Density-Functional Theory on Graphs

Markus Penz; Robert van Leeuwen

doi:10.1063/5.0074249

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arXiv · 2106.15370

Density-Functional Theory on Graphs

Markus Penz·Robert van Leeuwen

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Abstract

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional.

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Markus Penz, Robert van Leeuwen. 2021-06-29. Density-Functional Theory on Graphs. https://doi.org/10.1063/5.0074249

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