# On the evaluation of the non-interacting kinetic energy in density functional theory

### Michael J. G. Peach, David G. J. Griffiths, David J. Tozer, J. Chem. Phys., **136**, 144101, 2012.

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Another paper that came about as part of a 4th year research project, this paper investigates the practical usefulness of an expression developed by Levy and Ayers for the evaluation of the non-interacting kinetic energy in terms of a single Kohn–Sham orbital, which would have many computational advantages if it were practical. We highlighted some interesting problems arising from the approximate solution of the Kohn–Sham equation that leads to unphysical behaviour in orbitals that does not ordinarily manifest in practical calculations.

Further information, including details of subsequent work in this area, can be found on the research page. For the abstract, and access to the full text, see below.

## Abstract

The utility of both an orbital-free and a single-orbital expression for computing the non-interacting kinetic energy in density functional theory is investigated for simple atomic systems. The accuracy of both expressions is governed by the extent to which the Kohn–Sham equation is solved for the given exchange–correlation functional and so special attention is paid to the influence of finite Gaussian basis sets. The orbital-free expression is a statement of the virial theorem and its accuracy is quantified. The accuracy of the single-orbital expression is sensitive to the choice of Kohn–Sham orbital. The use of particularly compact orbitals is problematic because the failure to solve the Kohn–Sham equation exactly in regions where the orbital has decayed to near-zero leads to unphysical behaviour in regions that contribute to the kinetic energy, rendering it inaccurate. This problem is particularly severe for core orbitals, which would otherwise appear attractive due to their formally nodeless nature. The most accurate results from the single-orbital expression are obtained using the relatively diffuse, highest occupied orbitals, although special care is required at orbital nodes.

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