An analysis of limiting conditions on empirical nonbonded potential functions

Abstract

The use of empirical potential functions for describing the interaction between molecules has suffered from the difficulty of finding suitable potential constants. In particular, the barrier to rotation about a C-C bond is open to the question of how to partition the energy between nonbonded through space interactions and “intrinsic” resistance to bond rotation. Using the equation for the cohesive energy and its derivative for each of the three lattice parameters,a, b, andθ of the unit cell of polyethylene, we obtain four equations which are linear in the six potential constants required to write these quantities in terms of aMie potential. Instead of making additional assumptions, we have applied a series of inequalities and used linear programming to assess the range of permissible values. Many of the reported potential function parameters do not fall within this permissible range. The results show that the total contribution of nonbonded interactions to the barrier to rotation must be in the vicinity of 10–25%. Permissible ranges for the potential constants were very sensitive to the value of the chain setting angle,θ with no possible solutions lying outside the range 44°<θ<49°.