Approximating the kinetic energy functional T_s[ρ]: lessons from four-electron systems

Abstract

It is shown that for pairs of electron densities (ρ_α and

) obtained from mixing orbital densities in a spin-compensated four-electron system, the kinetic energy functional of the non-interacting reference system (T _s[ρ]) satisfies the general inequality

. This condition is discussed in the context of the gradient expansion approximation to T _s[ρ] and its possible use in variational orbital-free calculations. In particular, it is shown that the second-order term of the analytic form given by von Weizsäcker violates this inequality for the considered pairs.

Keywords:

• Kinetic energy functional Ts[ρ]
• Four-electron systems

Acknowledgements

The author dedicates this work to Professor Nicholas C. Handy on the occasion of his 60th birthday. This work was supported by the Swiss National Science Foundation within project 200020-100352.

Notes

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Additional information

Notes on contributors

Tomasz A. Wesołowski *

e-mail: [email protected]