THEORETICAL PREDICTION OF THE GUEST PERIODICITY OF ALKANE UREA INCLUSION-COMPOUNDS

A mathematical model of one-dimensional inclusion compounds, developed previously, is applied here to predict and rationalize structural pro perties of the alkane/urea family of inclusion compounds. Within this model, the one-dimensional inclusion compound is considered as a linea r infinite host tunnel (with periodic repeat distance c(h)) containing a finite periodic arrangement (with periodic repeat distance c(g)) of identical guest molecules. This mathematical model provides a formali sm that allows potential-energy functions (describing host-guest inter action, guest-guest interaction and intramolecular potential energies) computed for any one-dimensional inclusion compound to be used to pre dict and rationalize structural properties of the inclusion compound. Using this approach, the optimum c(g) has been determined for the seri es of urea inclusion compounds containing the alkane guest molecules C H3(CH2)(r)CH3, with r = 2-18, and the question of whether these inclus ion compounds exhibit commensurate or incommensurate behaviour has bee n assessed. It is predicted and demonstrated that the heptadecane/urea inclusion compound is commensurate (6c(g) = 13c(h)). The butane/urea inclusion compound is also predicted to be commensurate, whereas all o f 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 com pounds with guest molecules CH3(CH2)rCH3 (r = 7-15, 18) have been stud ied by single-crystal X-ray diffraction, and from these data the value of c(g) at room temperature has been determined. The values of c(g) p redicted theoretically for these inclusion compounds are in good agree ment with the values of c(g) determined experimentally. For all the ur ea inclusion compounds studied, the optimum c(g) is ca. 0.5 angstrom s horter than the value of c(g) corresponding to the minimum guest-guest interaction energy; this fact substantiates the claim that, at the op timum guest periodicity in alkane/urea inclusion compounds, the intera ction between adjacent guest molecules is repulsive.