New advances in conceptual-DFT: an alternative way to calculate the Fukui function and dual descriptor

  • Jesús Sánchez-MárquezEmail author
Original Paper


An alternative way of calculating the Fukui function and the partial derivative of second order of the electronic density with respect to the number of electrons N is presented, the new formulas agree with the usual ones but only in cases without degeneracy. The new operative formulas are more general than the previous ones and are the right ones for those problematic cases where one or both of the frontier molecular orbitals are degenerate. Finally, we present a new way of applying the finite difference approximation that leads to more realistic results than the usual formulas.

Graphical abstract

A new way of calculating the Fukui function is presented that results in a new operative formula of the function. It has also been obtained the partial derivative of second order of the electronic density with respect to the number of electrons N, and it agree with the usual formula of the dual descriptor function but only in cases without degeneration.


Reactivity descriptors Fukui function Dual descriptor Finite difference approximation UCA-FUKUI software Conceptual DFT 



Calculations were performed through CICA (Centro Informático Científico de Andalucía).

Supplementary material

894_2019_4000_MOESM1_ESM.doc (750 kb)
ESM 1 (DOC 749 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Química-Física, Facultad de Ciencias, Campus Universitario Río San PedroUniversidad de CádizPuerto RealSpain

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