Free energy extended generating functionals

See for example Oxtoby, D. W. Nucleation of first-order phase transitions, Acc. Chem. Res. 1998, 31, 91-97, and references therein. The classical nucleation theory (CNT) is challenged by extended theories, one of which was unfortunately called density functional theory because free energy is a functional of the average density profile of the nucleating site, generating some confusion, at least for theoretical chemists, with quantum chemical density functional theory. 

For the structure at higher energies, the agreement becomes better when the basis set is extended. The molecular orbital approximation has been proved to be efficient even for generation of continuum wave function of free-electron state when the extension of the basis set is sufficient. 

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