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.
為了持續優化網站功能與使用者體驗,本網站將Cookies分析技術用於網站營運、分析和個人化服務之目的。
若您繼續瀏覽本網站,即表示您同意本網站使用Cookies。