Assessment of the Ab Initio Bethe–Salpeter Equation Approach for the Low-Lying Excitation Energies of Bacteriochlorophylls and Chlorophylls

Abstract

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.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

“…GW/BSE has been of increasing interest in the molecular electronic structure community in recent years, , and we have recently presented a subsystem-based derivation . The high quality of GW/BSE results for chlorophyll and bacteriochlorophyll molecules makes this method ideally suited for many biological systems in the context of photosynthesis. An extension of the uncoupled methodology presented in ref to the coupled formalism would therefore be highly desirable, and work along these lines is currently in progress.…”

Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules

“…Recent applications include the calculation of band gaps and elucidation of charge-transfer in organic donor-acceptor compounds Caruso et al, 2014), applications to dye-sensitized solar cells (Marom et al, 2011;Faber et al, 2012;Umari et al, 2013;Marom et al, 2014;Mowbray and Migani, 2015), electronic level alignment in photocatalytic interfaces (Migani et al, 2013(Migani et al, , 2014, coreionization spectra of medium sized molecules (Van Setten et al, 2018;Golze et al, 2018Golze et al, , 2020 or photo-electron spectra of transition metal oxides (Berardo et al, 2017;Hung et al, 2017;Shi et al, 2018;Rezaei and Ögüt, 2021). Combined with the Bethe-Salpeter equation (BSE) formalism (Salpeter and Bethe, 1951;Strinati, 1988) the GWA has been used to calculate optical spectra of Cyanins (Boulanger et al, 2014), the Bacteriochlorin molecule (Duchemin et al, 2012) or Bacteriochlorophylls and Chlorophylls (Hashemi and Leppert, 2021). At the same time, the GWA has been implemented into an increasing number of molecular electronic structure codes (Ke, 2011;Caruso et al, 2012;Caruso et al, 2013;Ren et al, 2012;Van Setten et al, 2013;Kaplan et al, 2015Kaplan et al, , 2016Bruneval et al, 2016;Wilhelm et al, 2016;Tirimbò et al, 2020b).…”

Quasiparticle Self-Consistent GW-Bethe–Salpeter Equation Calculations for Large Chromophoric Systems

“…Next, we assess the accuracy of qs GW -BSE by comparison to experimental gas-phase data for Chla by Gruber et al In Table , we directly compare VEEs calculated with different computational methods to the experimental VEE, which has recently been extracted from the experimental spectrum by Sirohiwal et al The domain based local pair-natural orbital , (DLPNO)-STEOM-CCSD − results are taken from ref , while the ev GW@ LDA-BSE/6-311++G­(2d,2p) results calculated using MOLGW are by Hashemi and Leppert . Two different, gas-phase optimized structures have been used: one has been optimized at the CAM-B3LYP-D3­(BJ)/def2-TZVP level of theory by Sirohival et al., while the other has been optimized by Hashemi and Leppert using B3LYP/def2-TZVP.…”

“…Typically, the Dyson equation for G 1 is solved within the GWA first. Only afterward, the non-interacting 2-particle Green’s function and the corresponding kernel in its zero-frequency limit are constructed and one solves for a few or all roots of the generalized susceptibility. − If only a few excitonic states are needed, one may thereby use computationally efficient iterative diagonalization techniques. , This procedure is known as the GW -BSE method and is increasingly applied to compute the lowest electronically excited states of molecular systems. ,,− …”

“…The GW -BSE method has recently been shown to reproduce experimental low-lying excitation energies of Chls with high accuracy. , So far, it has only been applied to monomeric models of PSII. In this work, we will first give a brief account of the (low-scaling) implementation of the GW -BSE approach in Section .…”