Towards chemical applications of Dempster-Shafer-type approach: Case of variant ligands

In many practical situations, molecules can be obtained from a “template” molecule like benzene by replacing some of its hydrogen atoms with ligands (other atoms or atom groups). There can be many possible replacements of this type. To avoid time-consuming testing of all possible replacements, it is desirable to test some of the replacements and then extrapolate to others - so that only the promising molecules, for which the extrapolated values are desirable, will have to be synthesized and tested. For this extrapolation, D. J. Klein and co-authors proposed to use a Dempster-Shafer-type poset extrapolation technique developed by G.-C. Rota from MIT. One of the limitations of this approach is that this technique has been originally proposed on a heuristic basis, with no convincing justification of its applicability to chemical (or other) problems. In our previous paper, we showed that for the case when all the ligands are of the same type, the poset technique is actually equivalent to a more familiar (and much more justified) Taylor series extrapolation. In this paper, we show that this equivalence can be extended to the case when we have variant ligands.