An Algorithm on Interpolating between Two Shapes of a Molecule

Conformational behaviour analysis produces a sequence of shapes of a molecule which are only the key points on the entire path. They differ from one another significantly and an interpolation is necessary to achieve a smooth visualization. However, standard interpolation techniques cannot be used. We introduce a hypothesis on the nature of the shape changes and derive an interpolation algorithm. Conditions required for proper function as well as some ideas how to overcome the algorithm’s drawbacks are presented. 1 Chemical background A simulation of conformational behaviour is an important part of computational chemistry. Unlike reactions this behaviour of a molecule involves changes in the shape of the molecule (called geometry here) only, bonds are neither created nor destroyed (the topology does not change). Among all such possible geometries of a single molecule there are two categories of special interest • Conformers (or conformations) are the stable ones in terms of potential energy—local minima on the potential energy hypersurface. • Transition states are those of maximal potential energy on a minimal energy path connecting two conformers—saddle points on the hypersurface. Figure 1 shows an example, conformers of propylaldehyde CH3CH2CHO. Based on the assumption a molecule traverses only some minimal energy path it can be seen that describing geometries of visited conformers and transition states is sufficient to describe the entire conformation behaviour. Actually there is a recently developed software system strictly depending on that assumption [1, 2].