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. (C) 2014 Elsevier B.V. All rights reserved.