The Conceptual Density Functional Theory (cDFT) has been widely recognized as the potential apparatus for theoretical exploration aiming at a priori prediction of chemical reactivity of atoms and molecules. Its birth was marked by the landmark paper by Parr et al. where chemical potential derived from the Hohenberg and Kohn theorem 2 has been identified as electronegativity. Further development was clearly divided between the theory an application. In the theoretical advances, the significant step has been done with the paper by Perdew et al. where Hohenberg-Kohn theory was formulated for fractional number of electrons, for systems described by a quantum mixed state. The practical applications of this theoretical achievements were remarkably initiated by the paper by Parr and Pearson. While innumerable successes have been reported in both directions, coupling the two fields together into the coherent system of "molecular thermodynamics" is still in progress. The proposal of axiomatic approach to the chemical concepts by Ayers et al. exposed once again the ever-growing disparity between the language of chemistry with its traditional concepts (atoms, bonds) and the wealth of quantum chemistry tools. The short paper with the exhausting bibliography has confirmed the longstanding interest of the group in bridging the fields of practical chemistry and quantum theory. Interesting practical guidelines to possible merging these two separately developed and powerful methodologies have been presented: the role of observables, the free choice of basic axioms and the role of their mathematical formulation for the concept based upon them. Interestingly, the authors concentrate on the conceptual integrity of the possible results of that approach, rather than on the computational accuracy on the output from a theoretical effort.