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This includes the image-potential interaction with a static point charge. 68 The Thomas-Fermi response is discussed in detail, as well as the solutions to the relevant equations. Results are compared to those from self-consistent calculations (see below). 65 One can solve the Thomas-Fermi-Dirac equation numerically to obtain the electron density profile for any surface charge density, thus obtaining the capacitance of the metal surface as well as the surface potential. Here, one is not limited to the linearresponse regime.

Then the acceptable wave functions are = (2/ L) 1/2 sin nirx/L ($ = 0 for x = 0 and for x = L), with the familiar particle-in-a-box energies e + y0 = n2h27T2/2mL2 = n2h2/SmL2 Because of electron spin, each state can hold two electrons. Adding together contributions for all n from 1 to nl — (8mL2//i2)1/2(ei+ Vo)1/2, we should obtain the total number of electrons: Nz =l 2 = 2(SmL2/h2)1/2(£l + V0)1/2 i The Fermi energy eF — ex + Vo is then EF = (Nz/L)2(h2/32m) which is proportional to the square of the one-dimensional electron density Nz/ L.

Equation (32) is extremely important to the calculation of work functions. The work required to remove an electron from the interior of the metal to vacuum outside is where fxe, the chemical potential of the electron, is a bulk property The Metal-Electrolyte Interface 53 and the surface potential, xM, is a surface property. In the densityfunctional model, Me = d[nf(n)]/dn and x = ( > f {~0®) ~ fii0®) Equation (32) shows that there is some cancellation between the bulk and surface contributions; combining Eq.