Revised multi-structural approximations including torsional anharmonicity for partition function estimation

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. Zheng et al. (2011) proposed a family of multi-structural approximation methods that could satisfactorily deal with the torsional anharmonicity. However, these methods invoke a strong assumption that the potential barrier positions are equidistant from the local minimum on two sides in a specific torsion, and thereby resulting in the same barrier heights. It is unphysical when torsional motions present non-uniformly distributed local minima. In the present study, two improvements have been made to correct their methods based on the information about the local minima and the Voronoi tessellation. First, we estimated barrier heights by introducing two periodicity parameters and assuming that the exact barrier positions are at the boundaries of Voronoi cells. Second, we modified the Voronoi tessellation by defining a structure-related distance metric. These two improvements have been validated for two one-dimensional and one two-dimensional benchmark torsions.