1-Density operators and algebraic version of the Hohenberg-Kohn theorem

Interrelation of the Coleman's representabilty theory for 1‐density operators and algebraic form of the Hohenberg–Kohn (HK) theorem is studied in detail. Convenient realization of the HK set of classes of 1‐electron operators and the Coleman's set of ensemble representable 1‐density operators is presented. Dependence of the HK class structure on the boundary properties of the ground‐state 1‐density operator is established and is illustrated on concrete simple examples. An algorithm of restoration of many electron determinant ensembles from a given 1‐density diagonal is described. A complete description of the combinatorial structure of Coleman's polyhedrons is obtained. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007