Comparison of Available Orbital-Dependent Approximations for Ec

After establishing the basic ability of to deal with dispersion forces, the next step is a quantitative study of more conventional systems. In Table 2.9 the correlation energies obtained with this functional for closed-subshell atoms are compared with various other approximations and the exact correlation energies [83] (which have been extracted by combining variational results for two- and three-electron systems with experimental data for the ionization energies of the remaining electrons). The LDA energies show the 

In Table 2.9 the Ef component of the complete E is also listed separately. Ef vanishes for two-electron systems and is more than 2 orders of magnitude smaller than for all other atoms. This result suggests that Ef can be neglected in most situations, which definitively simplifies the application of o  

Ec do not completely vanish in this limit, so that the ISI correlation energy is slightly smaller than the exact result. 

A more sensitive test for correlation functionals than total atomic correlation energies is provided by atomic EAs. In Table 2.11 the EAs for obtained with various functionals are listed [62]. In all cases the exact exchange is used, only the correlation part of varies. As to be expected, the x-only calculation predicts H to be unbound, while LDA correlation 

Turning to the first-principles orbital-dependent correlation functionals, one realizes that Ec does not predict N2 to be bound at all. To understand this result one has to go back to (2.83) and examine the structure of this expression. represents the interaction of two simultaneous particle- 

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