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Variational calculation with general density functional to solve the electronic Schrödinger equation directly for ground state: a recipe for self-consistent field solution



AbstractUsing orbital-free framework, a simple numerical optimization of the density functional for ground state electronic energy is described for any type of functional approximation, demonstrated via the example of linear combinations of homogeneous functionals of the density. The numerical recipe is given and analyzed for solution: Originating from the linear dependence of nuclear-electron attraction functional on one-electron density (Vne[ρ0(r1)] = -ΣA = 1,…,MZA∫ρ0(r1)rA1-1dr1), and a quadratic LCAO approximation for ρ0, the optimization can be done with iterative use of lin-solver. This quadratic approximation, as simplest educated choice for ρ0, is compared and analyzed algebraically to the HF-SCF one in the Appendices. We call the attention that the introduction of a self-consistent field optimization of non-linear density functional is a new element in this part of the related, general theory.