More than 30,000 papers are published each year
in which modern density functional calculations are performed.
However, there is presently no systematic route to finding useful
approximations. Over 40 years ago, Lieb and Simon demonstrated
that the original version of density functional theory, Thomas-Fermi
theory, becomes relatively exact in a very particular
non-relativistic limit of large electron number. I will explain why I believe this
holds the key to a systematic treatment of such approximations, and
what my group has done in the last 8 years to use this insight.