Excitation Energy Transfer in Donor-Bridge-Acceptor Systems: A Combined Quantum-Mechanical/Classical Analysis of the Role of the Bridge and the Solvent

Discriminatory Resonance Energy Transfer Mediated by a Third Molecule

Relay of resonant excitation energy between two chiral molecules by an inert third particle is studied using molecular quantum electrodynamics theory. A single virtual photon propagates between each interacting pair. Fourth-order diagrammatic time-dependent perturbation theory is employed to compute the matrix element. Rate terms dependent upon the chirality of the donor and acceptor species are extracted using the Fermi golden rule. Interestingly, the mediated rate is discriminatory. For freely tumbling particles it exhibits an inverse-square dependence on each interparticle separation distance, indicating a purely radiative exchange mechanism. Furthermore, the isotropic rate is found to be a maximum for a collinear geometry and vanishes when the angle between the donor, mediator, and acceptor is 90°. The indirect rate is compared with direct transfer between two chiral molecules. Insight is gained into discriminatory migration of energy in a dielectric medium.

Resonance energy transfer mediated by a chiral molecule

The problem of resonant energy transfer (RET) between an electric dipole donor, D, and an electric dipole acceptor, A, mediated by a passive, chiral third-body, T, is considered within the framework of molecular quantum electrodynamics theory. To account for the optical activity of the mediator, magnetic dipole and electric quadrupole coupling terms are included in addition to the leading electric dipole interaction term. Fourth-order diagrammatic time-dependent perturbation theory is used to obtain the matrix element. It is found that the Fermi golden rule rate depends on pure multipole moment polarizabilities and susceptibilities of T, as well as on various mixed electric and magnetic multipole moment response functions. The handedness of T manifests through mixed electric-magnetic dipole and mixed electric dipole-quadrupole polarizabilities, which affect the rate and, respectively, require the use of fourth-rank and sixth-rank Cartesian tensor averages over T, yielding non-vanishing isotropic rate formulae applicable to a chiral fluid medium. Terms of a similar order of magnitude proportional to the product of electric dipole polarizability and either magnetic dipole susceptibility or electric quadrupole polarizability of T are also computed for oriented and freely tumbling molecules. Migration rates dependent upon the product of the pure electric dipole or magnetic dipole polarizability with the mixed electric-magnetic or electric dipole-quadrupole analogs, which require fourth- and fifth-rank Cartesian tensor averaging, vanish for randomly oriented systems. Asymptotically limiting rate expressions are also evaluated. Insight is gained into RET occurring in complex media.

Dynamics of Photoinduced Energy Transfer in Fully and Partially Conjugated Polymers Bearing π-Extended Donor and Acceptor Monomers

The photophysical properties of donor (D)-acceptor (A) polymers were studied by designing two types of polymers, (D-σ-A)_n and (D-π-A)_n, with non-conjugated alkyl (sp³) and π-conjugated (sp²) linkers using π-extended donor and acceptor monomers that exhibit planar A-D-A structures. The non-conjugated alkyl linker provides structural flexibility to the (D-σ-A)_n polymers, while the π-conjugated linker retains the rigid structure of the (D-π-A)_n polymers. Photoinduced energy transfer occurs from the large donor to acceptor units in both polymers. However, the photoinduced energy transfer dynamics are found to be dependent on the conformation of the polymers, where the difference is dictated by the types of linkers between the donor and acceptor units. In solution, intramolecular energy transfer is relatively favorable for the (D-σ-A)_n polymers with flexible linkers that allow the donor and acceptor units to be proximally located in the polymers. On the other hand, intermolecular (or interchain) energy transfer is dominant in the two polymer films because the π-extended donor and acceptor units in polymers are closely packed. The structural flexibility of the linkers between the donor and acceptor repeating units in the polymers affects the efficiency of energy transfer between the donor and acceptor units and the overall photophysical properties of the polymers.

Polariton mediated resonance energy transfer in a fluid

The focus of this work is on a microscopic quantum electrodynamical understanding of cumulative quantum effects in resonance energy transfer occurring in an isotropic and disordered medium. In particular, we consider quantum coherence, defined in terms of interferences between Feynman pathways, and analyze pure-amplitude and phase cross terms that appear in the Fermi golden rule rate equation that results from squaring the matrix element for mediated energy transfer. It is shown that pure-amplitude terms dominate in the near-zone when chromophores are close in proximity to one another (within a few nanometers), and phase cross terms dominate toward the far-zone when phase differences between different Feynman pathways begin to emerge. This can be understood in terms of physical attributes of the mediating photon, whose character becomes more real at long distances, coinciding with vanishing longitudinal components of the field, as transverse components begin to dominate.

Mediation of resonance energy transfer by two polarisable particles

The molecular quantum electrodynamics theory is employed to calculate the matrix element and Fermi golden rule rate for resonant transfer of electronic excitation energy between a donor and an acceptor in the vicinity of two neutral electric dipole polarizable particles, which play the role of bridging species. The emitter and absorber couple linearly to the electric displacement field via their electric dipole moments, while each mediator interacts quadratically with this field through its dynamic polarizability. This form of interaction Hamiltonian enables fourth-order perturbation theory to be used to compute the probability amplitude together with summation over 24 time-ordered diagrams representing a single virtual photon exchange between each pair of coupled particles. Expressions for the migration rate mediated by two inert molecules are obtained for an arbitrary arrangement of the four species that are in fixed mutual orientation or are freely tumbling. These formulae are valid for all interparticle separation distances outside the orbital overlap region. From the general result, rate equations applicable to an equidistant collinear configuration of the four bodies are evaluated. Near- and far-zone limiting forms of the transfer rate for the relay pathway are also calculated and exhibit inverse sixth and inverse square dependences on relative separation distances between pairs of particles, confirming the short-range (radiationless) and long-range (radiative) energy transfer mechanisms associated with two-body theory. The distance behavior of interference terms between two-, three-, and four-body terms is also examined, and the relative importance of each contribution to the total transfer rate is discussed.

A Quantum Electrodynamics Description of Quantum Coherence and Damping in Condensed-Phase Energy Transfer

Quantum coherence in condensed-phase electronic resonance energy transfer (RET) is described within the context of quantum electrodynamics (QED) theory. Mediating dressed virtual photons (polaritons) are explicitly incorporated into the treatment, and coherence is understood within the context of interfering Feynman pathways connecting the initial and final states for the RET process. The model investigated is that of an oriented three-body donor, acceptor, and mediator RET system embedded within a dispersive and absorbing polarizable medium. We show how quantum coherence can significantly enhance the rate of RET and give a rigorous picture for subsequent decoherence that is driven by both phase and amplitude damping. Energy-conserving phase damping occurs as a result of geometric and dispersive effects and is associated with destructive interference between Feynman pathways. Dissipative amplitude damping, on the other hand, is attributed to vibronic relaxation and absorptivity of the medium and can be understood as virtual photons (polaritons) leaking into the environment. This model offers insights into the emergence of coherence and subsequent decoherence for energy transfer in photosynthetic systems.

Quantum Chemical Studies of Light Harvesting

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

Quantum-Chemical Studies on Excitation Energy Transfer Processes in BODIPY-Based Donor-Acceptor Systems

BODIPY-based excitation energy transfer (EET) cassettes are experimentally extensively studied and serve as excellent model systems for the investigation of photophysical processes, since they occur in any photosynthetic system and in organic photovoltaics. In the present work, the EET rates in five BODIPY-based EET cassettes in which anthracene serves as the donor have been determined, employing the monomer transition density approach (MTD) and the ideal dipole approximation (IDA). To this end, a new computer program has been devised that calculates the direct and exchange contributions to the excitonic coupling (EC) matrix element from transition density matrices generated by a combined density functional and multireference configuration interaction (DFT/MRCI) calculation for the monomers. EET rates have been calculated according to Fermi's Golden Rule from the EC and the spectral overlap, which was obtained from the calculated vibrationally resolved emission and absorption spectra of donor and acceptor, respectively. We find that the direct contribution to the EC matrix element is dominant in the studied EET cassettes. Furthermore, we show that the contribution of the molecular linker to the EET rate cannot be neglected. In our best fragment model, the molecular linker is attached to the donor moiety. For cassettes in which the transition dipole moments of donor and acceptor are oriented in parallel manner, our results confirm the experimental findings reported by Kim et al. [J. Phys. Chem. A 2006, 110, 20-27]. In cassettes with a perpendicular orientation of the donor and acceptor transition dipole moments, dynamic effects turn out to be important.

Crucial Role of Nuclear Dynamics for Electron Injection in a Dye-Semiconductor Complex

We investigate the electron injection from a terrylene-based chromophore to the TiO2 semiconductor bridged by a recently proposed phenyl-amide-phenyl molecular rectifier. The mechanism of electron transfer is studied by means of quantum dynamics simulations using an extended Hückel Hamiltonian. It is found that the inclusion of the nuclear motion is necessary to observe the photoinduced electron transfer. In particular, the fluctuations of the dihedral angle between the terrylene and the phenyl ring modulate the localization and thus the electronic coupling between the donor and acceptor states involved in the injection process. The electron propagation shows characteristic oscillatory features that correlate with interatomic distance fluctuations in the bridge, which are associated with the vibrational modes driving the process. The understanding of such effects is important for the design of functional dyes with optimal injection and rectification properties.