# Förster Theodor

Erich Sackmann[[1]]

Professor Emeritus, Physics Department E22, Technische Universität München, D85747 Garching, Germany, EU and Am Perlacher Forst 204, D81545 München, 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)).

Figure 1.1. Theodor Förster as a lecturer. Middle: as adviser of his colleagues, and as experimentalist
Figure 1.2. Theodor Förster and David Dexter

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 the 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

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

Where $\varphi _{A}$ and $\varphi _{A}^{*}$ 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

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

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

The second outstanding achievement of Förster is the establishment of a correlation between the energy transfer rate $k_{ET}$ 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

$k_{ET}=\frac{1}{\tau _{D}}\left ( \frac{R_{0}}{R_{kl}} \right )^{6}\tag{3}$

In this equation $R_{0}$ is the critical distance over which energy transfer is efficient, which is now called the Förster Radius. $\tau_{D}$ is the life time of the donor in the excited state. In the earlier classical paper from 1946, Förster had already shown that $R_{0}$ is a function of three independent quantities: an orientation factor $\kappa$, the fluorescence quantum yield $\eta _{F}$ and the overlap between the absorption and the emission spectrum $\varepsilon _{A}\left ( \nu \right )$ and $\Phi_{D}(\nu)$, respectively(see Förster 1959)

$R_{0}^{6}=\left ( \frac{3\, c^{4}\, \kappa ^{2}\ln 10}{128\, \pi ^{5}\, N_{A}\, n^{4}} \right )\Phi_{F} \int_{0}^{\infty }\frac{\epsilon _{A}(\nu )\Phi _{D}\nu }{\nu ^{4}}\, d\nu \tag{4}$

The situation would have been hopeless complicated if Förster would not have found a simple method to measure the radius $R_{0}$ by determining the fraction $w_{DA}$ of energy transferred from the energy donor to the acceptor.

$w_{DA}=\frac{1}{1+(r/R_{0})^{6}}\tag{5}$

A compelling quantitative verification of the Förster theory was provided by Hans Kuhn (the other giant of photochemistry and photophysics in after-war Europe) in beautiful experiments. He measured the energy transfer between two chromophores anchored in lipid monolayers via hydrophilic tails. By embedding the monolayers in multi-lamellar Langmuir-Blodgett-Kuhn films, the distance of the chromophore containing monolayers could be varied by the intercalation of various numbers of dye-free monolayers between the dye exposing monolayers. Since one deals with a two-dimensional system the transfer rate depends on the fourth power of the Förster radius (Kuhn 1982). Thus Kuhn not only provided a beautiful proof of the Förster theory but also clearly demonstrated that the energy transfer rate depends on the dimensionality of the system studies.

## 4 Why was the Förster theory so revolutionary: the idea of supramolecular states.

Förster tacitly assumed that the excited states of complexes (AB)* can be described as super-molecules with fixed nuclear positions and with the two valence electrons moving in a supramolecular potential whereby the initial and final states (D*A and DA*), can be represented by the wave functions $\Psi _{initial}=\varphi _{k}(D^{*}A)$ and $\Psi _{final}=\varphi _{k}(DA^{*})$. The squares of these function are measures for the probability that the valence electron at the acceptor and the donor is excited (see (Hopfield 1974)).

With his keen concept of super-molecular states of molecular complexes, Förster paved the way for numerous theories of photophysical processes of molecular complexes including exciton formation in organic crystals, the red shift of the absorption band of chromophore complexes. This concept formed also the basis for the theories of photochemically induced electron transfer reaction between an excited electron donor (D*) and an acceptor in the ground state (A) by electron tunneling (Hopfield 1974; Jortner 1985) and intersystem crossing (Jortner 1980), (Markus and Stutin1985).

Försters keen dipolar theory had to go through a critical phase and was criticized by famous colleagues, such as Davydov (known for his treatment of excitation of crystals (Knox 2012)). However, during the ongoing discussion, the FRET theory stood its test. Försters theory was later extended for more tightly packed molecules by Dexter. By introducing electron exchange terms more complex cases such as energy transfer between triplet states could be explained. The history of this development is well described in common paper. In fact, Förster had proposed to treat situations of the closely packed chromophore by introducing quadrupole terms and discussed the transition between weak and strong coupling. An interesting discussion of the extension of the Förster theory to tightly packed chromophores can be found in a paper jointly written by Dexter, Förster and Knox (Knox 2012).

## 5 Försters impact on photobiology-energy and quantum efficiency of photosynthesis

Theodor Förster was always interested in photobiology as I remember from many visits by famous photochemists who came to Stuttgart to discuss with him the possible role of energy transfer reactions in photosynthesis. In fact, before he wrote his famous quantum mechanical theory in 1948 he had published a paper “on the theory of photo synthesis (Förster 1947). Based on estimations of the chlorophyll density he conjectured that the excitation energy captured by a chlorophyll molecule in the photosynthetic membrane can move over some 104 chlorophyll molecules by dipolar energy transfer and exciton diffusion. Most importantly he pointed out that carotenoids can be involved in the energy transfer process.

Today we know that that energy transfer processes play a key role for the light harvesting by bacteria and plants. Figure 2 (in the BOX) shows the present view of the arrangement of chlorophyll and carotenoids in the light harvesting complexes of purple bacteria based on electron microscopy, spectroscopic studies and sophisticated theories by the group of Klaus Schulten (for references see (Ritz, Damjanivic and Schulten 2002). Two Light harvesting complexes (LHC1 and LHC2) surround the photosynthetic reaction centres. They guide the light, absorbed by any chlorophyll molecule in a most effectively to the chlorophyll dimer, of the RZ which is often called the special pair).

Försters prominent pupil Klaus Schulten explained the role of carotenoids as protector of the photosynthetic reaction center and inhibitor of plant cell death. His theoretical studies provided strong evidence that a unique feature of excited carotenoids is their transition to long living triplet states by ultrafast internal conversion (in 0.2 psec). These states lie lower than the excited singlet states of oxygen $^{1}O_{2}^{*}$ and can thus quench these photo-damaging states. The low lying triplet states of Chlorophylls ($^{3}B-Chl$) can also be populated by energy transfer from chlorophyll triplet states according to

$BChl^{*}+^{1}Car\rightarrow ^{1}BChl+^{3}Car^{*}$

This intersystem crossing is enabled by strong interaction by exchange mechanisms and requires the tight packing of chromophores as already anticipated by Förster in 1947.

Here, another remark is appropriate. Today we assume that our knowledge of the molecular structure of the photosynthetic reaction centre is basically a result of X-ray and Electron Microscopy studies. However, our knowledge on the organisation and the function of the chromophores is due to spectroscopic studies and the wealth of knowledge about photophysical processes collected over a hundred years. One major triumph of spectroscopists was the discovery of the special chlorophyll pair, long before the structure determination by Deisenhofer and coworkers.

Förster-Schulten model of energy transfer in photosynthetic reaction centers.

Figure 2. (a) Generation of proto motoric forces (in terms of proton gradients-grad [H+]) across membrane of purple bacteria. The electrons are transported from the excited special pair (B-Chl)2, acting as primary electron donor, via the monomers of B-Chl, bacteria pheophytins (B-Ph) and two quinone-derivates: Qa and Qb. From there it is guided via the stack of cytochrome C proteins to the electron hole of the special pair (B-Chl2)+. The electron could cross the membrane with the help of the cytochromes (such as Cyt b) or directly via the stable electron donors hydroquinone (QbH2). The inset shows some of the players involved and the arrangement of the two chlorophylls in the special pair as calculated by Hans Kuhn (Kuhn 1986) (b). Fine structure of the two light harvesting complexes (LHC 1 und LHC 2) in the membrane of purple bacteria (redrawn after (Ritz, Damjanivic and Schulten 2002)). The fine-tuned energy ladder guides the excitation from the light harvesting complex LHC 1 (absorbing at 850 nm) to the LHC2 surrounding the reaction center with the chlorophyll dimer (called special pair) absorbing at 875 nm. The Carotenoids (marked by circles) are located at the periphery with the long axis oriented parallel to the membrane normal.

Figure 2 shows the present view of the arrangement of the chlorophyll and carotenoids in the light harvesting complexes which surround the photosynthetic reaction centres and guide the light, absorbed by any chlorophyll molecule in most effective way to the $h\nu$-receptor, of the reaction centres. More recent theoretical studies of the energy transport in photosynthetic systems by the Schulten group has shown that the energy transfer also involves the carotenoids embedded in the Light Harvesting Complexes (LHC). They play a key role for the protection of photosynthetic membranes from excess light intensities. In fact the subtle control of the energy transfer from the location of absorption to the reaction centres is one of the most stunning examples how nature exploits physical concepts to control life processes.

Today we assume that our knowledge of the molecular structure of the photosynthetic reaction centre is due to X-ray and Electron Microscopy studies. However, our knowledge on the organisation and the function of the chromophores, is due to spectroscopic studies based on the wealth of knowledge about photophysical processes collected over a hundred years. One major triumph of spectroscopists was the discovery of the special chlorophyll pair long before the structure determination by Deisenhofer In fact the array of chromophores in the reaction centre is based on spectroscopic studies.

## 6 The Förster Cycle

Chemistry in the excited state and how Förster measured excited state lifetimes long before the development of flash photolysis.

A surprising feature of the theoretical physicists Förster was his ongoing interest in the industrial application of photochemical techniques. He liked discussions with industrial researchers who frequently asked for his advice about all questions of photochemical synthesis of organic molecules or about strategies to avoid the bleaching of fabrics. This may have stimulated him to study the physical basis of photochemical reactions after he had moved to the University of Stuttgart in 1951. At that time photochemical reactions were utilized in industry to activate organic molecules by free radical mediated chlorination and nitrosation (replacement of hydrogen by groups with R-NO functionality) which serves the generation of activators of polymerization. An example is a caprolactam a precursor for the production of polyamides, such as perlon.

Förster realized that excited molecules can be considered as electronic isoforms of the ground state molecules with strongly modified chemical properties, such as the acidity and basicity of polar molecules. He concentrated on the photochemical modification of the chemistry of $\beta$-Naphtol (see Figure 3a) which was applied for the production of dyes (such as Sudan). In a ground breaking experiment, he showed that when $\beta$-Naphtol (ROH in Fig. 3a) is excited at very low pH~2-3 one observes the fluorescence of the anion (RO-). In striking contrast, in the ground state, the molecule dissociates only in very basic solutions (of pKa~9.6). This simple observation prompted him to develop the powerful concept of the Förster cycle allowing us to determine thermodynamic parameters and pK values of excited molecules (Förster 1950). Most interestingly, it allowed Förster to measure the life time of excited states (which was generally considered as measurably small) several years before flash photolysis was invented by Porter and Eigen.

In this ground breaking study, Förster showed that for a situation in which the fluorescence and absorption spectra are centro-symmetrically located about a wavelength $\lambda_{0}$ called the symmetry rule) the life time can be measured by application of Einstein’s law of induce excitation and spontaneous emission. He derived the following equation for the determination of the lifetime $\tau_{e}$

$\frac{1}{\tau _{e}}=2.88\times 10^{-9}\, n^{2}\int_{0}^{\infty }\frac{(2\tilde{\nu }_{0}-\tilde{\nu })}{\tilde{\nu }}\, \epsilon (\tilde{\nu })\, d\tilde{\nu }\tag{6}$

In this equation, n is the refractive index and is the wave number of the symmetry axis between the long wavelength absorption and the short wavelength emission band. For Naphtol in acidic aqueous solutions he obtained $\tau_{e}$=5.8$\times$10$^{-8}$ sec which is astonishingly close to the result measured by flash photolysis $\tau_{e}$=4$\times$10$^{-8}$sec. This equation was derived in a more rigorous way a decade later and the validity of this method was established experimentally for several aromatic molecules (Stickler and Berg 1962).

The concept of the Förster cycle was extended by his pupil Ernst Lippert to study the color changes of organic molecule due to a change in solvent polarity which enabled him for the first time to measure dipole moments of molecules in the excited states (Lippert 1955).

The major value of this discovery of Förster lies in the fact that it showed for the first time how to measure thermodynamic properties of photochemical reactions, such as heats of transition or dissociation constant of complex formation in the excited state, He developed a thermodynamic concept, now called Förster-cycle, for the evaluation of excited state equilibria, such as acid-base equilibria. This concept paved the way for the determination of the equilibrium constants $K_{a}$ in the excited states by considering the cycle processes shown in Figure 3a. The basic idea for measuring molar enthalpies was to consider only the difference in molar enthalpy changes in the ground and excited states, neglecting the changes of the entropy associated with the reaction. Consider the free energy change of deprotonation in the ground (0) and excited state (1) by assuming that $\Delta S_{1}=\Delta S_{0}$. The dissociation constants in the ground and excited state are then determined by the difference in the molar heats of transition $\Delta H_{i}$

$\delta \Delta H=\Delta H_{1}-\Delta H_{0}=-RT\ln \left \{ \frac{K_{a}^{*}}{K_{a}} \right \}.\tag{7}$

By considering the energy diagram of Fig 3a one obtains

$\Delta H+N_{A}h\nu _{1}-\Delta H^{*}-N_{A}h\nu _{2}=0\tag{8}$

and the dissociation constant is given by

$\ln K_{a}^{*}=\ln K_{a}+\frac{h(\nu _{1}-\nu _{0})}{k_{B}T}\tag{9}$

The thermodynamic basis of the Förster cycle was later refined by Grabowski and Rubaszewska ( Grabowski and Rubaszewska 1976).

Figure 3. a) Left: Förster cycle of the deprotonation reaction of <math\beta[/itex]-Naphtol. Right: term scheme for the calculation of thermodynamic properties of the reactions in the excited state. (b) Model of the chromophore (green) embedded into the peptide network of the protein (marked in black). The left side shows the fluorescent dye before and the right side after excitation at 396 nm resulting in the formation of phenolate ($-\Phi O^{-}$).The phenolate is supposed to form a link with histidine. The ionic form of the chromophore can remain in the dissociated state for an extended period of time and can thus be used as long wavelength emitting fluorescence probe. (c) The absorption spectrum of the neutral state and fluorescence spectrum of ionic form.

The interest in the Förster cycle has gained new impetus with the application of photophysical techniques in cell biology after it became possible to genetically express green fluorescent proteins (GFP) from jelly fish, reviewed in (Tsien 1998). The chromophore is embedded in a barrel like protein shell where it is protected from hydrolysis by enzymes. If the molecule is excited at 395 nm, the phenol (which has a pKa~0.1 in the ground state) dissociates, in close analogy to the behavior of $\beta$-naphtol. In contrast to the short lifetime of isolated phenols, the dissociated state of GFP is metastable and lives for extended periods of time. This fortunate situation allows us to average over many excitations of single molecules enabling the measurement of distances between molecules with nm precision.

There are still many open questions concerning the structure and function of the green fluorescent proteins and its isoforms. The chromophore can form a network with the amino acid scaffold by hydrogen bridges as indicated by arrows in Figure 3b. The ionic state is likely stabilized by formation of a link between the ionized phenolate and the histidine group of the protein (see Figure 3b). At present, several other models as that shown in Figure 3 are discussed in the literature. To the authors knowledge a systematic quantitative analysis of the function of GFP in terms of the thermodynamics of the Förster cycle is still missing. Such analyses would certainly necessary to test the validity of the various models.

## 7 From Excimers to Exciplexes –New applications in life science

Some years after he had moved to Stuttgart, Förster opened another new field of photophysics with the discovery of excited complexes between a ground state and an excited pyrene molecule (called excimers). Together with his pupil X. Kasper he observed the appearance of a new broad band (centred at 450nm) at the long wavelength end of the fluorescence spectrum (with the 0-0 transition located at 395 nm). The fluorescence band showed no vibrational fine structure and increased with increasing concentration (Förster and Kaspar 1955). Förster called this effect “Fluoreszenzumschlag” (english concentration transformation). With his unmatched insight into the behaviour of excited molecules he realized that this is due to the formation of sandwich-like complexes between a molecule in the ground and in the excited state, formed according to

$P^{*}+P\Rightarrow {PP}^{*}$

With the discovery of excimers Förster had found a case of strong interaction between excited and ground state molecules which he most likely had anticipated many years before. (see Förster 1957 and Förster 1969). Again Förster generalized the discovery of excimers formed by homodimers to excited hetero-complexes (now called exiplexes) and this concept paved the way for the new field of charge transfer reactions in the excited state. In his typical generosity he left the field to younger colleagues, in particular to his most important pupil Albrecht Weller who led the field of photochemistry of charge transfer complexes to the highest possible standard. In the paper written in 1969 Förster discussed many aspects of excimer formation including measurements of the enthalpies and entropies of excited complex formation and excimer formation in triplet states (Förster 1965, Förster 1969). In the impressive study of 1963 he cited 143 publications and this review most certainly summarizes the state of the art around 1970.

Both, the Förster energy transfer (FRET) and excimer forming molecules had been constantly used by material scientists and solid state physicists to study chemical reactions and dynamic properties of organic and biomimetic materials. The interest in these discoveries exploded in recent years after biophysicists and cell biologists realized that they provide us with molecular rulers that can dynamically measure molecular distances in the 5-50 nm range by labelling biomolecules either with energy donors and acceptors (FRET-techniques) or with excimer forming probes. The dyes can also serve as molecular beacon to localize nanomole molecules in solutions complex fluids and cells .The main advantage of fluorescent probes in biological physics applications, compared to classical super-resolution microscopy techniques, is the possibility to measure dynamic processes down to nanometer scales and with 10 nsec time resolution which, in the authors view, this is a major task of biological physicists.

The application of FRET as molecular ruler in living matter research is described in many reviews (references see (Knox 2012)) and I restrict myself to some critical remarks which had always been pointed out by Förster. First, due to the geometric factor $\kappa$ in Eq. (3), the energy transfer depends on the orientation of the chromophores and under certain conditions ($\theta =45^{\circ},\, \xi =90^{\circ}$) the geometric factor and thus the energy transfer probability can become very small. Moreover if the chromophores are confined to planar or linear targets the $R^{-6}$ - dependence of Eqs. (4) and (5) does not hold as shown in the above mentioned Kuhn experiments (Kuhn 1982). For quantitative studies of molecular interaction by FRET or the excimer technique, it is thus important to carefully consider the topology of the system studied.

In the following, I will address the problem of dimensionality by considering the use of excimer probes for studying dynamic properties in bio-membranes and new applications in genetic engineering. The excimer probe technique is not as popular as FRET. However, its usefulness and power have not been fully exploited yet. In other words, there is much room left for the application of excimer probe technique to study dynamic properties and dissipative processes in biomaterial research.

After switching to biological physics the author was encouraged by Förster to apply excimer probe technique for measuring micro-viscosities and diffusivities $D_{lat}$ in artificial and biological membranes, doped with a few mole% of pyrene or pyrene-labelled lipids. From the point of view of physics of condensed matter lipid membranes are of great interest as prototypes of two-dimensional fluids (Galla et al 1979). Diffusivities can be measured by stationary analysis of the excimer quantum yield and with non-stationary techniques, enabling the observation, of the formation and decay of excimer fluorescence. Hans Joachim Galla (a scientific grandson of Förster) first solved the problem by a stationary technique (neglecting the decay of excimers). It is based on the measurement of the jump frequency $\nu_{j}$ of pyrene labelled lipids between two neighboring sites (separated by a distance $\lambda$) in the lipid matrix. By application of a random walk model in 2D lattices, he could determine the two-dimensional jump frequency from which the diffusion coefficient $D_{lat}$ in the membrane plane obtained according to

$D_{lat}=\frac{1}{4}\nu _{j}\lambda ^{2}$

Figure 4. (a) Model system for studying reactions in two dimensional polymer solutions formed by anchoring of macrolipids in lipid monolayers at the air water interface of a Langmuir film balance. Some of the chains are labelled with pyrene. Please note the growing-in of the excimer fluorescence during the first 10 nsec, (b) Direct observation of time dependent of monomer fluorescence and excimer fluorescence of pyrene labelled phospholipids embedded in a fluid lipid monolayer. The inset on the right shows the reaction and the definition of the kinetic coefficients.

In order to measure diffusivities $D_{lat}$ and microviscosities of membranes with high precision nonstationary measurements of the time dependent reaction rate of excimer formation are required. The theoretical basis for such measurement in organic solvents was laid by Sienicki and Winnik (Sienicki and Winnik 1987). Birks and coworkers solved the experimental problems and measured the excimer formation rate r(t) (defined in Figure 4b) in organic solution (Birks, Dyson and Munro 1963). The diffusion coefficients were obtained by application of the Smoluchowski equation of chemical reactions in solutions.

The problem in 2D solutions is much more complex since the Smoluchovsky equation does not have stationary solutions. This problem was elegantly solved by Rudolf Merkel (another scientific grandchild of Förster) in his PH. D. thesis. He developed a technique to measure both the time evolution of monomer fluorescence decay and the parallel growing-in and decay of the excimer fluorescence. He studied monolayers of phospholipids on a Langmuir film balances that was equipped with a device for time resolved fluorescence spectroscopy (Merkel et al 1994). He determined diffusion coefficients by numerically solving the 2D diffusion equation. The values of $D_{lat}$ measured by the stationary and the non-stationary techniques agree reasonable well justifying the application of the stationary method.

An important result of the stationary and dynamic measurements of the temperature dependence of $D_{lat}$ was the first demonstration that the random walk in fluid membrane is determined by the free volume model rather than by the Arrhenius equation. This theory was introduced by Turnbull and Cohen to describe the molecular diffusion in glasses (see (Galla 1979)). The free volume model opens new possibilities to measure changes of the packing densities of lipids in membranes by solutes and temperature changes. Moreover it enables the determination of phase diagrams of lipid mixtures (Merkel and Sackmann 1994).

The great power of the excimer probe techniques for studying complex fluids was further demonstrated in corporation with the group of Helmut Ringsdorf in Mainz by measuring (for the first time) the time dependent reaction rate r(t) of pyren excimer formation in 2D polymer solutions (shown in Fig4a). The purpose of these experiments was to test a celebrated theoretical model of Pierre de Gennes. He predicted a scaling law of the time dependent reaction rate in 2D, with $r(t)=\left ( \frac{t}{t_{0}}\right )^{-\beta }$. The excimer technique yielded a value of $\beta$=0.45 in good agreement with the theoretical prediction of de Gennes (see (Merkel 1994).

### 7.1 Applications of Excimer Probes in Genetic Engineering

Figure 5. Application DNA as molecular beacon to detect specific DNA sequences in solution and cells with nano-molar sensitivity.

The interest in excimer forming molecular probes, has recently been revitalized in connection with the application of DNA and RNA scaffolds in molecular engineering and nano-electronics. One particularly interesting examples are oligomers of nucleic acid that recognize specific base sequences of nucleotides in solutions or cells which are typically present in nM concentrations. One type of such indicators called molecular beatons is shown in Figure 5. It consists of a loop-forming DNA sequence extending from a double helical stem which is stabilized by sequences of complementary base pairs comprising 4–6 bases. As indicators of the binding to targets either a donor and acceptor pair or excimer forming chromophores are coupled to both free ends. In this way nanomoles of specific bases sequences of DNA or protein folding can be detected in solutions or cells.

In the absence of targets the chromophores are close together and the fluorescence of the energy donor is quenched or the pyren excimers emission is observed. In the presence of DNA or RNA exhibiting DNA-strands that are complementary to one of the strands forming the stem the loop is opened. This is indicated by the emission of the acceptor of the FRET-pair or the abolishment of excimer emission. In this way nanomoles of DNA sequences in solutions can be detected. Owing to the well developed genetic engineering techniques whole libraries of loop forming aptamers have become available.

## 8 How Förster Tried to Bring Order into the Confusing Manifold of Photochemical Processes

In his last years, Förster endeavored to bring some order into the complex field of photochemistry (Förster 1970). He proposed that photochemical reactions may be classified as adiabatic or as diabatic, depending upon whether the chemical change occurs on the potential energy surface of the excited or not. He defined three types of reactions. First, photoreactions in which de-excitation occur in the reactant by thermal deactivation, a situation mainly occurring in gas phase reactions. Second, reactions in which the product is formed in the excited state and deactivates by fluorescence or in non-radiative ways. Third, anywhere on the reaction path, in which case it has to cross between different potential curves (called intersystem crossing). For the second type, he established two well studied universal prototypes, the pyrene excimer formation and the dissociation of excited $\beta$-naphtol (see Figure 3). In this case, the reactions proceed (diabatically) on the potential surface of the excited state from reactant to product.

Together with his postdoc Julian Menter, Förster tried hard to find prototypes for the third case by studying photo dissociation of anthracene and its derivative 9-methyl-anthracene (Menter and Förster 1972). The latter compound forms an excimer from which it dissociates via diabatic pathways. After his death, the concept of diabatic processes became popular by the discovery that such processes play a key role in the formation of photochemically induced charge transfer complexes (see Jortner 1980).

## 9 Some Personal Remarks on the Personality of Theodor Förster

While Förster was a shaker in science he was simultaneously the prototype of the modest scientist who dedicates his life to science and the education of students, which is often a hallmark of great scientists. For many of the students in the early fifties Theodor Förster was an antithesis of the classical German professor, who considered strict guidance of students the best academic education.

One had to get accustomed to his lecture style because he apparently suffered from slight speech impediment, which made his lectures for undergraduates sometimes difficult to follow. Later when I read my notes of his lecture to learn for my examinations I realized first, that he spoke slowly and iteratively because he reflected about each statement before he made it or wrote it down on the blackboard. Secondly I found out that when you had taken the effort to write down his presentation at the blackboard and his comments you did not need a textbook any more for the examination.

Figure 6. Dr. Theodor Förster

Förster’s international reputation was a tremendous benefit for his students and assistants. Since he was frequently visited by the most famous colleagues in the field of photophysics and photochemistry from abroad, Förster’s students had the privilege to learn about photochemistry and photobiology from the pioneers in the field.

Despite of his apparent shyness Förster must have had great self confidence in his science. Although he wrote excellent English he published most of his papers in German, and in German journals, such as Zeitschrift für Elektrochemie and Zeitschrift für Physikalische Chemie. Obviously he was convinced that his work is so fundamental that the international community would recognize its value despite of this drawback. However, from personal discussion with him I know that he deliberately published in German Journals because he wanted to re-establish the high pre-war standing of the German scientific journals. Moreover, he may have realized that it is easier to solve very complex problems by thinking in his mother language. Unfortunately, most of the publications in the German journals are not accessible via the internet. One example is the Förster equation for the determination of the fluorescence lifetimes by measuring fluorescence quantum yields which is only written down in his book (Förster 1951) and is therefore often attribute to other authors. However, his work was considered so important for the international scientific community that his most fundamental papers have been translated into English.

Theodor Förster was also unique concerning the planning of his professional future. During the time as professor in Posen he did not publish a paper. But the appearance of his famous publication on energy transfer between 1946 and 1948 shows that he was by no means idle but that he spent his time to think about one of the most tricky scientific problems of the time, besides starting a family.

The young Förster must have been a man of uttermost self-discipline. As recalled by his wife, he wrote his long papers on the classical and the quantum mechanical theory of energy transfer under awful conditions, that is, without a job, few food and heating in winter. His life became easier again after he received the offer from Karl-Friederich Bonhoeffer to work at the newly founded Max Planck Institute for Physical Chemistry in Göttingen, now called MPI for Biophysical Chemistry.

I think we all agree that Förster’s premature death was a catastrophe for the German scientific community in particular and the international community of Physical Chemists in general. It would have been interesting to learn more about his unmatched insights into adiabatic and non-adiabatic photochemical reactions. For the community of physicochemists in Germany it was a catastrophe considering his outstanding contribution to reestablish the pre-war standard of research at the interface between physics and chemistry. Stuttgart lost a scientific beacon.

The outstanding international reputation of Theodor Förster is best characterized by the following statement of George Porter, one of the founding fathers of short time spectroscopy and Chemistry Nobel Prize Winner of 1992. “Over the last quarter of a century few branches of science have enjoyed more progress than the physics and chemistry of excited molecules. Photochemistry which previously was concerned mainly with the final products of dark reactions of the intermediates such as free radicals has become a new science of the excited state No single person contributed more to this progress than Theodor Förster”.

## 10 Acknowledgements

I grateful acknowledges financial support by the Excellence Initiative of the Technical University Munich and The Center for NanoScience (CeNS) at the Ludwig-Maximilian University (LMU) Munich, where a large part of the article was written.

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