Förster Theodor

Erich Sackmann

Professor Emeritus, Physics Department E22, Technische Universität München, D85747Garching, Germany, EU.

1 Introduction

Our development as a scientist is guided by scientific giants who show us how complex scientific questions can be solved by smart experiments and thinking. One of these scientific lighthouses in photophysics and photochemistry is Theodor Förster; not only due to his great scientific discoveries but also owing to his devotion to science and his benevolent attitude towards students and young scientists. Looking back to my time as a student I find this most remarkable since in the post war years his personality and outstanding scientific competence contributed much to the renaissance of science in post-war Germany. Förster’s discoveries and his way of thinking influenced the research of generations of scientists working on photophysical and photochemical properties of molecules, including several of those obtaining Nobel Prizes, (see (Weller 1980) and (Porter 1976)). Most remarkably, Förster belongs to a tiny group of scientists whose fame is growing steadily after their death. The only other scientist of this group in Germany that comes to my mind is Alfred Wegener, the discoverer of the tectonic structure of the earth. One reason for Försters growing recognition is that his discovery of energy transfer and of fluorescent excited complexes (excimers and exciplexes) provided us with molecular rules that allow us to study dynamic processes in complex fluids and cells with nanometer resolution and time scales of 10nsec. It should also not be forgotten that Försters’ interest in applied science paved the way for the rational photochemical synthesis of polymers and pharmaceuticals in industry. In this overview, I first summarize some aspects of Förster’s life. Then I describe his ground breaking discoveries and their impact on photochemistry and photobiology. In the third part I describe the application of FRET and excimer forming probes as molecular rulers allowing us to study the dynamics and structure of complex materials cells and chromatin with nm spatial resolution on 10 nsec time scales.

2 Biographical Sketch

Theodor Förster was born May 15th, 1910 in Frankfurt am Main. In 1929 he finished school in his hometown and studied Theoretical Physics and Mathematics at the Wolfgang Goethe University of Frankfurt a. M. He did his PHD (on the polarisation of electrons by reflection) at the Institute of Prof Erwin Madelung, who was one of the most prominent solid state physicist in Germany in his time. Indeed, he finished his Ph.D. after only four years at the age of 24. The reason for this astonishing dead was that, at that time, students could study mathematics and physics without making specific examinations. They finished their studies with an oral examination after having completed their Ph.D. work (Weller 1980)

After finishing his Ph.D. Förster moved to the University of Leipzig, together with his young mentor Karl-Friedrich Bonhöfer, one of the discoverers of ortho- and para-hydrogen who (at the age of 32) had been appointed full professor and director of the Institute of Physical Chemistry at the 29-year-old University of Leipzig. This first Institute for Physical Chemistry in Germany had been founded by Walter Ostwald, one of the founding fathers of physical chemistry and colloid research. At the same time Peter Debye, Werner Heisenberg, and Friedrich Hund worked as professors at the Physics Faculty. For that reason, years Leipzig became for several an attractive center for physicists from all over the world. Most likely, Förster’s ongoing interest in applied science was stimulated by his contact with Peter Debey.

During the Leipzig years (1934-1942) Förster published about 10 papers on various fields of molecular physics, including the stabilization of organic molecules by the carbon valency and double bonds and on light absorption by aromatic molecules. In 1942, at the age of 32, Förster became Professor of Physical Chemistry at the University of Posen. This university had been founded in 1919 by the king of Poland after the reunification of the province Posen with Poland in 1914. It had been taken over by Germany during the occupation of Poland. Most remarkably, Förster did not publish any papers during his four years in Posen. He was certainly not idle and most likely spent his time to create a family, to establish a curriculum on Physical Chemistry and to think about new scientific directions.

In 1947 Förster returned to Karl-Friedrich Bonhöfer who had become director of the newly founded Max Planck Institute for Physical Chemistry in Göttingen. Here he accomplished his ground breaking theory on energy transfer between organic molecules. Moreover, he wrote his monography “Fluoreszenz organischer Verbindungen” which for many years became the bible of the photochemists and photophysicists, at least in German speaking countries. In this book, Förster demonstrated his outstanding ability to explain complex quantum mechanical concepts to chemists and experimental physicists.

In 1951 Förster accepted the chair for Physical Chemistry at the Technical University Stuttgart where he worked until his premature death in 1974. Förster’s life ended in a tragic way. While returning from swimming in his car he had a heart attack. His car went into the left lane and was hit by a truck. Most likely he was dead before the truck hit his car.

3 The conception of the dipolar model of intermolecular energy transfer

After the publication of Dirac's “The Quantum Theory of Emission and Absorption of Radiation” theory in 1927 the question of energy exchange between molecules was revisited by many physicists. It was generally thought to be determined by collisions between atoms or molecules. Around 1925 Jean Baptist Perrin (the man who proofed Einstein’s theory of Brownian motion) had estimated that two molecules (one of which is excited) can exchange energy when they approach a critical distance of ~15 nm (Perrin1927). However, sensitized fluorescence and fluorescence depolarization experiments with chromophores (such as Fluorescein) strongly suggested that energy exchange between chromophores can occur over distances of 50nm. In his first estimate, Perrin had assumed that the molecules are two oscillators with sharp frequencies. He conjectured that in order to explain this discrepancy one has to consider the Stokes shift of fluorescence spectra as well as the shape of the absorption and emission spectra of the energy exchanging molecules (see (Perrin 1927) and introductory remarks in (Förster 1946)).

Stimulated by Perrins suggestion Förster developed a classical model of energy transfer in 1946 (Förster 1946) and a rigorous quantum mechanical theory in 1948 (Förster 1948). Both theories are based on the assumption that the energy transfer is mediated by dipolar interaction between an excited electron (initially located at the donor D) and a ground state electron at the acceptor A. The classical theory is beautifully described in a review by Hans Kuhn (Kuhn1982), the second European hero of photophysics and photochemistry. Here I briefly focus on the salient features of Förster’s quantum mechanical theory which shows that he was a keen scientific pioneer.

To calculate the transfer rate in the quantum mechanical model he keenly applied the Dirac transition theory (Dirac 1927) which is also often attributed to Fermi and is then called Fermi’s Golden Rule. He wrote down the following expression for the rate of energy transfer between two molecules A and B

[math]k_{ET}=\frac{2\pi}{h}\int \int d\overrightarrow{r}_{k}d\overrightarrow{r_{l}}\varphi _{A}^{*}(\overrightarrow{r}_{k})\varphi _{B}(\overrightarrow{r}_{k})H(\overrightarrow {r}_{k},\overrightarrow{r}_{l})\overrightarrow{r_{l}}\varphi _{A}(\overrightarrow{r}_{k})\varphi _{B}^{*}(\overrightarrow{r}_{k})\tag{1}[/math]

Where [math]\varphi _{A}[/math] and [math]\varphi _{A}^{*}[/math] are the wave functions of the electrons (k and l) in the ground and excited state. For electron distances large compared to the size of the molecules, Förster assumed that the Hamiltonian H is determined by the dipolar interaction between the electron in the excited state of the donor and the electron located at the acceptor in the ground state

[math]H(\vec{r}_{k},\vec{r}_{l})\frac{e^{2}}{\epsilon \left | r_{k}-r_{l} \right |}\approx \frac{e\vec{p}\vec{r}}{\varepsilon r^{3}}\tag{2}[/math]

where [math]\vec{p}=e\vec{r}[/math]is the electric dipole moment and [math]\varepsilon[/math]the dielectric constant of the solvent.

The second outstanding achievement of Förster is the establishment of a correlation between the energy transfer rate [math]k_{ET}[/math] and the overlap integral between the emission spectrum of the donor and the absorption spectrum of the acceptor and he derived the famous equation for the transfer rate

[math]k_{ET}=\frac{1}{\tau _{D}}\left ( \frac{R_{0}}{R_{kl}} \right )\tag{3}[/math]