Maximum principles in DFT from reciprocal variational problem

• Published in: International journal of quantum chemistry Vol. 65; no. 5; pp. 499 - 501
• Main Authors: Tkacz-Śmiech, Katarzyna, Ptak, W. S.
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 1997
• Subjects: density-functional theory; maximum principle; reciprocal problem; variational principle
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/(SICI)1097-461X(1997)65:5<499::AID-QUA14>3.0.CO;2-Z

Formalism of density‐functional theory (DFT) is based on the calculus of variation. In the Hohenberg and Kohn theorem, a variational equation minimizing electronic energy with respect to an electron density is constructed. The calculus of variation allows one to formulate a problem which is reciprocal to an original one. Also, we may consider the problem of finding the electron density determining a given energy E=E[ρ] for a maximum number N=N[ρ] of the electrons forming the system. In this work, the reciprocal variational problem is discussed. Mathematical considerations are followed by a presentation of an application of the reciprocal problem (maximum entropy principle). Other possibilities of the applications are sketched. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 499–501, 1997