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Time-Dependent Density-Functional TheoryConcepts and Applications$
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Carsten A. Ullrich

Print publication date: 2011

Print ISBN-13: 9780199563029

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199563029.001.0001

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Long–range correlations and dispersion interactions

Long–range correlations and dispersion interactions

(p.333) 14 Long–range correlations and dispersion interactions
Time-Dependent Density-Functional Theory

Carsten A. Ullrich

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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