Signs of Exchange and Correlation Potentials

The exchange and correlation potentials refer to those defined in density functional theory. (See also <http://en.wikipedia.org/wiki/Local-density_approximation>)


Define the exchange potential as $V\_{x}(n) = \partial E\_x(n)/ \partial n$, when $E\_x(n)$ is the exchange energy density of the whole system(**not** per particle). Define a similar quantity $V\_c(n)$ for the correlation contribution. My question is, are the two potentials (generally) of the same sign?


Another question: It seems that the prediction of the ionization potential using the -ve energy of HOMO is not good (See the section *Exchange-correlation potential* on <http://en.wikipedia.org/wiki/Local-density_approximation>). Using a simple slater exchange potential and a reasonable correlation potential (for a uniform electron gas), the result (?; not sure about its correctness; feel free to point it out if you think it's wrong) is about 0.7\*13.6 eV, which is not good. Of course one need not use DFT for hydrogen; it however serves as a test case. Is there any reason to believe the results will improve as the atomic number increases? 


Thanks a lot.


