Electronic coupling calculations with transition charges, dipoles, and quadrupoles derived from electrostatic potential fitting

Molecular Mechanisms behind Circular Dichroism Spectral Variations between Channelrhodopsin and Heliorhodopsin Dimers

Channelrhodopsin (ChR) and heliorhodopsin (HeR) are microbial rhodopsins with similar structures but different circular dichroism (CD) spectra: ChR shows biphasic negative and positive bands, whereas HeR shows a single positive band. We explored the physicochemical factors underlying these differences through computational methods. Using the exciton model based on first-principles computations, we obtained the CD spectra of ChR and HeR. The obtained spectra indicate that the protein dimer structures and the quantum mechanical treatment of the retinal chromophore and its interacting amino acids are crucial for accurately reproducing the experimental spectra. Further calculations revealed that the sign of the excitonic coupling was opposite between the ChR and HeR dimers, which was attributed to the contrasting second term of the orientation factor between the two retinal chromophores. These findings demonstrate that slight variations in the intermolecular orientation of the two chromophores can result in significant differences in the CD spectral shape.

Spectral Tuning and Excitation-Energy Transfer by Unique Carotenoids in Diatom Light-Harvesting Antenna

The light-harvesting antennae of diatoms and spinach are composed of similar chromophores; however, they exhibit different absorption wavelengths. Recent advances in cryoelectron microscopy have revealed that the diatom light-harvesting antenna fucoxanthin chlorophyll a/c-binding protein (FCPII) forms a tetramer and differs from the spinach antenna in terms of the number of protomers; however, the detailed molecular mechanism remains elusive. Herein, we report the physicochemical factors contributing to the characteristic light absorption of the diatom light-harvesting antenna based on spectral calculations using an exciton model. Spectral analysis reveals the significant contribution of unique fucoxanthin molecules (fucoxanthin-S) in FCPII to the diatom-specific spectrum, and further analysis determines their essential role in excitation-energy transfer to chlorophyll. It was revealed that the specificity of these fucoxanthin-S molecules is caused by the proximity between protomers associated with the tetramerization of FCPII. The findings of this study demonstrate that diatoms employ fucoxanthin-S to harvest energy under the ocean in the absence of long-wavelength sunlight and can provide significant information about the survival strategies of photosynthetic organisms to adjust to their living environment.

Unravelling the Origin of the Vibronic Spectral Signatures in an Excitonically Coupled Indocarbocyanine Cy3 Dimer

The indocarbocyanine Cy3 dye is widely used to probe the dynamics of proteins and DNA. Excitonically coupled Cy3 dimers exhibit very unique spectral signatures that depend on the interchromophoric geometrical orientation induced by the environment, making them powerful tools to infer the dynamics of their surroundings. Understanding the origin of the dimeric spectral signatures is a necessity for an accurate interpretation of the experimental results. In this work, we simulate the vibronic spectrum of an experimentally well-studied Cy3 dimer, and we explain the origin of the experimental signatures present in its linear absorption spectrum. The Franck-Condon harmonic approximations, among other tests, are used to probe the factors contributing to the spectrum. It is found that the first peak in the absorption spectrum originates from the lower energy excitonic state, while the next two peaks are vibrational progressions of the higher energy excitonic state. The polar solvent plays a crucial role in the appearance of the spectrum, being responsible for the localized S1 minimum, which results in an increased intensity of the first peak.

Impact of Structure, Coupling Scheme, and State of Interest on the Energy Transfer in CP29

The Qy and Bx excitation energy transfer (EET) in the minor light-harvesting complex CP29 (LHCII B4.1) antenna complex of Pisum sativum was characterized using a computational approach. We applied Förster resonance energy transfer (FRET) and the transition density cube (TDC) method to estimate the Coulombic coupling, based on a combination of classical molecular dynamics and quantum mechanics/molecular mechanics calculations. Employing TDC instead of FRET mostly affects the EET between chlorophylls (Chls) and carotenoids (Crts), as expected due to the Crts being spatially more challenging for FRET. Only between Chls, effects are found to be small (about only 0.1 EET efficiency change when introducing TDC instead of FRET). Effects of structural sampling were found to be small, illustrated by a small average standard deviation for the Qy state coupling elements (FRET/TDC: 0.97/0.94 cm-1). Due to the higher flexibility of the Bx state, the corresponding deviations are larger (FRET/TDC between Chl-Chl pairs: 17.58/22.67 cm-1, between Crt-Chl pairs: 62.58/31.63 cm-1). In summary, it was found for the Q band that the coupling between Chls varies only slightly depending on FRET or TDC, resulting in a minute effect on EET acceptor preference. In contrast, the coupling in the B band spectral region is found to be more affected. Here, the S2 (1Bu) states of the spatially challenging Crts may act as acceptors in addition to the B states of the Chls. Depending on FRET or TDC, several Chls show different Chl-to-Crt couplings. Interestingly, the EET between Chls or Crts in the B band is found to often outcompete the corresponding decay processes. The individual efficiencies for B band EET to Crts vary however strongly with the chosen coupling scheme (e.g., up to 0.29/0.99 FRET/TDC efficiency for the Chl a604/neoxanthin pair). Thus, the choice of the coupling scheme must involve a consideration of the state of interest.

Determination of FRET orientation factor between artificial fluorophore and photosynthetic light-harvesting 2 complex (LH2)

The orientation factor of fluorescence resonance energy transfer (FRET) between photosynthetic light-harvesting 2 complex (LH2) and artificial fluorophore (Alexa Fluor 647: A647) was theoretically investigated. The orientation factor of 2/3, i.e., the isotropic mean, is widely used to predict the donor–acceptor distance from FRET measurements. However, this approximation seems inappropriate because the movement of A647 is possibly restricted by the bifunctional linker binding to LH2. In this study, we performed molecular dynamics (MD) simulations and electronic coupling calculations on the LH2-A647 conjugate to analyze its orientation factor. The MD results showed that A647 keeps a position approximately 26 Å away from the bacteriochlorophyll (BChl) assembly in LH2. The effective orientation factor was extracted from the electronic coupling calculated using the transition charge from electrostatic potential (TrESP) method. With MD snapshots, an averaged orientation factor was predicted to be 1.55, significantly different from the isotropic mean value. The analysis also suggested that the value of the refractive index employed in the previous studies is not suitable for this system. Furthermore, optimal orientations of A647 with larger orientation factors to improve FRET efficiency were searched using Euler angles. The present approach is useful for extending the applicability of FRET analysis.

Perturbative Expansion of Nonorthogonal Product Approach for Charge Transfer States

Modeling of the excited states of multichromophoric systems is crucial for the understanding of photosynthesis functioning. The excitonic Hamiltonian method is widely used for such calculations. Excited states of the combined system are constructed from the wave functions of individual chromophores while their interactions are described by excitonic couplings. In the current study, we enhance a previously proposed nonorthogonal product approach to incorporate dynamic correlation effects accounted for by the multireference perturbation theory. We discuss the problems of constructing the excitonic Hamiltonian including charge transfer states for the molecular systems where the overlap contribution to the excitonic couplings is non-negligible. The benchmark calculations were performed for a model system. It was shown that the overlap component of the excitonic coupling is of great importance. The enhanced method provides an accurate description of the excited state energies and other properties.

Surface Hopping Dynamics with the Frenkel Exciton Model in a Semiempirical Framework

We present an implementation of the Frenkel exciton model in the framework of the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method, aimed at simulating the dynamics of multichromophoric systems, in which excitation energy transfer can occur, by a very efficient approach. The nonadiabatic molecular dynamics is here dealt with by the surface hopping method, but the implementation we proposed is compatible with other dynamical approaches. The exciton coupling is computed either exactly, within the semiempirical approximation considered, or by resorting to transition atomic charges. The validation of our implementation is carried out on the trans-azobenzeno-2S-phane (2S-TTABP), formed by two azobenzene units held together by sulfur bridges, taken as a minimal model of multichromophoric systems, in which both strong and weak exciton couplings are present.

Electronic Couplings and Electrostatic Interactions Behind the Light Absorption of Retinal Proteins

The photo-functional chromophore retinal exhibits a wide variety of optical absorption properties depending on its intermolecular interactions with surrounding proteins and other chromophores. By utilizing these properties, microbial and animal rhodopsins express biological functions such as ion-transport and signal transduction. In this review, we present the molecular mechanisms underlying light absorption in rhodopsins, as revealed by quantum chemical calculations. Here, symmetry-adapted cluster-configuration interaction (SAC-CI), combined quantum mechanical and molecular mechanical (QM/MM), and transition-density-fragment interaction (TDFI) methods are used to describe the electronic structure of the retinal, the surrounding protein environment, and the electronic coupling between chromophores, respectively. These computational approaches provide successful reproductions of experimentally observed absorption and circular dichroism (CD) spectra, as well as insights into the mechanisms of unique optical properties in terms of chromophore-protein electrostatic interactions and chromophore-chromophore electronic couplings. On the basis of the molecular mechanisms revealed in these studies, we also discuss strategies for artificial design of the optical absorption properties of rhodopsins.

Spectral Tuning Mechanism of Photosynthetic Light-Harvesting Complex II Revealed by Ab Initio Dimer Exciton Model

Excited states of two kinds of bacteriochlorophyll (BChl) aggregates, B850 and B800, in photosynthetic light-harvesting complex II (LH2) are theoretically investigated by developing and using an extended exciton model considering efficiently evaluated excitonic coupling. Our exciton model based on dimer fragmentation is shown to reproduce the experimental absorption spectrum of LH2 with good accuracy, entailing their different redshifts originating from aggregations of B850 and B800. The systematic analysis has been performed on the spectra by quantitatively decomposing their spectral shift energies into the contributions of various effects: structural distortion, electrostatic, excitonic coupling, and charge-transfer (CT) effects. Our results show that the spectral redshift of B800 is mainly attributed to its electrostatic interaction with the protein environment, while that of B850 arises from the marked effect of the excitonic coupling between BChl units. The interchromophore CT excitation also plays a key role in the spectral redshift of B850. This CT effect can be effectively described using our dimer model. This suited characterization reveals that the pronounced CT effect originates from the characteristics of B850 that has closely spaced BChls as dimers. We highlight the importance of the refinement of the crystal structure with the use of quantum chemical methods for prediction of the spectrum.

Accurate Modeling of Excitonic Coupling in Cyanine Dye Cy3

Accurate modeling of excitonic coupling in molecules is of great importance for inferring the structures and dynamics of coupled systems. Cy3 is a cyanine dye that is widely used in molecular spectroscopy. Its well-separated excitation bands, high sensitivity to the surroundings, and the high energy transfer efficiency make it a perfect choice for excitonic coupling experiments. Many methods have been used to model the excitonic coupling in molecules with varying degrees of accuracy. The atomic transition charge model offers a high-accuracy and cost-effective way to calculating the excitonic coupling. The main focus of this work is to generate high-quality atomic transition charges that can accurately model the Cy3 dye's transition density. The transition density of the excitation of the ground to first excited state is calculated using configuration-interaction singles and time-dependent density functional theory and is benchmarked against the algebraic diagrammatic construction method. Using the transition density we derived the atomic transition charges using two approaches: Mulliken population analysis and charges fitted to the transition electrostatic potential. The quality of the charges is examined, and their ability to accurately calculate the excitonic coupling is assessed via comparison to experimental data of an artificial biscyanine construct. Theoretical comparisons to the supermolecule ab initio couplings and the widely used point-dipole approximation are also made. Results show that using the transition electrostatic potential is a reliable approach for generating the transition atomic charges. A high-quality set of charges, that can be used to model the Cy3 dye dimer excitonic coupling with high-accuracy and a reasonable computational cost, is obtained.

An effective potential for Frenkel excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is introduced that is valid in a wide range of intermolecular distances. The proposed approach is based on the effective elimination of electron repulsion integrals from the excitonic Hamiltonian matrix elements via the density-fitting approach and distributed multipole approximation. The excitonic Hamiltonian represented in a basis including charge transfer (CT) states is re-cast in terms of the effective one-electron potential functions (EOPs) and adapted into the effective fragment parameter (EFP) framework. Calculations for model systems indicate that the speedup of at least three orders of magnitude, as compared to the state-of-the-art methods, can be achieved while maintaining the accuracy of the EET couplings even at short intermolecular distances.

Photophysical properties of acetylene-linked syn bimane oligomers: a molecular photonic wire

Computational studies using correlated wave function methods and density functional theory were carried out on a series of acetylene-linked bimane oligomers with particular emphasis on their excitonic properties and implications for intra-chain excitation energy transfer (EET). The low energy barriers found for the rotation of bimane subunits about the longitudinal axis are such that the π-conjugation is easily disrupted. Nevertheless, a distinctive feature of the oligomer lies in the parallel alignment of the S₁ transition dipole along the longitudinal axis, which sustains electronic coupling between adjacent bimane subunits over a range of torsional angles and is crucial for driving intra-chain EET. Using a model that comprises hexameric donor and acceptor fragments, we evaluated electronic couplings and spectral overlaps, and applied Fermi's golden rule (in the weak electronic coupling regime) to approximate the lower limit of intra-chain EET in an acetylene-linked bimane photonic wire.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.