Many-Electron Densities and Reduced Density Matrices

Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil iary yet essential N-representability conditions turned quite bleak. How ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry.

Springer Book Archives

I. Properties of Reduced Density Matrices.- 1. RDMs: How Did We Get Here?.- 2. Some Theorems on Uniqueness and Reconstruction of Higher-Order Density Matrices.- 3. Cumulant Expansions of Reduced Densities, Reduced Density Matrices, and Green's Functions.- 4. On Calculating Approximate and Exact Density Matrices.- II. The Contracted Schr?dinger Equation.- 5. Density Equation Theory in Chemical Physics.- 6. Critical Questions Concerning Iterative Solution of the Contracted Schrödinger Equation.- 7. Cumulants and the Contracted Schrödinger Equation.- III. Density Matrix Functional Theory.- 8. Natural Orbital Functional Theory.- 9. The Pair Density in Approximate Density Functional Theory: The Hidden Agent.- 10. Functional N-representability in Density Matrix and Density Functional Theory: An Illustration for Hooke's Atom.- IV. Electron Intracule and Extracule Densities.- 11. Intracule and Extracule Densities: Historical Perspectives and Future Prospects.- 12. Topology of Electron Correlation.- 13. Electron-Pair Densities of Atoms.