  A necessary first step in the development of technologies such as artificial
photosynthesis is understanding the photoexcitation process within the basic
building blocks of naturally-occurring light harvesting complexes (LHCs). The
most important of these building blocks in biological LHCs such as LHC II from
green plants are the chlorophyll $a$ (Chl $a$) and chlorophyll $b$ (Chl $b$)
chromophores dispersed throughout the protein matrix. However, efforts to
describe such systems are still hampered by the lack of computationally
efficient and accurate methods that are able to describe optical absorption in
large biomolecules. In this work we employ a highly efficient linear
combination of atomic orbitals (LCAOs) to represent the Kohn--Sham (KS) wave
functions at the density functional theory (DFT) level and perform time
dependent density functional theory (TDDFT) in either the reciprocal space and
frequency domain (LCAO-TDDFT-$k$-$\omega$) or real space and time
(LCAO-TDDFT-$r$-$t$) calculations of the optical absorption spectra of Chl $a$
and $b$ monomers and dimers. We find our LCAO-TDDFT-$k$-$\omega$ and
LCAO-TDDFT-$r$-$t$ calculations reproduce results obtained with a plane wave
(PW) representation of the KS wave functions (PW-TDDFT-$k$-$\omega$), but with
a significant reduction in computational effort. Moreover, by applying the
GLLB-SC derivative discontinuity correction $\Delta_x$ to the KS eigenenergies,
with both LCAO-TDDFT-$k$-$\omega$ and LCAO-TDDFT-$r$-$t$ methods we are able to
semi-quantitatively reproduce the experimentally measured photoinduced
dissociation (PID) results. This work opens the path to first principles
calculations of optical excitations in macromolecular systems.
