- 期刊
- OpenAccess
A Second Variation of the Energy Functional: II. Possible Zero Hardness for the Density-Functional Theory
並列摘要
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.
並列關鍵字
無資料延伸閱讀
- Guo, Z. (2009). Density functional theory studies of selected hydrogen bond assisted chemical reactions [doctoral dissertation, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200015505
- CAI, K. (1988). AN APPLICATION OF STRESS ENERGY TENSOR TO THE VANISHING THEOREM OF OIFFERENTIAL FORMS. International Journal of Mathematics and Mathematical Sciences, 1988(), 675-682. https://doi.org/10.1155/S0161171288000821
- 李維崇（2008）。Phonon calculations on microwave dielectric material La(Mg1/2,Ti1/2)O3:Density-Functional Perturbation Theory Study〔碩士論文，淡江大學〕。華藝線上圖書館。https://doi.org/10.6846/TKU.2008.00581
- Ghsemi, A., & Ashrafi, F. (2012). Density Functional Theory (DFT) Study of O_2, N_2 Adsorptions on H-Capped (4,4) Single-Walled Carbon Nanotube. Research Journal of Applied Sciences, Engineering and Technology, 4(15), 2523-2528. https://www.airitilibrary.com/Article/Detail?DocID=20407467-201208-201510260013-201510260013-2523-2528
- 周育祥（2010）。Phonon studys on microwave dielectric material Ba(Zn1/3Nb2/3)O3 form Density-Functional Perturbation Theory Study〔碩士論文，淡江大學〕。華藝線上圖書館。https://doi.org/10.6846/TKU.2010.00586