Issue 28, 2014

Revisiting the density scaling of the non-interacting kinetic energy


Scaling relations play an important role in the understanding and development of approximate functionals in density functional theory. Recently, a number of these relationships have been redefined in terms of the Kohn–Sham orbitals [Calderín, Phys. Rev. A: At., Mol., Opt. Phys., 2013, 86, 032510]. For density scaling the author proposed a procedure involving a multiplicative scaling of the Kohn–Sham orbitals whilst keeping their occupation numbers fixed. In the present work, the differences between this scaling with fixed occupation numbers and that of previous studies, where the particle number change implied by the scaling was accommodated through the use of the grand canonical ensemble, are examined. We introduce the terms orbital and ensemble density scaling for these approaches, respectively. The natural ambiguity of the density scaling of the non-interacting kinetic energy functional is examined and the ancillary definitions implicit in each approach are highlighted and compared. As a consequence of these differences, Calderín recovered a homogeneity of degree 1 for the non-interacting kinetic energy functional under orbital scaling, contrasting recent work by the present authors [J. Chem. Phys., 2012, 136, 034101] where the functional was found to be inhomogeneous under ensemble density scaling. Furthermore, we show that the orbital scaling result follows directly from the linearity and the single-particle nature of the kinetic energy operator. The inhomogeneity of the non-interacting kinetic energy functional under ensemble density scaling can be quantified by defining an effective homogeneity. This quantity is shown to recover the homogeneity values for important approximate forms that are exact for limiting cases such as the uniform electron gas and one-electron systems. We argue that the ensemble density scaling provides more insight into the development of new functional forms.

Graphical abstract: Revisiting the density scaling of the non-interacting kinetic energy

Article information

Article type
13 Jan 2014
21 Mar 2014
First published
21 Mar 2014
This article is Open Access
Creative Commons BY license

Phys. Chem. Chem. Phys., 2014,16, 14578-14583

Author version available

Revisiting the density scaling of the non-interacting kinetic energy

A. Borgoo, A. M. Teale and D. J. Tozer, Phys. Chem. Chem. Phys., 2014, 16, 14578 DOI: 10.1039/C4CP00170B

This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. You can use material from this article in other publications without requesting further permissions from the RSC, provided that the correct acknowledgement is given.

Read more about how to correctly acknowledge RSC content.

Social activity