The Journal of Chemical Physics 139, 064104 (2013)
Linear-scaling time-dependent density-functional theory in the linear response formalism
Tim J. Zuehlsdorff1,2, Nicholas D. M. Hine2,3, James S. Spencer1,2, Nicholas M. Harrison4, D. Jason Riley2 and Peter D. Haynes1,2
1Department of Physics, Imperial College London,
Exhibition Road, London SW7 2AZ, United Kingdom
2Department of Materials, Imperial College London,
Exhibition Road, London SW7 2AZ, United Kingdom
3Cavendish Laboratory, J. J. Thomson Avenue,
Cambridge CB3 0HE, United Kingdom
4Department of Chemistry, Imperial College London,
Exhibition Road, London SW7 2AZ, United Kingdom
We present an implementation of time-dependent density-functional theory
(TDDFT) in the linear response formalism enabling the calculation of low
energy optical absorption spectra for large molecules and nanostructures.
The method avoids any explicit reference to canonical representations of
either occupied or virtual Kohn-Sham states and thus achieves linear-scaling
computational effort with system size. In contrast to conventional localised
orbital formulations, where a single set of localised functions is used to
span the occupied and unoccupied state manifold, we make use of two sets of
in situ optimised localised orbitals, one for the occupied and one
for the unoccupied space. This double representation approach avoids known
problems of spanning the space of unoccupied Kohn-Sham states with a minimal
set of localised orbitals optimised for the occupied space, while the
in situ optimisation procedure allows for efficient calculations with
a minimal number of functions. The method is applied to a number of medium
sized organic molecules and a good agreement with traditional TDDFT methods
is observed. Furthermore, linear scaling of computational cost with system
size is demonstrated on (11,0) carbon nanotubes of different lengths.
Last updated: 12 August 2013