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P. BadiaH is written as T[n(z)] "" f dz n(z}{to[n(z)] + tt[n(z)] + tz[n(z)] + ... } (18) The first term in the integrand corresponds to a simple ThomasFermi approximation. Developments up to second gradient terms ar--------------------------------------------------, ... ---- " ", . . . \~'~> . ' -- - - - ---- , '. \ \ ... '. \ , " ".. \ , \ . \ \ - ·5 -5 au br---------------------------------, -5 Figure 4. Calculated density profiles n(z)/n for " = 6 (a) and " = 2 (b) in the jellium model. (---) from Smith74; (---) from Lang and Kohn.

Then it will be sufficient to discuss a possible effect of the field related only to nonzero ionic size (in the electronion interaction energy) on the work function. Due to the diffuse nature of the ionic profile in the case of liquid metals, screening of external fields by the free electrons might be less efficient than for solids. The ionic profile may then vary with charge, with a possible effect on both 'Y and Xm. In this case, no definite conclusion can be reached prior to calculations. To summarize, at the pzc and for solids it seems that reasonable values of the work function may coexist within the same model with somewhat less satisfactory values of the surface energy.

This less familiar expression of cI> is a consequence of the general definition of the work function. 77 It may be understood as the change in energy (per unit area) of the metal when an infinitesimal charge is induced on its surface, due to the transfer of a few electrons from the metal to the vacuum. Since the induced charge is localized on the surface, this change in energy results from a change in surface energy. Because of the stationary property of E[n(z)] (viz. Us) with respect to a variation of the density profile, the IlSCF expression is much less sensitive to errors in the profile than the direct Koopman's theorem expression.