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.
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