DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Abstract

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum–classical description. To this end, Born−Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna−Matthews−Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Multiscale QM/MM molecular dynamics simulations of the trimeric major light-harvesting complex II

“…This kind of treatment is necessary to avoid artificial boundary effects in the non-periodic QM/MM excited state calculations 56,57 . The computational costs for the ground state QM/MM MD and the excited QM/MM calculations were similar to those of our previous study for a bacterial system 43 while numerically being cheaper than DFT-based approaches with similar accuracy 33 . After performing the TD-LC-DFTB calculations, the energies of the first excited state have been extracted along the QM/MM MD trajectories.…”

“…The 3OB-f is a variant of the standard 3OB set with an optimized description of the vibrational frequencies which especially improves the C=C, C=O and C=N stretching modes within the DFTB framework 51,52 . This enhancement has already shown to yield very reasonable results for the spectral densities in the bacterial Fenna-Matthews-Olson (FMO) complex 43 . For each pigment, a 60 ps NPT simulation with a 0.5 fs time step was carried out at 300 K using the GROMACS/DFTB+ interface 33, 53,54 .…”

“…where E m denotes the excitation energy gap of pigment m which is also called the site energy and V mn is the excitonic coupling between pigment molecules m and n. Depending on the theory used for the exciton dynamics, the Hamiltonian is either used directly in its time- In other investigations, the semi-empirical ZINDO/S-CIS method has been employed along classical MD trajectories for the LHCII complex leading to site energy values close to the experimental ones 60 . Although, the ZINDO/S-CIS approach is numerically very efficient and results in average site energies of Chl and BChl molecules that are rather accurate due to its parametrization for this molecule class, the fluctuations and the influence of environmental charges are less well represented 33,43 . This inadequacy of the ZINDO/S-CIS scheme is likely due to its parametrization for equilibrium conformations but not out-of-equilibrium ones 61,62 .…”

“…In this study we have employed a well-established technique which has been applied earlier to bacterial and algae LH complexes. In this formalism, a cosine transformation of the site-energy autocorrelation function decorated with a thermal factor is performed to determine the spectral density of each pigment molecule 22,36,43,[63][64][65] .…”

“…However, because of the size of the pigments in LH systems, it is numerically challenging to perform state of the art QM/MM MD simulations based on DFT 25 or even semi-empirical methods 41 . In this direction, our recent protocol based on the density functional tight-binding (DFTB) level of theory 42 is a numerically affordable alternative to perform an accurate ground state dynamics followed by excited state calculations for the relatively large pigment molecules 33,43 . Based on this strategy, in the present contribution we report on a DFTB-QM/MM MD ground state dynamics for the Chl-a molecules in connection with a classical description of the environment based on the OPLS force field.…”