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Journal of Chemical Sciences

Generalized density-functional theory: Conquering theN-representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

Paul W. Ayers, Mel Levy

Published Sep 1, 2005• 93 citations
Publisher
DOI
10.1007/bf02708356

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Abstract The variational determination of the second‐order reduced density matrices arising from N‐electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on‐top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second‐order reduced density matrix elements satisfy determined N‐representability variational conditions, as well as other constraints arising from the doubly‐occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many‐electron systems, shows the usefulness of our proposals.

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The N-representability conditions on the reduced second-order reduced density matrix (2-RDM), impose restrictions not only in the context of reduced density matrix theory (RDMT), but also on functionals advanced in one-matrix theory such as natural orbital functional theory (NOFT), and on functionals depending on the one-electron density such as those of density functional theory (DFT). We review some aspects of the applications of these N-representability conditions in these theories and present some conclusions.
Preface. I: Properties of Reduced Density Matrices. 1. RDMs: How Did We Get Here? A.J. Coleman. 2. Some Theorems on Uniqueness and Reconstruction of Higher-Order Density Matrices M. Rosina. 3. Cumulant Expansions of Reduced Densities, Reduced Density Matrices, and Green's Functions P. Ziesche. 4. On Calculating Approximate and Exact Density Matrices R. Erdahl, B. Jin. II: The Contracted Schroedinger Equation. 5. Density Equation Theory in Chemical Physics H. Nakatsuji. 6. Critical Questions Concerning Iterative Solution of the Contracted Schroedinger Equation C. Valdemoro, L.M. Tel, E. Perez-Romero 7. Cumulants and the Contracted Schroedinger Equation D.A. Mazziotti.. III: Density Matrix Functional Theory. 8. Natural Orbital Functional Theory S. Goedecker, C.J. Umrigar. 9. The Pair Density in Approximate Density Functional Theory: The Hidden Agent N.T. Maitra, K. Burke. 10. Functional N-representability in Density Matrix and Density Functional Theory: An Illustration for Hooke's Atom E.V. Ludena, V. Karasiev, A. Artemiev, D. Gomez.. IV: Electron Intracule and Extracule Densities. 11. Intracule and Extracule Densities: Historical Perspectives and Future Prospects E. Valderrama, J.M. Ugalde, R.J. Boyd. 12. Topology of Electron Correlation J. Cioslowski. 13. Electron-Pair Densities of Atoms T. Koga. Index.
Abstract The variational determination of the second‐order reduced density matrices arising from N‐electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on‐top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second‐order reduced density matrix elements satisfy determined N‐representability variational conditions, as well as other constraints arising from the doubly‐occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many‐electron systems, shows the usefulness of our proposals.