The holographic electron density theorem and quantum similarity measures

How much information about the complete molecule is present in a part of the molecule? Quantum similarity measures provide comparisons between molecular electron densities based on integration over the whole space. Such integration involves boundaryless electron densities, whereas an early application of the Hohenberg—Kohn theorem to local subsystems of molecules requires these molecules to be confined to bounded, finite regions of the space. However, actual molecules have no boundaries, they are not confined to any finite region of the space. In order to find deterministic relations between local and global, boundaryless electron densities, and to classify the link between quantum similarity measures involving the full space and local subsystems, the unique extension property called the holographic property of subsystems of complete, boundaryless electron densities is established. Any nonzero volume piece of the ground state electron density completely determines the electron density of the complete, bou...

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