Resonance Energy Transfer: From Fundamental Theory to Recent Applications

REVIEW published: 12 July 2019 doi: 10.3389/fphy.2019.00100 Resonance Energy Transfer: From Fundamental Theory to Recent Applications Garth A. Jones* and David S. Bradshaw* School of Chemistry, University of East Anglia, Norwich, United Kingdom Edited by: Olivier J. F. Martin, École Polytechnique Fédérale de Lausanne, Switzerland Reviewed by: George C. Schatz, Northwestern University, United States Cristian Leonardo Cortes, Argonne National Laboratory (DOE), United States *Correspondence: Garth A. Jones David S. Bradshaw Specialty section: This article was submitted to Optics and Photonics, a section of the journal Frontiers in Physics Received: 30 May 2019 Accepted: 28 June 2019 Published: 12 July 2019 Citation: Jones GA and Bradshaw DS (2019) Resonance Energy Transfer: From Fundamental Theory to Recent Applications. Front. Phys. 7:100. doi: 10.3389/fphy.2019.00100 Frontiers in Physics | www.frontiersin.org Resonance energy transfer (RET), the transport of electronic energy from one atom or molecule to another, has significant importance to a number of diverse areas of science. Since the pioneering experiments on RET by Cario and Franck in 1922, the theoretical understanding of the process has been continually refined. This review presents a historical account of the post-Förster outlook on RET, based on quantum electrodynamics, up to the present-day viewpoint. It is through this quantum framework that the short-range, R−6 distance dependence of Förster theory was unified with the long-range, radiative transfer governed by the inverse-square law. Crucial to the theoretical knowledge of RET is the electric dipole-electric dipole coupling tensor; we outline its mathematical derivation with a view to explaining some key physical concepts of RET. The higher order interactions that involve magnetic dipoles and electric quadrupoles are also discussed. To conclude, a survey is provided on the latest research, which includes transfer between nanomaterials, enhancement due to surface plasmons, possibilities outside the usual ultraviolet or visible range and RET within a cavity. Keywords: Förster theory, FRET, electronic energy transfer, photosynthesis, solar harvesting, plasmonics, cavity QED, interatomic Coulombic decay INTRODUCTION AND THE EARLY YEARS OF RET Resonance energy transfer (RET, also known as fluorescence resonance energy transfer, FRET, or electronic energy transfer, EET) is an optical process, in which the excess energy of an excited molecule—usually called the donor—is transferred to an acceptor molecule [1–4]; as depicted schematically in Figure 1. Fundamentally, RET involves two types of elementary particles: electrons and photons. In RET, all the electrons (including the dynamically active electrons) are bound to the nuclei of the molecules, and typically reside in their valence molecular orbitals. As such, the individual electrons do not migrate between molecules during the transfer process, since the molecular orbitals (the wavefunctions) do not overlap, but instead move between individual electronic states within the molecules. This is fundamentally different to the ultra-short-range Dexter energy transfer, where electrons do in fact migrate between molecules via covalent chemical bonds [5]. In RET, on relaxation of the electron to a lower energy electronic state in the donor, the excess energy is transported to the acceptor in the form of the emitted virtual photon—this transfer is facilitated by dipole-dipole couplings between the molecules. In fact, photons play two distinct roles toward the process: one as the mediator of donor-acceptor transfer, and the other as an external energy source that promotes donor valence electrons into an electronic excited state, via an absorption process prior to RET. 1 July 2019 | Volume 7 | Article 100 Jones and Bradshaw RET: Theory to Applications a non-quantized wave. For example, the wave-particle duality of light is uniquely portrayed within QED but not semi-classical theories. However, despite their deficiencies, classical and semiclassical theories can still be useful since, often, they are easier to implement analytically and more economic computationally. The first major QED publication is credited to Dirac who, in 1927, wrote a description of light emission and absorption that incorporated both quantum theory and special relativity [19]; this depiction later became known as the relativistic form of QED, which is used in systems that contain fast moving electrons. Three years later Dirac completed his classic book “The Principles of Quantum Mechanics” [20] in which, among other exceptional works, he derived a relativistic generalization of the Schrödinger equation. However, for elementary physical quantities such as the mass and charge of particles, calculations using this early form of QED produce diverging results. In the late 1940s, this problem was resolved (by renormalization) leading to a complete form of QED developed independently by Feynman [21–25], Schwinger [26–29], and Tomonaga [30, 31]—all three procedures were unified by Dyson [32]. The ability of QED to provide novel predictions is monumental, but its quantitative successes are even more impressive. In particular, the theory accurately predicts the electronic g-factor of the free electron to 12 decimal places. In Bohr magneton units, the most precise measurement of g/2 is 1.00115965218073(28) [33]; QED has a predicted value of 1.00115965218203(27) [34]. In addition, there are other staggering quantitative successes. For example, the numerical calculation of Lamb shift splitting of the 2S1/2 and 2P1/2 energy levels in molecular hydrogen predicts 1,057,838(6) kHz [35], which is highly accurate compared to the experimental value of 1,057,839(12) kHz [36]. QED also provides a number of predictions that are unobtainable by semi-classical theory. These include forecasts of spontaneous decay and the CasimirPolder forces, a deviation from London forces for long-range intermolecular interactions [37–41]. FIGURE 1 | Representation of energy transfer, the excited donor (on the left-hand side) transfers energy, represented by the red arrow, to the acceptor (on the right). In 1922, the pioneering work of Cario and Franck enabled the earliest observation of RET [6–8]. Their spectroscopy experiment involved the illumination of a mixture of mercury and thallium vapors at a wavelength absorbed only by the mercury; the fluorescence spectra that results show frequencies lines that can only be due to thallium. In 1927, the Nobel laureate J. Perrin provided the first theoretical explanation [9]: he recognized that energy could be transferred from an excited molecule to a nearby-unexcited molecule via dipole interactions. Five years later, his son F. Perrin developed a more accurate theory of RET [10] based on Kallman and London’s results [11]. Extending the works of both Perrins, Förster developed an improved theoretical treatment of RET [12–14]. Förs (...truncated)