Local and nonlocal counterparts of global descriptors: the cases of chemical softness and hardness

  • Marco Franco-Pérez
  • Carlos A. Polanco-Ramírez
  • José L. Gázquez
  • Paul W. Ayers
Original Paper
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday


A new strategy, recently reported by us to develop local and linear (nonlocal) counterparts of global response functions, is applied to study the local behavior of the global softness and hardness reactivity descriptors. Within this approach a local counterpart is designed to identify the most important molecular fragments for a given chemical response. The local counterpart of the global softness obtained through our methodology corresponds to the well-known definition of local softness and, in agreement with what standard conceptual chemical reactivity in density functional theory dictates, it simply reveals the softest sites in a molecule. For the case of the local hardness, we obtain two expressions that lead to different information regarding the values of the hardness at the different sites within a chemical species. The performance of these two proposal were tested by comparing their corresponding atom-condensed values to experimentally observed reactivity trends for electrophilic attack on benzene and ethene derivatives.


Global response functions Local and nonlocal reactivity indices Thermodynamic softness Chemical hardness Local softness Local hardness 



PWA thanks NSERC and support from the Canada Research Chairs and Compute Canada. We thank the Laboratorio de Supercómputo y Visualización of Universidad Autónoma Metropolitana-Iztapalapa and the Laboratorio Nacional de Cómputo de Alto Desempeño (LANCAD) for the use of their facilities. CPR was supported in part by Conacyt through a doctoral fellowship. JLG thanks Conacyt for grant 237045. We dedicate this work to Prof. Pratim Chattaraj on the occasion of his 60th anniversary for his great contributions to the density functional theory of chemical reactivity.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de QuímicaUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico
  2. 2.Departamento de QuímicaUniversidad Autónoma Metropolitana-IztapalapaCiudad de MéxicoMexico
  3. 3.Department of ChemistryMcMaster UniversityHamiltonCanada

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