# Long–range correlations and dispersion interactions

# Long–range correlations and dispersion interactions

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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