In ab initio quantum chemistry, the route that is followed, in many different ways, consists of finding computationally feasible and sufficiently accurate approximations to the full configurationinteraction (FCI) solution. One may call this a mathematicallyoriented approach. One can view DFT as an attempt -maybe often unconsciously -to follow the route of finding physical models for the pair-correlation function. The largest part of the LDA functional is the exchange functional, which is practically the same as Slater's original ρ 4/3 approximation. Slater derived his "exchange hole" from a simple model (local hole of constant depth integrating to -1) which leads to practically the same exchange energy expression (with ρ 4/3 density dependence) as the homogeneous electron gas of LDA. But the Slater construction shows that the interpretation is not necessarily that of an electrongas exchange approximation. Indeed, it has been realized that this simple local hole is much more like an exchange-correlation hole -for instance, accounting for considerable left-right cor-relation in the chemical bond (which is why it soon was called an exchange-correlation approximation) .The Slater (or LDA) hole yields much better bond energies for prototypical diatomic molecules than the exchange hole of the Hartree-Fock model: bonding changes from severe underbinding in Hartree-Fock theory to some overbinding in LDA. Also, the systematic errors in frequencies and bond distances that characterize the Hartree-Fock model disappear. This tells us that modelling of the exchangecorrelation energy may not be so difficult after all.