research papers
A
between benzene and ethane: a potential evaporite material for Saturn's moon TitanaBragg Institute, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia, bJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA, and cChemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853, USA
*Correspondence e-mail: helenmc@ansto.gov.au
Using synchrotron X-ray powder diffraction, the structure of a in situ at cryogenic conditions has been determined, and validated using dispersion-corrected density functional theory calculations. The structure comprises a lattice of benzene molecules hosting ethane molecules within channels. Similarity between the intermolecular interactions found in the and in pure benzene indicate that the C—H⋯π network of benzene is maintained in the however, this expands to accommodate the guest ethane molecules. The has a 3:1 benzene:ethane stoichiometry and is described in the with a = 15.977 (1) Å and c = 5.581 (1) Å at 90 K, with a density of 1.067 g cm−3. The conditions under which this forms identify it is a potential that forms from evaporation of Saturn's moon Titan's lakes, an evaporite material.
between benzene and ethane formed1. Introduction
Crystallographic studies of benzene have a history of moving scientific understanding significantly forward. Kathleen Lonsdale's pioneering work on the structure of hexamethylbenzene showed the community that the benzene molecule was flat (Lonsdale, 1929), a study which, at least in part, laid the groundwork for molecular crystallography as we know it today. Later studies of the of pure benzene (Cox et al., 1958) showed that the flat benzene rings fit together like `six-tooth bevel gear wheels' (Cox, 1932).
There is now growing interest in the structures of many simple hydrocarbons for a different reason. Titan, Saturn's largest moon, has in recent years been revealed, largely by the on-going Cassini mission, to have a `hydrological' cycle. Unlike the Earth's hydrological cycle, Titan's is not driven by water. The surface temperature on Titan is 91–95 K, and at these cryogenic temperatures the fluids that drive the cycle are small hydrocarbon molecules (Stofan et al., 2007) such as methane and ethane, as well as dissolved dinitrogen. Lakes and seas observed on the surface of Titan contain a mixture of methane and ethane (Cordier et al., 2009), which result from cloud formation and precipitation in the atmosphere. Additionally, there are a number of other small molecular species observed in the atmosphere, which are hypothesized to be present at Titan's surface. These include organic molecules such as hydrogen cyanide, acetylene, ethylene, acetonitrile and benzene, formed photochemically from CH4 and N2 in the upper atmosphere (Vuitton et al., 2008). In particular, benzene has been tentatively identified on the surface of Titan by the Huygens probe (Niemann et al., 2005).
The observation of Titan's hydrological cycle now encompasses lakes, seas, clouds and even rain of hydrocarbons – but it has been missing a vital piece. In light of the cycle observed at the surface, it is natural to ask whether Titan's surface materials could produce deposits analogous to evaporites on Earth. Cassini imagery has collated evidence for possible evaporite deposits (Barnes et al., 2011), but it remains a mystery as to what these materials could be made of. This is despite the important role that such materials would play in both the hydrological cycle and the surface chemistry of Titan.
In light of the discovery of Titan's hydrological cycle, investigations have been undertaken to identify possible evaporite materials that would form on the surface. Recent results with Raman spectroscopy (Cable et al., 2014; Vu et al., 2014) on the interaction of small molecules under Titan surface conditions identified the formation of a possible between benzene and ethane. Although spectroscopy and quantum-chemical calculations pointed to a specific local interaction between ethane and benzene molecules in the a crystallographic study is required to determine the structure unambiguously and consequently the composition of the as well as to ascertain its viability as an evaporite material on Titan.
2. Materials and methods
2.1. growth and data collection
Previous microscopic observations of the possible et al., 2014). Hence, we decided to pursue a powder X-ray diffraction study, using the high-resolution afforded by a synchrotron source. Approximately 2 µl of benzene (Sigma Aldrich 99.8%) was placed inside a 0.7 mm borosilicate capillary. The amount of benzene was tailored so that the length of the drop within the capillary was ∼ 2 mm. The capillary was then attached via a Swagelok fitting (Norby et al., 1998) to a valve allowing the system to be closed, and mounted on the powder diffraction beamline at the Australian Synchrotron (Wallwork et al., 2007), along with an Oxford Cryosystems cryostream (Cosier & Glazer, 1986) to control the sample temperature. The beamline was set up with λ = 0.826 (1) Å, verified by of a pattern measured from NIST LaB6 (SRM 660b) powder standard. The X-ray beam from the synchrotron is vertically focused to a height of 1 mm, and the width of the beam was constrained to 3 mm with lead slits. A MYTHEN strip detector (Bergamaschi et al., 2010) was used for all data collections.
showed that, on formation, the crystallite sizes were significantly reduced compared with that of frozen benzene (VuThe benzene within the capillary was frozen, and a diffraction pattern was measured at 170 K (Fig. 1; blue trace). The position of the capillary was then translated so that the edge of the frozen benzene was aligned with the centre of the X-ray beam, and the capillary system was attached to a bottle of ethane (Sigma Aldrich 99.9%). The temperature was reduced to 130 K, and ethane liquid was condensed adjacent to the frozen benzene. The interface was then monitored and cycling of the temperature between 130 and 90 K produced diffraction peaks additional to those of benzene, indicating the formation of the benzene:ethane (Fig. 1; red trace). These additional peaks cannot be attributable to solid ethane, which freezes at 89 K. The formation of the using this protocol was independently verified by Raman spectroscopic measurements (see the supporting information), in which a characteristic Raman feature at 2873 cm−1 (Vu et al., 2014) appears on warming the system from 90 to 130 K. Once the was formed at 130 K, the temperature was reduced to 90 K for a longer data acquisition. Acquiring the pattern at 90 K serves to minimize thermal motion in the and the longer acquisition time also revealed the signal from weaker peaks that may have been missed in the previous shorter acquisitions. The process of forming the was repeated and the result was verified.
To investigate the et al., 2014), and the smaller temperature intervals around this temperature allowed us to monitor the decomposition.
and stability properties of the sequential patterns (collected over 120 s) were taken at 5 K intervals from 90 K to 150 K, then at 1 K intervals to 170 K. Previous results had suggested that the would only be stable until ∼ 160 K (Vu2.2. Computational methods
Once the structure of the ), periodic DFT calculations were performed using VASP (Version 5.3.5; Kresse & Furthmüller, 1996; Kresse & Joubert, 1999) to validate the result. The Perdew–Burke–Ernzerhof (PBE; Perdew et al., 1996) GGA functional was used in combination with the DFT-D3 dispersion correction (Grimme et al., 2010), standard projected augmented wave (PAW) potentials (Kresse & Joubert, 1999; Blöchl, 1994) and a plane-wave energy cutoff of 800 eV. sampling was performed on a Monkhorst–Pack mesh, which spanned 3 × 3 × 9 k-points for the single Energies and forces were converged to < 1 meV per atom.
was established (as described in §3Molecular calculations were performed using ORCA 3.03 (Neese, 2012). The gas-phase geometry of the {C2H6–(C6H6)6} cluster was optimized at the PBE-D3(BJ)/Def2-TZVPP level of theory. Vibrational analysis at the same level of theory showed the geometry to be dynamically stable, and provided zero-point energy corrections. Single-point energy calculations were performed using the second-order perturbation corrected `double hybrid' density functional B2PLYP (Grimme, 2006) again together with the D3(BJ) dispersion correction (Grimme et al., 2011) and in conjuction with the RIJCOSX approximation (Neese et al., 2009) and auxillary def2-TZVPP/J and def2-TZVPP/C basis sets for separate coulomb and semi-numeric exchange integration. B2PLYP-D3(BJ) are expected to provide highly accurate energies. Specifically for intermolecular interactions, the reported mean absolute deviation is 1.2 kJ mol−1 (Grimme, 2011).
3. Results
Working with the diffraction pattern taken at 90 K, the peaks not attributed to benzene were fitted with pseudo-Voigt functions using TOPAS4.1 (Coelho, 2008) then indexed to an R-centred with a = 15.977 (1), c = 5.581 (1) Å, which gives a volume of 1233.8 Å3. Pawley (Pawley, 1981) in the R3 yielded wR = 0.031 and a goodness of fit (GoF) of 3.56. indicated either or Laue groups, giving five possible space groups: R3, , R32, R3m and . To begin our analysis of the the space groups (R32, R3m and ) were ruled out as they would require a disordered structure to accommodate the benzene and ethane molecules. It was noted that there were still a number of small peaks that were not accounted for, as shown in Fig. 2. Further investigation indicated that these peaks persisted after the melted in the first run but that they were not observed during the second run of the experiment. Hence, these peaks were judged not to belong to the and were not considered further in the structure solution process. Attempts were made to index these additional peaks, but at most 13 of them were identified (from the pattern collected at 160 K), which proved insufficient to determine a for this potentially new phase.
The determined volume of the −3 (van Nes & Vos, 1978) and benzene at 90 K is 1.103 g cm−3 (Bacon et al., 1964), so as a first assumption it was thought that the density of the would lie between these values. Also considering the trigonal there are only three possible combinations: a 1:1 benzene:ethane with six formula units per a 2:1 with three formula units, and a 3:1 also with three formula units. Unusual circumstances (i.e. the density of the being lower than that of ethane or higher than that of benzene) could also have been pursued, if the structure solution using these potential contents had not been successful. To minimize the number of during the structure solution process, the benzene and ethane molecules were constructed as rigid bodies, details of which are given in the supporting information. The arrangement of the rigid bodies was optimized against the 90 K pattern (Fig. 1), using a parallel-tempering algorithm within the Free Objects for Crystallography (FOX) program (Favre-Nicolin & Černý, 2002). The first co-crystallization run was used for the structure solution as the proportion of formed (relative to the residual benzene) was higher. Prior to the minimization, a Le Bail (Le Bail, 2005) of benzene was also undertaken in FOX to account for the peaks from this material in the pattern, the results of which were added to the parallel-tempering calculation. This process was undertaken for each of the three possible contents identified and in both potential space groups (R3 and ).
placed constraints on the likely contents and stoichiometry of the structure. The density of ethane in its solid phase at 89 K is 0.669 g cmA viable ) using TOPAS4.1 (Coelho, 2008), giving the fit shown in Fig. 3. The parameters varied for this were a scale factor, a background function, a zero error to account for displacement of the capillary, a single broad peak to account for the scattering of the borosilicate capillary, the lattice parameters for both of the phases, and the orientation and translation of the two rigid units used to build the structure (details given in the supporting information). Diffraction from the pure benzene in the pattern was described with the structure determined by Cox et al. (1958), with the atoms fixed to these positions. Additionally, to account for the in the pure benzene phase, a fourth-order spherical harmonic model was added. Peak-shape parameters (Thompson–Cox–Hasting model; Thompson et al., 1987) determined from the Pawley were used, but fixed for the structural with crystallite size refined. Additional pseudo-Voigt peaks were also entered into the to account for the intensity of the small peaks that were revealed at the indexing stage, as shown in Fig. 2. Atomic displacement parameters were constrained to be the same for the atoms within the benzene and ethane molecules, respectively. Table 1 lists the refined atomic coordinates for the The resultant density is 1.067 g cm−3 at 90 K, slightly less dense than solid benzene at 90 K (1.103 g cm−3). The determined H-atom positions are solely from geometric placement within the rigid bodies that were generated to solve the structure.
(judged by intermolecular distances and fit to the observed data) was obtained only for the 3:1 benzene:ethane model, with three formula units in the This structure was subjected to (Rietveld, 1969
|
Fourier difference methods were used to determine whether there was any systematic electron density not accounted for by the structure. Structure factors were extracted from the , and an |F(obs)| − |F(calc)| calculation was performed in the VESTA program (Momma & Izumi, 2008). The largest negative feature had a density of −0.02 e Å−3 and was situated between the ethane and benzene molecules; the largest positive feature was 0.05 e Å−3, which correlated with the C-atom positions within the ethane molecules. Given the small magnitude of the Fourier difference features, disordered models of the were not explored.
as presented in Fig. 3The model for the 3:1 benzene:ethane was also fitted (with the same procedure) to the pattern collected from the second formation of the at 90 K. Details of this fit are presented in the supporting information.
presented in Table 1Confirmation of the structure was sought from energy-minimization calculations. The periodic DFT calculations undertaken (results of which are detailed in the supporting information) include dispersion corrections and predict a structure in excellent agreement with the experimental determination of the benzene:ethane structure. The unit-cell volume is 1234 Å3 from experiment and 1206 Å3 on minimization, differing by only 2%. Additionally, molecular calculations on a dispersion-bound C2H6–(C6H6)6 cluster (Fig. 4) predict it to be vibrationally stable also in isolation, with a quite substantial binding energy of 108 kJ mol−1 near 0 K.
Using the model of the (a) shows how the lattice parameters vary over the temperature range. From this, it can be seen that the structure exhibits significant anisotropic with the majority of the expansion occurring along the a and b axes.
provided by the experimental structure solution process, each of the patterns from 90 to 165 K was refined and the lattice parameters and proportion of each phase (either benzene or co-crystal) were extracted from each pattern. Fig. 5The stability of the (b), which charts the relative proportion of the benzene and refined in each diffraction pattern collected; the patterns measured between 150 and 170 K are presented in Fig. 5(c). The proportion of to benzene in the patterns is steady at ∼ 89% and ∼ 11% benzene from 90 to 145 K. Above 145 K, the proportion of the in the refined pattern decreases monotonically. This is consistent with previous observations of the decomposition of the at elevated temperatures (Cable et al., 2014; Vu et al., 2014). It is likely that, given sufficient time, above 145 K the would decompose entirely without any increase of temperature.
structure is demonstrated by Fig. 54. Discussion
Inspection of the π interactions very similar to those found in crystalline benzene. Fig. 6 compares the benzene (as determined by Bacon et al., 1964) with the benzene:ethane The ring of six benzene molecules around each of the ethane molecules is a feature that is `inherited' from the pure benzene structure. In the the ethane molecules replace a quarter of the benzene molecules, and the benzene molecules move into a symmetry arrangement. This creates one-dimensional channels through the structure where the ethane molecules reside on the axes. Crucially, the benzene molecules maintains very similar C—H⋯π interactions (as shown by the distances highlighted in Fig. 6) compared to those in pure benzene.
over a number of unit cells shows that the structure is maintained by a network of C—H⋯The similarities between the benzene:ethane . Additionally, the structure is compared with the only other between benzene and a small hydrocarbon, namely a 1:1 benzene:acetylene (Boese et al., 2003). This shows how the C—H⋯π interactions between the benzene molecules create planes that run through both the benzene:ethane and the benzene structure. The higher symmetry of the benzene:ethane means that the benzene interactions create the channels parallel to the c axis where the ethane molecules are situated. The interactions in the benzene:ethane and pure benzene are in stark contrast to the intermolecular interaction in the 1:1 benzene:acetylene Here, the benzene molecules are arranged so that they do not interact with each other, and instead are seen to form C—H⋯π interactions with the acetylene molecules which sit perpendicular to the benzene rings.
and pure benzene are explored further in Fig. 7The similarity in the arrangement of benzene molecules in the et al. (2014), which are summarized in Table 2. The Raman modes of the benzene molecules show only modest shifts, of 0.3 cm−1 for ν1 and −3.1 and −1.8 cm−1 for ν7, indicating that the interactions of the molecules remain largely unchanged. This contrasts starkly with the observed changes in the Raman shifts of the ethane molecules in the from the pure (liquid) form at 90 K. This, itself, is perhaps not surprising but the co-crystal's ethane molecule Raman modes show a significant shift compared to that seen in solid ethane at 80 K [−4.4 cm−1 for ν1(a1g) and −6.7 cm−1 for ν11(eg)]. In the absence of the crystalline structure, Vu et. al. (2014) used electrostatic potential surface calculations of three benzene–ethane dimers to rationalize the origin of these Raman shifts. This previous work found the largest shift for the ethane molecules among the dimers studied to be −7 cm−1, arising from a monodentate interaction between the benzene and ethane molecules. These shifts can now be discussed in light of the structure.
and in its pure form is echoed in the experimental Raman shifts observed by Vu
|
The first point arising is that the experimental Raman shifts are not due to specific C—H⋯π interactions between the ethane and benzene molecules in the The closest distance between an ethane H atom and the centre of a benzene ring is 4.15 (3) Å. This distance is large, compared with the C—H⋯π distance of 2.447 Å in the benzene:acetylene (Boese et al., 2003), the closest H(benzene)⋯benzene ring centroid distance in the structure of 2.77 (3) Å, and the furthest C—H⋯π distance of 3.57 Å calculated by Vu et al. for a tridentate dimer between benzene and ethane. The next point is considering the orientation of the ethane molecules within the `channels' of symmetry between the benzene rings (Fig. 6). It is interpreted that the ethane molecules are in a more constrained local environment within the than in the monoclinic form of pure ethane (van Nes & Vos, 1978). This places more constraints on the motion of the ethane molecules, generating the noted experimental Raman shift.
The quantum mechanical calculations on the isolated subunit of ethane surrounded by six benzene molecules (Fig. 4) illustrates how effectively the arrangement of benzene molecules around each ethane molecules in the maximizes the number of favourable C—H⋯π contacts beyond what is possible in pure benzene, or other co-crystals (Fig. 7). This specific coordination geometry allows for quite sizable dispersion (van der Waals) interactions (binding energy ∼ 108 kJ mol−1 of this cluster). Due to the relatively high association strength of this supramolecular entity, and its expected consequential persistence in solution at low temperature, we can speculate that it is one plausible seed structure in the build-up of the co-crystal.
The determined . This arises because the C—H⋯π interactions are aligned closer to the a and b axes in the Along the c axis, these chains of interactions interlock with each other (Fig. 7) and thereby restrict the expansion in this direction. As well as exhibiting anisotropic Fig. 8 shows that the weak C—H⋯π interactions in the lead to significantly higher relative compared to other possible Titan `minerals', methane clathrate and ammonia dihydrate, which are dominated by hydrogen bonding (Fortes et al., 2003; Belosludov et al., 2002).
structure can also explain the anisotropic noted in Fig. 5It seems likely that, given the channels the ethane molecules occupy within the benzene:ethane
the other guest species could form similar co-crystals with benzene or partially substitute for ethane within the structure. Exchange of ethane with other linear hydrocarbons, or with HCN for example, is a target for future investigations, in the hope of further enriching our picture of Titan's icy mineralogy.5. Conclusions
This study confirms the existence and structure of a 3:1 benzene:ethane π, which could shape the surface of Titan. The structure of the is substantially different from any known of benzene. It is in significant contrast to a formed between benzene and acetylene (Boese et al., 2003), where the linear acetylene molecules align perpendicular to the benzene rings. The similarity of the interactions between the and the structure of pure benzene show that the C—H⋯π network of benzene is maintained as a `host', but expanded to allow the ethane `guest' to situate within the channels that result from this network. We anticipate that this work will be followed by a number of other investigations charting the formation and stability of other small molecular species that could become Titan's `minerals' and contribute to the understanding of the geology and potential habitability of this icy moon.
The structure was solved using synchrotron powder X-ray diffraction and confirmed to be viable by dispersion-corrected DFT calculations. Conditions of the formation of this suggest that it is a candidate evaporite material that will exist on the surface of Saturn's moon Titan. It is, in fact, the first potential `cryogenic mineral' to be identified where its intermolecular interactions are not dominated by hydrogen bonding. The can therefore be presented as part of a new group of materials fused only by weak intermolecular interactions such as C—H⋯Supporting information
10.1107/S2052252516002815/bi5052sup1.cif
contains datablocks global, benzene_ethane_cocrystal, benzene, refinedPDpattern. DOI:DFT-D optimized structure for the benzene:ethane 10.1107/S2052252516002815/bi5052sup2.txt
DOI:x | y | z | Biso*/Beq | ||
C1b | 0.547 (2) | 0.000 (1) | −0.213 (2) | 1.93 (3) | |
C2b | 0.451 (2) | −0.070 (2) | −0.175 (3) | 1.93 (3) | |
C3b | 0.596 (2) | 0.071 (2) | −0.038 (2) | 1.93 (3) | |
H1b | 0.417 (2) | −0.001 (2) | 0.378 (2) | 1.93 (3) | |
H2b | 0.588 (2) | 0.125 (2) | 0.310 (3) | 1.93 (3) | |
H3b | 0.329 (2) | −0.127 (2) | 0.067 (3) | 1.93 (3) | |
C1e | 0.000 | 0.000 | 0.363 (2) | 2.2 (1) | |
H1e | −0.040 (2) | 0.031 (2) | 0.284 (2) | 2.2 (1) |
x | y | z | Biso*/Beq | ||
C1 | −0.0569 | 0.1387 | −0.0054 | 1 | |
C2 | −0.1335 | 0.046 | 0.1264 | 1 | |
C3 | 0.0774 | 0.0925 | −0.1295 | 1 | |
H1 | −0.0976 | 0.2447 | −0.0177 | 1 | |
H2 | −0.2409 | 0.0794 | 0.2218 | 1 | |
H3 | 0.1371 | 0.1631 | −0.2312 | 1 |
Acknowledgements
We acknowledge the Australian Synchrotron for the award of beamtime EPN 3200 and Justin Kimpton for his assistance during the experiment. Calculations presented in this work used the Extreme Science and Engineering Discovery Environment (XSEDE) (Towns et al., 2014), which is supported by NSF grant number ACI-1053575. NSF support from grant CHE-1305872 is gratefully acknowledged. Additionally, the authors acknowledge ideas and advice from participants of the `Don't follow (Just) the water: does life occur in non-aqueous media?' workshop organized by the W. M. Keck Institute for Space Studies. RH acknowledges the support of the NASA Astrobiology Institute (Titan as a Prebiotic Chemical System) and NASA's Outer Planets Research program. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
References
Bacon, G. E., Curry, N. A. & Wilson, S. A. (1964). Proc. R. Soc. A: Math. Phys. Engineering Sci. 279, 98–110. Google Scholar
Barnes, J. W., Bow, J., Schwartz, J., Brown, R. H., Soderblom, J. M., Hayes, A. G., Vixie, G., Le Mouélic, S., Rodriguez, S., Sotin, C., Jaumann, R., Stephan, K., Soderblom, L. A., Clark, R. N., Buratti, B. J., Baines, K. H. & Nicholson, P. D. (2011). Icarus, 216, 136–140. Web of Science CrossRef CAS Google Scholar
Belosludov, V. R., Inerbaev, T. M., Subbotin, O. S., Belosludov, R. V., Kudoh, J.-I. & Kawazoe, Y. (2002). J. Supramol. Chem. 2, 453–458. CrossRef CAS Google Scholar
Bergamaschi, A., Cervellino, A., Dinapoli, R., Gozzo, F., Henrich, B., Johnson, I., Kraft, P., Mozzanica, A., Schmitt, B. & Shi, X. (2010). J. Synchrotron Rad. 17, 653–668. Web of Science CrossRef CAS IUCr Journals Google Scholar
Blöchl, P. E. (1994). Phys. Rev. B, 50, 17953–17979. CrossRef Web of Science Google Scholar
Boese, R., Clark, T. & Gavezzotti, A. (2003). Helv. Chim. Acta, 86, 1085–1100. Web of Science CSD CrossRef CAS Google Scholar
Cable, M. L., Vu, T. H., Hodyss, R., Choukroun, M., Malaska, M. J. & Beauchamp, P. (2014). Geophys. Res. Lett. 41, 5396–5401. Web of Science CrossRef CAS Google Scholar
Coelho, A. (2008). TOPAS 4.1. Bruker AXS, Wisconsin, USA. Google Scholar
Cordier, D., Mousis, O., Lunine, J. I., Lavvas, P. & Vuitton, V. (2009). ApJ, 707, L128–L131. Web of Science CrossRef CAS Google Scholar
Cosier, J. & Glazer, A. M. (1986). J. Appl. Cryst. 19, 105–107. CrossRef CAS Web of Science IUCr Journals Google Scholar
Cox, E. G. (1932). Proc. R. Soc. A: Math. Phys. Engineering Sci. 135, 491–498. Google Scholar
Cox, E., Cruickshank, D. & Smith, J. (1958). Proc. R. Soc. A: Math. Phys. Engineering Sci. 247, 1–21. Google Scholar
Favre-Nicolin, V. & Černý, R. (2002). J. Appl. Cryst. 35, 734–743. Web of Science CrossRef CAS IUCr Journals Google Scholar
Fortes, A. D., Wood, I. G., Brodholt, J. P., Alfredsson, M., Vočadlo, L., McGrady, G. S. & Knight, K. S. (2003). J. Chem. Phys. 119, 10806–10813. Web of Science CrossRef CAS Google Scholar
Grimme, S. (2006). J. Chem. Phys. 124, 034108. Web of Science CrossRef PubMed Google Scholar
Grimme, S. (2011). WIREs Comput. Mol. Sci. 1, 211–228. Web of Science CrossRef CAS Google Scholar
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. (2010). J. Chem. Phys. 132, 154104. Web of Science CrossRef PubMed Google Scholar
Grimme, S., Ehrlich, S. & Goerigk, L. (2011). J. Comput. Chem. 32, 1456–1465. Web of Science CrossRef CAS PubMed Google Scholar
Kresse, G. & Furthmüller, J. (1996). Phys. Rev. B, 54, 11169–11186. CrossRef CAS Web of Science Google Scholar
Kresse, G. & Joubert, D. (1999). Phys. Rev. B, 59, 1758–1775. Web of Science CrossRef CAS Google Scholar
Le Bail, A. (2005). Powder Diffr. 20, 316–326. Web of Science CrossRef CAS Google Scholar
Lonsdale, K. (1929). Proc. R. Soc. A: Math. Phys. Engineering Sci. 123, 494–515. Google Scholar
Momma, K. & Izumi, F. (2008). J. Appl. Cryst. 41, 653–658. Web of Science CrossRef CAS IUCr Journals Google Scholar
Neese, F. (2012). WIREs Comput. Mol. Sci. 2, 73–78. Web of Science CrossRef CAS Google Scholar
Neese, F., Wennmohs, F., Hansen, A. & Becker, U. (2009). Chem. Phys. 356, 98–109. Web of Science CrossRef CAS Google Scholar
Nes, G. J. H. van & Vos, A. (1978). Acta Cryst. B34, 1947–1956. CSD CrossRef IUCr Journals Web of Science Google Scholar
Niemann, H., Atreya, S., Bauer, S., Carignan, G., Demick, J., Frost, R., Gautier, D., Haberman, J., Harpold, D., Hunten, D., Israel, G., Lunine, J. I., Kasprzak, W. T., Owen, T. C., Paulkovich, M., Raulin, F., Raaen, E. & Way, S. H. (2005). Nature, 438, 779–784. Web of Science CrossRef PubMed CAS Google Scholar
Norby, P., Cahill, C., Koleda, C. & Parise, J. B. (1998). J. Appl. Cryst. 31, 481–483. Web of Science CrossRef CAS IUCr Journals Google Scholar
Pawley, G. S. (1981). J. Appl. Cryst. 14, 357–361. CrossRef CAS Web of Science IUCr Journals Google Scholar
Perdew, J. P., Burke, K. & Ernzerhof, M. (1996). Phys. Rev. Lett. 77, 3865–3868. CrossRef PubMed CAS Web of Science Google Scholar
Rietveld, H. M. (1969). J. Appl. Cryst. 2, 65–71. CrossRef CAS IUCr Journals Web of Science Google Scholar
Stofan, E. R., Elachi, C., Lunine, J. I., Lorenz, R. D., Stiles, B., Mitchell, K. L., Ostro, S., Soderblom, L., Wood, C., Zebker, H., Wall, S., Janssen, M., Kirk, R., Lopes, R., Paganelli, F., Radebaugh, J., Wye, L., Anderson, Y., Allison, M., Boehmer, R., Callahan, P., Encrenaz, P., Flamini, E., Francescetti, G., Gim, Y., Hamilton, G., Hensley, S., Johnson, W. T. K., Kelleher, K., Muhleman, D., Paillou, P., Picardi, G., Posa, F., Roth, L., Seu, R., Shaffer, S., Vetrella, S. & West, R. (2007). Nature, 445, 61–64. Web of Science CrossRef PubMed CAS Google Scholar
Thompson, P., Cox, D. E. & Hastings, J. B. (1987). J. Appl. Cryst. 20, 79–83. CrossRef CAS Web of Science IUCr Journals Google Scholar
Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., Hazlewood, V., Lathrop, S., Lifka, D., Peterson, G. D., Roskies, R., Scott, J. R. & Wilkens-Diehr, N. (2014). Comput. Sci. Eng. 16, 62–74. CrossRef Google Scholar
Vu, T. H., Cable, M. L., Choukroun, M., Hodyss, R. & Beauchamp, P. M. (2014). J. Phys. Chem. A, 118, 4087–4094. Web of Science CrossRef CAS PubMed Google Scholar
Vuitton, V., Yelle, R. & Cui, J. (2008). J. Geophys. Res.: Planets, 113, E10003. Web of Science CrossRef Google Scholar
Wallwork, K. S., Kennedy, B. J. & Wang, D. (2007). AIP Conf. Proc. pp. 879–882. CrossRef Google Scholar
This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.