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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.

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.

Photochemical isomerization in sterically crowded chiral alkenes is the driving force for molecular rotary motors in nanoscale machines. Here the excited-state dynamics and structural evolution of the prototypical light-driven rotary motor are followed on the ultrafast time scale by femtosecond stimulated Raman spectroscopy (FSRS) and transient absorption (TA). TA reveals a sub-100-fs blue shift and decay of the Franck-Condon bright state arising from relaxation along the reactive potential energy surface. The decay is accompanied by coherently excited vibrational dynamics which survive the excited-state structural evolution. The ultrafast Franck-Condon bright state relaxes to a dark excited state, which FSRS reveals to have a rich spectrum compared to the electronic ground state, with the most intense Raman-active modes shifted to significantly lower wavenumber. This is discussed in terms of a reduced bond order of the central bridging bond and overall weakening of bonds in the dark state, which is supported by electronic structure calculations. The observed evolution in the FSRS spectrum is assigned to vibrational cooling accompanied by partitioning of the dark state between the product isomer and the original ground state. Formation of the product isomer is observed in real time by FSRS. It is formed vibrationally hot and cools over several picoseconds, completing the characterization of the light-driven half of the photocycle.