Mediation of resonance energy transfer by a third molecule

Waveguided energy transfer in pseudo-two-dimensional systems

Resonance energy transfer (RET) is an important and ubiquitous process whereby energy is transferred from a donor chromophore to an acceptor chromophore without contact via Coulombic coupling. There have been a number of recent advances exploiting the quantum electrodynamics (QED) framework for RET. Here, we extend the QED RET theory to investigate whether real photon exchange can allow for excitation transfer over very long distances if the exchanged photon is waveguided. To study this problem, we consider RET in two spatial dimensions. We derive the RET matrix element using QED in two dimensions, consider an even greater confinement by deriving the RET matrix element for a two-dimensional waveguide using ray theory, and compare the resulting RET elements in 3D and 2D and for the 2D waveguide. We see greatly enhanced RET rates over long distances for both the 2D and 2D waveguide systems and see a great preference for transverse photon mediated transfer in the 2D waveguide system.

Two bridge-particle-mediated RET between chiral molecules

The problem of resonance energy transfer between a pair of chiral molecules mediated by two electrically polarizable bridging particles is solved using molecular QED theory. In this framework a single virtual photon propagates between any two-coupled entities and is responsible for the conveyance of excitation energy from emitter to absorber. Electric dipole and quadrupole, and magnetic dipole couplings linear in the Maxwell fields are employed for donor and acceptor, while each mediator scatters two virtual photons and responds quadratically to the electric displacement field via its electric dipole polarizability. This enables fourth-order diagrammatic perturbation theory to be used to compute the probability amplitude for the process. Individual multipole moment contributions to the Fermi golden rule rate are then extracted for oriented and isotropic systems. Discriminatory transfer rates arise when either the donor or the acceptor are electric-magnetic dipole and the other has a pure multipole moment, or when both are chiral, with mixed electric dipole-quadrupole contributions vanishing in the fluid phase. The bridge-mediated transfer rate is found to be a maximum for a collinear geometry. Moreover, a multi-level model of the mediator is necessary for energy migration. Asymptotically limiting rates for arbitrary and collinear geometries are also obtained for one centre purely electric dipolar and the other purely quadrupolar, or both donor and absorber purely quadrupolar. Understanding is gained of radiationless and radiative transfer mechanisms between chiral moieties in a dielectric medium.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

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.

Bridge-Mediated RET between Two Chiral Molecules

Molecular quantum electrodynamics (QED) theory is employed to calculate the rate of resonance energy transfer (RET) between a donor, D, described by an electric dipole and quadrupole, and magnetic dipole coupling, and an identical acceptor molecule, A, that is mediated by a third body, T, which is otherwise inert. A single virtual photon propagates between D and T, and between T and A. Time-dependent perturbation theory is used to compute the matrix element, from which the transfer rate is evaluated using the Fermi golden rule. This extends previous studies that were limited to the electric dipole approximation only and admits the possibility of the exchange of excitation between a chiral emitter and absorber. Rate terms are computed for specific pure and mixed multipole-dependent contributions of D and A for both an oriented arrangement of the three particles and for the freely tumbling situation. Mixed multipole moment contributions, such as those involving electric–magnetic dipole or electric dipole–quadrupole coupling at one center, do not survive random orientational averaging. Interestingly, the mixed electric–magnetic dipole D and A rate term is non-vanishing and discriminatory, exhibiting a dependence on the chirality of the emitter and absorber, and is entirely retarded. It vanishes, however, if D and A are oriented perpendicularly to one another. Near- and far-zone asymptotes of isotropic contributions to the rate are also evaluated, demonstrating radiationless short-range transfer and inverse-square radiative exchange at very large separations.

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.

Impact of a charged neighboring particle on Förster resonance energy transfer (FRET)

Förster resonance energy transfer (FRET) is an important physical phenomenon which demands precise control over the FRET rate for its wide range of applications. Hence, enhancing the FRET rate using different techniques has been extensively studied in the literature. Research indicates that introducing additional particles to a system consisting of a donor-acceptor pair can change the behaviour of FRET in the system. One such technique is to utilize the collective oscillations of the surface electrons of a neighboring electrically-neutral metal nanoparticle (MNP). However, the perceived changes on the FRET rate between the donor and the acceptor, when the MNP carries excess electrical charges are yet unknown. In this paper, we study these changes by introducing a charged MNP, in the proximity of an excited donor and a ground state acceptor. We deploy the classical Green's tensor to express the FRET rate in the system. We consider an effective dielectric response for the MNP, which accounts for the extraneous surface charge effects. We analyze the electrical potential at the acceptor position due to the changed dipole moment of the donor molecule as a result of the electric field induced at the donor position, and obtain the FRET rate of the system. This model considers arbitrary locations and orientations of the two molecular dipole moments with regard to the position of the spherical MNP. We present the enhancement of the FRET rate, predominantly caused by both the surface plasmon excitations and the extraneous surface electrical charges carried by the neighboring MNP. We obtain the results by varying the separation distance between the molecules and the MNP, the transition frequency of the donor-acceptor pair and the size of the metallic sphere. Specifically, we demonstrate that a donor-acceptor pair placed in the vicinity of an electrically-charged Silver MNP exhibits a remarkable improvement in the FRET rate. Furthermore, the aggregate FRET enhancement is determined by other characteristics such as the location of the donor, transition frequency, separation distances and the radius of the MNP. In essence, these findings reveal an approach to realize the enhanced FRET rate in a larger span in a more controlled manner that is desirable in many FRET-based applications including spectroscopic measurements.

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.

Virtual Photon Approximation for Three-Body Interatomic Coulombic Decay

Interatomic Coulombic decay (ICD) is a mechanism that allows microscopic objects to rapidly exchange energy. When the two objects are distant, the energy transfer between the donor and acceptor species takes place via the exchange of a virtual photon. On the contrary, recent ab initio calculations have revealed that the presence of a third passive species can significantly enhance the ICD rate at short distances due to the effects of electronic wave function overlap and charge transfer states [Phys. Rev. Lett. 119, 083403 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.083403]. Here, we develop a virtual photon description of three-body ICD, allowing us to investigate retardation and geometrical effects which are out of reach for current ab initio techniques. We show that a passive atom can have a significant influence on the rate of the ICD process at fairly large interatomic distances, due to the scattering of virtual photons off the mediator. Moreover, we demonstrate that in the retarded regime ICD can be substantially enhanced or suppressed depending on the position of the ICD-inactive object, even if the latter is far from both donor and acceptor species.

Near-Zone Mediation of RET by One and Two Proximal Particles

The effect of two inert, electric dipole polarizable molecules in relaying electronic excitation energy resonantly between a donor-acceptor pair is studied within the framework of molecular QED theory. Since transfer is efficacious when the coupled particles are close to one another, the matrix element is calculated in the near-zone approximation by employing static dipolar interaction potentials and third-order diagrammatic perturbation theory. For isotropic species, the Fermi golden rule exchange rate exhibits a Förster-like inverse sixth power dependence on each pair separation distance, is proportional to the modulus squares of the transition electric dipole moments of donor and acceptor, and depends on the polarizabilities of the two mediators. Comparison is made with direct (2-body) and third-body mediated near-zone transfer. Matrix elements for these last two processes are used to evaluate contributions to the rate due to 2-body-3-body, 2-body-4-body, and 3-body-4-body interference terms. In each of these cases, an inverse cubic dependence on each of the relative particle displacements is found.

The Unified Theory of Resonance Energy Transfer According to Molecular Quantum Electrodynamics

An overview is given of the molecular quantum electrodynamical (QED) theory of resonance energy transfer (RET). In this quantized radiation field description, RET arises from the exchange of a single virtual photon between excited donor and unexcited acceptor species. Diagrammatic time-dependent perturbation theory is employed to calculate the transfer matrix element, from which the migration rate is obtained via the Fermi golden rule. Rate formulae for oriented and isotropic systems hold for all pair separation distances, R, beyond wave function overlap. The two well-known mechanisms associated with migration of energy, namely the R−6 radiationless transfer rate due to Förster and the R−2 radiative exchange, correspond to near- and far-zone asymptotes of the general result. Discriminatory pair transfer rates are also presented. The influence of an environment is accounted for by invoking the polariton, which mediates exchange and by introducing a complex refractive index to describe local field and screening effects. This macroscopic treatment is compared and contrasted with a microscopic analysis in which the role of a neutral, polarizable and passive third-particle in mediating transfer of energy is considered. Three possible coupling mechanisms arise, each requiring summation over 24 time-ordered diagrams at fourth-order of perturbation theory with the total rate being a sum of two- and various three-body terms.

Perspective: Quantum Hamiltonians for optical interactions

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Controlling resonance energy transfer in nanostructure emitters by positioning near a mirror

The ability to control light-matter interactions in quantum objects opens up many avenues for new applications. We look at this issue within a fully quantized framework using a fundamental theory to describe mirror-assisted resonance energy transfer (RET) in nanostructures. The process of RET communicates electronic excitation between suitably disposed donor and acceptor particles in close proximity, activated by the initial excitation of the donor. Here, we demonstrate that the energy transfer rate can be significantly controlled by careful positioning of the RET emitters near a mirror. The results deliver equations that elicit new insights into the associated modification of virtual photon behavior, based on the quantum nature of light. In particular, our results indicate that energy transfer efficiency in nanostructures can be explicitly expedited or suppressed by a suitably positioned neighboring mirror, depending on the relative spacing and the dimensionality of the nanostructure. Interestingly, the resonance energy transfer between emitters is observed to "switch off" abruptly under suitable conditions of the RET system. This allows one to quantitatively control RET systems in a new way.

A revisitation of the Förster energy transfer near a metallic spherical nanoparticle: (1) Efficiency enhancement or reduction? (2) The control of the Förster radius of the unbounded medium. (3) The impact of the local density of states

The central motivation of this theoretical revisitation comes from the fact that some experimental works about Förster energy transfer report improvement of the Förster efficiency when the donor-acceptor molecular pair is in the vicinity of a metallic particle, while others found efficiency deterioration. In the presence of a nanoscale metallic sphere, we calculate contour plots of the Förster energy transfer rate KF and the Förster efficiency η as a function of the acceptor position rA for a fixed donor position. These contour plots clearly highlight the influence of the sphere on KF and η as the donor position, the orientations of donor and acceptor dipoles, and the particle size are varied; also the impact on KF(rA) and η due to the excitation of surface plasmons is easily noticeable from these contour plots. Moreover, we obtain the enhancement factor KF/KF0 (KF0 refers to the case without sphere) against the donor-surface separation for particular donor-acceptor spatial distributions, several particle sizes, and distinct molecular dipole orientations. Therefore, our calculations provide a systematic analysis of the Förster energy transfer in the presence of a metallic nanosphere. Based on these results, we formulate hypotheses for explaining the aforementioned contradictory experimental results about η. To complement our study, we examine the impact of the local density of states ρ on KF. KF is practically unperturbed by sphere when the intermolecular separation R is ≲ 3 nm, since the direct donor-acceptor electromagnetic interaction is dominant. On the contrary, when R ≳ 3 nm, the nanosphere perturbs KF and this perturbation is stronger if plasmonic resonances are excited. KF/KF0 can greatly be enhanced in certain regions, but these regions coincide with low-efficiency regions, compromising applications involving the Förster process. In the presence of the nanosphere, the high Förster efficiency region (η ≥ 0.5) has the same shape as that for the case without sphere, but its extension (Förster radius Ro) is reduced; this effect is a consequence of the large increase of the donor direct decay rate and Ro depends strongly on donor position. Consequently, the sphere controls Ro that is associated with the efficiency pattern that corresponds to the unbounded medium; this effect can be exploited in the measuring technique of nanoscale displacements of proteins that is based on the fluorescence resonant energy transfer. The functional form of KF(ρ) is determined by the intermolecular separation R, the spatial configuration and the dipole orientations of the molecular pair, and the donor proximity to the nanoparticle.

Resonance energy transfer: influence of neighboring matter absorbing in the wavelength region of the acceptor

In many of the materials and systems in which resonance energy transfer occurs, the individual chromophores are embedded within a superstructure of significantly different chemical composition. In accounting for the influence of the surrounding matter, the simplest and most widely used representation is commonly cast in terms of a dependence on local refractive index. However, such a depiction is a significant oversimplification, as it fails to register the electronic and local geometric effects of material specifically in the vicinity of the chromophores undergoing energy transfer. The principal objective of this study is to construct a detailed picture of how individual photon interaction events are modified by vicinal, non-absorbing chromophores. A specific aim is to discover what effects arise when input excitation is located in the neighborhood of other chromophores that have a slightly shorter wavelength of absorption; this involves a passive effect exerted on the transfer of energy at wavelengths where they themselves display no significant absorption. The theory is based on a thorough quantum electrodynamical analysis that allows the identification of specific optical and electronic chromophore attributes to expedite or inhibit electronic energy transfer. The Clausius-Mossotti dispersion relationship is then deployed to elicit a dependence on the bulk refractive index of the surroundings. A distinction is drawn between cases in which the influence on the electromagnetic coupling between the donor and the acceptor is primarily due to the static electric field produced by a polar medium, and converse cases in which the mechanism for modifying the form of energy transfer involves the medium acquiring an induced electric dipole. The results provide insights into the detailed quantum mechanisms that operate in multi-chromophore systems, pointing to factors that contribute to the optimization of photosystem characteristics.