The effect of temperature and pressure on the crystal structure of piperidine
- Laura E Budd^{1},
- Richard M Ibberson^{2, 3},
- William G Marshall^{2} and
- Simon Parsons^{1}Email author
https://doi.org/10.1186/s13065-015-0086-3
© Budd et al.; licensee Springer. 2015
Received: 29 October 2014
Accepted: 5 February 2015
Published: 12 April 2015
Abstract
Background
The response of molecular crystal structures to changes in externally applied conditions such as temperature and pressure are the result of a complex balance between strong intramolecular bonding, medium strength intermolecular interactions such as hydrogen bonds, and weaker intermolecular van der Waals contacts. At high pressure the additional thermodynamic requirement to fill space efficiently becomes increasingly important.
Results
The crystal structure of piperidine-d_{11} has been determined at 2 K and at room temperature at pressures between 0.22 and 1.09 GPa. Unit cell dimensions have been determined between 2 and 255 K, and at pressures up to 2.77 GPa at room temperature. All measurements were made using neutron powder diffraction. The crystal structure features chains of molecules formed by NH…N H-bonds with van der Waals interactions between the chains. Although the H-bonds are the strongest intermolecular contacts, the majority of the sublimation enthalpy may be ascribed to weaker but more numerous van der Waals interactions.
Conclusions
Analysis of the thermal expansion data in the light of phonon frequencies determined in periodic DFT calculations indicates that the expansion at very low temperature is governed by external lattice modes, but above 100 K the influence of intramolecular ring-flexing modes also becomes significant. The principal directions of thermal expansion are determined by the sensitivity of different van der Waals interactions to changes in distance. The principal values of the strain developed on application of pressure are similarly oriented to those determined in the variable-temperature study, but more isotropic because of the need to minimise volume by filling interstitial voids at elevated pressure.
Background
In cyclohexane-II the molecules are distributed in layers which stack in the ABCABC… pattern characteristic of cubic close packing. In piperidine and piperazine the NH groups are capable of forming hydrogen bonds. In piperazine the arrangement of the molecular centroids is the same as in cyclohexane-II, but the molecules are rotated to enable H-bonds to form between the layers [3]. The structure of piperidine can also be considered to consist of layers, but the distribution of the molecules with respect to inversion centres in the space group makes the topology hexagonally close-packed. H-bonds form only between alternate layers, and the structure can be considered to be a hybrid of cyclohexane and piperazine. The rotations necessary for H-bond formation optimise interactions between the NH groups, but at the expense of breaking the van der Waals interactions formed within the layers of cyclohexane, and piperidine has a somewhat lower packing coefficient [4] (0.66) than either cyclohexane or piperazine (0.71).
The low packing coefficient suggests that piperidine may be susceptible to formation of different phases. This suggestion is supported by differential scanning calorimetry data presented by Parkin [3], which show that piperidine appears to form one phase on cooling from the liquid, which then transforms to another phase at 239 K. However, the higher temperature phase is not recovered on warming. In addition, during preliminary crystal growth experiments Parkin et al. obtained a weakly-diffracting form of piperidine with a cell volume approximately half of that of the phase they eventually characterised. The cell dimensions of this smaller-volume phase were a = 7.033(3), b = 5.224(3), c = 7.852(4) Å and β = 108.03(3)°. However, despite numerous attempts in which the cooling rate and sample size were varied this phase was never observed again.
The primary aim of the present investigation was therefore to determine if new forms of piperidine (in its perdeuterated form) could be identified under different conditions of temperature and pressure. The data collected also enable a detailed analysis of the thermodynamic properties of piperidine which are analysed with the aid of periodic DFT simulations and PIXEL packing energy calculations.
Experimental
Piperidine-d_{11} was obtained from Aldrich and used as received.
Variable temperature measurements
Variable temperature time-of-flight neutron powder diffraction data were recorded using the HRPD instrument at ISIS [5]. As piperidine is liquid under ambient conditions, piperidine-d_{11} was poured into a liquid nitrogen chilled stainless steel mortar [6] and cold-ground before being loaded into a rectangular aluminium sample can fitted with a heater. The sample was then placed in a cryostat held at 100 K. After confirming the sample was in the known phase, the temperature was reduced to 2 K and data collected at this temperature. Data were then collected in 5 K steps from 5 K to 250 K; there was no indication of a phase transition in this range. No evidence of a pre-melting transition was found on increasing the temperature further to 255 K.
In order to investigate the possibility of a second phase close to the melting point, the sample was removed from the cryostat and allowed to melt. It was then transferred to a cylindrical vanadium can containing glass wool (to promote formation of a randomly-oriented powder) before being placed in a cryostat held at 245 K. This should have been well above the transition temperature (239 K) reported in ref. [3], however upon crystallisation the known low temperature phase was obtained.
Quenching a similar sample of piperidine in liquid nitrogen also resulted in the sample crystallising into the same phase. No evidence for a second phase of piperidine was observed.
High pressure measurements
Ambient temperature, high pressure neutron powder diffraction data were collected using the time-of-flight technique on the PEARL beamline high pressure facility at ISIS [7,8]. Piperidine-d_{11} was contained in a null-scattering Ti-Zr alloy capsule gasket [9] and loaded into a Paris-Edinburgh press [10-12]. The sample was loaded with powdered silica wool as previous work has shown it to aid formation of a well-oriented powder when crystallising liquids in situ; a small pellet of lead was included as a pressure marker. The pressure was calculated from the refined lead cell parameter using a Birch-Murnaghan equation of state [13,14] with V _{0} = 30.3128 Å^{3}, B = 41.92 GPa, B’ = 5.72. These parameters were derived by Fortes [15,16] by refitting data obtained in three earlier studies [17-19].
On increasing the pressure to 0.22 GPa the sample crystallised in the monoclinic phase observed at low temperature. Diffraction data were collected at 0.22, 0.49, 0.80, 1.09 and 1.36 GPa for ca 700 μA h, with shorter (ca 100 μA h) collections at 2.06 and 2.77 GPa. Peak broadening was pronounced above 1.09 GPa, because of the lack of a hydrostatic medium, and therefore the sample was decompressed to approximately 0.23 GPa. Over a period of four hours the pressure decreased slightly resulting in the sample melting. Recompressing the sample to 0.30 GPa resulted in the sample recrystallising in the same phase.
Structure refinement
Crystal and refinement data
Pressure (GPa) | 0.22 | 0.49 | 0.80 | 1.09 | Ambient |
Temperature (K) | 298 | 298 | 298 | 298 | 2 |
Chemical formula | C_{5}D_{11}N | C_{5}D_{11}N | C_{5}D_{11}N | C_{5}D_{11}N | C_{5}D_{11}N |
M_{r} | 96.17 | 96.17 | 96.17 | 96.17 | 96.17 |
Cell setting, space group | Monoclinic, P2_{1}/c | Monoclinic, P2_{1}/c | Monoclinic, P2_{1}/c | Monoclinic, P2_{1}/c | Monoclinic, P2_{1}/c |
a, b, c (Å) | 8.6994(17), 5.2552(9), 11.9045(16) | 8.5969(12), 5.2010(7), 11.7936(12) | 8.5150(14), 5.1577(8), 11.6988(14) | 8.4452(15), 5.1204(9), 11.6181(16) | 8.59695(4), 5.21506(2), 11.93271(4) |
α, β, γ (°) | 90, 96.468(17), 90 | 90, 96.507(14), 90 | 90, 96.532(15), 90 | 90, 96.558(17), 90 | 90, 96.8790(4), 90 |
V (Å^{3}) | 540.77(16) | 523.93(12) | 510.45(13) | 499.11(14) | 531.135(4) |
Z | 4 | 4 | 4 | 4 | 4 |
D_{calc} (g cm^{−3}) | 1.181 | 1.219 | 1.251 | 1.280 | 1.203 |
Diffractometer | PEARL, ISIS | HRPD, ISIS | |||
Collection method | Time of flight | Time of flight | Time of flight | Time of flight | Time of flight |
Fitted range of d (Å) | 0.75 – 4.17 | 0.75 – 4.17 | 0.75 – 4.17 | 0.75 – 4.12 | 0.83 – 2.51 |
R_{p} (%) | 5.329 | 4.484 | 4.370 | 4.363 | 4.626 |
R_{wp} (%) | 4.226 | 3.485 | 3.265 | 3.396 | 5.589 |
S | 1.294 | 1.432 | 1.344 | 1.395 | 1.544 |
Background | 9 term Chebychev polynomial | 6 term Chebychev polynomial | |||
Profile function | Back-to-back exponential convoluted with Voigt function | ||||
Number of parameters | 42 | 42 | 42 | 42 | 74 |
During refinement of the data collected at 2 K the piperidine molecules were treated using the Z-matrix formalism in TOPAS-Academic. Bond lengths and angles were refined, though all C-D distances were constrained to be equal. Anisotropic displacement parameters were modelled using the TLS formalism [23,24]. In spite of cold-grinding it was necessary to include a fourth order spherical harmonic correction for preferred orientation. The Rietveld refinement profile is shown in Figure 1c with crystal and refinement data given in Table 1. Pawley fits [25] were carried out on the rapid-scan data to obtain the lattice parameters.
DFT calculations
DFT calculations were performed on piperidine-d_{11} using the plane-wave pseudopotential method in the CASTEP code [26] as incorporated into Materials Studio version 7 [27]. The PBE exchange-correlation functional [28] was used with norm-conserving pseudopotentials and a basis set cut-off energy of 950 eV. Brillouin zone integrations were performed with a Monkhorst-Pack [29] k-point grid spacing of 0.07 Å^{−1}, corresponding to a grid of 2 × 3 × 1 points. These parameters gave an energy convergence of < 0.1 meV/atom.
For analysis of the effect of pressure and temperature on intermolecular interactions geometry optimisations were carried out while holding the unit cell parameters fixed to those observed experimentally. The total energy convergence tolerance was 5×10^{−6} eV/atom, with a maximum force tolerance of 0.01 eV Å^{−1} and a maximum displacement of 5×10^{−4} Å. The SCF convergence criterion was 5×10^{−7} eV/atom, and the space group symmetry was retained during geometry optimisation.
For frequency calculations, the geometry optimisation was carried out in two stages. The coordinates and unit cell dimensions were optimised using the Tkatchenko-Scheffler correction for dispersion (DFT-D) [30,31] starting from the experimentally determined structure determined at 2 K. The convergence criteria at this stage were the same as those given above with the additional requirement of a maximum stress tolerance of 0.02 GPa. The optimised cell parameters and volume were: a = 8.537417 [expt at 2 K: 8.59695(4)] Å, b = 5.169532 [5.21506(2)] Å, c = 11.923783 [11.93271(4)] Å, β = 96.834764 [96.8790(4)]° and V = 522.509783 [531.14(1)] Å^{3}, reproducing the cell dimensions to within 1% and the volume to 1.6%. Linear response [32] calculations are not yet possible in CASTEP with dispersion-corrected functionals, and so a second stage of optimisation was carried out with the pure PBE functional holding the cell dimensions fixed. At this stage the energy convergence tolerance was 5×10^{−7} eV/atom, with a maximum force tolerance of 0.002 eV Å^{−1} and a maximum displacement of 5×10^{−5} Å; the SCF convergence criterion was 5×10^{−10} eV/atom. The maximum force on any atom at convergence was 0.00012 eV Å^{−1}. Phonon density-of-states and dispersion curves were calculated with Fourier interpolation [33]. No imaginary frequencies were observed at any point in the Brillouin zone. Generation of structures distorted along phonon modes was accomplished with MODE_FOLLOW [34].
PIXEL calculations
Electron densities were calculated using Gaussian09 [35] at the MP2 level of theory with the 6-31G** basis set using molecular geometries derived from the crystal structures. The PIXEL method [36-40], as implemented in the program OPiX [41], was then used to calculate the intermolecular interaction energies.
Other programs used
Structures were visualised with XP [42], MERCURY [43] and DIAMOND [44]. Strain tensor calculations were carried out using a locally written program [45], based on the discussion by Ohashi and Burnham [46,47] and employing the JACOBI subroutine Numerical Recipes [48]. Equation-of-state calculations were performed using EOSfit [49]. ORIGIN was used for fitting of the unit cell parameters to variable temperature unit cell data. Animated GIFs were created from images generated in MERCURY using the web-site http://www.gifmaker.me/#003.
Results and discussion
The crystal structure of piperidine has been previously determined from X-ray data at 150 K. Variable temperature neutron powder diffraction revealed the structure exists between 2 K and 255 K. Attempts to access another phase by crystallisations via rapid cooling to 245 K and 77 K were not successful. Crystallisation via the application of pressure resulted in the same phase as obtained at low temperature. No phase transitions were evident upon compression to 2.77 GPa.
The crystal structure of piperidine
Intermolecular contact distances in piperidine-d _{ 11 } as determined by neutron powder diffraction, and molecule-molecule contact energies E estimated in PIXEL calculations
Contact | Symmetry operation | − E _{ COUL } / kJmol ^{ −1 } | − E _{ POL } / kJmol ^{ −1 } | − E _{ DISP } / kJmol ^{ −1 } | E _{ REP } / kJmol ^{ −1 } | − E _{ TOT } / kJmol ^{ −1 } | Distance/Å | Distance/Å | Distance/Å |
---|---|---|---|---|---|---|---|---|---|
T or P | T = 2 K | P = 0.22 GPa | P = 1.09 GPa | ||||||
Contacts formed within H-bonded chains | |||||||||
1. N1…H1-N1 | [−x + 1,y − ½, −z + ½] | 30.5 | 11.8 | 19.2 | 38.9 | 22.7 | 2.141(3) | 2.18 | 2.09 |
2. N1-H1…N1 | [−x + 1,y + ½, −z + ½] | 30.5 | 11.8 | 19.2 | 39 | 22.6 | 2.141(3) | 2.18 | 2.09 |
3. C1-H2…H5 | [x,y + 1,z] | 4.2 | 1.9 | 15.5 | 13.4 | 8.2 | 2.365(6) | 2.41 | 2.27 |
4. C2-H5…H2 | [x,y − 1,z] | 4.2 | 1.9 | 15.5 | 13.4 | 8.2 | 2.365(6) | 2.41 | 2.27 |
Contacts formed between H-bonded chains | |||||||||
5. C2-H4…H2 | [−x + 2,y − ½, −z + ½] | 2.2 | 1.2 | 12.1 | 9.5 | 6.0 | 2.373(9) | 2.42 | 2.31 |
6. C1-H2…H4 | [−x + 2,y + ½, −z + ½] | 2.2 | 1.2 | 12.1 | 9.5 | 6.0 | 2.373(9) | 2.42 | 2.31 |
7. C4-H8…H6 | [−x + 2, −y, −z + 1] | 2.4 | 1.0 | 11.2 | 8.8 | 5.7 | 2.446(14) | 2.49 | 2.38 |
8. C5-H11…H9 | [−x + 1, −y, −z + 1] | 3.0 | 1.5 | 10.5 | 9.7 | 5.4 | 2.382(13) | 2.44 | 2.26 |
9. C5-H10…H3 | [x, −y + ½,z + ½] | 1.1 | 0.4 | 6.8 | 3.9 | 4.4 | 2.588(9) | 3.04 | 2.51 |
10. C1-H3…H10 | [x, −y + ½,z − ½] | 1.1 | 0.4 | 6.8 | 3.9 | 4.4 | 2.588(9) | 3.04 | 2.51 |
11. C4-H8…H5 | [x, −y − ½,z + ½] | 1.7 | 0.7 | 8.0 | 6.3 | 4.1 | 2.443(6) | 2.51 | 2.33 |
12. C2-H5…H8 | [x, −y − ½,z − ½] | 1.7 | 0.7 | 8.0 | 6.3 | 4.1 | 2.443(6) | 2.51 | 2.33 |
The effect of temperature on the structure of piperidine
Fitting of volume versus temperature data using equation (5) yields values of θ, V(T _{0}) and X which can be interpreted in terms of vibrational, structural and heat capacity data.
Einstein model fitting parameters
X _{ 0 } /Å or Å ^{ 3 } | X _{ 1 } /Å or Å ^{ 3 } | X _{ 2 } /Å or Å ^{ 3 } | Θ _{ 1 } /K | Θ _{ 2 } /K | |
---|---|---|---|---|---|
V | 531.142(13) | 12.4(3) | 116(7) | 101.6(14) | 773(18) |
a | 8.59703(13) | 0.108(3) | 1.52(16) | 118(2) | 936(33) |
b | 5.21490(4) | 0.0481(12) | 0.40(3) | 117.1(17) | 791(22) |
c | 11.93275(9) | 0.0246(16) | 0.090(8) | 48(2) | 431(33) |
Structures of piperidine were optimised by periodic DFT using cell dimensions fixed to the experimentally-determined values at 2 K and in 25 K steps from 25 K to 250 K. The resulting structures were then combined into a movie, available in the Additional file 2: Movie S1, enabling the thermal expansion to be visualised. The H-bonded chains are arranged in rows which run parallel to c; these rows move apart as temperature is increased. Interestingly, the largest expansion component is the one approximately aligned with the axis (a) associated with the largest Einstein temperatures given in Table 3; similarly the smallest component lies approximately along c, which is associated with the smallest Einstein temperatures. In part, this may be the result of applying Equ. 5 to cell dimension data, when it strictly applies only to volume. However, the strain tensors components obtained from the variable temperature and pressure experiments adopt a similar alignment, suggesting that the anisotropy of thermal expansion is determined by the compressibility of the structure along different directions (see below).
The effect of pressure on the unit cell dimensions of piperidine
Comparison of eigenvalues and eigenvectors of the temperature and pressure induced strain tensors
T (255 K versus 2 K) | P (0.22 GPa versus 0.80 GPa) | ||
---|---|---|---|
Eigenvalue | Eigenvector | Eigenvalue | Eigenvector |
−0.026281(14) | [0.113 0.000 0.021] | −0.0213(3) | [0.115 0.000 0.016] |
−0.019036(10) | [0.000 0.188 0.000] | −0.0186(2) | [0.000 0.190 0.000] |
−0.011088(16) | [−0.016 0.000 0.081] | −0.01725(17) | [−0.009 0.000 0.083] |
The bulk modulus (B) refined for a third order Birch-Murnaghan equation of state [14] is 6.4(4) GPa, though the data-set used to calculate this quantity is admittedly rather limited. The values of V _{0} and B’ refined to 557.0(15) Å^{3} and 8.2(8) respectively (χ^{2} = 0.74). Molecular solids typically have B < 30 GPa and the following B values are useful for comparison [62]: Ru_{3}(CO)_{12} 6.6 GPa, L-alanine [63] and salicylaldoxime [64] 13.3 GPa, NaCl 25 GPa, quartz 37 GPa, ceramics 50–300 GPa and diamond 440 GPa. Piperidine is thus quite soft compared to other hydrogen bonded materials.
The effect of pressure on the structure of piperidine
The neutron powder diffraction data obtained at elevated pressure were of medium resolution and modest statistical precision, and during structure refinement the piperidine molecules were treated as rigid bodies with bond distances and angles taken from the X-ray structure at 150 K. To test the validity of the rigid-body assumption, the experimental structures were optimised using periodic DFT, holding the unit cell dimensions fixed to experimental values. Such calculations have been shown to reproduce experimentally determined atomic positions with crystal packing similarity values^{a} of < 0.1 Å [65]. For piperidine, crystal packing similarities [43,66] of the experimental and optimised structures were between 0.021 and 0.037 Å, confirming that the rigid-body assumption is reasonable.
Over the course of the first one or two kbars of applied pressure, provided the symmetry remains unchanged and volume changes are small, the path of compression might be expected to follow the path of a low-energy lattice vibration. Specifically, the mode would be expected to lie at the Γ-point and belong to the totally symmetric representation, in the present case, where the lattice point symmetry is 2/m, A _{1g}. The lowest totally symmetric phonon, which has a calculated frequency of 36 cm^{−1} is shown as an animation in the Additional file 4: Movie S3a) and can be compared to a sequential animation of the structures obtained at 0.22 and 0.49 GPa (Additional file 4: Movie S3b). The similarity between the two animations is striking, suggesting that structure determinations at pressures of a few kbar can potentially be used to visualise low-frequency phonons.
Comparison of the effects of pressure and temperature
The strain induced by cooling or compression is characterised by similarly orientated strain tensors, with largest principal axis lying approximately along a, the middle lying exactly along b and the smallest approximately along c (Figure 3c). Though the principal axes are similarly orientated, the tensor describing the response to pressure is more isotropic.
In an attempt to gain some insight into the structural reasons for these similarities and differences the DFT-optimised structure at 0.22 GPa was reoptimised with first the a and then the c axis reduced in length by 5%. PIXEL calculations were then carried out on all three optimised structures, referred to as ‘opt’, ‘A’, and ‘C’ respectively. The lattice energies were −55.2, −53.8 and −53.1 kJ mol^{−1}, respectively; though the differences between these figures are small, they are consistent with the greater compressibility along a. The H-bond energies (kJ mol^{−1}) are −21.7 (opt), −21.4 (A) and −21.9 (C), indicating that compression along c actually stabilises the H-bonds, while compression along a destabilises them. The H-bond distances (Å) are opt 2.136, A 2.074 and C 2.111, and though in both A and C the electrostatic term is more negative as a result of the shorter N…H distance, it is outweighed by a more positive repulsion term in A.
Conclusions
We have explored the crystal structure of piperidine under a range of different conditions of temperature and pressure. Although a previous study had indicated another phase exists, no new phases have been identified here, and it is possible that the alternative phase identified by Parkin on the basis of cell dimensions was a metastable form. The crystal structure of piperidine is characterised by chains of molecules linked by NH…N hydrogen bonds which are disposed about a 2_{1} axis running along b. The unit cell of the metastable phase has a b axis length very similar to that of the b-axis of the phase discussed in this paper, and both phases are likely to feature similar H-bond chains. Though our original crystal growth experiments and DSC measurements indicated formation of a metastable form, there is no mention of transitions in the report of heat capacity measurements in ref. [52], and it is possible that its formation is dependent on rather specific crystallisation conditions which remain unidentified. Deuteration is also known to influence formation of alternative phases [67].
Though the H-bonds have a characteristic and easily recognisable structural signature, the same is not true of van der Waals interactions [68], but their influence can be appreciated with the aid of packing energy calculations, such as the PIXEL method used here. In the case of piperidine, though H-bonds are the most energetic contacts, around 60% of the sublimation enthalpy is the result of van der Waals interactions in which individual interatomic distances teeter on the brink of insignificance when assessed in the conventional manner using van der Waals radii.
Periodic DFT calculations reproduce the experimental cell dimensions of piperidine at 2 K to within 1%. The phonon frequencies calculated using this optimised structure, though they are obtained on the basis of a harmonic model for the energies of small atomic displacements, also reproduce experimental heat capacity data well. These calculations enable the thermal expansion of piperidine to be understood in terms of a simple quantitative model for how energy in the form of heat is absorbed into lattice vibrations.
The response of piperidine to pressure is superficially similar to its response to cooling. Although the principal directions of strain are essentially the same under both sets of varying conditions, the tensor describing the strain developed under pressure is more isotropic. PIXEL calculations demonstrate that the energetic imbalance between the weak van der Waals interactions and the relatively strong H-bonds determines the anisotropy of the strain tensor on cooling. Under pressure the need to fill space efficiently competes with minimisation of free energy though intermolecular contacts, making the strain less anisotropic.
Endnote
^{a}This is a parameter quantifying the similarity of two crystal structures, and it is defined as the root-mean square deviation calculated for a cluster of 15 molecules taken from each structure. Crystal packing similarities were calculated in MERCURY.
Declarations
Acknowledgements
We thank STFC and ISIS through The Centre for Molecular Structure and Dynamics and EPSRC for studentship funding to LEB. We also thank the ISIS Facility for provision of neutron beam time on the HRPD and PEARL instruments. We also thank the referees for their careful reading of the manuscript.
Authors’ Affiliations
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