Orbital-Free Effective Embedding Potential: Density-Matrix Functional Theory Case

Minimization of the Hohenberg-Kohn total energy functional E-HK[rho] in the presence of the constraint rho - rho(B) >= 0, where rho(B) is some arbitrarily chosen electron density comprising integer number of electrons is considered. To access better numerical accuracy of approximations to E-HK[rho] in practice, the search for optimal rho - rho(B) is performed using auxiliary quantities such as orbitals of a reference system of non-interacting electrons [Wesolowski and Warshel, J Phys Chem 1993, 97, 8050] or a wavefunction-like object corresponding to interacting electrons [Wesolowski, Phys. Rev A 2008, 77, 012504]. In both cases, the condition rho - rho(B) >= 0 leads to a local potential (orbital-free effective embedding potential) of the same general form if expressed by means of universal density functionals. In this work, it is shown that the same local potential is obtained if the search for optimal rho - rho(B) is performed among one-particle reduced density matrices. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2520-2525, 2009