Title: Present state of the Density Functional Theory studies, the spin problem, and following from quantum mechanics limits on its application

Abstract

The Density Functional Theory (DFT) approach elaborated by Kohn with co-authors almost 60 years ago, at present became the most widely used method for studying molecules and solids. It can be applied to systems with million atoms, if the modern computation facilities are used. The application of the Density Functional Theory (DFT) approaches to large systems, which were not available to be studied before, induced a euphoria in the DFT community that led to using the DFT methods without an analysis of the limitations following from quantum mechanics. In this report, I will discuss the modern state of DFT studies basing on the last publications and will consider two cases when the conventional DFT approaches, cannot be applied. As the author rigorously proved for an arbitrary N-electron state by group theoretical methods, the electron density does not depend on the total spin S of the state. From this follows that the Kohn–Sham equations have the same form for states with different S. I will present the critical survey of elaborated DFT procedure taking into account the spin and show that they modify only exchange functionals, while correlation functionals do not correspond to the spin of the state. The conception of spin in principle cannot be defined in the framework of the electron density formalism. It is the main reason of the problems arising in the study by DFT methods the magnetic properties of the transition metals. The possible way of resolving spin problems can be found in the two-particle reduced density matrix formulation of DFT. Then, I will consider the case of the degenerated states. In the end of my report, I will present some results obtained in my studies of the Pauli Exclusion Principle (PEP), in which PEP was substantiated and also the review published recently. I will demonstrate that if PEP is not fulfilled, this leads to contradictions with the concepts of particle independence and their identity. It will be proved that the particles, described by wave functions with the permutation symmetry not allowed by PEP, may not exist. From this follows a very important conclusion: we may not expect that in future some unknown elementary particles that have not fermion or boson symmetries can be discovered.