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15.3. ENERGY DENSITY 119 120 CHAPTER 15. ANALYSIS TOOLS
our analysis, we may rewrite this as
1 ∞
E LDA = dr s g(r s ) & unif (r s ). (15.4)
XC 0 XC
Thus the contribution to E LDA for a given r s value is given by g 1 (r s ) times the weighting
XC
factor & unif (r s ). Clearly, from Fig. 15.3, we see that, to get a good value for the exchange-
XC
correlation energy of the Ar atom, LDA must do well for r s ≤ 2, but its performance for
larger r s values is irrelevant.
Typical r s values are small for core electrons (at the origin, a hydrogenic atom has r s =
0.72/Z), but valence electrons have r s between about 1 and 6. These produce the dominant
contribution to chemical processes, such as atomization of molecules, but core relaxations
with r s 0 1 can also contribute. The valence electrons in simple metal solids have r s between
2 and 6.

15.3 Energy density

15.4 Questions