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