Descripción: This work describes a simple spatial decomposition of the first-order reduced density matrix corresponding to an N -electron system into first-order density matrices, each of them associated to an atomic domain defined in the theory of atoms in molecules. A study of the representability of the density matrices arisen from this decomposition is reported and analyzed. An appropriate treatment of the eigenvectors of the matrices defined over atomic domains or over unions of these domains allows one to describe satisfactorily molecular properties and chemical bondings within a determined molecule and among its fragments. Numerical determinations, performed in selected molecules, confirm the reliability of our proposal. © 2005 American Institute of Physics.

Descripción: This paper describes a matrix formulation for the correlated hole theory within the framework of the domain-averaged model in many electron systems (atoms, molecules, condensed matter, etc.). General relationships between this quantity and one-particle reduced density matrices for any independent particle or correlated state functions are presented. This formulation turns out to be suitable for computational purposes due to the straightforward introduction of cumulants of two-particle reduced density matrices within the quantum field structure. Numerical calculations in selected simple molecular systems have been performed in order to determine preliminary correlated values for such a quantity.

Descripción: In this paper we propose a functional of the many-body cumulant of the second-order reduced density matrix within the spin-free formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spin-adapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems. © 2010 American Institute of Physics.

Descripción: This article is a continuation of our previous paper on schemes of energy decompositions of molecular systems in the real space [D. R. Alcoba, J. Chem. Phys. 122, 074102 (2005)] now using correlated state functions. We study, according to physical arguments, the appropriate management of the density cumulant arising from the second-order reduced density matrix at correlated level, whose contributions can be assigned to one-center or to two-center terms in the energy partitioning. Our treatments are applied within two physical space partitioning schemes: the Bader partitioning into atomic basins and the fuzzy atom procedure. The results obtained in selected molecules are analyzed and discussed in detail. © 2007 American Institute of Physics.

Descripción: Grand-canonical like descriptions of many electron atomic and molecular open systems which are characterized by a non-integer number of electrons are presented. Their associated reduced density matrices (RDMs) are obtained by introducing the contracting mapping for this type of distributions. It is shown that there is loss of information when connecting RDMs of different order by partial contractions. The energy convexity property of these systems simplifies the description. Consequently, this formulation opens the possibility to a new look for chemical descriptors such as chemical potential and reactivity among others. Examples are presented to discuss the theoretical aspects of this work. © 2013 AIP Publishing LLC.