  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. A family of multi-structural approximation methods have been
proposed and applied in recent years to deal with the torsional
anharmonicity.However, these methods approximate the exact "almost periodic"
potential energy as a summation of local periodic functions with symmetric
barrier positions and heights. In the present theoretical study, we illustrated
that the approximation is inaccurate when torsional modes present non-uniformly
distributed local minima. Thereby, we proposed an improved method to
reconstruct approximate potential to replace the periodic potential by using
information of the local minima and their Voronoi tessellation. First, we
established asymmetric barrier heights by introducing two periodicity
parameters and assuming that the exact barrier positions are at the boundaries
of Voronoi cells. Second, we used multiplicatively weighted Voronoi
tessellation to refine the barrier heights and positions by defining a
structure-related distance metric. The proposed method has been tested for a
few higher-dimensional cases, all of which show promising improved accuracy.
