In many applications, we have numerous molecules that are obtained from a "template" molecule like benzene C6H6 or cubane C8H8 by replacing some of its hydrogen atoms with other atoms or atom groups (called ligands). Depending on how many original atoms are replaced and which ones are replaced, we obtain a large number of different chemical substances. It is desirable to be able, based on the measurements performed on a small number of such substances, to accurately predict the characteristics (such as energy) of all similar substances.
Such predictions are very important, since, e.g. cubanes, while kinetically stable, are highly explosive. As a result, at present, they are actively used as high-density, high-energy fuels and explosives, and researchers are investigating the potential of using cubanes (and similarly high-energy molecules) in medicine and nanotechnology.
In a 2007 paper in the Journal of Mathematical Chemistry, one of the authors (DJK) showed that accurate predictions can be obtained by using the ideas of the famous MIT mathematician Gian-Carlo Rota on partially ordered sets. In this paper, we show that similar predictions can be made by using much simpler Taylor series techniques.