简介
This volume records the proceedings of a Forum attended by many leading researchers working in the field of Electron Density, Density Matrix and Density Functional Theory held at the Coseners' House, Abingdon-on-Thames, Oxfordshire, UK in early summer 2002.
It has long been recognized that "All the necessary information required for the energy and for calculating the properties of molecules is embodied in the first- and second-order density matrices". The wave function contains much more information than is required to yield the energy or other property. But the density matrices must correspond to some physically acceptable wave function. Coleman, one of the distinguished participants in the Forum, has dubbed this "Coulson's challenge". His paper describing recent work on the N-representability problem is included in this volume. McWeeny discusses some unsolved problems in density matrix theory and density functional theory; and Bader discusses the use of the electron density in explaining the structure and properties of atoms and molecules.
Density Functional Theory is widely used in studies of molecular and solid state systems. Yet the theoretical apparatus for this approach remains under active development. Theophilou describes a new formulation of density functional theory. Gross and his coworkers present a time-dependent theory for molecules in strong laser pulses. Nagy considers pair density functional theory, while Ludena and his colleagues examine functional N-representability in density matrix and density functional theory.
The meeting concluded with a Forum, ably chaired by B.T. Sutcliffe, in which the latest research and results were discussed. A record of this Forum is included in this volume.
This book will be of value to researchers and research students in theoretical chemistry and theoretical physics whose work involves the theoretical study of atoms, molecules and the solid state. It will be of interest to quantum chemists and solid state physicists, to materials scientists and applied mathematicians.
目录
Table Of Contents:
Preface xi
Contributing Authors xiii
Part I The Workshop
The Fundamental of Electron Density, Density Matrix and Density Functional Theory for Atoms, Molecules and the solid state 3(6)
B.T. Sutcliffe
1 Introduction 3(1)
2 Density Matrix Theory (DMT) 4(1)
3 Density Functional Theory (DFT) 5(2)
4 Conclusions 7(2)
The Programme 9(6)
Abstracts of Talks and Posters 15(18)
List of Participants 33(10)
Part II The Proceedings
The Keldysh formalism applied to time-dependent current-density-functional theory 43(26)
Robert van Leeuwen
1 Introduction 43(2)
2 Keldysh action 45(4)
3 Kohn-Sham equations and linear response 49(3)
4 TDOPM equations 52(3)
5 Integral equation for the xc-kernel 55(3)
6 The exchange-only kernel for the electron gas 58(2)
7 Conclusions 60(1)
Appendix: A 61(1)
Appendix: B 62(1)
Appendix: C 63(2)
Appendix: D 65(4)
Towards time-dependent density-functional theory for molecules in strong laser pulses 69(10)
T. Kreibich, N.I. Gidopoulos, R. van Leeuwen, and E.K.U. Gross
1 Introduction 69(2)
2 Formulation of DFT approach, absence of e-n correlation functional 71(1)
3 Ansatz to describe e-n correlation 72(7)
Pair density functional theory 79(10)
A. Nagy
1 Introduction 79(1)
2 Pair density functional theory 80(6)
3 Discussion 86(3)
The Kummer Variety for N-particles 89(8)
A.J. Coleman
1 Introduction 89(1)
2 Key Definitions 90(2)
3 Results 92(2)
4 Next steps? 94(3)
Some Unsolved Problems in Density Matrix Theory and Density Functional Theory 97(18)
Roy McWeeny
1 Preliminaries: the density functions 98(5)
2 Density matrices to density functionals 103(2)
3 Examples: density functions for simple systems 105(3)
4 A group theoretical approach 108(5)
5 Conclusion 113(2)
The new formulation of the density functional theory, the limitation of accuracy of the Kohn-Sham potential and its expression in terms of the external potential 115(14)
Andreas K. Theophilou
1 Introduction 115(1)
2 The New Formulation of DFT 116(10)
3 The KS potential as a mapping of the external potential. 126(3)
Functional N-representability in density matrix and density functional theory 129(16)
E.V. Ludeiia, V.V. Karasien, P. Nieto
1 Introduction 130(2)
2 Functional N-representability 132(2)
3 Functional N-representability through built-in pure-state N representability conditions 134(2)
4 Functional N-representability in DFT: Application to Hooke's atom 136(4)
4.1 General considerations 136(1)
4.2 Constructive approach based on local-scaling transformations 137(1)
4.3 Construction of exact functional for Hooke's atom 138(2)
5 Conclusions 140(2)
6 Acknowledgments 142(3)
Density-functional theory for the Hubbard model 145(24)
K. Capelle, N.A. Lima, M.F. Silva, and L.N. Oliveira
1 The Hubbard model and density-functional theory 146(3)
2 Exchange-correlation energy of the Hubbard model 149(5)
3 Applications 154(11)
3.1 Luttinger liquids 154(2)
3.2 Impurity models 156(4)
3.3 Spin-density waves 160(2)
3.4 Mott insulator 162(3)
4 Summary and outlook 165(4)
Demonstrating the effectiveness of a nonlocal density functional description of exchange and correlation 169(16)
Philip P. Rushton and Stewart J. Clark
1 Introduction 169(2)
2 WDA theory 171(1)
3 Cosine-wave electron gas. 172(5)
3.1 XC-energy density exc(r) 173(1)
3.2 Total XC-energy 174(1)
3.3 XC-potentials 175(1)
3.4 XC-holes 175(2)
3.5 Pair-correlation functions 177(1)
4 Large amplitude perturbations 177(2)
5 Conclusions 179(3)
6 Acknowledgements 182(3)
Incorporating the Virial Field into the Hartree-Fock Equations 185(10)
R.F.W. Bader
1 Introduction 186(3)
2 Incorporation of V(r) into the Hartree-Fock Equations 189(6)
Hohenber -Kohn Theorem and Constrained Search Formulation for Diagonal spin Density Functional Theory 195(14)
Nikitas I. Gidopoulos
1 Introduction 195(1)
2 Spin-Density-Factional Theory 196(5)
3 Diagonal-Spin-Density-Functional theory 201
Part III The Forum
The Forum - Questions 209(2)
The Forum - Discussion 211(8)
A Glossary 219(2)
A Selected Bibliography 221(2)
Index 223
Preface xi
Contributing Authors xiii
Part I The Workshop
The Fundamental of Electron Density, Density Matrix and Density Functional Theory for Atoms, Molecules and the solid state 3(6)
B.T. Sutcliffe
1 Introduction 3(1)
2 Density Matrix Theory (DMT) 4(1)
3 Density Functional Theory (DFT) 5(2)
4 Conclusions 7(2)
The Programme 9(6)
Abstracts of Talks and Posters 15(18)
List of Participants 33(10)
Part II The Proceedings
The Keldysh formalism applied to time-dependent current-density-functional theory 43(26)
Robert van Leeuwen
1 Introduction 43(2)
2 Keldysh action 45(4)
3 Kohn-Sham equations and linear response 49(3)
4 TDOPM equations 52(3)
5 Integral equation for the xc-kernel 55(3)
6 The exchange-only kernel for the electron gas 58(2)
7 Conclusions 60(1)
Appendix: A 61(1)
Appendix: B 62(1)
Appendix: C 63(2)
Appendix: D 65(4)
Towards time-dependent density-functional theory for molecules in strong laser pulses 69(10)
T. Kreibich, N.I. Gidopoulos, R. van Leeuwen, and E.K.U. Gross
1 Introduction 69(2)
2 Formulation of DFT approach, absence of e-n correlation functional 71(1)
3 Ansatz to describe e-n correlation 72(7)
Pair density functional theory 79(10)
A. Nagy
1 Introduction 79(1)
2 Pair density functional theory 80(6)
3 Discussion 86(3)
The Kummer Variety for N-particles 89(8)
A.J. Coleman
1 Introduction 89(1)
2 Key Definitions 90(2)
3 Results 92(2)
4 Next steps? 94(3)
Some Unsolved Problems in Density Matrix Theory and Density Functional Theory 97(18)
Roy McWeeny
1 Preliminaries: the density functions 98(5)
2 Density matrices to density functionals 103(2)
3 Examples: density functions for simple systems 105(3)
4 A group theoretical approach 108(5)
5 Conclusion 113(2)
The new formulation of the density functional theory, the limitation of accuracy of the Kohn-Sham potential and its expression in terms of the external potential 115(14)
Andreas K. Theophilou
1 Introduction 115(1)
2 The New Formulation of DFT 116(10)
3 The KS potential as a mapping of the external potential. 126(3)
Functional N-representability in density matrix and density functional theory 129(16)
E.V. Ludeiia, V.V. Karasien, P. Nieto
1 Introduction 130(2)
2 Functional N-representability 132(2)
3 Functional N-representability through built-in pure-state N representability conditions 134(2)
4 Functional N-representability in DFT: Application to Hooke's atom 136(4)
4.1 General considerations 136(1)
4.2 Constructive approach based on local-scaling transformations 137(1)
4.3 Construction of exact functional for Hooke's atom 138(2)
5 Conclusions 140(2)
6 Acknowledgments 142(3)
Density-functional theory for the Hubbard model 145(24)
K. Capelle, N.A. Lima, M.F. Silva, and L.N. Oliveira
1 The Hubbard model and density-functional theory 146(3)
2 Exchange-correlation energy of the Hubbard model 149(5)
3 Applications 154(11)
3.1 Luttinger liquids 154(2)
3.2 Impurity models 156(4)
3.3 Spin-density waves 160(2)
3.4 Mott insulator 162(3)
4 Summary and outlook 165(4)
Demonstrating the effectiveness of a nonlocal density functional description of exchange and correlation 169(16)
Philip P. Rushton and Stewart J. Clark
1 Introduction 169(2)
2 WDA theory 171(1)
3 Cosine-wave electron gas. 172(5)
3.1 XC-energy density exc(r) 173(1)
3.2 Total XC-energy 174(1)
3.3 XC-potentials 175(1)
3.4 XC-holes 175(2)
3.5 Pair-correlation functions 177(1)
4 Large amplitude perturbations 177(2)
5 Conclusions 179(3)
6 Acknowledgements 182(3)
Incorporating the Virial Field into the Hartree-Fock Equations 185(10)
R.F.W. Bader
1 Introduction 186(3)
2 Incorporation of V(r) into the Hartree-Fock Equations 189(6)
Hohenber -Kohn Theorem and Constrained Search Formulation for Diagonal spin Density Functional Theory 195(14)
Nikitas I. Gidopoulos
1 Introduction 195(1)
2 Spin-Density-Factional Theory 196(5)
3 Diagonal-Spin-Density-Functional theory 201
Part III The Forum
The Forum - Questions 209(2)
The Forum - Discussion 211(8)
A Glossary 219(2)
A Selected Bibliography 221(2)
Index 223
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