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

Abstract

The GW-Bethe−Salpeter equation (BSE) method is promising for calculating the low-lying excitonic states of molecular systems. However, so far it has only been applied to rather small molecules and in the commonly implemented diagonal approximations to the electronic self-energy, it depends on a mean-field starting point. We describe here an implementation of the self-consistent and starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on large molecules. We herein show that eigenvalue-only self-consistency can lead to an unfaithful description of some excitonic states for chlorophyll dimers while the qsGW-BSE vertical excitation energies (VEEs) are in excellent agreement with spectroscopic experiments for chlorophyll monomers and dimers measured in the gas phase. Furthermore, VEEs from time-dependent density functional theory calculations tend to disagree with experimental values and using different range-separated hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use the new qsGW-BSE implementation to calculate the lowest excitation energies of the six chromophores of the photosystem II (PSII) reaction center (RC) with nearly 2000 correlated electrons. Using more than 11,000 (6000) basis functions, the calculation could be completed in less than 5 (2) days on a single modern compute node. In agreement with previous TD-DFT calculations using RSH kernels on models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters in the low-energy spectrum of the hexameric complex. Earlier works with RSH kernels have demonstrated that the protein environment facilitates the experimentally observed interchromophoric charge transfer. Therefore, future research will need to combine correlation effects beyond TD-DFT with an explicit treatment of environmental electrostatics.

Mapping Charge-Transfer Excitations in Bacteriochlorophyll Dimers from First Principles

“…While this method was initially primarily applied to solids, recent years have witnessed a multitude of studies that have demonstrated the accuracy and predictive power of the GW +BSE method for small molecules [54-56] and larger molecular complexes [57][58][59][60][61]. In particular, we [62] and others [61] benchmarked the accuracy of the GW +BSE approach against experiment and wavefunction-based methods and found excellent agreement for the Q y and Q x excitations of a range of BCL and Chlorophyll molecules. We showed that both eigenvalue selfconsistent GW calculations and one-shot G 0 W 0 calculations where the zeroth-order singleparticle Green's function G 0 and screened Coulomb interaction W 0 were constructed from a DFT eigensystem obtained with an optimally-tuned range-separated hybrid functional lead to the best results.…”

“…An alternative approach for calculating charge-transfer excitations of molecules and solids is the GW +Bethe-Salpeter Equation (GW +BSE) approach [52,53]. While this method was initially primarily applied to solids, recent years have witnessed a multitude of studies that have demonstrated the accuracy and predictive power of the GW +BSE method for small molecules [54-56] and larger molecular complexes [57][58][59][60][61]. In particular, we [62] and others [61] benchmarked the accuracy of the GW +BSE approach against experiment and wavefunction-based methods and found excellent agreement for the Q y and Q x excitations of a range of BCL and Chlorophyll molecules.…”

Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy

“…The same projector can also be applied to orbital coefficients in order to reduce errors in post-SCF methods. This strategy has already been successfully employed in the past for many-body perturbation theory (MBPT) based calculations. , However, systematic benchmarks against other codes using the same basis sets were not yet performed. For this purpose, we report here an implementation of PADF-MP2 and PADF-RPA in the numerical atomic orbital (NAO) based code BAND. − This implementation allows us to use Gaussian type orbitals (GTO) as basis sets and therefore to systematically investigate the accuracy of the PADF-MP2 and PADF-RPA implementations in AMS for relative correlation energies with respect to global DF-based implementations (DF-MP2, DF-RPA) in Psi4 and TURBOMOLE .…”

“…This strategy has already been successfully employed in the past for many-body perturbation theory (MBPT) based calculations. 59,105 However, systematic benchmarks against other codes using the same basis sets were not yet performed. For this purpose, we report here an implementation of PADF-MP2 and PADF-RPA in the numerical atomic orbital (NAO) based code BAND.…”

Non-adiabatic couplings and conversion dynamics between localized and charge transfer excitations from Many-Body Green's Functions Theory

“…Especially for the conversion of charge-neutral excitations, e.g., after photo absorption from localized exciton (LE) to charge-transfer (CT) state as an example of a photoinduced electron transfer reaction, the energetics of both LEs and CTs need to be described on an equal footing. In this context, the use of many-body Green's functions Theory employing the GW approximation and the Bethe-Salpeter equation (BSE) [9] has become attractive to model electronically excited states on top of a ground-state reference calculation typically performed on the level of density-functional theory (DFT) [10,11]. It was shown that GW -BSE provides an effective single-and two-particle picture with accurate energies of LE and CT states without the need for any adaptations [12][13][14].…”