Use of ab initio methods to classify four existing energy density functionals according to their possible variational validity

Density functional theory is, of course, fundamentally a variational method. Therefore, in this Letter we suggest a classification of available energy density functionals into two groups, which we term (i) heuristic (H) and (ii) possibly variationally valid (PV). Quantum-chemical ab initio methods are employed on some selected neutral and anionic atomic systems and the molecules H2O and LiOB to make this separation into H and PV groups in the case of the exchange-correlation functionals LDA, PBE, PW91 and B3LYP. This study shows that while the PBE is a potential candidate for being variationally valid, the B3LYP, today's other most widely used density functional, shows its strongly heuristic character. The investigation of variational validity can be an important part of systematic functional development, which is today's biggest challenge in DFT.