Crystal Structures and Intermolecular Forces of Rare Gases

Abstract

By means of models of intermolecular potential U ( r ), the total energy of molecular crystals is calculated provided the additivity of intermolecular forces is valid. If the Lennard-Jones model, U ( r )= U 0 ( s -6) -1 [6( r 0 / r ) s - s ( r 0 / r ) 6 ], is used, the lattice of hexagonal closest packing has always a lower energy than that of cubic closet packing. If the model, U ( r )= U 0 (σ-6) -1 [6 exp (σ-σ r / r 0 )-σ( r 0 / r ) 6 ] is used, there is a critical value of σ, σ 0 =8.675, above which the hexagonal is stable and below which the cubic is stable. In general, in order that the cubic structure has a lower energy as in the case of rare gases, it is necessary (although not sufficient) that the hollow part of the intermolecular potential is wide enough, much wider than that of U ( r ) = U 0 [ r 0 / r ) 12 -2( r 0 / r ) 6 ] for instance. These results are in agreement with the conclusions which Kihara has obtained by investigating the third virial coefficients of the equation of state for rare gases.