Excitation energy transfer pathways in light‐harvesting proteins: Modeling with PyFREC

Excitation energy transfer (EET) determines the fate of sunlight energy absorbed by light‐harvesting proteins in natural photosynthetic systems and photovoltaic cells. As previously reported (D. Kosenkov, J. Comput. Chem. 2016, 37(19), 1847), PyFREC software enables computation of electronic couplings between organic molecules with a molecular fragmentation approach. The present work reports implementation of direct fragmentation‐based computation of the electronic couplings and EET rates in pigment–protein complexes within the Förster theory in PyFREC. The new feature enables assessment of EET pathways in a wide range of photosynthetic complexes, as well as artificial molecular architectures that include light‐harvesting proteins or tagged fluorescent biomolecules. The developed methodology has been tested analyzing EET in the Fenna–Matthews–Olson (FMO) pigment–protein complex. The pathways of excitation energy transfer in FMO have been identified based on the kinetics studies. © 2017 Wiley Periodicals, Inc.     

Contact effects on electronic transport in donor-bridge-acceptor complexes interacting with a thermal bath

A model for electron transfer in donor-bridge-acceptor complexes with electronic coupling to nuclear bridge modes is studied using the Redfield formulation. We demonstrate that the transport mechanism through the molecular bridge is controlled by the location of the electronic-nuclear coupling term along the bridge. As the electronic-nuclear coupling term is shifted from the donor/acceptor-bridge contact sites into the bridge, the mechanism changes from kinetic transport (incoherent, thermally activated, and bridge-length independent) to coherent tunneling oscillations. This study joins earlier works aiming to explore the factors which control the mechanism of electronic transport through molecular bridges and molecular wires.     

Excitation energy transfer in ion pairs of polymethine cyanine dyes: efficiency and dynamics

The present work deals with singlet excitation energy transfer (EET) occurring in contact ion pairs (CIPs) of several anionic oxonol analogues (acting as EE donors) and cationic cyanines (acting as acceptors) characterized by off resonance individual transitions. Combining conductometric and spectroscopic measurements with decreasing solvent polarity, we were able to observe a progressive ion pairing leading first to solvent-separated ion pairs (SSIPs) and then to CIPs. Analysis of the absorption spectra of three selected salts (A2,C1, A2,C2, and A1,C4) in chloroform-toluene mixtures showed that the transformation of SSIP into CIP involves the appearance of a certain exciton coupling, the extent of which decreases regularly with increasing gap between the local excitation energies. Fluorescence excitation spectra showed that EET occurs in CIP, and EET efficiencies were evaluated with a procedure expressly devised for weakly emitting donors. These were between 0.2 and 0.65 for the examined ion pairs involving anions A1 and A2. The spectroscopic study was complemented by a theoretical investigation aimed at establishing the dynamic regime of the observed EET. From classical MD simulations and local full geometry optimizations, A2,C1 and A2,C2 were found to form rather stable sandwich-type CIP structures with interchromophore distances (R) of about 0.45-0.50 nm. The donor-acceptor electronic coupling was calculated in terms of Coulombic interactions between atomic transition charges. For CIP, the electronic coupling was decidedly beyond the limit of the weak coupling required for an incoherent F?rster-type mechanism. Thus, we tried to arrange the EET dynamics within the theory developed by Kimura, Kakitani, and Yamato (J. Phys. Chem. B 2000, 104, 9276) for the intermediate coupling case, which provides analytical expressions of time-dependent occupation probability, EET rate, and coherency in terms of two basic quantities: the electronic coupling and a correlation time related to the Franck-Condon factor. The latter was shown to be primarily modulated by F?rster's spectral overlap integral (related in turn to the excitation energy gap). Calculations were carried out for the three sample systems using three values of the electronic coupling roughly corresponding to CIP, 1.0, and 2.0 nm interchromophore distances. At the CIP distance, EET in both A2,C1 and A2,C2 was predicted to occur with a partial exciton mechanism, very short transfer times (about 10 fs), and high degree of coherence. In A1,C4 (having the largest energy gap), EET was found to occur with a hot-transfer mechanism. More or less hot-transfer dynamics appeared to be retained by all three systems at R = 1.0 nm. Fully incoherent EET appeared to become operative only at distances larger than 2.0 nm.     

Intramolecular electronic energy transfer in bichromophoric macrocyclic complexes

Efficient intramolecular electronic energy transfer (EET) has been demonstrated for three novel bichromophoric compounds utilizing a macrocyclic spacer as the bridge between the electronic energy donor and acceptor fragments. As their free base forms, emission from the electronically excited donor is absent and the acceptor emission is reductively quenched via photoinduced oxidation of proximate amine lone pairs. As their Zn(II) complexes, excitation of the donor results in sensitization of the electronic acceptor emission.     

Intermolecular electronic excitation transfer in a confined space: a first-principles study.

The process of intermolecular electronic excitation transfer (EET) in a monodimensional supramolecular arrangement of molecules in confined space has been modelled and investigated by means of first-principles molecular dynamics simulations. The chosen model system consists of a wire of chlorine molecules hosted in the noncrossing channels of the zeolite bikitaite. The time evolution of the system in its first excited singlet state has been described by the restricted open shell Kohn-Sham formalism. Simulation results have highlighted that excitation, initially localized on a guest molecule, is transferred to an adjacent moiety in the molecular wire on the picosecond scale via a collision-induced Dexter-type short range EET. Analysis of the modifications of the electronic structure of the system brought about by EET has given insight into the microscopic details of the process.     

Theory and calculation for the electronic coupling in excitation energy transfer

Excitation energy transfer (EET) is a process where the electronically excitation is transferred from a donor to an acceptor. EET is widely seen in both natural and in artificial systems, such as light‐harvesting in photosynthesis, the fluorescence resonance energy transfer technique, and the design of light‐emitting molecular devices. In this work, we outline the theories describing both singlet and triplet EET (SEET and TEET) rates, with a focus on the physical nature and computational methods for the electronic coupling factor, an important parameter in predicting EET rates. The SEET coupling is dominated by the Coulomb coupling, and the remaining short‐range coupling is very similar to the TEET coupling. The magnitude of the Coulomb coupling in SEET can vary much, but the contribution of short‐range coupling has been found to be similar across different excited states in naphthalene. The exchange coupling has been believed to be the major physical contribution to the short‐range coupling, but it has been pointed out that other contribution, such as the orbital overlap effect is similar or even larger in strength. The computational aspects and the subsequent physical implication for both SEET and TEET coupling values are summarized in this work. © 2013 The Authors. International Journal of Quantum Chemistry Published by Wiley Periodicals, Inc.     

Photophysical properties of natural light-harvesting complexes studied by subsystem density functional theory

In this study, we investigate the excited states and absorption spectra of a natural light-harvesting system by means of subsystem density functional theory. In systems of this type, both specific interactions of the pigments with surrounding protein side chains as well as excitation energy transfer (EET) couplings resulting from the aggregation behavior of the chromophores modify the photophysical properties of the individual pigment molecules. It is shown that the recently proposed approximate scheme (J. Chem. Phys. 2007, 126, 134116) for coupled excitations within a subsystem approach to time-dependent DFT is capable of describing both effects in a consistent manner, and is efficient enough to study even the large assemblies of chromophores occurring in the light-harvesting complex 2 (LH2) of the purple bacterium Rhodopseudomonas acidophila. A way to extract phenomenological coupling constants as used in model calculations on EET rates is outlined. The resulting EET coupling constants and spectral properties are in reasonable agreement with the available reference data. Possible problems related to the effective exchange-correlation kernel are discussed.     

Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments

In this perspective, we present an overview of recent progress on Time-Dependent Density Functional Theory (TD-DFT) with a specific focus on its accuracy and on models able to take into account environmental effects, including complex media. To this end, we first summarise recent benchmarks and define an average TD-DFT accuracy in reproducing excitation energies when a conventional approach is used. Next, coupling of TD-DFT with models able to account for different kinds of interactions between a central chromophore and nearby chemical objects (solvent, organic cage, metal as well as semi-conducting surface) is investigated. Examples of application to excitation properties are presented, allowing to briefly describe several recent computational strategies. In addition, an extension of TD-DFT to describe a phenomenon involving interacting chromophores, e.g. the electronic energy transfer (EET), is presented to illustrate that this methodology can be applied to processes beyond the vertical excitation. This perspective therefore aims to provide to non-specialists a flavour of recent trends in the field of simulations of excited states in "realistic" situations.     

Mechanisms of excitation transfer in multichromophoric systems

The nature of the interactions which promote interchromophore electronic excitation transfer are examined. They are partitioned into direct and relayed components, where direct electronic coupling takes the form of a dipole—dipole interaction at large separations. Factors which modify this interaction at short to intermediate separations are discussed (with particular reference to aromatic polymer systems). The direct interaction is partitioned into coulombic, exchange and penetration terms; the significance of the penetration interaction at close separation (proposed recently for the first time) is elaborated upon here. The relayed interaction involves mediation of all these interactions over lage direct separations via intervening moieties. It is demonstrated, using a model poly(acenaphtylene) dyad as an example, that relayed interactions, mediated via the σ bonds connecting two chromophores, are capable of increasing substantially the rate of electronic excitation transfer.     

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene units placed between the chromophores. We find that the polarizability of the bridge significantly enhances the effective interaction. We compare our calculations to single molecule experiments on two types of dyads and find reasonable agreement between theory and experiment.     

Towards a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems. II. The through-bond contribution

In this paper we present a quantum-mechanical investigation on the mechanisms which promote intramolecular EET coupling. This investigation is done by using a new computational strategy in which we combine a configuration-interaction and a linear response approach. The combined use of these two methods allows a direct identification and a quantification of both "direct" (coulomb and exchange) and through-bond (superexchange and charge-transfer) contributions. In addition, solvent effects are introduced using the polarizable continuum model. The method is applied to a family of naphthalene-bridge-naphthalene and naphthalene-bridge-anthracene systems, and the results obtained are compared with experiments. The results found suggest that the through-bond charge-transfer effects are not significant when the EET goes through permitted excitations on distant chromophores (see DN4 and DN6) while they become as important as (or even more important than) the covalent terms for EETs involving weakly allowed excitations (see A6N). By contrast, the presence of a very short bridge (in DN2) allows a very efficient delocalization of the excitation energy which is also largely modified by the presence of a solvent.     

Parameters for excess electron transfer in DNA. Estimation using unoccupied Kohn-Sham orbitals and TD DFT

We show that the energetics and electronic couplings for excess electron transfer (EET) can be accurately estimated by using unoccupied Kohn-Sham orbitals (UKSO) calculated for neutral pi stacks. To assess the performance of different DFT functionals, we use MS-PT2 results for seven pi stacks of nucleobases as reference data. The DFT calculations are carried out by using the local spin density approximation SVWN, two generalized gradient approximation functionals BP86 and BLYP, and two hybrid functionals B3LYP and BH&HLYP. Best estimations within the UKSO approach are obtained by the B3LYP and SVWN methods. TD DFT calculations provide less accurate values of the EET parameters as compared with the UKSO data. Also, the excess charge distribution in the radical anions is well described by the LUMOs of neutral systems. In contrast, spin-unrestricted DFT calculations of radical anions considerably overestimate delocalization of the excess electron. The excellent results obtained for the ground and excited states of the radical anions (excitation energy, transition dipole moment, electronic coupling, and excess electron distribution) by using UKSO of neutral dimers suggest an efficient strategy to calculate the EET parameters for DNA pi stacks.     

Electronic to vibrational energy transfer assisted by interacting transition dipole moments: a quantum model for the nonadiabatic I2(E) + CF4 collisions

We report a theoretical study of nonadiabatic transitions within the first-tier ion-pair states of molecular iodine induced by collisions with CF(4). We propose a model that treats the partner as a spherical particle with internal vibrational structure. Potential energy surfaces and nonadiabatic matrix elements for the I(2)-CF(4) system are evaluated using the diatomics-in-molecule perturbation theory. A special form of the intermolecular perturbation theory for quasi-degenerate electronic states is implemented to evaluate the corrections to the long-range interaction of transition dipole moments of colliding molecules. The collision dynamics is studied by using an approximate quantum scattering approach that takes into account the coupling of electronic and vibrational degrees of freedom. Comparison with available experimental data on the rate constants and product state distributions demonstrates a good performance of the model. The interaction of the transition dipole moments is shown to induce very efficient excitation of the dipole-allowed upsilon(3) and upsilon(4) modes of the CF(4) partner. These transitions proceed predominantly through the near-resonant E-V energy transfer. The resonant character of the partner's excitation and the large mismatch in vibrational frequencies allow one to deduce the partner's vibrational product state distributions from the distributions measured for the molecule. The perspectives of the proposed theoretical model for treating a broad range of molecular collisions involving the spherical top partners are discussed.     

MS-CASPT2 calculation of excess electron transfer in stacked DNA nucleobases

Calculations using the complete active space self-consistent field (CASSCF) and complete active space second-order perturbation (CASPT2) methods, and the multistate formulation of CASPT2 (MS-CASPT2), are performed for the ground and excited states of radical anions consisting of two pi-stacked nucleobases. The electronic couplings for excess electron transfer (EET) in the pi-stacks are estimated by using the generalized Mulliken-Hush approach. We compare results obtained within the different methods with data derived using Koopmans' theorem approximation at the Hartree-Fock level. The results suggest that although the one-electron scheme cannot be applied to calculate electron affinities of nucleobases, it provides reasonable estimates for EET energies. The electronic couplings calculated with KTA lie between the CASPT2 and the MS-CASPT2 based values in almost all cases.     

Toward a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems

This paper presents a quantum-mechanical study of the intramolecular excitation energy transfer (EET) coupling in naphthalene-bridge-naphthalene systems in gas phase and in solution. ZINDO and TDDFT response schemes are compared using both an exact and an approximate solution. The approximate solution based on a perturbative approach uses the single chromophore properties to reconstruct the real system coupling thus neglecting possible through-bond effects which conversely are accounted for in the exact solution. The comparison of the results of the two approaches with the experiments allows a detailed analysis of the relative importance of through-bond and through-space effects as well as a more complete understanding of the modifications in the EET coupling with the size of the system, the chromophore-chromophore distance, and solvation.     

Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling T(DA) of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate T(DA). Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable T(DA) for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.