To obtain the electronic structure of molecules, the formidable task of solving highly dimensional Schrödinger equations would be needed. Density functional theory provides an alternative way. Although obtaining exact solutions would be even more difficult, it opens a path by suggesting a simple way to construct models. However, these are constructed by "cutting the Gordian knot". Thus, there is no path indicating how approach the exact solution.  Furthermore, one chooses to use a simple model (called by its authors Kohn-Sham), that provides speed in calculation, but misses quantum effects.The quality of such approximations is judged by comparison with reference data. With the rapidity of present computers a wealth of data is available , and the comparison uses statistical tools. This needs special care, that is not always taken.A possibility to improve on these problems is to define a family of models connecting the Kohn-Sham Hamiltonian with the physical one. Thus, the role of the rough density functional approximations can be reduced, and the missing quantum effects introduced.A second approach is to give up using density functionals, but simply use mathematical corrections to the models. Two examples of constructing such corrections are given. In the first, a basis is constructed that respects the analytically derived way the corrections approach the exact solution. The second solves the physical problem in a basis of functions provided by the solutions of the models.