure observed in piperazine. Projection of the structure onto the ac plane reveals a close-packed-like arrangement of chains; perpendicular to this direction the piperidine molecules in neighbouring chains are interleaved (Fig. 5c).
The melting point of piperidine is 250 K, although under cooling conditions of the DSC experiment the sample did not freeze until 244 K (Fig. 1). A phase transformation occurred at 239 K. This second phase is stable to cooling to 120 K and is presumably that described in this paper. The ®rst phase was not recovered by warming the second phase above 238 K.

Morpholine
Morpholine is structurally related to piperazine by the substitution of one NH group by oxygen. It crystallizes at 267 K in the space group P2 1 2 1 2 1 with one molecule per asymmetric unit occupying a general position. The maximum MOGUL combined ®gure-of-merit for primary bond distances and angles was 1.0. Like piperazine and piperidine, it has a chair conformation (98% of the puckering can be described with an ideal cyclohexane chair) with the H atom in an equatorial position (Fig. 6a)  NHÐNHÐ chains which characterized the structures of piperazine and piperidine are also observed in morpholine. The NHÁ Á ÁN distance is 2.35 (3) A Ê ( Table 2). Packing of the chains is reminiscent of those in piperidine, except that they are oriented in such a way that weak CHÁ Á ÁO interactions (2.63 A Ê ) are formed between the molecules in neighbouring chains (Fig. 6b).

General structural features and phase behaviour
Although amines are fairly weak hydrogen-bond donors, they are strong acceptors, and piperazine, piperidine and morpholine all exhibit chain-like structures developed through NHÁ Á ÁN hydrogen bonds. NHÁ Á ÁO hydrogen bonding is in principle possible in morpholine, although the stronger acceptor character of amine versus ether is presumably the reason that this is not observed. The NÁ Á ÁN distances in the three structures vary only slightly (range: 3.18±3.23 A Ê ) and the distances compare closely with a mean [3.22 (14) A Ê ] for such interactions in the Cambridge Database (Allen, 2002;Version 5.24, November 2002). Morpholine exhibits weak CHÁ Á ÁO interactions in which the HÁ Á ÁO distance (2.63 A Ê ) is slightly less than the sum of the van der Waals radii of H and O (2.72 A Ê ). Although this interaction must be very weak, in the crystal structure the molecules of morpholine do seem to be oriented in order to engage in it, and interactions of similar dimensions are observed in the crystal structures of 1,4-  dioxane (CSD refcodes CUKCIU and CUKCIU01;Buschmann et al., 1986).
Differential scanning calorimetry measurements show that piperidine appears to form one phase on cooling from the liquid, which then transforms to the phase described here at 239 K. However, the higher temperature phase cannot be recovered by warming the low-temperature phase to 238 K, although a shoulder on the melting transition suggests that some phase alteration may occur immediately prior to melting.
A further very weak transition occurs at 219 K. The formation of the ®rst phase appears to depend on experimental conditions and is not always observed. On our ®rst attempt to crystallize piperidine we measured metrically monoclinic primitive unit-cell dimensions of a = 7.033 (3), b = 5.224 (3), c = 7.852 (4) A Ê and = 108.03 (3) . The crystal was of low quality, however, and data collection on this sample was not pursued. Sadly, we have been unable to repeat this result. Similar behaviour is observed in acetone (Allan et al., 1999). We are currently investigating the phase behaviour of this compound more closely.

Structural relationship with cyclohexane
The three compounds studied here are related to cyclohexane by the substitution of one or more of the CH 2 groups for NH and/or O, and it might be anticipated that some relationship should exist between the crystal structures of all four compounds. Cyclohexane has a rich phase diversity and it has been studied under varying degrees of temperature and pressure. Phase I, which occurs between the melting point (279.82 K) and 186.1 K, is a plastic phase crystallizing in the space group Fm " 3m, in which the molecules undergo rapid molecular reorientations about the lattice points. On cooling below 186.1 K an order±disorder transition occurs to give phase II (space group C2/c; Kahn et al., 1973). The application of pressure to cyclohexane-d 12 initially yields phase I at 5 kbar and room temperature, but this transforms to phases III (Pmnn) and IV (P2 1 /n) at 280 and 250 K, respectively (Wilding et al., 1991(Wilding et al., , 1993. Phase IV has also been observed at ambient pressure by rapidly cooling cyclohexane-h 12 to 77 K. The coordination environment of a molecule in a crystal structure can be visualized using a Voronoi±Dirichlet polyhedron or VDP (Peresypkina & Blatov, 2000a,b). Voronoi± Dirichlet analysis is a method for partitioning space amongst points which occupy that space. A point is separated from a neighbouring point by a plane which bisects the vector between them. This construction is repeated for every pair of points to yield a subdivision of the space into cells which each contain one point. VDP analysis carried out using individual atoms to de®ne the points leads to a molecular VDP. In general, the molecular VDP is non-convex (see, for example, Fig. 2 in Peresypkina & Blatov, 2000a). If the VDP is constructed using only the molecular centroids, the result is a convex lattice VDP. This characterizes the topology of crystal packing. In cases of crystal structures of non-isometric mole-Acta Cryst.   Although cyclohexane-I has a low packing coef®cient (0.62), and cannot be described as`close-packed', the coordination number of the average positions is 12, with a distribution which follows the familiar ABC layering characteristic of a cubic close-packed (c.c.p.) hard-sphere structure. The results of the topological VDP analysis presented in Table 3 show that the coordination sequence (whether calculated using smoothed or lattice VDPs) in cyclohexane-II is 14±50± 110; that is, there are 14 molecules in the ®rst coordination sphere, 50 in the second and 110 in the third. This makes the structure topologically equivalent to a body-centred cubic (b.c.c.) hard-spheres structure. However, two centroid-tocentroid intermolecular distances are very long compared with the other 12 (7.95 compared with 5.21±6.47 A Ê ) and omitting these from the calculation yields a coordination sequence of 12±42±92, which is characteristic of a cubic close-packed (c.c.p.) structure. The lattice VDP of cyclohexane-II is compared with those of perfect b.c.c. and c.c.p. in Fig. 3, and it clearly resembles the latter more closely. This interpretation of the topology is supported by the covering coef®cient (K cov ), de®ned by Blatov as V s /V VDP , where V VDP is the volume of the VDP and V s is the volume of the sphere circumscribed around it. K cov adopts a value of 1.46 for a perfect b.c.c. structure and 2.09 for a close-packed structure; with a value of 1.93 cyclohexane-II more resembles the latter.
The molecular centroids in cyclohexane-II thus retain a coordination number of 12 with the ABC layered arrangement present in the plastic phase (I) (Fig. 7). This is also the case for cyclohexane-III and cyclohexane-IV. The deviation of the distribution of the molecular centroids from perfect c.c.p. can be quanti®ed using the continuous symmetry measure parameter described by Pinsky & Avnir (1998). In general, this measure has a physical bound of 0 to 100, and we obtain values of 2.0, 0.9 and 1.1 for cyclohexane-II, -III and -IV, respectively, where a value of 0.0 corresponds to perfect c.c.p. Cyclohexane-III and -IV are both high-pressure polymorphs and the distribution of their centroids more closely resembles perfect c.c.p. than in cyclohexane-II; this often seems to be the case in crystal structures determined at high pressure.
The crystal structures of piperazine, piperidine and morpholine also contain molecules which, although formally 14-coordinate, exhibit two centroid-to-centroid distances much longer than the other 12, and in all three structures the molecular coordination number is best considered to be 12. Lattice VDP plots are shown in Figs. 3(f)±(h). The molecular centroids in piperazine also adopt a CCP distribution (coordination sequence 12±42±92), with a continuous symmetry measure of 2.2 relative to a c.c.p. structure. While the positions of the molecules within each layer are similar to those in cyclohexane-II, hydrogen bonding occurs between the ABC layers and in order to accommodate this the molecules are rotated relative to those in cyclohexane-II (Fig. 8). Since there are four threefold rotational axes of symmetry in a c.c.p. structure, these layers can be chosen in four different ways. The choice here was made to facilitate comparison with morpholine and piperidine, and in the latter hydrogen bonds can be considered to be formed between alternate layers (Fig.  9). Piperidine is therefore a kind of hybrid between the cyclohexane and piperazine structures, as would be expected on the basis of the molecular structures.   The piperazine and cyclohexane structures both consist of centrosymmetric molecules with their centroids on inversion centres. The piperidine molecule is non-centrosymmetric and in its (centrosymmetric) crystal structure the inversion centres lie between molecules. This is incompatible with a c.c.p. distribution of centroids and piperidine therefore adopts a hexagonally close-packed (h.c.p.) arrangement (coordination sequence 12±44±96), with a continuous symmetry measure of 2.0 relative to perfect h.c.p. The crystal structure of morpholine is non-centrosymmetric (space group P2 1 2 1 2 1 ). This is a common space group for molecules which lack inversion symmetry and it is usually the case that in this space group molecules tend to avoid the screw axes (Motherwell, 1997).
Here the molecules lie very close to the unit-cell origin and if only the molecular centroids are considered the space group is Pnma, with the centroids lying on mirror planes either side of the inversion centres. The packing in morpholine yields a coordination sequence of 12±44±96 and this structure can therefore also be considered to be based on h.c.p.; this is illustrated in Fig. 10. The continuous symmetry measure is 1.4 relative to perfect h.c.p. Both NHÁ Á ÁN and CHÁ Á ÁO hydrogen bonds are formed between the layers.
Although recent work by Peresypkina & Blatov (2000a,b) and other workers reveals that the molecular coordination number 14 is most common in molecular crystal structures, 12 is far from rare. Indeed, Kitaigorodski (1973) noted that 12 was most common, although this may have been dependent on his method of calculation. There is a clear relationship between the crystal structures of cyclohexane-II, piperazine, piperidine and morpholine, all forming layered structures with either a c.c.p. or h.c.p. distribution of molecular centroids depending on whether these coincide with a molecular inversion centre. All four molecules have packing coef®cients in Kitaigorodski's typical range (0.65±0.77: cyclohexane-II and piperazine, 0.71; piperidine, 0.66, and morpholine, 0.70), although piperidine is notably rather low and this perhaps explains why at least two different phases are observed between 77 K and its melting point.