Partition theory: A very simple illustration

TL;DR

This paper demonstrates a simple example illustrating a new ensemble density functional theory method for dividing complex molecules into parts, providing analytic densities and finite chemical hardness for the parts.

Contribution

It introduces a straightforward illustration of a recent method that rigorously partitions molecules and assigns finite chemical hardness to the parts.

Findings

Analytic densities for molecular parts are derived.

The method yields finite, positive chemical hardness for the parts.

The approach clarifies reactivity potential in molecular systems.

Abstract

We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229 (2007)]. The illustrative system is an analog of the hydrogen molecule for which analytic expressions for the densities of the parts (hydrogen "atoms") are found along with the "reactivity potential" that enters the theory. While previous formulations of Chemical Reactivity Theory lead to zero, or undefined, values for the chemical hardness of the isolated parts, we demonstrate they can acquire a finite and positive hardness within the present formulation.