Stabilization of Charge-Transfer Excited States in Biological Systems: A Computational Focus on the Special Pair in Photosystem II Reaction Centers.

Charge-transfer (CT) excited states play an important role in many biological processes. However, many computational approaches often inadequately address the equilibration effects of nuclear and environmental degrees of freedom on these states. One prominent example of systems in which CT states are of utmost importance is reaction centers (RC) in photosystems. Here we use a multiscale approach combined with time-dependent density functional theory to explore the lowest CT excited state of the special pair PD1-PD2 in the Photosystem II-RC of a cyanobacterium. We find that the nonequilibrium CT excited state resides near the Soret band, making an exciton the lowest-energy excited state. However, accounting for nuclear and state-specific dielectric equilibration along the CT potential energy surface (PES), the CT state PD1--PD2+ stabilizes energetically below the excitonic state. This underscores the crucial role of state-specific solvation in mapping the PES of CT states, as demonstrated in a simplified dimer model.

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms.

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

Phase separation of passive particles in active liquids.

The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of activity and attractive effective potential between the colloids. The strength of the effective potential is set by the size ratio of passive particles to the active ones. As the relative size of the passive particles increases, the effective potential becomes stronger and the average size of the clusters grows. The simulations reveal a macroscopic phase separation at sufficiently large size ratios. We will discuss the effect of density fluctuations of active particles on the nature of effective interactions between passive ones.

Multifidelity Machine Learning for Molecular Excitation Energies.

The accurate but fast calculation of molecular excited states is still a very challenging topic. For many applications, detailed knowledge of the energy funnel in larger molecular aggregates is of key importance, requiring highly accurate excitation energies. To this end, machine learning techniques can be a very useful tool, though the cost of generating highly accurate training data sets still remains a severe challenge. To overcome this hurdle, this work proposes the use of multifidelity machine learning where very little training data from high accuracies is combined with cheaper and less accurate data to achieve the accuracy of the costlier level. In the present study, the approach is employed to predict vertical excitation energies to the first excited state for three molecules of increasing size, namely, benzene, naphthalene, and anthracene. The energies are trained and tested for conformations stemming from classical molecular dynamics and density functional based tight-binding simulations. It can be shown that the multifidelity machine learning model can achieve the same accuracy as a machine learning model built only on high-cost training data while expending a much lower computational effort to generate the data. The numerical gain observed in these benchmark test calculations was over a factor of 30 but certainly can be much higher for high-accuracy data.

Incoherent Energy Transfer between the Baseplate and FMO Protein Explored at Ideal Geometries.

The Förster resonance energy transfer (FRET) between the Fenna-Matthews-Olson (FMO) protein complex and the chlorosomal baseplate (CBP) is investigated by using an idealized model. This simplified model is based on crystal structure and molecular dynamics conformations. Some of the further input, such as the transition dipole moments, was extracted from earlier molecular-level simulations. The resulting model mimics the effects of the relative position between the CBP and the FMO complex on the corresponding FRET efficiency under ideal conditions, involving about 1.3 billion FRET calculations per investigated model. In this idealized model and employing some approximations, it is found that FRET efficiency is almost completely independent of the FMO trimer orientation (displacement, distance, and rotation), despite FMO and CBP being highly structured complexes. Even removing individual FMO BChl triples will only reduce the FRET efficiency by up to 8.6%. An FMO containing only the least efficient BChl triple will retain about 25% of the FRET efficiency of a full FMO complex. In addition to its proposed function as an energetic funnel, FMO is thus identified to act as a highly robust spatial funnel for CBP excitation harvesting, independent of the mutual CBP-FMO orientation.

Correction: Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes.

Correction for 'Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes' by Beatrix M. Bold et al., Phys. Chem. Chem. Phys., 2020, 22, 10500-10518, https://doi.org/10.1039/C9CP05753F.

Stabilizing Polar Domains in MAPbBr3 via the Hydrostatic Pressure-Induced Liquid Crystal-like Transition.

Pressure-induced phases of MAPbBr3 were investigated at room temperature in the range of 0-2.8 GPa by ab initio molecular dynamics. Two structural transitions at 0.7 GPa (cubic → cubic) and 1.1 GPa (cubic → tetragonal) involved both the inorganic host (lead bromide) and the organic guest (MA). MA dipoles behave like a liquid crystal undergoing isotropic → isotropic and isotropic → oblate nematic transitions as pressure confines their orientational fluctuations to a crystal plane. Beyond 1.1 GPa, the MA ions lie alternately along two orthogonal directions in the plane forming stacks perpendicular to it. However, the molecular dipoles are statically disordered, leading to stable polar and antipolar MA domains in each stack. H-Bond interactions, which primarily mediate host-guest coupling, facilitate the static disordering of MA dipoles. Interestingly, high pressures suppress CH3 torsional motion, emphasizing the role of C-H···Br bonds in the transitions.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review.

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

Spectral densities and absorption spectra of the core antenna complex CP43 from photosystem II.

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings.

Robust Strategy for Photoprotection in the Light-Harvesting Antenna of Diatoms: A Molecular Dynamics Study.

Diatoms generate a large portion of the oxygen produced on earth due to their exceptional light-harvesting properties involving fucoxanthin and chlorophyll-binding proteins (FCP). At the same time, an efficient adaptation of these complexes to fluctuating light conditions is necessary to protect the diatoms against photodamage. So far, structural and dynamic data for the interaction between FCP and the photoprotective LHCX family of proteins in diatoms are lacking. In this computational study, we provide a structural basis for a remarkable pH-dependent adaptation at the molecular level. Upon binding of the LHCX1 protein to the FCP complex together with a change in pH, conformational changes within the FCP protein result in a variation of the electronic coupling in a specific chlorophyll-fucoxanthin pair, leading to a change in the exciton transfer rate by almost an order of magnitude. A common strategy for photoprotection between diatoms and higher plants is identified and discussed.

Time-dependent atomistic simulations of the CP29 light-harvesting complex.

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Pressure induced topochemical polymerization of solid acrylamide facilitated by anisotropic response of the hydrogen bond network.

The pressure induced polymerization of molecular solids is an appealing route to obtain pure, crystalline polymers without the need for radical initiators. Here, we report a detailed density functional theory (DFT) study of the structural and chemical changes that occur in defect free solid acrylamide, a hydrogen bonded crystal, when it is subjected to hydrostatic pressures. While our calculations are able to reproduce experimentally measured pressure dependent spectroscopic features in the 0-20 GPa range, our atomistic analysis predicts polymerization in acrylamide at a pressure of ∼23 GPa at 0 K albeit through large enthalpy barriers. Interestingly, we find that the two-dimensional hydrogen bond network in acrylamide templates topochemical polymerization by aligning the atoms through an anisotropic response at low pressures. This results not only in conventional C-C, but also unusual C-O polymeric linkages, as well as a new hydrogen bonded framework, with both N-HO and C-HO bonds. Using a simple model for thermal effects, we also show that at 300 K, higher pressures significantly accelerate the transformation into polymers by lowering the barrier. Thus, application of pressure offers an alternative route for topochemical polymerization when higher temperatures are undesirable.

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

Photosynthetic processes are driven by sunlight. Too little of it and the photosynthetic machinery cannot produce the reductive power to drive the anabolic pathways. Too much sunlight and the machinery can get damaged. In higher plants, the major Light-Harvesting Complex (LHCII) efficiently absorbs the light energy, but can also dissipate it when in excess (quenching). In order to study the dynamics related to the quenching process but also the exciton dynamics in general, one needs to accurately determine the so-called spectral density which describes the coupling between the relevant pigment modes and the environmental degrees of freedom. To this end, Born-Oppenheimer molecular dynamics simulations in a quantum mechanics/molecular mechanics (QM/MM) fashion utilizing the density functional based tight binding (DFTB) method have been performed for the ground state dynamics. Subsequently, the time-dependent extension of the long-range-corrected DFTB scheme has been employed for the excited state calculations of the individual chlorophyll-a molecules in the LHCII complex. The analysis of this data resulted in spectral densities showing an astonishing agreement with the experimental counterpart in this rather large system. This consistency with an experimental observable also supports the accuracy, robustness, and reliability of the present multi-scale scheme. To the best of our knowledge, this is the first theoretical attempt on this large complex system is ever made to accurately simulate the spectral density. In addition, the resulting spectral densities and site energies were used to determine the exciton transfer rate within a special pigment pair consisting of a chlorophyll-a and a carotenoid molecule which is assumed to play a role in the balance between the light harvesting and quenching modes.

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

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.

Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes.

The chromophores of rhodopsins (Rh) and light-harvesting (LH) complexes still represent a major challenge for a quantum chemical description due to their size and complex electronic structure. Since gradient corrected and hybrid density functional approaches have been shown to fail for these systems, only range-separated functionals seem to be a promising alternative to the more time consuming post-Hartree-Fock approaches. For extended sampling of optical properties, however, even more approximate approaches are required. Recently, a long-range corrected (LC) functional has been implemented into the efficient density functional tight binding (DFTB) method, allowing to sample the excited states properties of chromophores embedded into proteins using quantum mechanical/molecular mechanical (QM/MM) with the time-dependent (TD) DFTB approach. In the present study, we assess the accuracy of LC-TD-DFT and LC-TD-DFTB for rhodopsins (bacteriorhodopsin (bR) and pharaonis phoborhodopsin (ppR)) and LH complexes (light-harvesting complex II (LH2) and Fenna-Matthews-Olson (FMO) complex). This benchmark study shows the improved description of the color tuning parameters compared to standard DFT functionals. In general, LC-TD-DFTB can exhibit a similar performance as the corresponding LC functionals, allowing a reliable description of excited states properties at significantly reduced cost. The two chromophores investigated here pose complementary challenges: while huge sensitivity to external field perturbation (color tuning) and charge transfer excitations are characteristic for the retinal chromophore, the multi-chromophoric character of the LH complexes emphasizes a correct description of inter-chromophore couplings, giving less importance to color tuning. None of the investigated functionals masters both systems simultaneously with satisfactory accuracy. LC-TD-DFTB, at the current stage, although showing a systematic improvement compared to TD-DFTB cannot be recommended for studying color tuning in retinal proteins, similar to some of the LC-DFT functionals, because the response to external fields is still too weak. For sampling of LH-spectra, however, LC-TD-DFTB is a viable tool, allowing to efficiently sample absorption energies, as shown for three different LH complexes. As the calculations indicate, geometry optimization may overestimate the importance of local minima, which may be averaged over when using trajectories. Fast quantum chemical approaches therefore may allow for a direct sampling of spectra in the near future.

Structural Basis for Allosteric Regulation in the Major Antenna Trimer of Photosystem II.

The allosteric regulation of protein function proves important in many life-sustaining processes. In plant photosynthesis, LHCII, the major antenna complex of Photosystem II, employs a delicate switch between light harvesting and photoprotective modes. The switch is triggered by an enlarged pH gradient (ΔpH) across the thylakoid membranes. Using molecular simulations and quantum calculations, we show that ΔpH can tune the light-harvesting potential of the antenna via allosteric regulation of the excitonic coupling in chlorophyll-carotenoid pairs. To this end, we propose how the LHCII excited state lifetime is coupled to the environmental conditions. In line with experimental findings, our theoretical model provides crucial evidence toward the elucidation of the photoprotective switch of higher plants at an all-atom resolution.