Configurational properties of water clathrates: Monte Carlo and multidimensional integration versus the Lennard-Jones and Devonshire approximation

To quantify the inadequacies associated with the use of the spherically symmetric Lennard-Jones Devonshire smooth cell approximation, Monte Carlo and multidimensional quadrature integrations were performed for various water clathrate cavity geometries while accounting for the asymmetries of the host lattice using complete crystallographic structural data with effects included for multiple coordination shells. Using the van der Waals-Platteeuw model as a basis, the configurational partition function was evaluated for typical hydrate host-lattice systems containing small (Ar, CH4, C2H6, CO2,...; structure I type) and large (C3H6, C4H8, CHCl3,...; structure II type) guest molecules. A range of intermolecular potential energy and size parameters were used to characterize configurational effects for structure I and II guest-host interactions. Additionally, angle-averaged potential energy profiles were calculated in order to compare with those determined using the Lennard-Jones Devonshire approximation. It was found that the Lennard-Jones Devonshire approximation gives quantitatively correct results for smaller guest molecules (sigma > 3.0 Angstrom) but completely incorrect results for larger guest molecules (sigma > 3.0 Angstrom). In addition, quadrature calculations must include four coordination shells or more to provide an accurate estimation of physical properties.