Approximate noninteracting kinetic energy functionals from a nonuniform scaling requirement

Abstract

AbstractWe have recently proven an inequality for the exact noninteracting kinetic energy density functional \documentclass{article}\pagestyle{empty}\begin{document}$ T_s [n]:\mathop {\lim }\limits_{x \to \infty } T_s [n_\lambda ^x] \le T_s [n_s^y [n] + T_S^2 [n] < \infty,where{\rm }n_\lambda ^x (x,{\rm }y,{\rm }z) = \lambda n(\lambda x,{\rm }\lambda {\rm y, }\lambda z) $\end{document}. It is known that the gradient expansion through fourth order, T[n], violates this inequality. Toward improving TsGE[n], we have constructed two new functionals, Ts1[n] and Ts2[n], by keeping the zeroth and second orders in TsGE[n] and replacing the fourth order with two simple terms, respectively, so that these new functionals satisfy the inequality. Numerical tests are presented for Ts1[n], Ts2[n], and TsGE[n] and for the gradient expansion through second order. Hartree–Fock and hydrogenic atomic densities are employed.