Synopsis and Future Trends

Abstract

The problem of how to envelop an immensity is certainly a very difficult one, particularly, if we consider the rather limited extension of the present book. Because, all the branches, sub-branches and sub-sub-branches, etc., of the density functional tree which has grown for already over sixty years, do represent an immensity. But, in truth, the authors have not pursued this goal, for in the first place, it is quite hopeless and in the second place, it is unadvisable, because in.hat case this book would have become a mere collection of ideas borrowed from rather different and sometimes opposite quarters. We have renounced to the task of presenting an unrelated description of particular branches of this tree and have opted for a more comprehensive presentation built around a basic and unifying idea. This has been the method of local-scaling transformations in $\mathcal{R}^3$. Perhaps this basic idea will also be vital for future developments and we expect that it will contribute substantially to create a unified picture of the different branches of density functional theory. Briefly, in what follows, we describe some of the topics which were not discussed in the present book but which certainly constitute important aspects of the theory.