A Second Variation of the Energy Functional: II. Possible Zero Hardness for the Density-Functional Theory

Der-Ruenn Su

Chinese Journal of Physics

33卷5期（1995 / 10 / 01）

513 - 529

英文

The frontier function (FF) introduced in the electron transfer process for a chemical reaction as appeared in a previous paper (Chin. J. Phys. 32, 433 (1994)) is investigated along with the total number of particle integral in the density-functional theory (DFT). We find that the weight function of this integral is the inverse function of the FF. In order to have mathematics of variations correct in the DFT, we conclude that the variational (functional) derivatives are not the quotient of two variations in general at thermal equilibrium. For a two-atom system, we need a 'two-potential' at a space point in parallel to our previous finding for the quantum well theory. The definition of the FF indicates that two-potential problems are actually common. The few particle transfer process is newly interpreted. Consistency of the theory implies that the hardness is zero for the DFT. We have derived a new formula for the variational derivative of the energy functional when there are electron transfers. For thermal non-equilibrium cases in semiconductors, we find the driven-mechanism which is accompanied by a charge transfer and thus involves a FF.