Reduced-Density-Matrix Mechanics (eBook)

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.

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