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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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Applications to atomic and molecular systems

Applications to atomic and molecular systems

(p.176) 9 Applications to atomic and molecular systems
Time-Dependent Density-Functional Theory

Carsten A. Ullrich

Oxford University Press

This chapter contains an overview of applications of time-dependent density-functional theory (TDDFT) for excitation energies in atoms and molecules. The first section begins with a discussion of the spectrum of Kohn-Sham excitations, which in general is close to the exact excitation spectrum, provided the exact exchange-correlation (xc) potential is used. The importance of the correct asymptotic behaviour of the xc potential is emphasized. The second section considers various trends and features of molecular excitation energies, comparing TDDFT with wave-function based approaches. TDDFT has a lower computational cost and performs very well compared to traditional approaches of quantum chemistry. Challenging cases such as double excitations and charge-transfer excitations are studied. The frequency dependence and the long-range behaviour of the exchange-correlation kernel are important for describing these challenging cases correctly. Other methods to obtain excitation energies with TDDFT, such as the Sternheimer equation and real-time propagation, are also described.

Keywords:   excitation energies, real-time propagation, double excitations, charge-transfer excitations, exchange-correlation kernel, Sternheimer equation, density-functional theory, quantum chemistry

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