Derivative of the Lieb definition for the energy functional of density-functional theory with respect to the particle number and the spin number
- General Chemistry Department (ALGC), Member of the QCMM Alliance Ghent-Brussels, Free University of Brussels (VUB), B-1050 Brussels (Belgium)
The nature of the explicit dependence on the particle number N and on the spin number N{sub s} of the Lieb definition for the energy density functional is examined both in spin-independent and in spin-polarized density functional theory. It is pointed out that the nonuniqueness of the external magnetic field B(r{yields}) corresponding to a given pair of ground-state density n(r{yields}) and spin density s(r{yields}) in spin-polarized density functional theory implies the nonexistence of the total derivative of the SDFT Lieb functional F{sub N,N{sub s}{sup L}[n,s] with respect to N{sub s}}. By giving a suitable extension of F{sub N}{sup L}[n] and F{sub N,N{sub s}{sup L}[n,s] for N{ne}{integral}n(r{yields})dr{yields} and N{sub s{ne}{integral}}}s(r{yields})dr{yields}, it is then shown that their derivatives with respect to N and N{sub s} are equal to the derivatives, with respect to N and N{sub s}, of the total energies E[N,v] and E[N,N{sub s},v,B] minus the external-field energy components, respectively.
- OSTI ID:
- 21408418
- Journal Information:
- Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032512; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
74 ATOMIC AND MOLECULAR PHYSICS
DENSITY
DENSITY FUNCTIONAL METHOD
ENERGY DENSITY
GROUND STATES
MAGNETIC FIELDS
SPIN
SPIN ORIENTATION
ANGULAR MOMENTUM
CALCULATION METHODS
ENERGY LEVELS
ORIENTATION
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
VARIATIONAL METHODS