Hardness and the Potential Energy Function in Internal Rotations: A Generalized Symmetry-Adapted Interpolation Procedure

Abstract

Density functional theory (DFT) has provided the theoretical basis to study reactivity parameters of molecular systems, this is, to its resistance to change its electron density distribution, namely the molecular hardness (ŋ). Its evolution along a given reaction coordinate is examined in order to better understand the chemical reactivity of the system of interest. In this work, compounds that are often used as prototypes to study their linkage in proteins are shown.In the DFT framework, for which the total number of electrons must be con­served, rotational isomerization reactions can be regarded as a reorganization / redistribution of electron density among atoms in a system.The relation between the molecular hardness and the potential energy function (E) (both global properties) is here studied. It is shown that ŋ is analytically related to E. Correction terms to the definition for ŋ, that include a molecular symmetry parameter (b), are included. An expression for the activation hardness in terms of the activation potential energy function and b for the molecular system under study are derived. A qualitative proof of the principle of maximum hardness (PMH) is shown. The procedure is tested with nine molecular systems. Our results show to be in excellent agreement with those available in the literature.KeywordsTransition StateInternal RotationMolecular SystemReaction CoordinatePotential Energy FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.