  Real time, density matrix based, time dependent density functional theory
proceeds through the propagation of the density matrix, as opposed to the
Kohn-Sham orbitals. It is possible to reduce the computational workload by
imposing spatial cut-off radii on sparse matrices, and the propagation of the
density matrix in this manner provides direct access to the optical response of
very large systems, which would be otherwise impractical to obtain using the
standard formulations of TDDFT. Following a brief summary of our
implementation, along with several benchmark tests illustrating the validity of
the method, we present an exploration of the factors affecting the accuracy of
the approach. In particular we investigate the effect of basis set size and
matrix truncation, the key approximation used in achieving linear scaling, on
the propagator unitarity and optical spectra. Finally we illustrate that, with
an appropriate density matrix truncation range applied, the computational load
scales linearly with the system size and discuss the limitations of the
approach.
