Density-functional theory on graphs.
Markus Penz, Robert van Leeuwen
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.
Topics & Concepts
ConvexityDensity functional theoryMathematicsGraph theoryVoid (composites)Property (philosophy)Lattice (music)Functional theorySet (abstract data type)Pure mathematicsTopology (electrical circuits)Discrete mathematicsComputer scienceCombinatoricsPhysicsQuantum mechanicsMaterials scienceProgramming languageFinancial economicsComposite materialPhilosophyAcousticsEconomicsEpistemologyAdvanced Chemical Physics StudiesTheoretical and Computational PhysicsMachine Learning in Materials Science