Density-Functional Theory on Graphs

• URL: http://arxiv.org/abs/2106.15370v2
• Date: Tue, 11 Jan 2022 20:38:17 GMT
• Title: Density-Functional Theory on Graphs
• Authors: Markus Penz, Robert van Leeuwen
• Abstract summary: The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn is found void in general.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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