- 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

# Properties of the time-dependent xc potential

# Properties of the time-dependent xc potential

- Chapter:
- (p.91) 6 Properties of the time-dependent xc potential
- Source:
- Time-Dependent Density-Functional Theory
- Author(s):
### Carsten A. Ullrich

- Publisher:
- Oxford University Press

This chapter reviews the properties of the time-dependent exchange-correlation (xc) potential. It starts with a discussion of the meaning of the universal xc functional, and then covers a number of exact conditions: the adiabatic limit, the zero-force theorem, freedom of self-interaction, sum rules, and various scaling properties. Next, Galiean invariance of the xc potential and the harmonic potential theorem are discussed. The xc potential has the intriguing property that it has a memory of the previous history of the system. The ramifications of this memory dependence are discussed, as well as causality properties. Another property is the dependence on the initial state of the system. Then, a time-dependent variational principle is presented which yields the xc potential, provided that one pays attention to certain boundary conditions. Finally, it is shown that the time-dependent xc potential has a discontinuity upon change of particle number.

*Keywords:*
exchange-correlation potential, variational principle, harmonic potential theorem, Galiean invariance, derivative discontinuity, zero-force theorem, scaling properties

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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