Analytic calculation of Fukui functions and related reactivity descriptors

The electronic Fukui functions are calculated analytically as the linear response of molecular electronic density with respect to changes on orbital occupation numbers. The dual descriptor is also calculated analytically as a special combination of electrodonating and electroaccepting Fukui functions. The global descriptors are obtained, including ionization energy, electron affinity, electrodonating hardness, electroaccepting hardness, as well as electrodonating and electroaccepting powers which are calculated analytically using a second-order truncated Taylor approximation. Comparison with numerical estimates show that analytic electrodonating power is around a factor of two smaller than the values obtained using experimental ionization energy and electron affinities for atoms ranging from hydrogen to xenon. Surprisingly, electroaccepting powers follow very closely previously reported values for main group elements. All these quantities are computed for two conformers of the molecule of the anthraquinone derivative disperse red 60, as an example application where many valence orbitals are considered. Additionally, the values for electrodonating and electroaccepting powers calculated analytically are provided for a large set of small molecules as reference for future implementations.