Bacteriochlorophyll
and chlorophyll molecules are crucial building
blocks of the photosynthetic apparatus in bacteria, algae, and plants.
Embedded in transmembrane protein complexes, they are responsible
for the primary processes of photosynthesis: excitation energy and
charge transfer. Here, we use
ab initio
many-body
perturbation theory within the
GW
approximation and
Bethe–Salpeter equation (BSE) approach to calculate the electronic
structure and optical excitations of bacteriochlorophylls
a
,
b
,
c
,
d
, and
e
and chlorophylls
a
and
b
. We systematically study the effects of the structure,
basis set size, partial self-consistency in
GW
, and
the underlying exchange–correlation approximation and compare
our calculations with results from time-dependent density functional
theory, multireference RASPT2, and experimental literature results.
We find that optical excitations calculated with
GW
+BSE are in excellent agreement with experimental data, with an average
deviation of less than 100 meV for the first three bright excitations
of the entire family of (bacterio)chlorophylls. Contrary to state-of-the-art
time-dependent density functional theory (TDDFT) with an optimally
tuned range-separated hybrid functional, this accuracy is achieved
in a parameter-free approach. Moreover,
GW
+BSE predicts
the energy differences between the low-energy excitations correctly
and eliminates spurious charge transfer states that TDDFT with (semi)local
approximations is known to produce. Our study provides accurate reference
results and highlights the potential of the
GW
+BSE
approach for the simulation of larger pigment complexes.