Abstract
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.
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