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 1Chapter 1 N-representability 3By A. John ColemanChapter 2 historical Introduction 11By Mitja RosinaPart II 19Chapter 3 variational Two-electron Reduced-density-matrix Theory 21By David A. MazziottiChapter 4 the Lower Bound Method for Density Matrices And Semidefinite Programming 61By Robert M. ErdahlChapter 5 the T1 and T2 Representability Conditions 93By Bastiaan J. Braams, Jerome K. Percus, and Zhengji ZhaoChapter 6 semidefinite Programming: Formulations and Primal–dual Interior-point Methods 103By Mituhiro Fukuda, Maho Nakata, and Makoto YamashitaPart III 119Chapter 7 theory and Methodology of the Contracted Schrödinger Equation 121By C. ValdemoroChapter 8 contracted Schrödinger Equation 165By David A. MazziottiChapter 9 purification of Correlated Reduced Density Matrices: Review and Applications 205By D. R. AlcobaChapter 10 Cumulants, Extensivity, and the Connected Formulation of the Contracted Schrödinger Equation 261By John M. Herbert and John E. HarrimanChapter 11 Generalized Normal Ordering, Irreducible Brillouin Conditions, and Contracted Schrödinger Equations 293By Werner Kutzelnigg and Debashis MukherjeeChapter 12 Anti-hermitian Formulation of the Contracted Schrödinger Theory 331By David A. MazziottiChapter 13 Canonical Transformation Theory for Dynamic Correlations in Multireference Problems 343By Garnet Kin-Lic Chan and Takeshi YanaiPart IV 385Chapter 14 Natural Orbital Functional Theory 387By Mario PirisChapter 15 Geminal Functional Theory 429By B. C. RinderspacherChapter 16 Linear Inequalities for Diagonal Elements Of Density Matrices 443By Paul W. Ayers and Ernest R. DavidsonPart V 485Chapter 17 Parameterization of the 2-rdm 487By A. John ColemanChapter 18 Entanglement, Electron Correlation, And Density Matrices 493By Sabre KaisAuthor Index 537Subject Index 551

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 1Chapter 1 N-representability 3By A. John ColemanChapter 2 historical Introduction 11By Mitja RosinaPart II 19Chapter 3 variational Two-electron Reduced-density-matrix Theory 21By David A. MazziottiChapter 4 the Lower Bound Method for Density Matrices And Semidefinite Programming 61By Robert M. ErdahlChapter 5 the T1 and T2 Representability Conditions 93By Bastiaan J. Braams, Jerome K. Percus, and Zhengji ZhaoChapter 6 semidefinite Programming: Formulations and Primal–dual Interior-point Methods 103By Mituhiro Fukuda, Maho Nakata, and Makoto YamashitaPart III 119Chapter 7 theory and Methodology of the Contracted Schrödinger Equation 121By C. ValdemoroChapter 8 contracted Schrödinger Equation 165By David A. MazziottiChapter 9 purification of Correlated Reduced Density Matrices: Review and Applications 205By D. R. AlcobaChapter 10 Cumulants, Extensivity, and the Connected Formulation of the Contracted Schrödinger Equation 261By John M. Herbert and John E. HarrimanChapter 11 Generalized Normal Ordering, Irreducible Brillouin Conditions, and Contracted Schrödinger Equations 293By Werner Kutzelnigg and Debashis MukherjeeChapter 12 Anti-hermitian Formulation of the Contracted Schrödinger Theory 331By David A. MazziottiChapter 13 Canonical Transformation Theory for Dynamic Correlations in Multireference Problems 343By Garnet Kin-Lic Chan and Takeshi YanaiPart IV 385Chapter 14 Natural Orbital Functional Theory 387By Mario PirisChapter 15 Geminal Functional Theory 429By B. C. RinderspacherChapter 16 Linear Inequalities for Diagonal Elements Of Density Matrices 443By Paul W. Ayers and Ernest R. DavidsonPart V 485Chapter 17 Parameterization of the 2-rdm 487By A. John ColemanChapter 18 Entanglement, Electron Correlation, And Density Matrices 493By Sabre KaisAuthor Index 537Subject Index 551