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- Title Pages
- Preface
- List of abbreviations
- 1 Introduction
- 2 Review of ground-state density-functional theory
- 3 Fundamental existence theorems
- 4 The time-dependent Kohn–Sham scheme
- 5 Time-dependent observables
- 6 Properties of the time-dependent xc potential
- 7 The formal framework of linear-response TDDFT
- 8 The frequency-dependent xc kernel
- 9 Applications to atomic and molecular systems
- 10 Time-dependent current-DFT
- 11 The time-dependent optimized effective potential
- 12 Extended systems
- 13 TDDFT and many-body theory
- 14 Long–range correlations and dispersion interactions
- 15 Nanoscale transport and molecular junctions
- 16 Strong-field phenomena and optimal control
- 17 Nuclear motion
- Appendix A Atomic units
- Appendix B Functionals and functional derivatives
- Appendix C Densities and density matrices
- Appendix D Hartree–Fock and other wave-function approaches
- Appendix E Constructing the xc potential from a given density
- Appendix F DFT for excited states
- Appendix G Systems with noncollinear spins
- Appendix H The dipole approximation
- Appendix I A brief review of classical fluid dynamics
- Appendix J Constructing the scalar xc kernel from the tensor xc kernel
- Appendix K Semiconductor quantum wells
- Appendix L TDDFT in a Lagrangian frame
- Appendix M Inversion of the dielectric matrix
- Appendix N Review literature on DFT and many-body theory
- Appendix O TDDFT computer codes
- References
- Index

# (p.455) Appendix J Constructing the scalar xc kernel from the tensor xc kernel

# (p.455) Appendix J Constructing the scalar xc kernel from the tensor xc kernel

- Source:
- Time-Dependent Density-Functional Theory
- Publisher:
- Oxford University Press

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- Title Pages
- Preface
- List of abbreviations
- 1 Introduction
- 2 Review of ground-state density-functional theory
- 3 Fundamental existence theorems
- 4 The time-dependent Kohn–Sham scheme
- 5 Time-dependent observables
- 6 Properties of the time-dependent xc potential
- 7 The formal framework of linear-response TDDFT
- 8 The frequency-dependent xc kernel
- 9 Applications to atomic and molecular systems
- 10 Time-dependent current-DFT
- 11 The time-dependent optimized effective potential
- 12 Extended systems
- 13 TDDFT and many-body theory
- 14 Long–range correlations and dispersion interactions
- 15 Nanoscale transport and molecular junctions
- 16 Strong-field phenomena and optimal control
- 17 Nuclear motion
- Appendix A Atomic units
- Appendix B Functionals and functional derivatives
- Appendix C Densities and density matrices
- Appendix D Hartree–Fock and other wave-function approaches
- Appendix E Constructing the xc potential from a given density
- Appendix F DFT for excited states
- Appendix G Systems with noncollinear spins
- Appendix H The dipole approximation
- Appendix I A brief review of classical fluid dynamics
- Appendix J Constructing the scalar xc kernel from the tensor xc kernel
- Appendix K Semiconductor quantum wells
- Appendix L TDDFT in a Lagrangian frame
- Appendix M Inversion of the dielectric matrix
- Appendix N Review literature on DFT and many-body theory
- Appendix O TDDFT computer codes
- References
- Index