Toward Ab Initio Optical Spectroscopy of the Fenna-Matthews-Olson Complex

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Explicit environmental and vibronic effects in simulations of linear and nonlinear optical spectroscopy

Accurately simulating the linear and nonlinear electronic spectra of condensed phase systems and accounting for all physical phenomena contributing to spectral line shapes presents a significant challenge. Vibronic transitions can be captured through a harmonic model generated from the normal modes of a chromophore, but it is challenging to also include the effects of specific chromophore-environment interactions within such a model. We work to overcome this limitation by combining approaches to account for both explicit environment interactions and vibronic couplings for simulating both linear and nonlinear optical spectra. We present and show results for three approaches of varying computational cost for combining ensemble sampling of chromophore-environment configurations with Franck-Condon line shapes for simulating linear spectra. We present two analogous approaches for nonlinear spectra. Simulated absorption spectra and two-dimensional electronic spectra (2DES) are presented for the Nile red chromophore in different solvent environments. Employing an average Franck-Condon or 2DES line shape appears to be a promising method for simulating linear and nonlinear spectroscopy for a chromophore in the condensed phase.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

The ONETEP linear-scaling density functional theory program

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Microscopic calculation of absorption spectra of macromolecules: An analytic approach

We develop a cross-disciplinary approach to analytically compute optical response functions of open macromolecular systems by exploiting the mathematical formalism of quantum field theory (QFT). Indeed, the entries of the density matrix for the electronic excitations interacting with their open dissipative environment are mapped into vacuum-to-vacuum Green's functions in a fictitious relativistic closed quantum system. We show that by re-summing appropriate self-energy diagrams in this dual QFT, it is possible to obtain analytic expressions for the response functions in Mukamel's theory. This yields physical insight into the structure and dynamics of vibronic resonances, since their frequency and width is related to fundamental physical constants and microscopic model parameters. For illustration, we apply this scheme to compute the linear absorption spectrum of the Fenna-Matthews-Olson light harvesting complex, comparing analytic calculations, numerical Monte Carlo simulations, and experimental data.

Unraveling electronic absorption spectra using nuclear quantum effects: Photoactive yellow protein and green fluorescent protein chromophores in water

Many physical phenomena must be accounted for to accurately model solution-phase optical spectral line shapes, from the sampling of chromophore-solvent configurations to the electronic-vibrational transitions leading to vibronic fine structure. Here we thoroughly explore the role of nuclear quantum effects, direct and indirect solvent effects, and vibronic effects in the computation of the optical spectrum of the aqueously solvated anionic chromophores of green fluorescent protein and photoactive yellow protein. By analyzing the chromophore and solvent configurations, the distributions of vertical excitation energies, the absorption spectra computed within the ensemble approach, and the absorption spectra computed within the ensemble plus zero-temperature Franck-Condon approach, we show how solvent, nuclear quantum effects, and vibronic transitions alter the optical absorption spectra. We find that including nuclear quantum effects in the sampling of chromophore-solvent configurations using ab initio path integral molecular dynamics simulations leads to improved spectral shapes through three mechanisms. The three mechanisms that lead to line shape broadening and a better description of the high-energy tail are softening of heavy atom bonds in the chromophore that couple to the optically bright state, widening the distribution of vertical excitation energies from more diverse solvation environments, and redistributing spectral weight from the 0-0 vibronic transition to higher energy vibronic transitions when computing the Franck-Condon spectrum in a frozen solvent pocket. The absorption spectra computed using the combined ensemble plus zero-temperature Franck-Condon approach yield significant improvements in spectral shape and width compared to the spectra computed with the ensemble approach. Using the combined approach with configurations sampled from path integral molecular dynamics trajectories presents a significant step forward in accurately modeling the absorption spectra of aqueously solvated chromophores.

Impact of Single-Point Mutations on the Excitonic Structure and Dynamics in a Fenna-Matthews-Olson Complex

Hole burning (HB) spectroscopy and modeling studies reveal significant changes in the excitonic structure and dynamics in several mutants of the FMO trimer from the Chlorobaculum tepidum. The excited-state decay times ( T₁) of the high-energy excitons are significantly modified when mutation occurs near bacteriochlorophyll (BChl) 1 (V152N mutant) or BChl 6 (W184F). Longer (averaged) T₁ times of highest-energy excitons in V152N and W184F mutants suggest that site energies of BChls 1 and 6, believed to play an important role in receiving excitation from the baseplate BChls, likely play a critical role to ensure the femtosecond (fs) energy relaxation observed in wild-type FMO. HB spectroscopy reveals preferentially slower T₁ times (about 1 ps on average) because fs times prohibit HB due to an extremely low HB quantum yield. Uncorrelated (incoherent) excitation energy transfer times between monomers, the composition of exciton states, and average, frequency-dependent, excited-state decay times ( T₁) are discussed.

Combining the ensemble and Franck-Condon approaches for calculating spectral shapes of molecules in solution

The correct treatment of vibronic effects is vital for the modeling of absorption spectra of many solvated dyes. Vibronic spectra for small dyes in solution can be easily computed within the Franck-Condon approximation using an implicit solvent model. However, implicit solvent models neglect specific solute-solvent interactions on the electronic excited state. On the other hand, a straightforward way to account for solute-solvent interactions and temperature-dependent broadening is by computing vertical excitation energies obtained from an ensemble of solute-solvent conformations. Ensemble approaches usually do not account for vibronic transitions and thus often produce spectral shapes in poor agreement with experiment. We address these shortcomings by combining zero-temperature vibronic fine structure with vertical excitations computed for a room-temperature ensemble of solute-solvent configurations. In this combined approach, all temperature-dependent broadening is treated classically through the sampling of configurations and quantum mechanical vibronic contributions are included as a zero-temperature correction to each vertical transition. In our calculation of the vertical excitations, significant regions of the solvent environment are treated fully quantum mechanically to account for solute-solvent polarization and charge-transfer. For the Franck-Condon calculations, a small amount of frozen explicit solvent is considered in order to capture solvent effects on the vibronic shape function. We test the proposed method by comparing calculated and experimental absorption spectra of Nile red and the green fluorescent protein chromophore in polar and non-polar solvents. For systems with strong solute-solvent interactions, the combined approach yields significant improvements over the ensemble approach. For systems with weak to moderate solute-solvent interactions, both the high-energy vibronic tail and the width of the spectra are in excellent agreement with experiments.

Excitonic Energy Landscape of the Y16F Mutant of the Chlorobium tepidum Fenna-Matthews-Olson (FMO) Complex: High Resolution Spectroscopic and Modeling Studies

We report high-resolution (low-temperature) absorption, emission, and nonresonant/resonant hole-burned (HB) spectra and results of excitonic calculations using a non-Markovian reduced density matrix theory (with an improved algorithm for parameter optimization in heterogeneous samples) obtained for the Y16F mutant of the Fenna-Matthews-Olson (FMO) trimer from the green sulfur bacterium Chlorobium tepidum. We show that the Y16F mutant is a mixture of FMO complexes with three independent low-energy traps (located near 817, 821, and 826 nm), in agreement with measured composite emission and HB spectra. Two of these traps belong to mutated FMO subpopulations characterized by significantly modified low-energy excitonic states. Hamiltonians for the two major subpopulations (Sub₈₂₁ and Sub₈₁₇) provide new insight into extensive changes induced by the single-point mutation in the vicinity of BChl 3 (where tyrosine Y16 was replaced with phenylalanine F16). The average decay time(s) from the higher exciton state(s) in the Y16F mutant depends on frequency and occurs on a picosecond time scale.

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.

Evidence of Correlated Static Disorder in the Fenna-Matthews-Olson Complex

Observation of excitonic quantum beats in photosynthetic antennae has prompted wide debate regarding the function of excitonic coherence in pigment-protein complexes. Much of this work focuses on the interactions of excitons with the femto-to-picosecond dynamical fluctuations of their environment. However, in experiments these effects can be masked by static disorder of the excited-state energies across ensembles, whose microscopic origins are challenging to predict. Here the excited-state properties of ∼2000 atom clusters of the Fenna-Matthews-Olson complex are simulated using a unique combination of linear-scaling density functional theory and constrained geometric dynamics. While slow, large amplitude protein motion leads to large variations in the Q_y transitions of two pigments, we identify pigment-protein correlations that greatly reduce variations in the energy gap across the ensemble, which is consistent with experimental observations of suppressed inhomogeneous dephasing of quantum beats.

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.

Toward an Understanding of the Excitonic Structure of the CP47 Antenna Protein Complex of Photosystem II Revealed via Circularly Polarized Luminescence

Identification of the lowest energy pigments in the photosynthetic CP47 antenna protein complex of Photosystem II (PSII) is essential for understanding its excitonic structure, as well as excitation energy pathways in the PSII core complex. Unfortunately, there is no consensus concerning the nature of the low-energy state(s), nor chlorophyll (Chl) site energies in this important photosynthetic antenna. Although we raised concerns regarding the estimations of Chl site energies obtained from modeling studies of various types of CP47 optical spectra [Reinot, T; et al., Anal. Chem. Insights 2016, 11, 35-48] recent new assignments imposed by the shape of the circularly polarized luminescence (CPL) spectrum [Hall, J.; et al., Biochim. Biophys. Acta 2016, 1857, 1580-1593] necessitate our comments. We demonstrate that other combinations of low-energy Chls provide equally good or improved simultaneous fits of various optical spectra (absorption, emission, CPL, circular dichroism, and nonresonant hole-burned spectra), but more importantly, we expose the heterogeneous nature of the recently studied complexes and argue that the published composite nature of the CPL (contributed to by CPL₆₈₅, CPL₆₉₁, and CPL₆₉₅) does not represent an intact CP47 protein. A positive CPL₆₉₅ is extracted for the intact protein, which, when simultaneously fitted with multiple other optical spectra, provides new information on the excitonic structure of intact and destabilized CP47 complexes and their lowest energy state(s).

Atomistic non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model

We present GPU-accelerated ab initio molecular dynamics simulations of nonadiabatic dynamics in the LH2 complex in full atomistic detail.

Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

Applications of large-scale density functional theory in biology

Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

On the Conflicting Estimations of Pigment Site Energies in Photosynthetic Complexes: A Case Study of the CP47 Complex

We focus on problems with elucidation of site energies (E0n) for photosynthetic complexes (PSCs) in order to raise some genuine concern regarding the conflicting estimations propagating in the literature. As an example, we provide a stern assessment of the site energies extracted from fits to optical spectra of the widely studied CP47 antenna complex of photosystem II from spinach, though many general comments apply to other PSCs as well. Correct values of E0n for chlorophyll (Chl) a in CP47 are essential for understanding its excitonic structure, population dynamics, and excitation energy pathway(s). To demonstrate this, we present a case study where simultaneous fits of multiple spectra (absorption, emission, circular dichroism, and nonresonant hole-burned spectra) show that several sets of parameters can fit the spectra very well. Importantly, we show that variable emission maxima (690–695 nm) and sample-dependent bleaching in nonresonant hole-burning spectra reported in literature could be explained, assuming that many previously studied CP47 samples were a mixture of intact and destabilized proteins. It appears that the destabilized subpopulation of CP47 complexes could feature a weakened hydrogen bond between the 13¹-keto group of Chl29 and the PsbH protein subunit, though other possibilities cannot be entirely excluded, as discussed in this work. Possible implications of our findings are briefly discussed.

Biomolecular Force Field Parameterization via Atoms-in-Molecule Electron Density Partitioning

Molecular mechanics force fields, which are commonly used in biomolecular modeling and computer-aided drug design, typically treat nonbonded interactions using a limited library of empirical parameters that are developed for small molecules. This approach does not account for polarization in larger molecules or proteins, and the parametrization process is labor-intensive. Using linear-scaling density functional theory and atoms-in-molecule electron density partitioning, environment-specific charges and Lennard-Jones parameters are derived directly from quantum mechanical calculations for use in biomolecular modeling of organic and biomolecular systems. The proposed methods significantly reduce the number of empirical parameters needed to construct molecular mechanics force fields, naturally include polarization effects in charge and Lennard-Jones parameters, and scale well to systems comprised of thousands of atoms, including proteins. The feasibility and benefits of this approach are demonstrated by computing free energies of hydration, properties of pure liquids, and the relative binding free energies of indole and benzofuran to the L99A mutant of T4 lysozyme.

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.

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.

Limits and potentials of quantum chemical methods in modelling photosynthetic antennae

A critical overview of quantum chemical approaches to simulate the light-harvesting process in photosynthetic antennae is presented together with a perspective on the developments that need to be introduced to reach a quantitative predictive power.

Identifying and tracing potential energy surfaces of electronic excitations with specific character via their transition origins: application to oxirane

We show that the transition origins of electronic excitations identified by quantified natural transition orbital (QNTO) analysis can be employed to connect potential energy surfaces (PESs) according to their character across a wide range of molecular geometries.

Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer

The trimeric Fenna-Mathews-Olson (FMO) complex of green sulphur bacteria is a well-studied example of a photosynthetic pigment-protein complex, in which the electronic properties of the pigments are modified by the protein environment to promote efficient excitonic energy transfer from antenna complexes to the reaction centres. By a range of simulation methods, many of the electronic properties of the FMO complex can be extracted from knowledge of the static crystal structure. However, the recent observation and analysis of long-lasting quantum dynamics in the FMO complex point to protein dynamics as a key factor in protecting and generating quantum coherence under laboratory conditions. While fast inter- and intra-molecular vibrations have been investigated extensively, the slow, conformational dynamics which effectively determine the optical inhomogeneous broadening of experimental ensembles has received less attention. The following study employs constrained geometric dynamics to study the flexibility in the protein network by efficiently generating the accessible conformational states from the published crystal structure. Statistical and principle component analyses reveal highly correlated low frequency motions between functionally relevant elements, including strong correlations between pigments that are excitonically coupled. Our analysis reveals a hierarchy of structural interactions which enforce these correlated motions, from the level of monomer-monomer interfaces right down to the α-helices, β-sheets and pigments. In addition to inducing strong spatial correlations across the conformational ensemble, we find that the overall rigidity of the FMO complex is exceptionally high. We suggest that these observations support the idea of highly correlated inhomogeneous disorder of the electronic excited states, which is further supported by the remarkably low variance (typically <5%) of the excitonic couplings of the conformational ensemble.

Large-Scale Density Functional Theory Transition State Searching in Enzymes

Linear-scaling quantum mechanical density functional theory calculations have been applied to study the rearrangement of chorismate to prephenate in large-scale models of the Bacillus subtilis chorismate mutase enzyme. By treating up to 2000 atoms at a consistent quantum mechanical level of theory, we obtain an unbiased, almost parameter-free description of the transition state geometry and energetics. The activation energy barrier is calculated to be lowered by 10.5 kcal mol(-1) in the enzyme, compared with the equivalent reaction in water, which is in good agreement with experiment. Natural bond orbital analysis identifies a number of active site residues that are important for transition state stabilization in chorismate mutase. This benchmark study demonstrates that linear-scaling density functional theory techniques are capable of simulating entire enzymes at the ab initio quantum mechanical level of accuracy.

The Fenna-Matthews-Olson protein revisited: a fully polarizable (TD)DFT/MM description

We report a combined molecular dynamics and quantum mechanics (QM)/molecular mechanics (MM) analysis of the excitonic properties of the Fenna-Matthews-Olson (FMO) protein by using a polarizable MM model combined with a time-dependent density functional theory description. Overall, our results indicate that structural fluctuations, electrostatic interactions, and short-range quantum effects can significantly modulate the model Hamiltonian parameters (site energies and couplings). We find that the specific interactions with the axial ligand and the hydrogen-bonded residues are responsible for the energy ladder, with their effects being mainly due to electrostatic interactions, but with short-range quantum contributions that are not negligible. In addition, a striking modulation of the screening effects experienced by the BChl pairs, due to the heterogeneous polarizability of the FMO and solvent environment, is observed. Finally, we find that the exciton model gives a reliable description of the delocalized excited states in the complex.