An up-to-date account of this cutting-edge research in a consistent and understandable framework, of special interest to experts in other areas of electronic structure and/or quantum many-body theory. It will serve equally well as a self-contained guide to learning about reduced density matrices either through self-study or in a classroom as well as an invaluable resource for understanding the critical advancements in the field.
Table of Content
Part I 1
Chapter 1 N-representability 3
By A. John Coleman
Chapter 2 historical Introduction 11
By Mitja Rosina
Part II 19
Chapter 3 variational Two-electron Reduced-density-matrix Theory 21
By David A. Mazziotti
Chapter 4 the Lower Bound Method for Density Matrices And Semidefinite Programming 61
By Robert M. Erdahl
Chapter 5 the T1 and T2 Representability Conditions 93
By Bastiaan J. Braams, Jerome K. Percus, and Zhengji Zhao
Chapter 6 semidefinite Programming: Formulations and Primal-dual Interior-point Methods 103
By Mituhiro Fukuda, Maho Nakata, and Makoto Yamashita
Part III 119
Chapter 7 theory and Methodology of the Contracted Schrödinger Equation 121
By C. Valdemoro
Chapter 8 contracted Schrödinger Equation 165
By David A. Mazziotti
Chapter 9 purification of Correlated Reduced Density Matrices: Review and Applications 205
By D. R. Alcoba
Chapter 10 Cumulants, Extensivity, and the Connected Formulation of the Contracted Schrödinger Equation 261
By John M. Herbert and John E. Harriman
Chapter 11 Generalized Normal Ordering, Irreducible Brillouin Conditions, and Contracted Schrödinger Equations 293
By Werner Kutzelnigg and Debashis Mukherjee
Chapter 12 Anti-hermitian Formulation of the Contracted Schrödinger Theory 331
By David A. Mazziotti
Chapter 13 Canonical Transformation Theory for Dynamic Correlations in Multireference Problems 343
By Garnet Kin-Lic Chan and Takeshi Yanai
Part IV 385
Chapter 14 Natural Orbital Functional Theory 387
By Mario Piris
Chapter 15 Geminal Functional Theory 429
By B. C. Rinderspacher
Chapter 16 Linear Inequalities for Diagonal Elements Of Density Matrices 443
By Paul W. Ayers and Ernest R. Davidson
Part V 485
Chapter 17 Parameterization of the 2-rdm 487
By A. John Coleman
Chapter 18 Entanglement, Electron Correlation, And Density Matrices 493
By Sabre Kais
Author Index 537
Subject Index 551
About the author
David A. Mazziotti is Assistant Professor in the Department
of Chemistry at the University of Chicago. His current research
interests lie at the intersection of chemistry, physics, biology,
and applied mathematics with special interest in advanced
electronic structure and quantum control theory.
Stuart Rice is Frank P. Hixon Distinguished Service
Professor in the James Franck Institute and the Department of
Chemistry at the University of Chicago.
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