# 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.

• This would really be two questions. Can you separate your second (about ionization potentials in DFT) into a distinct question? Then this is about exchange vs. correlation potentials and there are separate pages and discussions for each. – Geoff Hutchison Mar 5 '15 at 18:27
• What is the ''-ve energy''? – TheFox Mar 22 '17 at 12:37
• "Of course one need not use DFT for hydrogen; it however serves as a test case." No, it doesn't. Systems with one electron are those where any standard DFT must inevitably fail. $\ce{H}$ might be the smallest testcase, but that's about it. – TheFox Mar 22 '17 at 12:41