N D LANG AND W. KOHN TABLE L. The work function u of the uniform-back- Other, more recently suggested, forms of the cor round model, and its bulk and surface-barrier compo- relation energy give substantially similar results nents. The Wigner-Seitz radius r& characterizes the in terior density.面=△d-园, where u=量h》+Hxe, The bar The quantity H and its two components 2k and rier term Ap is given with a self-consistency of 0. 03 eV uxe are shown in Table I for rs in the metallic or better (this is a somewhat greater self-consistency than that of the preliminary report, Ref. 4) the bulk contribution to , It will be seen from Table I that, for metals of low electron density respectively),-H is much larger than the othe 212.52 9.61 6,803.89 term△φ. The rather good agreement with ex 2.58.01790 11 3.83 3. 72 periment(see Table II)constitutes 5.57 5.92-1.18 2.32 3.50 good confirmation of the expression (3. 3)for 5. 28.83 1.43 3. 26 This is especially meaningful since the theory of -2.31 0.91 3.06 the correlation energy is most difficult at low elec- 0.56 2.00 4.38 2.38 tron densities 2.38 We turn now to the double-layer contribution 1.39 3.76-2.370,042.41 △中. By Poisson' s equation, p=d()-(-)=4mJxm(x)-n,()dx (3.5) nd Are is the exchange and correlation part of with n(x)and n,(x), respectively the electron the chemical potential of an infinite uniform elec and positive-background densities in the uniform tron gas of density n. Axe is given by the relation model. n(x), calculated in LK-I with a self-con sistency of better than 1% of n, was recalculated (3. 2) for the present work to an accuracy of 0. 2% or better. The resulting values of Ap are listed in with Exc the exchange and correlation energy per Table i, as is the total work function in the uni- particle of the uniform gas. In our computations, form model we have used the expression (3.6) ∈x)=-(0.458/ys)-0.44/(+7.8) (3.3) It will be noted that while△φ is negligible for here the wigner-Serls C analysis of the electron gas; nant for high-eledr and 4p separately change by from wigner’ s class metals of low electron density, it becomes domi radius rs is given by on-density metals. It is also trik mr3=1/ 5.3 and 6.8 ev, respectively, over the metallic Theoretical and experimental work functions of nine simple metals. u is the work function for the uni- ound model; ois the first-order pseudopotential correction: =u+o (rounded to the nearest 0.05 eV) potential core radii re are taken from the work of Ashcroft and Langreth (Refs. 18-20). In the cases in which these authors give two possible values of r for a metal, the choice which yields agreement with experiment for were taken from Refs. 25-27(see text for details of selection). [The most densely packed faces for the various struc tures are: fcc (111), hep(0001), bec(110).] Metal Structure rs 4ulev) b币(eV) 西ev) (110) 00) (111) (110)(100) (111)(polycrystalline) 2.073,871,12 0.210 0.193.654.204.05 2.303.801.12 0 0.130.063.803.953.8 2,303,801.270.36for(0001) face 4.15 for(0001) face 0.38 for (0001) face 4,05for(0001)fac 3,283,371.06*0,19-0,050,133.553,303,25 2.00-0.99-0.95-1.052.402.402.30 bcc 393.102.752.65 4.96 2.7 0,01 0 2,402.35 2 2.63 2.61 0.45-0.53-0.602.202.102.05 2.21 0.26-0.32652.352.30 bcc 0.23 0.61 2.14 0.10-0.21