Theoretical prediction of the guest periodicity of alkane/urea inclusion compounds

Abstract

A mathematical model of one-dimensional inclusion compounds, developed previously, is applied here to predict and rationalize structural properties of the alkane/urea family of inclusion compounds. Within this model, the one-dimensional inclusion compound is considered as a linear infinite host tunnel (with periodic repeat distance ch) containing a finite periodic arrangement (with periodic repeat distance cg) of identical guest molecules. This mathematical model provides a formalism that allows potential-energy functions (describing host–guest interaction, guest–guest interaction and intramolecular potential energies) computed for any one-dimensional inclusion compound to be used to predict and rationalize structural properties of the inclusion compound. Using this approach, the optimum cg has been determined for the series of urea inclusion compounds containing the alkane guest molecules CH3(CH2)rCH3, with r= 2–18, and the question of whether these inclusion compounds exhibit commensurate or incommensurate behaviour has been assessed. It is predicted and demonstrated that the heptadecane/urea inclusion compound is commensurate (6cg= 13ch). The butane/urea inclusion compound is also predicted to be commensurate, whereas all of the other alkane/urea inclusion compounds investigated are predicted to exhibit incommensurate behaviour. The wider issue of assessing the commensurate vs. incommensurate nature of such inclusion compounds by this theoretical approach is discussed.The alkane/urea inclusion compounds with guest molecules CH3(CH2)rCH3(r= 7–15, 18) have been studied by single-crystal X-ray diffraction, and from these data the value of cg at room temperature has been determined. The values of cg predicted theoretically for these inclusion compounds are in good agreement with the values of cg determined experimentally. For all the urea inclusion compounds studied, the optimum cg is ca. 0.5 A shorter than the value of cg corresponding to the minimum guest–guest interaction energy; this fact substantiates the claim that, at the optimum guest periodicity in alkane/urea inclusion compounds, the interaction between adjacent guest molecules is repulsive.