Abstract
Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.
Highlights
The Hohenberg–Kohn theorems [1] form the foundation of density functional theory (DFT), on which most ab initio electronic structure methods currently are based
Using that formalism, we show analytically that differentiating the non-interacting kinetic energy for a v-representable wave function leads to the negative potential (Kohn–Sham potential), up to a constant
We have shown the formalism determines the potential exact from wave functions by functional differentiation of the kinetic energy, where it is known that all orbitals originate from the same potential, the condition for v-representability
Summary
The Hohenberg–Kohn theorems [1] form the foundation of density functional theory (DFT), on which most ab initio electronic structure methods currently are based. Using that formalism, we show analytically that differentiating the non-interacting kinetic energy for a v-representable wave function leads to the negative potential (Kohn–Sham potential), up to a constant. This does not hold for arbitrary wave functions leading to the density. This provides a test establishing whether a given wave function (non-interacting), leading to a density, is non-interacting v-representable We illustrate these procedures on the one-dimensional particle in a box problem as well as the harmonic oscillator
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