Fourier type potential energy function for conformational change of selected organic functional groups

The energy changes associated with internal rotation of a functional group in a molecule depend on the topology of the chemical environment. Energies obtained from electron structure and force-field calculations have been analyzed by Fourier expansions. The findings show that rotation around bonds connecting atoms without lone pairs can be described with a one term Fourier-series. In contrast, two or three terms are needed if the connected atoms have lone pairs. The analysis inspires adoption of a simplified Fourier expansion that reproduces the data well, suggesting that Fourier-type-series with few terms are useful in describing any internal rotation analytically.