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Many references exist in the density functional theory (DFT) literature tothe chemical potential of the electrons in an atom or a molecule. The origin ofthis notion has been the identification of the Lagrange multiplier $\mu =\partial E/\partial N$ in the Euler-Lagrange variational equation for theground state density as the chemical potential of the electrons. We firstdiscuss why the Lagrange multiplier in this case is an arbitrary constant andtherefore cannot be a physical characteristic of an atom or molecule. Theswitching of the energy derivative ("chemical potential") from $-I$ to $-A$when the electron number crosses the integer, called integer discontinuity orderivative discontinuity, is not physical but only occurs when the nonphysicalnoninteger electron systems and the corresponding energy and derivative$\partial E/\partial N$ are chosen in a specific discontinuous way. Thequestion is discussed whether in fact the thermodynamical concept of a chemicalpotential can be defined for the electrons in such few-electron systems asatoms and molecules. The conclusion is that such systems lack importantcharacteristics of thermodynamic systems and do not afford the definition of achemical potential. They also cannot be considered as analogues of the opensystems of thermodynamics that can exchange particles with an environment (aparticles bath or other members of a Gibbsian ensemble). Thermodynamical(statistical mechanical) concepts like chemical potential, open systems, grandcanonical ensemble etc. are not applicable to a few electron system like anatom or molecule. A number of topics in DFT are critically reviewed in thelight of these findings: jumps in the Kohn-Sham potential when crossing aninteger number of electrons, the band gap problem, thedeviation-from-straight-lines error, the role of ensembles in DFT.

physical chemistry chemical physics/pccp. physical chemistry chemical physics

Chemical potential, derivative discontinuity, fractional electrons, jump  of the Kohn-Sham potential, atoms as thermodynamic open systems, and other  (mis)conceptions of the density functional theory of electrons in molecules