- 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

# Long–range correlations and dispersion interactions

# Long–range correlations and dispersion interactions

- Chapter:
- (p.333) 14 Long–range correlations and dispersion interactions
- Source:
- Time-Dependent Density-Functional Theory
- Author(s):
### Carsten A. Ullrich

- Publisher:
- Oxford University Press

This chapter focuses on the treatment of long-range correlation effects and dispersion interactions via time-dependent density-functional theory. It first derives an exact expression for the ground-state correlation energy of an electronic system, using the so-called adiabatic-connection fluctuation-dissipation approach. This expression gives the correlation energy as an imaginary-frequency integral over the response functions. The random-phase approximation (RPA) for the correlation energy is introduced, and applications for molecules are discussed. The second section focuses on van der Waals interactions. These long-range forces are due to the interaction between induced fluctuating dipoles, and can be expressed in principle exactly using time-dependent density-functional theory. Simple and seamless van der Waals density functionals are presented and discussed. These functionals allow the possibility of accurate calculations of the properties of sparse matter using density-functional theory.

*Keywords:*
adiabatic-connection fluctuation-dissipation approach, correlation energy, random-phase approximation, van der Waals interactions, sparse matter, van der Waals density functionals

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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