An important chemical property emerging from density-functional theory is the hardness, which can be evaluated as half of the difference between the vertical ionisation energy and electron affinity of the system. For many gas phase molecules, however, the electron affinity is negative and standard ways of evaluating this property are troublesome. In this contribution, we investigate an unconventional approximation for the electron affinity, based on the Kohn-Sham orbital energies of the frontier orbitals and the ionisation potential. It is shown that, for a large series of molecules possessing negative electron affinities, this methodology yields reasonable values for this quantity and that the correlation of the computed values with the experimental affinities from electron transmission spectroscopy is superior to other theoretical approaches. In a second part of this contribution, the hardness of a series of stable negative ions is evaluated in aqueous solution.

Calculations of conceptual density functional theory (DFT) reactivity indices are mainly restricted to global quantities and local functions, whereas values for the nonlocal kernels are rarely presented. We used a molecular orbitalbased expression to calculate the atom-condensed linear response kernel. The results are the first published values of this quantity that have been obtained through a direct and generally applicable methodology. This letter focuses on the off-diagonal elements, which provide insight into the nonlocal contributions to chemical reactivity. A detailed study of a set of eight functionalized alkane and polyalkene derivatives enabled us to quantify inductive and resonance effects. SECTION Molecular Structure, Quantum Chemistry, General Theory S everal authors 1-4 have recently been paying attention to higher order derivatives and functional derivatives of the electronic energy E within the context of conceptual or chemical density functional theory (DFT). [5][6][7][8][9] The linear response function or polarizability kernel χ(r,r 0 ), which is defined as

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The Fukui function is a frequently used DFT concept in the description of a system's regioselective preferences to undergo electrophilic, nucleophilic, or radical attacks. Until now, this function has usually been evaluated using finite difference approximations. The first paper in this series proposed a method for obtaining the Fukui function by a direct calculation of the functional derivative of the chemical potential with respect to the external potential. This paper extends the method to condensed Fukui functions and applies it to an extensive testing set of molecules. Results are promising, which demonstrates the usefulness of the new formalism.