Cioslowski’s approach

It is clear, therefore, that Cioslowski s approach based on density-driven orbitals [74, 75, 77], corresponds to a finite orbital representation of the local-scaling transformation version of density functional theory [38]. 

The explicit construction to which Cioslowski refers is that provided by the density-driven approach, advanced in 1988. But, already in 1986, an alternative way for carrying out this explicit construction had been set forward by Kryachko, Petkov and Stoitsov [28]. This new approach - based on localscaling transformations - was further developed by these same authors [29, 30, 32, 34], by Kryachko and Ludena [1, 20, 31, 33, 35-37], and by Koga [51]. In this Section we show that Cioslowski s density-driven method corresponds to a finite basis representation of the local-scaling transformation version of density functional theory [38]. 

The gist of Cioslowski s work is to set up an energy functional that depends on the density, in the context of the constrained-search approach of Levy [84]. This functional is, therefore, defined by ... 

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