Reduced density matrix application

Reduced-Density-Matrix Mechanics. With Application to Many-Electron Atoms and Molecules,... 

G. Gidofalvi and D. A. Mazziotti, Application of variational reduced-density-matrix theory to organic molecules. J. Chem. Phys. 122, 094107 (2005). 

D. A. Mazziotti, Variational reduced-density-matrix method using three-particle N-represent-ability conditions with application to many-electron molecules. Phys. Rev. A 74, 032501 (2006). 

C. Valdemoro, Reduced density matrix versus wave function recent developments, in Strategies and Applications in Quantum Chemistry, (Y. Ellinger and M. Defranceschi, eds.), Kluwer, Dordrecht, 1996, p. 55. 

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

The A-representability constraints presented in this chapter can also be applied to computational methods based on the variational optimization of the reduced density matrix subject to necessary conditions for A-representability. Because of their hierarchical structure, the (g, R) conditions are also directly applicable to computational approaches based on the contracted Schrodinger equation. For example, consider the (2, 4) contracted Schrodinger equation. Requiring that the reconstmcted 4-matrix in the (2, 4) contracted Schrodinger equation satisfies the (4, 4) conditions is sufficient to ensure that the 2-matrix satisfies the rather stringent (2, 4) conditions. Conversely, if the 2-matrix does not satisfy the (2, 4) conditions, then it is impossible to construct a 4-matrix that is consistent with this 2-matrix and also satisfies the (4, 4) conditions. It seems that the (g, R) conditions provide important constraints for maintaining consistency at different levels of the contracted Schrodinger equation hierarchy. 

REDUCED-DENSITY-MATRIX MECHANICS WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES... 

This volume in Advances in Chemical Physics provides a broad yet detailed survey of the recent advances and applications of reduced-density-matrix mechanics in chemistry and physics. With advances in theory and optimization, Coulson s challenge for the direct calculation of the 2-RDM has been answered. While significant progress has been made, as evident from the many contributions to this book, there remain many open questions and exciting opportunities for further development of 2-RDM methods and applications. It is the hope of the editor and the contributors that this book will serve as a guide for many further advenmres and advancements in RDM mechanics. 

Elements of second order reduced density matrix of a fermion system are written in geminal basis. Matrix elements are pointed out to be scalar product of special vectors. Based on elementary vector operations inequalities are formulated relating the density matrix elements. While the inequalities are based only on the features of scalar product, not the full information is exploited carried by the vectors D. Recently there are two object of research. The first is theoretical investigation of inequalities, reducibility of the large system of them. Further work may have the chance for reaching deeper insight of the so-called N-representability problem. The second object is a practical one examine the possibility of computational applications, associate conditions above with known methods and conditions for calculating density matrices. 

The concept of the molecular orbital and their occupation is, however, not restricted to the HF model. It has much wider relevance and is applicable also for more accurate wave functions. For each wave function we can form the first-order reduced density matrix. This matrix is Hermitian and can be diagonalized. The basis for this diagonal form of the density matrix are the Natural Orbitals first introduced in quantum chemistry by Per-Olof Lowdin [4]. 

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