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Förster’s seminal papers that successfully outlined the theory behind FRET were published in the 1940’s and 50’s, however the idea that molecules could donate and accept energy at distances beyond their collision cross section was well established and was first observed experimentally shortly after 1900. Below is a short account that briefly mentions some of the major events and people involved in understanding how FRET came to be understood; a more in depth analysis is beyond the scope of this thesis but is given by Clegg.135

The foundation of the theory describing FRET relies on an electromagnetic interaction between two species and requires the notion of an electromagnetic field. The movement of objects as a result of magnetism is an ancient knowledge, and has been used practically in navigation for centuries. A link between electricity and magnetism had been suspected since before the 1800’s, however the first mention in the literature that describes communication between two places via electromagnetic interactions was published in 1822, when Ampère observed wires would attract or

repel each other once currents were passed through them. Later Faraday’s experiments on magnetic lines of force enabled Maxwell to piece together his famous mathematical description of an electromagnetic field. It is his equations that are familiar to all physics students and were used by Hertz to derive a mathematical description of an electromagnetic field emanating from a vibrating electric dipole. These experiments were published in 1889 and the Hertzian oscillating dipole serves as a beginning point for the classical description of fluorescence and energy transfer.135

The emergence of quantum theory was evident at the turn of the 20th century. Plank had solved the blackbody radiation problem, by suggesting energy changes in matter could only take place through well defined leaps, before Einstein then suggested light itself could be quantified, by using wave-particle duality to explain the photoelectric effect.135 In 1913 Bohr managed to piece together many of these ideas as well as others, including notable contributions from Conway, to present his atomic model. Electromagnetic interactions of an electron orbiting an atomic nucleus provided a cornerstone for spectroscopy, and its extension to multi-electron systems was made possible through Heisenberg’s and Schrödinger’s work on quantum mechanics during the 1920’s. This was in turn was applied by Kallman and London, F. Perrin and ultimately Förster to describe transfers of energy in vapours and solution.136, 137

The first observation of energy transfer was recorded as the emission of radiation from thallium atoms that were indirectly stimulated through the excitation of mercury atoms. A comparison between the atomic radii and the calculated

‘spectroscopic’ cross section showed that the donor and acceptor species were too far apart to transfer energy through collisions. Cario and Franck published this sensitised luminescence in the 1920’s,138

and the dependence on the resonance between the energy levels of the sensitiser and acceptor was demonstrated by Beutler and Josephi shortly afterwards through spectroscopic studies of many pairs of acceptors and donors.139

Many classical theories of energy transfer involving dipole interactions were being developed in 1920’s and some were arriving at the distance dependence typical of Förster long range dipole coupling. Kallman and London published the first quantum explanation of energy transfer in vapours in 1928,136 which was the basis for F. Perrin’s quantum theories on energy transfer in condensed systems in 1932 and 1933.137 Both explanations were impractical to use, and F. Perrin overestimated the distances involved, but laid the foundations for Förster to extend and improve a theory of energy transfer after World War II.

Like many, Förster was partly motivated to study energy transfer by the supposedly overly efficient mechanism for plant photosynthesis. The surface area of ‘reaction centres’ on a leaf where electron transfer reactions took place was considered small when compared to the number of photons being absorbed. It was reasoned that the larger surrounding area was capable of absorbing photons and transferring energy to the reaction centre.135

Oppenheimer, also interested in photosynthesis, arrived at a correct solution and actually published before Förster. However, due to the short length of the abstract he did not arrive at an expression for general energy transfer and because it was placed in a relatively obscure journal during the war, the publication was largely ignored by the spectroscopic community.140

What sets Förster’s work apart is that he managed to integrate experimentally observable spectra into his theory. Kallman and London included unrealistically sharp spectra which did not take in to account spectral broadening due to the fluorphores’ interaction with the environment and therefore made any practical use of their theory difficult.136 Both J. and F. Perrin, using classical and quantum mechanical explanations respectively, again only looked at sharp spectra from over simplified and identical acceptor and donor species which gave exact resonance and overestimated the distance required for energy transfer between the pairs as a result. Broadening of the spectra through collisions in solution was considered by F. Perrin and did bring his distance closer to Förster’s but it was still too large.135, 137

Förster realised that broadening of the spectra of the donor and acceptor species reduced the chances of resonance between the two species, and that he could use statistics to calculate the number of pairs that were well matched in energy at any one time. The probability that a pair is in perfect resonance with each other can be calculated from the spectral overlap between emission of the donor and the absorption of the acceptor, and is known as the overlap integral ( ). This probability is typically much less than one, and so dramatically shortens the required distance for

energy transfer to occur. Förster also included a dependence on the orientation of the two dipoles into his expression for the rate of energy transfer, which in solution can be average due to molecular tumbling of the donor and acceptor. Overall, Förster pieced together a theory and used a fully quantum mechanical approach to produce expressions that used experimentally obtainable values in its derivation which made it both accessible and extremely useful.133