J. MATER. CHEM., 1994, 4(11), 1731-1735 Properties of the Guest Molecules in the 1,lo-Dibromodecane/Urea Inclusion Compound A Molecular Dynamics Simulation Study Ashley R. Georgeayband Kenneth D. M. Harris*a a Department of Chemistry, University College London, 20 Gordon Street, London, UK WCI H OAJ The Royal Institution, 21 Albemarle Street, London, UK W1X 4BS A molecular dynamics (MD) simulation of the 1 ,lo-dibromodecane/urea inclusion compound has been carried out at a temperature of 300 K to investigate various local structural properties of the 1,lO-dibromodecane guest molecules within the urea tunnel structure. The bromine radial distribution function determined from the MD simulation indicates a broad distribution for the intermolecular Br.. -Br distance, but considerably narrower distributions for intramolecular Br.-.C distances.This supports information determined experimentally via bromine K-edge EXAFS spectroscopy. The MD simulation provides evidence that a small proportion of the 1,lO-dibromodecane molecules contain a gauche end-group, and provides direct evidence for the interconversion between gauche and trans end-group conformations on a timescale of the order of picoseconds. The MD simulation indicates that there is substantial dynamic disorder of the 1,lO-dibromodecane guest molecules within the urea tunnel structure. These local structural properties and dynamic properties of the 1,lO-dibromodecane guest molecules, determined from the MD simulation, are compared directly with corresponding information established via experimental approaches.Urea inclusion compounds have been investigated widely from the viewpoint of their fundamental physico-chemical proper tie^.'-^ The ‘host’ substructure in the ‘conventional’ urea inclusion compounds comprises an extensively hydrogen- bonded arrangement of urea molecules, and this structure contains a regular arrangement of one-dimensional, parallel ‘Guest’ molecules of appropriate dimensions can be accommodated within these tunnels. The cross-section of the tunnels (defined by the van der Waals s;rface of the tunnel wall) is comparatively narrow (ca. 5.5-5.8 A) and, as a conse- quence, only guest molecules based on a sufficiently long n-alkane chain and with an appropriately limited degree of substitution (e.g.a, m-dibromoalkanes [Br(CH,),Br)] can fit within these tunnels. Within the urea tunnel structure, these guest molecules must adopt a linear, extended conformation, and inclusion within the urea tunnel structure has often been used as a means of constraining molecules in such confor- mations. Importantly, these conformations may differ substan- tially from the preferred conformations of the same molecules in other solid-state environments or in dispersed phases. The urea inclusion compounds have thus been exploited as proto- typical materials for understanding the structural, dynamic and spectroscopic properties of molecules in linear, extended conformations. The physico-chemical properties of urea inclusion com-pounds containing alkane guest molecules have been studied extensively2 via a wide range of experimental techniques, although, at present, much less is known about the corre- sponding properties of urea inclusion compounds containing functionalized alkane guests.In this paper, we consider the application of MD simulation techniques to study local structural properties and dynamic properties of the 1,lO-dibromodecane [Br(CH,),,Br] guest molecules in the Br(CH2 ),,Br/urea inclusion compound, and we first review relevant experimental information on this material. The periodic repeat distance of the guest molecules along the urea tunnel (c,) is, in general, incommensurate with the periodic repeat distance of the host substructure along the tunnel; a detailed discussion of incommensurate us.commen-surate behaviour in one-dimensional inclusion compounds (typified by the urea inclusion compounds) has been given else~here.~?~The periodic repeat distance, c,, of guest mol- ecules in the :conventional’ urea inclusion compounds is always ca. 0.5 A shorter than the ‘van der Waals length’ of the guest molecule in its ‘all-trans’ conformation.’ This arises from the fact that, in the energetically most stable state of the inclusion compound, there is a repulsive interaction between adjacent guest molecules in the same t~nnel.~,~ Recent incoherent quasielastic neutron scattering studies’ of the dynamic properties of the guest molecules in Br(CH,),Br/urea inclusion compounds (n=8-10) have shown that both reorientational motions of the guest molecules about the tunnel axis and translational motions of the guest mol- ecules along the tunnel axis are effective on the picosecond timescale.The translation olength depends critically upon temperature, and is ca. 2.3 A for Br(CH,),Br/urea at 280 K. The possibility to determine dynamic properties of the guest molecules from the MD simulations carried out in this work is discussed further below. A recent Br K-edge EXAFS investigation” assessed the feasibility of determining local structural information for the guest substructures of ‘conventional’ urea inclusio11 com-pounds containing Br(CH,),Br (n=7-1 1) guest molecules. One major aim of these Br EXAFS studies was to determine the Br...Br distance between adjacent guest molecules in the urea tunnel.(This is particularly important in vieu of the theoretical prediction that the interaction between adjacent guest molecules in the urea tunnel is repulsive, corresponding to a short intermolecular Br--.Br distance.) However, the Br..-Br distance could not be determined accurately from the Br EXAFS data collected between room temperature and 77 K [and also at 9 K for Br(CH,),,Br/urea]; this can be attributed to dynamic disorder in the guest substructure at high temperature and static positional disorder at lcjw tem-perature. In these Br EXAFS studies, backscattering from the first three intramolecular C neighbours was detected. As a consequence of the incommensurate structural relationship between the host and guest substructures along the tunnel axis, no well defined features arising from backscattering by atoms of the host substructure were observed in the Br EXAFS data.Raman spectroscopic investigations of urea inclusion com- pounds containing Br(CH,),Br (n=7-1 1) guest molecules have been reported,” with the C-Br stretching vibration J. MATER. CHEM., 1994, VOL. 4 studied as a function of the length (n) of the guest molecule, temperature and pressure. From these results, trends in the relative amounts of gauche and trans end-groups for the Br(CH,),Br guest molecules within the urea tunnel structure were assessed. For Br(CH,),,Br/urea, both trans and gauche end-group conformations were detected, with ca.11.5% of end-groups in the gauche conformation at room temperature. Computational Details In the MD simulation, a single tunnel of the Br(CH,),,Br/urea inclusion compound was considered. Despite the approxi- mations used here, our model for the Br(CH,),,Br/urea inclusion compound is nevertheless more sophisticated than that used in recent simulations12 of similar inclusion com- pounds, in which only a single guest molecule was considered. The urea tunnel structure determined previously5 for Br(CH,),,Br/urea from room-temperature single-crystal X- ray diffraction data was used; this is the hexagonal tunnel structure of the conventional urea inclusion compounds. In the MD simulation, the length of the tunnel corresponded to 18 unit ce!ls of the host substructure (periodic repeat distance, ch =11.0 A), and 11 guest molecules [Br(CH,),,Br] were considered.Because both host and guest substructures are confined within the simulation cell, a commensurate relation- ship between the host and guest substructures is effectively imposed upon the system in the MD simulation; nevertheless, the host :guest ratio for the simulation cell considered here is acceptably close to the experimental host :guest ratio (the experimental periodic repeat dist?nce of the guest molecules along the tunnel axis is cg=18.0A at room temperature). In the MD simulation, the host substructure was held rigid and the position of the Br atom at each end of the tunnel was fixed (in their fixed positions, these two Br atoms were on the 61 symmetry axis of the host structure).These constraints represent an approximation to a constant-volume simulation. Apart from the restriction that the positions of two Br atoms in the structure were fixed, the Br(CH,),,Br molecules were allowed to move freely in the MD simulation. Although these constraints limit the ability of the simulation to provide meaningful information on certain properties (e.g. diffusion parameters) of the guest molecules, they nevertheless allow reliable information to be derived for local structural proper- ties of the guest molecules provided only those guest molecules close to the centre of the simulation cell are considered. The MD simulation was carried out within the DISCOVER program package,13 and the potential-energy parameterization embodied within this package was used.The Coulombic energy contribution of a molecular system of the type con- sidered here is comparatively small, and thus the use of an Ewald summation is not essential (unlike the situation for simulations of ionic systems). The MD simulation was run for 20 x s for equilibration, and then for 200 x s during which the structural properties were determined every 1OOx lo-’’ s. The thermal energy was equivalent to a tem- perature of 300K and a numerical integration step of 1 x s was used in the Verlet a1g0rithm.l~ The evolution of the structure was monitored during the MD simulation, and selected properties were calculated sub- sequently for those guest molecules close to the centre of the simulation cell.The Br radial distribution function (RDF) was measured for the nearest intramolecular C neighbours and for the nearest intermolecular Br neighbour. The end- group conformations were probed by monitoring the intra- molecular Br-C( l)-C(2)-C(3) torsion angles; plots show- ing the variation of this angle as a function of time yield information on the dynamics of the conformational changes in the guest molecule. Results and Discussion Fig. l(u) shows the structure at the beginning of the MD simulation, with all Br(CH,),,Br molecules taken to be in the ‘all-trans’ conformation. Fig. l(b) shows a snapshot of the structure, viewed along the direction of the urea tunnel axis, at the end of the MD simulation.It is clear that there is substantial positional and orientational disorder of guest molecules within the host tunnel. The extent of disorder of the guest molecules will result in a rapid diminution in the intensity of X-ray scattering from the guest substructure with increasing diffraction angle, as observed experimentally.* The occurrence of substantial motion of the guest molecules in the Br(CH,),,Br/urea inclusion compound is in agreement with conclusions from incoherent quasielastic neutron scattering’ and ,H NMR” studies of this material. Fig.2(u) shows the Br RDF determined during the MD simulation. This RDF contains sharp, well defined peaks for the first four intramolecular Br...C distances (Table 1); the linewidth increases for C neighbours further away from the Br atom, in the manner expected for a flexible molecule.The very broad peak at 3.7A in the Br RDF [expanded in Fig. 2(b)] represents the intermolecular Br-.. Br distance for neighbouring Br(CH,),,Br molecules in the urea tunnel. The P 9 P Fig. 1 (a) Structure of Br(CH,),,Br/urea (both host and guest substructures shown) at the start of the MD simulation, viewed along the urea tunnel axis. Note that all guest molecules are in the all-trans conformation, although the exact orientations of the guest molecules differ slightly. (b) Structure of Br(CH,),,Br/urea at the end of the MD simulation, illustrating the extent of disorder within the guest substructure. J.MATER. CHEM., 1994, VOL. 4 1 (I I1 I' I' I' c I' I! I distance/A Fig.2 Bromine RDF for Br(CH,),,Br/urea determined for the five guest molecules towards the centre of the simulation cell in the MD simulation: (a) the full Br RDF; (b) the Br RDF expanded in the region of the Br...Br peak. (-) Br..-Br; (---) Br...C(l); (---) Br...C(2); (-.-) Br..C(3);(--.-) Br-..C(4). Table 1 Intramolecular Br-C distances (r) and root-mean-squared displacements (CT)in these distances for Br(CH,),,Br/urea r/A CT/A experimental calculated experimental calculated Br-C( 1) 1.96 1.921 0.083 0.036 Br--C( 2) 2.83 2.824 0.124 0.056 Br--C( 3) 3.91 4.232 0.114 0.074 Br--C( 4) -5.373 -0.082 Calculated data were obtained from the MD simulation (at 300 K) reported here, and experimental data were obtained from the Br EXAFS studies (at 296 K) reported in ref.10. large width of this peak, in comparison to the widths of the peaks for intramolecular Br.. .C distances, is particularly significant in view of the fact that the Br.-.Br distance could not be determined from Br EXAFS data on Br(CH,),Br/urea inclusion compounds. Specifically, the width of the distri- bution for the Br..-Br distance (corresponding to substantial local structural disorder and/or dynamic disorder) will render backscattering due to the intermolecular Br neighbour essen- tially insignificant in the Br EXAFS experiment. The asym- metry of the Br-..Br peak in the Br RDF is noteworthy [see Fig.2(b)],There is a well defined low-distance cut-off just above 3 A, whereas at large tistances the RDF tails off gradually, extending beyond 6 A. Note that the sum ,of the van der Waals radii for a pair of Br atoms is ca. 3.9 A. The neighbouring Br atoms are apparently located mainly in regions corresponding to a repulsive Br- .Br interaction (in agreement with theoretical predictions6) although local con- figurations with an attractive Br..-Br interaction are also sampled. The Br-..C distances are sufficiently well defined to allow these distances to be extracted from the Br EXAFS data; this is vindicated by the presence of sharp peaks for Br...C distances in the Br RDF determined from the MD simulation. The Br.-.C distances determined from the MD siniulation and from the Br EXAFS data are compared in Table 1.For the third and fourth neighbouring C atoms, the Br-..C distance is represented by a pair of peaks in the Br RDF: a main peak and a small broad peak on the low-distance side of the main peak. The small broad peak can be attributed to confor- mations [containing gauche end-groups (vide infra)] that differ substantially from the major (all-trans) conformation as dis- cussed in more detail below. In principle, it should be feasible to correlate roo t-mean- squared displacements in the Br.--C distances extracted from the appropriate peaks in the calculated Br RDF with the experimental root-mean-squared displacements determined from Debye-Waller factors obtained in fitting the Br EXAFS spectra.However, acceptable agreement between these calcu- lated and experimental root-mean-squared displacemmts was not obtained (Table l), and this failure is attributed to a combination of factors arising, in part, from the ;tpproxi- mations embodied within our MD simulation (particularly the fact that the terminal Br atoms in the simulation cell were fixed in position), and, in part, from the fact that Debye- Waller factors extracted from the Br EXAFS spectra can often subsume substantial errors in the fitting procedure. €or these reasons, it is not appropriate here to attempt a detailed comparison of calculated and experimental root-mean-squared displacements, but rather it is prudent to recognize the potential difficulties in attempting to make comparisons of this type.The existence of a proportion of gauche end-group.; for the guest molecules in the Br(CH,),,Br/urea inclusion compound is in agreement with our findings from Raman spectroscopy." From the conformational trajectory, the variation in the torsion angles in the guest molecules has been determined as a function of time; Fig. 3 reports the variation of the terminal torsion angles [Br-C( 1)-C(2)-C(3)] for two different mol- ecules located towards the centre of the simulation cell. The molecule probed in Fig. 3(a) has remained in the trans confor-mation during the simulation, with fluctuations (up to ca.+25") in this torsion angle attributed to thermal vibration." For the molecule probed in Fig.3(b), on the other hand, a trans-gauche-trans conformational charige has occurred during the simulation. The lifetime of thc gauche conformation is ca. 4.8x s, and is appreciabl? shorter than the lifetime of the trans conformation (as sampled for other molecules). Fig.4 shows snapshots of sections of the guest substructure illustrating the conformations ot interest (for clarity, the host substructure is not shown). In Fig. 4(a) all the molecules shown have trans end-groups, whereas in Fig. 4(b) the central molecule has a gauche end-group. The proportion of gauche end-groups, averaged over the simu- lation, is ca. 1.9% (the corresponding value determined exper- imentally" is ca. 11.5%). Thus, our MD simulation has verified the existence of gauche end-groups for Br((:H,),,Br guest molecules within the urea tunnel structure, although it is important to emphasize that good quantitative agreement between the results from the MD simulation and the exper- imental results is not necessarily expected, in view of the approximations embodied within our simulation, and in view of the fact that the number of trans-gauche interconversions observed in the MD simulation was insufficient to give an accurate time average of the conformational populations.Concluding Remarks As discussed above, computer simulation of incommensurate materials requires the use of large simulation cells, often J. MATER. CHEM., 1994, VOL. 4 t -80.-12 J I I I I I 0 -40 -80 -1 20 trans end-group \'gauche end-group -1 60 I I I I I I I I I I 8000 16000 24000 32000 40000 time/fs Fig.3 Conformational trajectories, as a function of time, for the Br-C( l)-C(2)-C(3) torsion angles of two Br(CH,),,Br molecules towards the centre of the simulation cell. [The value of angle reported on the graphs represents the deviation of the Br-C( 1 )-C(ZtC( 3) torsion angle from the value (180 "C) for a trans end-group.] For (a)the end-group has remained trans during the simulation, whereas for (bl the end-group has undergone a trans-gauche-trans conformational change during the simulation. gauche end-group \ Fig. 4 Snapshots of the structure of Br(CH,),,Br/urea (with the host substructure omitted for clarity) illustrating: (a) a section of the set of guest molecules in which all end-groups are trans; (b)a section of the set of guest molecules in which one molecule has a gauche end-group.prohibitively large. Nevertheless, if valid simplifying assump- tions can be made, the extent of the problem can often be reduced to manageable proportions. In the present case, the approximation of considering a single tunnel of the inclusion compound, without the application of periodic boundary conditions, has been shown to produce results on local structural properties that agree well, at least qualitatively (and in some cases quantitatively), with information derived from experimental approaches. Specifically, in the present case: (i) the Br RDF determined from the MD simulation is consistent with information determined experimentally uia Br K-edge EXAFS spectroscopy; (ii) the MD simulation has demonstrated the existence of gauche end-group confor- mations of the guest molecules and has provided direct J.MATER. CHEM., 1994, VOL. 4 evidence for the interconversion between trans and gauche end-group conformations on a timescale of the order of picoseconds; (iii) the MD simulation implies that there is substantial dynamic disorder of the Br(CH,),,Br guest mol- ecules within the urea tunnel structure. The present work has illustrated the usefulness of computer simulation as an aid to the interpretation of experimental data and the rationalization of experimental observations. For example, the MD simulation of Br(CH,),,Br/urea reported here has provided a clear understanding of the absence of information from Br EXAFS data on the intermol- ecular Br..-Br distance, and has provided direct evidence for interconversion between trans and gauche end-group confor- mations and an estimate of the lifetime of the gauche con-formation. Nevertheless, in order to derive a deeper understanding of the dynamic properties and the long-range structural properties of the Br( CH,),,Br/urea inclusion com-pound, MD simulations are required in which some of the simplifying approximations embodied within the present work have been eliminated. We are grateful to SERC for financial support (studentship to A.R.G.), and to BIOSYM Technologies Inc. for providing the INSIGHT/DISCOVER suite of programs.Professor Sir John Meurig Thomas, Professor C. R. A. Catlow and Dr. G. Sankar are thanked for useful discussions in connection with this work. References 1 K. Takemoto and N. Sonoda, in Inclusion Compoiinds, ed. J. L. Atwood, J. E. D. Davies and D. D. MacNicol, Academic Press, London, 1984, vol. 2, p. 47. 2 K. D. M. Harris, J. Solid State Chem., 1993, 106, 83. 3 F. Guillaume, A. El Baghdadi and A-J. Dianoux, Phyx. Scr. T, 1993, 49,691. 4 A. E. Smith, Acta Crystallogr., 1952, 5,224. 5 K. D. M. Harris, and J. M. Thomas, J. Chem. Soc., Faraday Trans., 1990, 86, 2985. 6 A. J. 0.Rennie, and K. D. M. Harris, Proc. R. Soc. LCndon, A, 1990,430,615. 7 A. J. 0. Rennie, and K. D. M. Harris, J. Chem. Ph.:ts., 1992, 96, 7117. 8 K. D. M. Harris, S. P. Smart and M. D. Hollingsworth, J. Chem. Soc., Faraday Trans., 1991,87, 3423. 9 F. Guillaume, S. P. Smart, K. D. M. Harris and A-J. Ilianoux, J. Phys.: Condensed Matter, 1994,6,2169. 10 I. J. Shannon, K. D. M. Harris, A. Mahdyarfar, P. Johnston and R. W. Joyner, J. Chem. SOC.,Faraday Trans., 1993,89,3[199. 11 S. P. Smart, A. El Baghdadi, F. Guillaume and K. D. hl. Harris, J. Chem. SOC., Faraday Trans., 1994,90, 1313. 12 K. J. Lee, W. L. Mattice and R. G. Snyder, J. Chem. Phys., 1992, 96,9138. 13 DISCOVER, BIOSYM Technologies Inc., San Diego, ('A, USA, 1993. 14 L. Verlet, Phys. Rev., 1967,159,98. 15 A. E. Aliev, S. P. Smart, I. J. Shannon and K. D. hi. Harris, manuscript in preparation. 16 B. D. Hudson, A. R. George, M. G. Ford and D. J. Lixingstone, J. Comput. Aided Mol. Des., 1992,6, 191. Paper 4/02385D; Received 22nd April, 1994