  The accuracy of approximate methods for calculating linear optical spectra
depends on many variables. In this study, we fix most of these parameters to
typical values found in photosynthetic light-harvesting complexes of plants and
determine the accuracy of approximate spectra with respect to exact calculation
as a function of the energy gap and interpigment coupling in a pigment dimer.
We use a spectral density with the first eight intramolecular modes of
chlorophyll a and include inhomogeneous disorder for the calculation of
spectra. We compare the accuracy of absorption, linear dichroism, and circular
dichroism spectra calculated using the Full Cumulant Expansion (FCE), coherent
time-dependent Redfield (ctR), and time-independent Redfield and modified
Redfield methods. As a reference we use spectra calculated with the Exact
Stochastic Path Integral Evaluation method. We find the FCE method to be the
most accurate for the calculation of all spectra. The ctR method performs well
for the qualitative calculation of absorption and linear dichroism spectra when
pigments are moderately coupled ($\sim 15\text{ cm}^{-1}$), but ctR spectra may
differ significantly from exact spectra when strong interpigment coupling
($\sim 100\text{ cm}^{-1}$) is present. The dependence of the quality of
Redfield and modified Redfield spectra on molecular parameters is similar, and
these methods almost always perform worse than ctR, especially when the
interpigment coupling is strong or the excitonic energy gap is small (for a
given coupling). The accuracy of approximate spectra is not affected by
resonance between the excitonic energy gap and intramolecular modes when
realistic inhomogeneous disorder is included.
