Quantum chemical description of absorption properties and excited-state processes in photosynthetic systems

Convergence Analysis of the Stochastic Resolution of Identity: Comparing Hutchinson to Hutch++ for the Second-Order Green's Function

Stochastic orbital techniques offer reduced computational scaling and memory requirements to describe ground and excited states at the cost of introducing controlled statistical errors. Such techniques often rely on two basic operations, stochastic trace estimation and stochastic resolution of identity, both of which lead to statistical errors that scale with the number of stochastic realizations (Nξ) as N ξ - 1 . Reducing the statistical errors without significantly increasing Nξ has been challenging and is central to the development of efficient and accurate stochastic algorithms. In this work, we build upon recent progress made to improve stochastic trace estimation based on the ubiquitous Hutchinson's algorithm and propose a two-step approach for the stochastic resolution of identity, in the spirit of the Hutch++ method. Our approach is based on employing a randomized low-rank approximation followed by a residual calculation, resulting in statistical errors that scale much better than N ξ - 1 . We implement the approach within the second-order Born approximation for the self-energy in the computation of neutral excitations and discuss three different low-rank approximations for the two-body Coulomb integrals. Tests on a series of hydrogen dimer chains with varying lengths demonstrate that the Hutch++-like approximations are computationally more efficient than both deterministic and purely stochastic (Hutchinson) approaches for low error thresholds and intermediate system sizes. Notably, for arbitrarily large systems, the Hutchinson-like approximation outperforms both deterministic and Hutch++-like methods.

A Simple Expression for the Screening of Excitonic Couplings between Chlorophylls as Inferred for Photosystem I Trimers

The Coulomb coupling between transition densities of the pigments in photosynthetic pigment-protein complexes, termed excitonic coupling, is a key factor for the description of optical spectra and energy transfer. A challenging question is the quantification of the screening of the excitonic coupling by the optical polarizability of the environment. We use the equivalence between the sophisticated quantum chemical polarizable continuum (PCM) model and the simple electrostatic Poisson-TrEsp approach to analyze the distance and orientation dependence of the dielectric screening between chlorophylls in photosystem I trimers. On the basis of these calculations we find that the vacuum couplings Vmn(0) and the couplings in the dielectric medium Vmn=fmnVmn(0) are related by the empirical screening factor fmn=0.60+39.6θ(|κmn|-1.17)exp(-0.56Rmn/Å), where κmn is the usual orientational factor of the dipole-dipole coupling between the pigments, Rmn is the center-to-center distance, and the Heaviside-function θ(|κmn|-1.17) ensures that the exponential distance dependence only contributes for in-line type dipole geometries. We are confident that the present expression can be applied also to other pigment-protein complexes with chlorophyll or related pigments of similar shape. The variance between the Poisson-TrEsp and the approximate coupling values is found to decrease by a factor of 8 and 3-4 using the present expression, instead of an exponential distance dependent or constant screening factor, respectively, assumed previously in the literature.

Excitation landscape of the CP43 photosynthetic antenna complex from multiscale simulations

Photosystem II (PSII), the principal enzyme of oxygenic photosynthesis, contains two integral light harvesting proteins (CP43 and CP47) that bind chlorophylls and carotenoids. The two intrinsic antennae play crucial roles in excitation energy transfer and photoprotection. CP43 interacts most closely with the reaction center of PSII, specifically with the branch of the reaction center (D1) that is responsible for primary charge separation and electron transfer. Deciphering the function of CP43 requires detailed atomic-level insights into the properties of the embedded pigments. To advance this goal, we employ a range of multiscale computational approaches to determine the site energies and excitonic profile of CP43 chlorophylls, using large all-atom models of a membrane-bound PSII monomer. In addition to time-dependent density functional theory (TD-DFT) used in the context of a quantum-mechanics/molecular-mechanics setup (QM/MM), we present a thorough analysis using the perturbed matrix method (PMM), which enables us to utilize information from long-timescale molecular dynamics simulations of native PSII-complexed CP43. The excited state energetics and excitonic couplings have both similarities and differences compared with previous experimental fits and theoretical calculations. Both static TD-DFT and dynamic PMM results indicate a layered distribution of site energies and reveal specific groups of chlorophylls that have shared contributions to low-energy excitations. Importantly, the contribution to the lowest energy exciton does not arise from the same chlorophylls at each system configuration, but rather changes as a function of conformational dynamics. An unexpected finding is the identification of a low-energy charge-transfer excited state within CP43 that involves a lumenal (C2) and the central (C10) chlorophyll of the complex. The results provide a refined basis for structure-based interpretation of spectroscopic observations and for further deciphering excitation energy transfer in oxygenic photosynthesis.

Reaction Center Excitation in Photosystem II: From Multiscale Modeling to Functional Principles

Oxygenic photosynthesis is the fundamental energy-converting process that utilizes sunlight to generate molecular oxygen and the organic compounds that sustain life. Protein-pigment complexes harvest light and transfer excitation energy to specialized pigment assemblies, reaction centers (RC), where electron transfer cascades are initiated. A molecular-level understanding of the primary events is indispensable for elucidating the principles of natural photosynthesis and enabling development of bioinspired technologies. The primary enzyme in oxygenic photosynthesis is Photosystem II (PSII), a membrane-embedded multisubunit complex, that catalyzes the light-driven oxidation of water. The RC of PSII consists of four chlorophyll a and two pheophytin a pigments symmetrically arranged along two core polypeptides; only one branch participates in electron transfer. Despite decades of research, fundamental questions remain, including the origin of this functional asymmetry, the nature of primary charge-transfer states and the identity of the initial electron donor, the origin of the capability of PSII to enact charge separation with far-red photons, i.e., beyond the "red limit" where individual chlorophylls absorb, and the role of protein conformational dynamics in modulating charge-separation pathways.In this Account, we highlight developments in quantum-chemistry based excited-state computations for multipigment assemblies and the refinement of protocols for computing protein-induced electrochromic shifts and charge-transfer excitations calibrated with modern local correlation coupled cluster methods. We emphasize the importance of multiscale atomistic quantum-mechanics/molecular-mechanics and large-scale molecular dynamics simulations, which enabled direct and accurate modeling of primary processes in RC excitation at the quantum mechanical level.Our findings show how differential protein electrostatics enable spectral tuning of RC pigments and generate functional asymmetry in PSII. A chlorophyll pigment on the active branch (ChlD1) has the lowest site energy in PSII and is the primary electron donor. The complete absence of low-lying charge-transfer states within the central pair of chlorophylls excludes a long-held assumption about the initial charge separation. Instead, we identify two primary charge separation pathways, both with the same pheophytin acceptor (PheoD1): a fast pathway with ChlD1 as the primary electron donor (short-range charge-separation) and a slow pathway with PD1PD2 as the initial donor (long-range charge separation). The low-energy spectrum is dominated by two states with significant charge-transfer character, ChlD1δ+PheoD1δ- and PD1δ+PheoD1δ-. The conformational dynamics of PSII allows these charge-transfer states to span wide energy ranges, pushing oxygenic photosynthesis beyond the "red limit". These results provide a quantum mechanical picture of the primary events in the RC of oxygenic photosynthesis, forming a solid basis for interpreting experimental observations and for extending photosynthesis research in new directions.

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.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

The charge-transfer states and excitation energy transfers of halogen-free organic molecules from first-principles many-body Green's function theory

The organic solar cells based on halogen-free components, have been the new favorites to develop green and renewable energy. PBDB-T and its derivatives are considered the superior electron donors to construct the solar cells. Although there are plenty of researches about them, the charge-transfer mechanisms and excitation energy transfers of relative organic solar cells are still unclear, the developments of photovoltaic devices are restricted consequently. In this work, we calculate the electronic structures and excited-state properties of PBDB-T, PBT1-C, PBT1-O and PBT1-S donors in the gas phase from the many-body Green's function theory. With BTP-IC and BTP-IS as the acceptors, we consider the Förster, Dexter, and overlap electronic couplings to compute the excitation energy transfers of the dimers. The ionization energies and excited-state energies of the four donors calculated by GW + BSE are in good agreement with experiments, and they are sensitive to the functionals in the computation. We find two charge transfer schemes. The thienyl of PBDB-T molecule makes its charge-transfer state at the lowest energy, and the total electronic coupling of PBDB-T based dimer is the strongest. The Dexter, and overlap types electronic couplings are significant to study the excitation energy transfer of organic heterojunctions. We provide a theoretical guide in the design and synthesis of higher-performance halogen-free donors.

An efficient protocol for excited states of large biochromophores

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Q_y transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies.

Modeling Luminescence Spectrum of BaZrO3:Ti Including Vibronic Coupling from First Principles Calculations

Herein, we present a methodology based on constrained density functional theory and vibrational mode computations to simulate and interpret the luminescence spectra of periodic solids. A multi-dimension harmonic model is used to combine electronic and vibrational contributions into an overall vibrationally resolved emission spectrum. We applied it to Ti-doped BaZrO₃ to accurately reproduce its blue luminescence and unambiguously assign the observed luminescence to a Ti³⁺ + O^- → Ti⁴⁺ + O^2- charge transfer.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

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

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

Photosynthetic Light-Harvesting (Antenna) Complexes-Structures and Functions

Chlorophylls and bacteriochlorophylls, together with carotenoids, serve, noncovalently bound to specific apoproteins, as principal light-harvesting and energy-transforming pigments in photosynthetic organisms. In recent years, enormous progress has been achieved in the elucidation of structures and functions of light-harvesting (antenna) complexes, photosynthetic reaction centers and even entire photosystems. It is becoming increasingly clear that light-harvesting complexes not only serve to enlarge the absorption cross sections of the respective reaction centers but are vitally important in short- and long-term adaptation of the photosynthetic apparatus and regulation of the energy-transforming processes in response to external and internal conditions. Thus, the wide variety of structural diversity in photosynthetic antenna “designs” becomes conceivable. It is, however, common for LHCs to form trimeric (or multiples thereof) structures. We propose a simple, tentative explanation of the trimer issue, based on the 2D world created by photosynthetic membrane systems.

Understanding the Relation between Structural and Spectral Properties of Light-Harvesting Complex II

Light-harvesting complex II (LHCII) is a pigment-protein complex present in higher plants and green algae. LHCII represents the main site of light absorption, and its role is to transfer the excitation energy toward the photosynthetic reaction centers, where primary energy conversion reactions take place. The optical properties of LHCII are known to depend on protein conformation. However, the relation between the structural and spectroscopic properties of the pigments is not fully understood yet. In this respect, previous classical molecular dynamics simulations of LHCII in a model membrane [Sci. Rep. 2015, 5, 1-10] have shown that the configuration and excitonic coupling of a chlorophyll (Chl) dimer functioning as the main terminal emitter of the complex are particularly sensitive to conformational changes. Here, we use quantum chemistry calculations to investigate in greater detail the effect of pigment-pigment interactions on the excited-state landscape. While most previous studies have used a local picture in which electrons are localized on single pigments, here we achieve a more accurate description of the Chl dimer by adopting a supramolecular picture where time-dependent density functional theory is applied to the whole system at once. Our results show that specific dimer configurations characterized by shorter inter-pigment distances can result in a sizable intensity decrease (up to 36%) of the Chl absorption bands in the visible spectral region. Such a decrease can be predicted only when accounting for Chl-Chl charge-transfer excitations, which is possible using the above-mentioned supramolecular approach. The charge-transfer character of the excitations is quantified by two types of analyses: one focusing on the composition of the excitations and the other directly on the observable total absorption intensities.

The integrative biology of pigment organelles, a quantum chemical approach

Coloration is a complex phenotypic trait involving both physical and chemical processes at a multiscale level, from molecules to tissues. Pigments, whose main property is to absorb specific wavelengths of visible light, are usually deposited in specialized organelles or complex matrices comprising proteins, metals, ions and redox compounds, among others. By modulating electronic properties and stability, interactions between pigments and these molecular actors can lead to color tuning. Furthermore, pigments are not only important for visual effects but also provide other critical functions, such as detoxification and antiradical activity. Hence, integrative studies of pigment organelles are required to understand how pigments interact with their cellular environment. In this review, we show how quantum chemistry, a computational method that models the molecular and optical properties of pigments, has provided key insights into the mechanisms by which pigment properties, from color to reactivity, are modulated by their organellar environment. These results allow to rationalize and to predict the way pigments behave in supramolecular complexes, up to the complete modelling of pigment organelles. We also discuss the main limitations of quantum chemistry, emphasizing the need for carrying experimental work with identical vigor. We finally suggest that taking into account the ecology of pigments (i.e. how they interact with these various other cellular components and at higher organizational levels) will lead to a greater understanding of how and why animals are vividly and variably colored, two fundamental questions in organismal biology.

Spectral tuning of chlorophylls in proteins - electrostatics vs. ring deformation

In photosynthetic complexes, tuning of chlorophyll light-absorption spectra by the protein environment is crucial to their efficiency and robustness. Recombinant type II water soluble chlorophyll-binding proteins from Brassicaceae (WSCPs) are useful for studying spectral tuning mechanisms due to their symmetric homotetramer structure, and the ability to rigorously modify the chlorophyll's protein surroundings. Our previous comparison of the crystal structures of two WSCP homologues suggested that protein-induced chlorophyll ring deformation is the predominant spectral tuning mechanism. Here, we implement a more rigorous analysis based on hybrid quantum mechanics and molecular mechanics calculations to quantify the relative contributions of geometrical and electrostatic factors to the absorption spectra of WSCP-chlorophyll complexes. We show that when considering conformational dynamics, geometry distortions such as chlorophyll ring deformation accounts for about one-third of the spectral shift, whereas the direct polarization of the electron density accounts for the remaining two-thirds. From a practical perspective, protein electrostatics is easier to manipulate than chlorophyll conformations, thus, it may be more readily implemented in designing artificial protein-chlorophyll complexes.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

How Can We Predict Accurate Electrochromic Shifts for Biochromophores? A Case Study on the Photosynthetic Reaction Center

Protein-embedded chromophores are responsible for light harvesting, excitation energy transfer, and charge separation in photosynthesis. A critical part of the photosynthetic apparatus are reaction centers (RCs), which comprise groups of (bacterio)chlorophyll and (bacterio)pheophytin molecules that transform the excitation energy derived from light absorption into charge separation. The lowest excitation energies of individual pigments (site energies) are key for understanding photosynthetic systems, and form a prime target for quantum chemistry. A major theoretical challenge is to accurately describe the electrochromic (Stark) shifts in site energies produced by the inhomogeneous electric field of the protein matrix. Here, we present large-scale quantum mechanics/molecular mechanics calculations of electrochromic shifts for the RC chromophores of photosystem II (PSII) using various quantum chemical methods evaluated against the domain-based local pair natural orbital (DLPNO) implementation of the similarity-transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD). We show that certain range-separated density functionals (ωΒ97, ωΒ97X-V, ωΒ2PLYP, and LC-BLYP) correctly reproduce RC site energy shifts with time-dependent density functional theory (TD-DFT). The popular CAM-B3LYP functional underestimates the shifts and is not recommended. Global hybrid functionals are too insensitive to the environment and should be avoided, while nonhybrid functionals are strictly nonapplicable. Among the applicable approximate coupled cluster methods, the canonical versions of CC2 and ADC(2) were found to deviate significantly from the reference results both for the description of the lowest excited state and for the electrochromic shifts. By contrast, their spin-component-scaled (SCS) and particularly the scale-opposite-spin (SOS) variants compare well with the reference DLPNO-STEOM-CCSD and the best range-separated DFT methods. The emergence of RC excitation asymmetry is discussed in terms of intrinsic and protein electrostatic potentials. In addition, we evaluate a minimal structural scaffold of PSII, the D1-D2-CytB559 RC complex often employed in experimental studies, and show that it would have the same site energy distribution of RC chromophores as the full PSII supercomplex, but only under the unlikely conditions that the core protein organization and cofactor arrangement remain identical to those of the intact enzyme.

Electronic couplings for photo-induced processes from subsystem time-dependent density-functional theory: The role of the diabatization

Subsystem time-dependent density-functional theory (sTDDFT) making use of approximate non-additive kinetic energy (NAKE) functionals is known to be capable of describing excitation energy transfer processes in a variety of applications. Here, we show that sTDDFT, especially when combined with projection-based embedding (PbE), can be employed for the entire range of photo-induced electronic couplings essential for modeling photophysical properties of complex chemical and biological systems and therefore represents a complete toolbox for this class of problems. This means that it is capable of capturing the interaction/coupling associated with local- and charge-transfer (CT) excitons. However, this requires the choice of a reasonable diabatic basis. We therefore propose different diabatization strategies of the virtual orbital space in PbE-sTDDFT and show how CT excitations can be included in sTDDFT using NAKE functionals via a phenomenological approach. Finally, these electronic couplings are compared to couplings from a multistate fragment excitation difference (FED)-fragment charge difference (FCD) diabatization procedure. We show that both procedures, multistate FED-FCD and sTDDFT (with the right diabatization procedure chosen), lead to an overall good agreement for the electronic couplings, despite differences in their general diabatization strategy. We conclude that the entire range of photo-induced electronic couplings can be obtained using sTDDFT (with the right diabatization procedure chosen) in a black-box manner.

Protein Matrix Control of Reaction Center Excitation in Photosystem II

Photosystem II (PSII) is a multisubunit pigment-protein complex that uses light-induced charge separation to power oxygenic photosynthesis. Its reaction center chromophores, where the charge transfer cascade is initiated, are arranged symmetrically along the D1 and D2 core polypeptides and comprise four chlorophyll (PD1, PD2, ChlD1, ChlD2) and two pheophytin molecules (PheoD1 and PheoD2). Evolution favored productive electron transfer only via the D1 branch, with the precise nature of primary excitation and the factors that control asymmetric charge transfer remaining under investigation. Here we present a detailed atomistic description for both. We combine large-scale simulations of membrane-embedded PSII with high-level quantum-mechanics/molecular-mechanics (QM/MM) calculations of individual and coupled reaction center chromophores to describe reaction center excited states. We employ both range-separated time-dependent density functional theory and the recently developed domain based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD), the first coupled cluster QM/MM calculations of the reaction center. We find that the protein matrix is exclusively responsible for both transverse (chlorophylls versus pheophytins) and lateral (D1 versus D2 branch) excitation asymmetry, making ChlD1 the chromophore with the lowest site energy. Multipigment calculations show that the protein matrix renders the ChlD1 → PheoD1 charge-transfer the lowest energy excitation globally within the reaction center, lower than any pigment-centered local excitation. Remarkably, no low-energy charge transfer states are located within the "special pair" PD1-PD2, which is therefore excluded as the site of initial charge separation in PSII. Finally, molecular dynamics simulations suggest that modulation of the electrostatic environment due to protein conformational flexibility enables direct excitation of low-lying charge transfer states by far-red light.

Accurate Computation of the Absorption Spectrum of Chlorophyll a with Pair Natural Orbital Coupled Cluster Methods

The ability to accurately compute low-energy excited states of chlorophylls is critically important for understanding the vital roles they play in light harvesting, energy transfer, and photosynthetic charge separation. The challenge for quantum chemical methods arises both from the intrinsic complexity of the electronic structure problem and, in the case of biological models, from the need to account for protein–pigment interactions. In this work, we report electronic structure calculations of unprecedented accuracy for the low-energy excited states in the Q and B bands of chlorophyll a. This is achieved by using the newly developed domain-based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD) in combination with sufficiently large and flexible basis sets. The results of our DLPNO–STEOM-CCSD calculations are compared with more approximate approaches. The results demonstrate that, in contrast to time-dependent density functional theory, the DLPNO–STEOM-CCSD method provides a balanced performance for both absorption bands. In addition to vertical excitation energies, we have calculated the vibronic spectrum for the Q and B bands through a combination of DLPNO–STEOM-CCSD and ground-state density functional theory frequency calculations. These results serve as a basis for comparison with gas-phase experiments.

Exciton transfer free energy from Car-Parrinello molecular dynamics

A computational approach is presented which allows the calculation of free energies profiles for exciton transfer processes within the framework of ab initio molecular dynamics (AIMD) simulations, sampling both the electronic and the nuclear degrees of freedom. To achieve this, restraining potentials are imposed on the centres of maximally localized Wannier orbitals. The resulting quantum-mechanical orbital forces are derived analytically and implemented in an AIMD program. In analogy to classical umbrella sampling techniques, these restraints are used to control an exciton transfer by incrementally moving the Wannier centres corresponding to the electron-hole pair along a suitable reaction coordinate. The new method is applied to study exciton transfer between two stacked penta(3-methylthiophene) molecules as a function of intermolecular distance. From the resulting free energy profiles, exciton transfer rates and diffusion constants are estimated, which prove to be in line with experimental results.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Vibronic structure of photosynthetic pigments probed by polarized two-dimensional electronic spectroscopy and ab initio calculations

Bacteriochlorophyll a (Bchl a) and chlorophyll a (Chl a) play important roles as light absorbers in photosynthetic antennae and participate in the initial charge-separation steps in photosynthetic reaction centers. Despite decades of study, questions remain about the interplay of electronic and vibrational states within the Q-band and its effect on the photoexcited dynamics. Here we report results of polarized two-dimensional electronic spectroscopic measurements, performed on penta-coordinated Bchl a and Chl a and their interpretation based on state-of-the-art time-dependent density functional theory calculations and vibrational mode analysis for spectral shapes. We find that the Q-band of Bchl a is comprised of two independent bands, that are assigned following the Gouterman model to Q x and Q y states with orthogonal transition dipole moments. However, we measure the angle to be ∼75°, a finding that is confirmed by ab initio calculations. The internal conversion rate constant from Q x to Q y is found to be 11 ps-1. Unlike Bchl a, the Q-band of Chl a contains three distinct peaks with different polarizations. Ab initio calculations trace these features back to a spectral overlap between two electronic transitions and their vibrational replicas. The smaller energy gap and the mixing of vibronic states result in faster internal conversion rate constants of 38-50 ps-1. We analyze the spectra of penta-coordinated Bchl a and Chl a to highlight the interplay between low-lying vibronic states and their relationship to photoinduced relaxation. Our findings shed new light on the photoexcited dynamics in photosynthetic systems where these chromophores are primary pigments.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

Robust and Fragile Quantum Effects in the Transfer Kinetics of Delocalized Excitons between B850 Units of LH2 Complexes

Aggregates of light harvesting 2 (LH2) complexes form the major exciton-relaying domain in the photosynthetic unit of purple bacteria. Application of a generalized master equation to pairs of the B850 units of LH2 complexes, where excitons predominantly reside, provides quantitative information on how the inter-LH2 exciton transfer depends on the distance, relative rotational angle, and the relative energies of the two LH2s. The distance dependence demonstrates significant enhancement of the rate due to quantum delocalization of excitons, the qualitative nature of which remains robust against the disorder. The angle dependence reflects isotropic nature of exciton transfer, which remains similar for the ensemble of disorder. The variation of the rate on relative excitation energies of LH2 exhibits resonance peaks, which, however, is fragile as the disorder becomes significant. Overall, the average transfer times between two LH2s are estimated to be in the range of 4-25 ps for physically plausible inter-LH2 distances.

Computational modelling of singlet excitation energy transfer: a DFT/TD-DFT study of the ground and excited state properties of a syn bimane dimer system using non-empirically tuned range-separated functionals

Range-tuned DFT/TD-DFT improves predicted properties for the sequence of events leading to excitation energy transfer (EET) in bimanes.

Photosynthesis, pigment-protein complexes and electronic energy transport: simple models for complicated processes

In this review, we discuss our recent work on modelling biological pigment-protein complexes, such as the Fenna-Matthews-Olson complex and light-harvesting complex-II, to explain their electronic energy transport properties. In particular, we highlight how a network-based analysis approach, where the light-absorbing pigments are treated as a network of interconnected nodes, can provide a qualitative picture of quantum dynamic energy transport. With this in mind, we demonstrate how other properties such as robustness to environmental changes can be assessed in a simple and computationally tractable manner. Such analyses could prove useful for the design of artificial energy transport networks such as those which might find application in solar cells.

Photosynthetic pigment-protein complexes as highly connected networks: implications for robust energy transport

Photosynthetic pigment-protein complexes (PPCs) are a vital component of the light-harvesting machinery of all plants and photosynthesizing bacteria, enabling efficient transport of the energy of absorbed light towards the reaction centre, where chemical energy storage is initiated. PPCs comprise a set of chromophore molecules, typically bacteriochlorophyll species, held in a well-defined arrangement by a protein scaffold; this relatively rigid distribution leads to a viewpoint in which the chromophore subsystem is treated as a network, where chromophores represent vertices and inter-chromophore electronic couplings represent edges. This graph-based view can then be used as a framework within which to interrogate the role of structural and electronic organization in PPCs. Here, we use this network-based viewpoint to compare excitation energy transfer (EET) dynamics in the light-harvesting complex II (LHC-II) system commonly found in higher plants and the Fenna-Matthews-Olson (FMO) complex found in green sulfur bacteria. The results of our simple network-based investigations clearly demonstrate the role of network connectivity and multiple EET pathways on the efficient and robust EET dynamics in these PPCs, and highlight a role for such considerations in the development of new artificial light-harvesting systems.

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.

Strong Impact of an Axial Ligand on the Absorption by Chlorophyll a and b Pigments Determined by Gas-Phase Ion Spectroscopy Experiments

The microenvironments in photosynthetic proteins affect the absorption by chlorophyll (Chl) pigments. It is, however, a challenge to disentangle the impact on the transition energies of different perturbations, for example, the global electrostatics of the protein (nonbonded environmental effects), exciton coupling between Chl's, conformational variations, and binding of an axial ligand to the magnesium center. This is needed to distinguish between the two most commonly proposed mechanisms for energy transport in photosynthetic proteins, relying on either weakly or strongly coupled pigments. Here, on the basis of photodissociation action spectroscopy, we establish that the redshift of the Soret absorption band due to binding of a negatively charged carboxylate (as present in aspartic acid and glutamic acid residues) is 0.1-0.2 eV for Chl a and b. This effect is almost enough to reproduce the well-known green color of plants and can account for the strong spectral variation between Chl's. The experimental data serve to benchmark future high-level calculations of excited-state energies. Finally, we demonstrate that complexes between Chl a and histidine, tagged by a quaternary ammonium ion, can be made in the gas phase by electrospray ionization, but more work is needed to produce enough ions for gas-phase spectroscopy.

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.

Virtual eyes for technology and cultural heritage: toward computational strategy for new and old indigo-based dyes

A cost-effective, robust, and reliable computational strategy is applied to simulate peak positions and band-shapes of UV-vis spectra together with the dye colours perceived by human eyes. The features of our virtual multifrequency spectrometer (VMS) relevant to this topic are sketched with special focus on the selection of density functional, vibronic model, and solvent description. Furthermore, the new VMS-Draw graphical user interface (GUI) is employed for user-friendly pre- and post-processing of the computed data. The family of indigo dyes is used as case study in view of their continued use in the field of cultural heritage, together with new promising applications for photonics and sustainable energy. After assessment of different simplified models employed in previous studies, the role of several substituents and of dimerization in tuning the colour and spectral features are analyzed in detail by means of both accurate computations and interpretative models. The results are in remarkable agreement with experiment and allow to rationalize the behaviour of this class of dyes.