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Torsional modes within a complex molecule containing various functionalgroups are often strongly coupled so that the harmonic approximation andone-dimensional torsional treatment are inaccurate to evaluate their partitionfunctions. A family of multi-structural approximation methods have beenproposed and applied in recent years to deal with the torsionalanharmonicity.However, these methods approximate the exact "almost periodic"potential energy as a summation of local periodic functions with symmetricbarrier positions and heights. In the present theoretical study, we illustratedthat the approximation is inaccurate when torsional modes present non-uniformlydistributed local minima. Thereby, we proposed an improved method toreconstruct approximate potential to replace the periodic potential by usinginformation of the local minima and their Voronoi tessellation. First, weestablished asymmetric barrier heights by introducing two periodicityparameters and assuming that the exact barrier positions are at the boundariesof Voronoi cells. Second, we used multiplicatively weighted Voronoitessellation to refine the barrier heights and positions by defining astructure-related distance metric. The proposed method has been tested for afew higher-dimensional cases, all of which show promising improved accuracy.

Approximate Reconstruction of Torsional Potential Energy Surface based on Voronoi Tessellation