Are the Unconventional Density Variations Really Unconventional?

Based on numerical evidence and theoretical arguments, we demonstrate that the unconventional density variations are not really unconventional and should be included in the density variational domain of any ground-state density. As a result, Lieb’s Theorem 3.10 (Lieb, Int J Quantum Chem 1983, 24, 243) is reconfirmed. More specifically, the energy variation delta E-v is of order higher than linear order of the density variation delta n(r) about the ground-state density n(0)(r) of a system with a fixed number of electrons in Hilbert space, whereas delta E-v is of linear order of delta n(r) about the ground-state density of a system with a varied number of electrons in Fock space. The unconventional density variations are not the cause for the linear-order behavior of delta E-v in Fock space and the derivative discontinuity of the total energy. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 3199-3216, 2009