Additivity Schemes in Conformational Analysis. Concept and Demonstration

Additivity schemes are of fundamental importance in molecular modeling. It is the goal of an additivity scheme to predict the value of parameter for a complex system based on the knowledge of the respective parameters for prototypical systems. The commonly employed method is based on the identification of energy factors, the quantification of these energy factors, and the evaluation of trial functions that depend on these factors. We describe a non-iterative method to derive energy factor expressions. While energy factors occur in the derivation of the energy factor expressions, the values of the energy factors are not determined and they are expressed instead as series of the known parameters of the minimal set of prototypes. The non-iterative energy factor analysis is illustrated by application to conformational preference energies for a series of spiro(THF)cyclohexanes for which the results of a traditional analysis are available. We demonstrate that the contributions to the conformational preference energy are additive, clarify the precise meaning of the terms " gauche interaction" and "1,3-interaction", and state a more general hypothesis that provides opportunities for testing by future experimental and computational studies.