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Generator coordinate method in time-dependent density-functional theory: Memory made simple

J. Chem. Phys. 127, 124101 (2007); doi:10.1063/1.2768368

Published 24 September 2007

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E. Orestes
Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, Caixa Postal 780, São Carlos, São Paulo 13560-970, Brazil; Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, São Paulo 13560-970, Brazil; and Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA

K. Capelle
Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, São Paulo 13560-970, Brazil

A. B. F. da Silva
Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, Caixa Postal 780, São Carlos, São Paulo 13560-970, Brazil

C. A. Ullrich
Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation. ©2007 American Institute of Physics
History: Received 23 April 2007; accepted 10 July 2007; published 24 September 2007
Permalink: http://link.aip.org/link/?JCPSA6/127/124101/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.Ew
    Density-functional theory (atoms and molecules)
  • 31.15.Pf
    Variational techniques (atoms and molecules)
  • 31.25.-v
    Electron correlation calculations for atoms and molecules
  • YEAR: 2007

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ISSN:
0021-9606 (print)   1089-7690 (online)
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