ETF-LDA

The ETF-LDA energy functional, etf[p] is obtained by replacing the kinetic energy term, 7[p], in the usual LDA functional, namely in the expression... 

The optimal ETF-LDA total energy is obtained by minimization of etf[p] with respect to the density. In our calculations, we use for the trial densities parameterized profiles P( i K/ ) [60, 25, 26] with y, as variational parameters (the ETF-LDA optimal density is denoted as p). The single-particle eigenvalues, in Eq. (6) are obtained then as the solutions to the single-particle Hamiltonian of Eq. (7) with Vi replaced by Vetf (given by Eq. (8) with p "(r) replaced by p(r)). Hereafter, these single-particle eigenvalues will be denoted by ,. ... 

Parameterize results of ETF-LDA calculations for spherical neutral jellia according to Eq. (18). 

The LDA-SCM approach, which has been shown to yield results in excellent agreement with self-consistent KS-LDA calculations [25, 26], is equivalent to a Harris functional [53] approximation ( Harris[p "], see below) to the KS-LDA total energy [50] ( Ks[PKs]) with the input density obtained through a variational minimization of an extended Thomas-Fermi (ETF) energy functional, etf[p1-The property of the nonselfconsistent Harris functional to yield total energies close to the KS-LDA ones is based on the following equality ... 

For materials with high electronic densities, it is known that the usual LDA fails to provide adequate values for the surface tension. Therefore, in Ref. [40] (see also Ref. [28] for the case of fullerenes), in the case of Cu and Li clusters, we have carried an ETF calculation... 

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