Keywords density functional, atomization energy, electronic structure theory
IntroductionThis year is the 50th anniversary of Kohn-Sham density functional theory [1], which from a humble beginning has grown up to be the most widely-used method of electronic structure calculation in condensed matter physics, quantum chemistry, and materials engineering. The popularity of this theory arises first because it is computationally efficient, with an orbital structure like that of Hartree or Hartree-Fock theory, and second because it is usefully accurate. There is an underlying exact theory for the ground-state energy and electron density, which inspires the continuing and successful (if slow) search for more accurate but still computationally tractable approximations to the needed density functional for the exchange-correlation energy. This is also the tenth anniversary of collaboration among the authors of this paper. In 2005, three of us (GIC, AR, JPP) published the first [2] of 35 collaborative research papers in density functional theory. (One year later, another of us (JS) started research in this theory as a graduate student with JPP.) That first collaborative paper raised questions about the atomization energies of molecules, which up to that time had been widely regarded as a "gold standard" of accuracy for density functional approximations. In 2015, when three of us (JS, AR, and JPP) have proposed what we regard as an optimally accurate functional that preserves computational efficiency [3], we return to the issue in the title of this article and present an explanation which is supported by numerical evidence at this high level of approximation.