The goal of the work presented in this thesis was to develop and implement a method for
calculating optical absorption spectra for large electronic systems within a linear-scaling
density-functional theory (LS-DFT) formalism. The key feature of this method was the
development of a scheme for optimizing a set of localized orbitals to accurately represent
unoccupied Kohn-Sham states, which are not well represented by the localized orbital basis
sets used for ground state LS-DFT calculations.
Three different schemes were compared for the calculation of unoccupied states using
a one-dimensional “toy model” and the most promising of these, based on the use of a
projection operator, was implemented in a fully-functional LS-DFT code.
Using the toy model, two methods for the calculation of band structures within a
localized basis set were investigated and some of the features required by localized basis
sets in order to produce accurate band structures were identified.
The method was tested by the application to both molecular and extended systems,
with calculations of densities of states, band structures and optical absorption spectra.
The results for the smaller systems were validated by comparison with a cubic-scaling
plane-wave density-functional theory code, with which excellent agreement was achieved.
Additionally, the method was shown to be linear-scaling for a conjugated polymer for
system sizes up to 1000 atoms.
The use of the projection method was shown to be crucial for calculating the above
results, as was the implementation of a momentum operator based formalism for the calculation
of spectra. Finally, it was shown that the method can be used to identify the transitions
responsible for particular peaks in the spectra and is sensitive enough to distinguish
between spectra for systems with very similar structures, demonstrating the capabilities of
the method to aid the interpretation of experimental results.