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A new representation for ground states and its legendre transforms
Author(s) -
Cedillo Andrés
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560520824
Subject(s) - legendre transformation , legendre polynomials , representation (politics) , ground state , mathematics , reduction (mathematics) , variable (mathematics) , regular polygon , legendre function , associated legendre polynomials , energy (signal processing) , energy functional , computational chemistry , pure mathematics , quantum mechanics , mathematical analysis , chemistry , physics , geometry , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , politics , political science , law , statistics
The ground‐state energy of an electronic system is a functional of the number of electrons ( N ) and the external potential ( v ): E = E [ N , v ], this is the energy representation for ground states. In 1982, Nalewajski defined the Legendre transforms of this representation, taking advantage of the strict concavity of E with respect to their variables (concave respect v and convex respect N ), and he also constructed a scheme for the reduction of derivatives of his representations. Unfortunately, N and the electronic density (ρ) were the independent variables of one of these representations, but ρ depends explicitly on N . In this work, this problem is avoided using the energy per particle (ϵ) as the basic variable. In this case ϵ is a strict concave functional respect to both of his variables, and the Legendre transformations can be defined. A procedure for the reduction of derivatives is generated for the new four representations and, in contrast to the Nalewajski's procedure, it only includes derivatives of the four representations. Finally, the reduction of derivatives is used to test some relationships between the hardness and softness kernels. © 1994 John Wiley & Sons, Inc.