Static polarizability and hyperpolarizability in atoms and molecules through a Cartesian-grid DFT

  • Tanmay Mandal
  • Abhisek Ghosal
  • Amlan K. RoyEmail author
Regular Article


Static electric response properties of atoms and molecules are reported within the real-space Cartesian-grid implementation of pseudopotential Kohn–Sham density functional theory. A detailed systematic investigation is made for a representative set of atoms and molecules, through a number of properties like total ground-state electronic energies, permanent dipole moment (\(\varvec{\mu }\)), static average dipole polarizability (\(\overline{\alpha }\)). This is further extended to first hyperpolarizability (\(\varvec{\beta }\)) in molecules. It employs a recently developed non-uniform grid-optimization technique, with a suitably chosen fixed initial applied field. A simple variant of the finite-field method, using a rational function fit to the dipole moment with respect to electric field, is adopted. We make use of Labello–Ferreira–Kurtz basis set, which has performed quite well in these scenarios. To assess the efficacy and feasibility, four XC functionals such as LDA, BLYP, PBE and LBVWN are chosen. The present results are compared with available literature (both theoretical and experimental) values, whenever possible. In all instances, they show excellent agreement with the respective atom-centered-grid results, very widely used in many quantum chemistry programs. This demonstrates a viable alternative toward accurate prediction of response properties of many-electron systems in Cartesian coordinate grid.


Density functional theory Polarizability Hyperpolarizability Exchange-correlation functional Cartesian grid Basis set 



AG thanks UGC for a Senior Research Fellowship. TM very much appreciates a Junior Research fellowship from IISER Kolkata. Financial support from DST SERB, New Delhi, India (sanction order number EMR/2014/000838) is sincerely acknowledged. Constructive comments from anonymous referee have helped in improving the quality of this manuscript.


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Copyright information

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

Authors and Affiliations

  1. 1.Department of Chemical SciencesIndian Institute of Science Education and Research (IISER) KolkataMohanpur, NadiaIndia

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