Hans Kuhn

Hans Kuhn, 1998 Photo and © U. Anders

Hans Kuhn was born in 1919 in Bern, Switzerland. He studied chemistry at the ETH Zuerich and later at Basel. He did his thesis under Werner Kuhn (not related) in Basel concerning the flow of polymers in liquids. He postdoced with Pauling in 1947, became professor at the Univ. of Basel in 1951. In 1953 he went to Marburg (Germany), followed by a move in 1970 to the Max Planck Institut for Biophysical Chemistry at Goettingen (Germany) where he retired in 1985. His autobiography you may find here. You'll find his free electron gas theory, among other topics, in : Hans Kuhn and H.-D. Försterling, Principles of Physical Chemistry : Understanding molecules, molecular assemblies, supramolecular machines. Wiley, Chichester and Weinheim, 2000. 970 pages. A Jananese edition may be found here.

Personal recollections, recalling personally exciting events in research, is a welcome opportunity to look back and reflect. Watching the emergence and the growth of molecular biology, seeing, in atomic precision, how things are constructed and operate was a great excitement to me. Equally fascinating to me was the search for the motifs behind all this, the attempt to grasp the logic frame of a process that has lead to the concrete existenee of biosystems.

Finding motifs describing the essence of complex phenomena is of general importance in physical chemistry: the search for theoretieal models, replacing reality, that focus on what is relevant in a complex process. I was fascinated by theoretieal modeling, searching for lucidity and simplieity since I had been a Ph.D. student. I think this kind of approach is useful and it is important to transmit to young people the fascination of finding simple motifs in complex patterns.


1920s and 1930s


I think the determining factors are set early in life. A great adventure to me as a little boy was my father showing me how to develop a photographie plate, to renew the Leclanché cell for carbide and to use it for the lamp light of bis bicycle. My father died when I was 10, but his input on my excitement for simple chemical and physical effects was enormous. Soon I made all kind of silly chemical experiments, and my mother, on the one hand anxious about my dangerous hobby, on the other hand, silently appreciating my interests, supported my excitement for chemistry.

I enjoyed observing and reflecting on natural events when I went to school in Bern. It was great fun to me to see how chemical processes can be understood as an interplay of atoms and molecules. Living organisms appeared as molecular assemblies, but it was hard to believe that these assemblies are purely driven by what follows from the laws of physics; some strange additional influences seemed to direct processes. But even more puzzling to me was the idea that I should consist of molecules. Molecules cannot have fun and do not suffer; so what am I? As teenagers, I think, we worry more about fundamental questions - what we are, where we come from, where we go - than later in life when things become more settled.

Recalling that time and reflecting on how we feel today, I think there is a most important elucidation in our thinking: molecular biology has consolidated the idea that the world perceived through our senses is governed by the laws of physics because it has not been falsified that what we perceive through our senses is in agreement with these laws. However, the mystery of why we perceive, our speechless astonishment, has not changed since I was a teenager.

The astonishment about why there is a certain relation between our personal awareness and distinct processes in the brain is unchanged but it appears in clearer focus and the possibility to investigate the relation between distinct personal occurrences and distinct processes in the brain appears much more realistic. It was a dream at the time when I worried about this problem as a teenager and it is the great challenge of the twenty first century. Finding the laws describing this relation is an immense task.

It is worth reflecting on another remarkable clarification. When I was a teenager, eminent physicists dreamt of quantum mechanical indeterminacy allowing unknown influences to guide processes in living systems. In today's view quantum mechanics, of course, is the basis to understand atoms and chemical bonds linking atoms to form molecules. But for describing the interplay between the molecules thus formed, the simplifying views of classical physics are sufficient to grasp the essence and it is reasonable to assume that the interplay of molecules determining the function of the brain can be described in the context of classical physics - at least as long as this assumption has not been falsified.

When I had finished high school in 1938 in Bern, I felt that biology is too far from a basic understanding in molecular terms and so I decided to study chemistry at the Eidgenössische Technische Hochschule in Zürich. It was a hectic time. World War II began when I had just started my studies in Zürich, and I was alternating between studying and doing military service in the Swiss army. Zürich was the Mecca of natural product chemistry; Ruzicka was my professor in organic chemistry, while Karrer was at the university next door. This was interesting chemistry, but I missed the relation to what really happens in the living organism. I was excited by the lectures on botany by Frey-Wissling, who put things on a general molecular basis as far as this was possible at that time; biology appeared to me in a new light.


Werner Kuhn and modeling polymer molecules


During my studies in Zürich I heard about Werner Kuhn; his fundamental work in several fields in physical chemistry, his theories on optical activity and on separation processes were world famous. I heard that he had recently come to Basel escaping Nazi Germany. In spring 1942, when I had passed my diploma as a chemical engineer, I thought it might be exciting to do my work for the Ph.D. with Werner Kuhn, and so, with my fresh diploma in the pocket, I took the train from Zürich to Basel and just took the chance to see Werner Kuhn whom I had not seen before. I took my courage and knocked at the door of his office and luckily he was in. I asked him if he might possibly accept me as a Ph.D. student. He had time for his unexpected and unknown visitor, and explained to me some possible subjects for a thesis. I was delighted about his proposal and immediately started to work in Basel with great enthusiasm. I did not know that Werner Kuhn's proposal gave me a key I would use throughout my life: attempting to invent models that are as simple as possible but still including essential points to describe complex phenomena.

My thesis was concerned with Werner Kuhn's theory on the shape of polymer molecules and on properties determined by this shape. The problem to be solved theoretically was: what happens with a molecular coil in dilute solution when applying a flow gradient? The coil will be stretched, turned round, coiled together and changed in shape by thermal motion. The problem appeared to me to be much too complicated to be solved. However, Werner Kuhn proposed a model which was astonishingly simple: replace the molecule by a dumb-bell, the two spheres being at the ends of the molecular chain. These spheres are assumed to be connected by a spring replacing the molecular coil. The spring takes account of the fact that the chain ends are attracted to each other (by the thermal collisions of the molecules of the solvent with the chain). The hydrodynamic resistance of the chain (acting against the viscous forces exhibited by the flowing solvent) are assurned to be concentrated in these spheres (Fig. 1). Then these spheres and the spring replacing the molecule behave like particles in Brownian motion, attracting each other and being driven by hydrodynamic forces. My task was to find the spatial distribution function of the distance between the chain ends for different flow gradients, and for coils of different size, and the resulting relations for viscosity of solutions and streaming birefringence [1]. I was greatly surprised to find an



excellent agreement of the theoretical expectation with the experimental data at low flow gradient and fascinated by Werner Kuhn's intuitivity in focusing on the essence.

The example demonstrates Werner Kuhn's way to go: to begin with a model in which the real situation is drastically simplified but which still takes into consideration what is physically essential and is sufficiently simple to allow a mathematical treatment that is transparent in each single step. He aimed for an immediate check of the results with experimental data and investigated his models very carefully by studying all consequences. Werner Kuhn had more confidence in an elementary mathematical treatment than in an abstract formalism; he wanted to really understand what is important for an effect considered.

The basic idea to understand the properties of polymers proposed by Werner Kuhn was to divide the molecular chain into N segments of length A where A is the distance between the end points of the segment [2]. N is arbitrary but sufficiently large, such that the direction of a given segment can be considered as independent of the direction in the neighboring segments. Then the shape of the coil and the distribution of shapes is a simple statistical problem. The average of the square of the distance h between the chainends then is (random walk)

(1)

I think that the importance of this work in paving the way for molecular biology is not sufficiently appreciated. It allowed the first quantitative theoretical description of the shape of a macromolecule and its properties when changing the shape by external forces. Werner Kuhn had explained the elasticity of rubber in this way. Subdividing the chain in sections of sufficiently large but then arbitrary length was an early thinking in fractals and this basic idea fascinated me very much.

But amusingly I had my first friendly argument with Werner Kuhn on this point and I think the question is of interest in today's view. I must explain this by again considering a polymer molecule in a flow gradient or an even simpler case, considering the molecule during sedimentation in the ultracentrifuge.

Qualitatively, the resistance is quite different in the case of a relatively short chain (open coil) and a long chain (dense coil): the hydrodynamic forces act on each part of the chain in the first case (drained chain), and the solvent inside the coil is immobilized in the second case (non-drained coil; Fig. 2). Werner Kuhn, in those days, was interested in a quantitative description of the sedimentation velocity in the general case including these limits. He had great confidence in a hydrodynamic description (considering the solvent as continuum), but even with this simplifying assumption the problem was formidable.



I thought why not avoid the difficulty by making macroscopic models by bending wire accordingly and measuring the sedimentation velocity of the models in a viscous liquid. The form factor of the model should be the same as that of the corresponding molecule. I took a piece of wire with the ratio length/cross-section as representing the molecule to be modeled. L corresponds to the length of the contour line of the molecular thread (after applying the enlargement factor). I divided the wire into sections of length A where A was fixed by

     (2)

for given (average of the square of the distance between the ends of the molecule (after applying the enlargement factor)). Each section was bent by an arbitrary angle. This way I obtained models corresponding to snapshots of the corresponding molecules and measured the sedimentation velocities.

Werner Kuhn strongly disagreed with my disfigured statistical chain element, and, of course, he was right. It was against his clear thinking: defining A as a sufficiently large section of the molecular chain was the basis for the statistical treatment of the problem. On the other hand, for my experiments, I needed good models at the expense of conceptual clearness. Werner Kuhn reflected again and again until he agreed with me to consider chain segments defined in this way as useful [1]. The essence was: Werner Kuhn's statistical chain elements are to be considered as sections of the true molecule. With the additional fixation NA = L we described a model which is explicitly different from the true molecule but resembles the molecule in a simple way. Segments fixed in this way are widely used today without seeing the critical basis in their use. Werner Kuhn's original considerations should be kept in mmd. In the following, I use N and A for these segments defined by = NA² and L = NA. The segments A are particularly useful in theoretically modeling polymer molecules in many different situations.

I made models mimicking a large number of random forms and measured the translational and rotational resistance in a viscous liquid. The experiments showed a strong deviation from free draining, even for loose coils. The resulting relations for sedimentation, streaming birefringence and viscosity agreed well with experimental findings; even the diameter of the wire mimicking the molecule (applying the enlargement factor) almost agreed with the diameter of the molecular thread. All this confirmed Werner Kuhn's simplifying description of polymer properties by hydrodynamic models [3,4].

The macroscopic models did a good job as naive analogue computer. I was interested in getting the probability distribution P(R)dR of the maximum extension of a coil (R, Fig. 2); of course, R &grt;= h. I derived the distribution function of a projection of R [5] but was unable to derive P(R). Thus, naively, I determined P(R) by measuring R at a number of models [6]. Today, R can be directly measured in the case of fluorescence- labeled DNA double helices [7] and the result is evaluated for P(R). Agreement with the 'theoretical' distribution was observed [8].

The force f (considered above) acting on the chain ends assumed to be fixed at distance h, on the average, is given by [1]

      (3)

where k is the Bolzmann constant and T is the absolute temperature.

Today this force (Fig. 3) can be directly measured by fixing



Fig. 3. Force f acting (on average) on chain ends fixed at distance h.

the molecular thread at the ends and an exact agreement with Eq. (3) is found [9]. At larger values, Eq. (3) is no longer valid, and at stretching forces of the order of 10 pN the elastic modulus of the stretched thread which is still elastically deformed can be measured for a DNA duplex strand. The elastic modulus is 1/1000 of the modulus of steel. The force to disrupt the DNA duplex chain is 500 pN, so that the force divided by the cross-sectional area (10⁸ Nm^-2) comes close to the value for steel. The experimentally determined length A = 100 nm gives the value of the bending modulus by comparing the elastic energy for bending the segment by 900 with kT. This is similar to the bending modulus of a laboratory tube and the same is true for the torsion modulus [10]. I mention this because such comparisons with everyday objects are not easily found in the modern literature. It was always important for Werner Kuhn to have a vivid picture. Intelligent modeling of molecular processes requires an intuition related to very lively imagining ofthe molecular process by considering processes in everyday life.

I mentioned the behavior of molecular coils in dilute solution at low flow gradient and the good agreement between theory and experiment. Werner Kuhn, when proposing the subject for my Ph.D. thesis, had another problem in mind: I should demonstrate the unraveling of a coil in a flowing solvent at large flow gradients. In those days it was generally assumed that there is free rotation about single bonds, and in this case the coil, under the influence of hydrodynamic forces, should immediately adapt its shape to the motion of the solvent. In a cycle, the coil should be stretched and unraveled (Fig. 1), turned around, compressed and its shape restored. As a consequence, flow birefringence of dilute solutions should overproportion- ally increase with flow gradient.

When checking with the experiment (the important work of Signer on dilute solutions of nitrocellubose and methylcellulose [11]), I found an increase which was less than proportional and it was immediately clear that the coil must be stiff such that when turning round there is no time for the coil to unra- vel, compress and restore its shape (shape-resistance).

We extended the model to the general case of arbitrary shape-resistance of the coil. Comparison with the experiment (measurement of viscosity and streaming birefringence) allowed us to calculate potential barrier heights for bond rotation [12]. Similar barrier heights had been obtained for the rotation of one CH₃ group in ethane about C-C bond axis [13,14].

Werner Kuhn and I were engaged at that time with a more basic theoretical question relevant to a quantitative description of the viscosity of dilute solutions of macromolecules. In calculating the energy dissipation in flowing solutions of small elongated particles, I considered a term (diffusion term) which had been neglected in the literature, and I obtained a dissipation energy twice as large as the dissipation energy calculated earlier by Werner Kuhn [15]. We both were most worried - which calculation was correct? Amusingly, Werner Kuhn felt my calculation was right and I felt I was wrong. We discussed the problem again and again and finally realized on the basis of simple thought experiments that the diffusion term must indeed be added [16].

Investigating the consequences of including the shape resistance was my main job [12] but, on the other hand, I wanted to solve the task originally set by Werner Kuhn, namely to unravel a coil. Thus, I was looking for a way which would be independent of the shape resistance. I tried to solve the problem by bringing a chain of methyl cellulose (with an electrically charged carboxylate group at one end) into a high electric field, acting on the charged end, and pulling the chain through the solvent. I observed a small double refraction in a solution of such chains which was increasing proportionally with the square of the field. The accessible fields were too small to unravel the coil [17].

It is fascinating to see how this problem can be solved today with a single fluorescent-labeled DNA duplex chain in water



Fig. 4. Coil held at one end and pulled through solvent.

fixed at one end and exposed to a weak flow or by attaching the end to a small particle and pulling the particle through the water. The partial or complete unraveling is directly observed [18] and the force applied to pull the chain can be measured as a function of the speed v (Fig. 4); it can be quantitatively described [19]. Restoring a coil from a fully unraveled chain can be directly observed [20]. The hydrodynamic experiments with macroscopic models facilitate the easy evaluation of the experimental data. An excellent agreement between theory and experiment is found [21]. It is fun to mention that these exciting experiments got me busy again working on ideas in my Ph.D. thesis 56 years ago!

Gel electrophoresis of DNA can be treated accordingly; it is assumed that the molecular chain is imprisoned in a network. It is driven by the applied electric field and exposed to fluctuation. The resistance of the solvent (water) is again approximated by hydrodynamics [22]. This picture gives the speed as a function of chain length. It is found to be in good agreement with the experiment.

Werner Kuhn's confidence in using hydrodynamics to approximate the behavior of macromolecules was by no means obvious in the 1940s. According to Kirkwood and Rise- man [23], in theoretically approaching the sedimentation velocity of a polymer, one assumed a friction factor (which they considered as an adjustable parameter) about ten times smaller than according to the hydrodynamic model. This appeared unreasonable. The message was not heard. The Kirkwood- Riseman paper, with the free parameter appropriately adjusted, is the classical paper today.

An important aspect in Werner Kuhn's way of thinking is largely forgotten; the example illustrates it. He did not like to play with parameters, he wanted to stay on solid grounds. A free parameter in a theory is a kind of built-in excuse for a failure.

In the very first attempt to describe a polymer molecule in a flow gradient [1], Werner Kuhn and I used the picture of a free-draining coil, and we often discussed an extension of the dumb-bell model which seemed easy within this limit: a row of spheres connected by springs replacing the chain section in between instead of just two spheres (Fig. 1). The result of the experiments with macroscopic models made it clear that the free-draining coil was a quite unrealistic limiting case, and for that reason we felt that such an extension would not lead to a better description. However, it didn't go this way and it is just this extension (the paper by Prince Rouse [24]) that was important for further developments.

Approaching problems by inventing theoretical models was a success story in physical chemistry in the past. The flair to invent simple models in order to extract essentials should be kept alive, in spite of the marvelous possibilities created by the computer. It is crucial that powerful, simple models serve as paradigms. Werner Kuhn's dumb-bell model was a masterpiece and it is a pity that the scientific community has not kept in mind the model and the work based on it (see Ref. [25]).

I was fascinated by the wide aspect in the work of Werner Kuhn. Shortly before I came to Basel he had discovered a principle for a particularly efficient fractional distillation in a narrow tube and he was on the way to developing a system for an efficient separation of isotopes [26]. He realized soon that the action of the kidney is based on this principle and he developed a theory of the kidney function [27]. Later he saw that the air-bladder of fish is based on the same principle and he was able to explain how deep sea fish can produce air under a pressure of 200 bar, which appeared mysterious before [28]. It is astonishing how Werner Kuhn grasped an important problem in a fleld which had been completely unknown to him before. He was a deep thinker, considering the particular problem again and again and in this way he discovered important and totally new aspects. Werner Kuhn died in 1962; this year would have been his lOOth birthday.




Linus Pauling and attempts in quantum chemistry


In 1946 I was completing my work for the 'Habilitation' allowing me to give lectures at the University of Basel, but the war was over and it became possible to get a dispense from the Swiss army and I was happy to obtain a Swiss fellowship for one year to do postdoctoral work with Linus Pauling. Traveling was still an adventure. I came to New York from Le Havre on a boat used before to transport American Army soldiers with cabins with 20 beds, now for a happy new generation of settlers. When I arrived at Cal Tech I found my desk in the room of Eddie Hughes. Eddie was not only a famous crystallographer but an absolutely charming person. His immediate friendliness made my stay so enjoyable. Being for the first time outside Switzerland and having great problems with English, I really needed help and Eddie had always time to care for me and to explain things. I enjoyed very much my stay in Pasadena. I was impressed by Linus Pauling's work in very diverse fields. His intuitive imagination fascinated me. I felt that his sparkling ideas and his enthusiasm were enormously fruitful, even in cases where he was later shown to be wrong (e.g. his theory on antibodies which he had proposed in those days). Linus Pauling suggested that I should investigate transition metals in the light of the valence bond theory which he had used so successfully for treating chemical bonds. I did not obtain useful results, but in this way, by looking into metal theories, I came in touch with Sommerfeld's free electron model and I thought why not go the other way around, using free electron considerations to treat chemical bonding. I tried to understand the absorption of polyenes in this way, assuming that the pi electrons, pairwise, occupy the lowest electron states in a one-dimensional box, and with this idea I obtained Eq. (4) for the absorption maximum

lambda_max = (16m_e cd² / h)(n + 1/2) = 129 nm (n + 1/2)      (4)

where n is the number of double bonds, h is Planck's constant, c is the speed of light, m_e is the mass of the electron, and d is the average CC-bond length (140 pm). The equation predicts a 129 nm bathochromic shift with each additional double bond in the chain. I found this to be in strong disagreement with the experiment, so again I felt quite unsuccessful, but I did not care too much because the stay at Cal Tech and the contact with Linus Pauling and with many interesting people around him was just too exciting. Lazlo Zechmeister, a natural products chemist who is famous for his work on chromatography, strongly activated my interest in polyenes. His students were separating the different cis-trans isomers of carotinoids [29], and understanding their absorption spectra was a challenging problem.

Back in Basel in mid-1947, my disappointment with the polyene spectra turned into excitement by a fortuitous event. Tadeus Reichstein had asked Werner Kuhn to give a seminar on spectroscopy for his students, and Werner Kuhn, after having given the first lecture, was too busy with other duties and turned the job over to me. In preparing my seminar, I discovered the work on cyanine dyes by Leslie Brooker [30]. These dyes show a bathochromic shift of about 100 nm with each additional double bond in the chemical formula, just about what I had wrongly predicted for the absorption of polyenes [31] and it immediately occurred to me that the discrepancy in the polyenes must be due to an instability of equal bonds leading to bond length alternation [32], as expressed by the chemist's writing of alternating double bonds and single bonds (Fig. 5).

I tried to apply these considerations to treat quantitatively the light absorption of other classes of organic dyes, viewing them as pi electron systems between the limiting cases of the



Fig. 5. Free electron model of butadiene. pi electron wave functions and charge density. Maxima at formal double bonds: attraction of nuclei toward maxima of charge density. Formation of double bonds and single bond in between.

symmetric cyanine dyes and the polyenes, and came to the conclusion that these limiting cases play a key role in understanding pi electron systems. I was fascinated by the similarity between cyanine dyes (with a half-filled energy level band) and metals on the one hand, and by the similarity of polyenes (with a filled band separated from an empty band by a band gap caused by the instability of equal bonds) and semiconductors on the other [33]. Peierls later emphasized the more general aspect of this kind of instability called 'Peierls instabil- ity' [34].

I was so fascinated to see Eq. (4) describing the spectra of the cyanine dyes with no adjustable parameter. In contrast, the Hückel approximation, with the adjusted value of beta used at that time, predicted values for the wavelengths of the absorption maxima which were four times larger than the experimental values, an absorption far in IR. I thought that this new approach would be a real progress in treating pi electrons.

In spring 1948 Linus Pauling was in Oxford as a visiting professor and I joined him, together with some people from Cal Tech. This was the time when he had his legendary flu and the idea of the x-helical structure of proteins - I remember how enthusiastically he told me about his idea just after his recovery. This was when I had prepared a manuscript and showed it to him. I had noticed that the hybrid bond orbitals used in quadricovalent complexes of transition elements are composed of 4/9 s, 14/9 d and two p orbitals, the strength being 2.943, while Pauling's best bond orbitals (sp² d) had a considerably smaller strength (2.694). Therefore, I felt somewhat uncomfortable showing him my manuscript [35]. He read it very carefully, sentence for sentence, and finally expressed his happy appreciation - I think this little occurrence is typical of Pauling's friendly and easy-going nature.



Fig. 6. Branched string model. (a) Dye I (see below); wave functions in highest occupied and lowest unoccupied molecular orbitals. (b) Bacterio- chlorophyll; location of charge density accumulations (antinodes of wave functions) of HOMO and LUMO. lambda_max and f.

When extending the free electron model to branched pi electron systems (considering standing de Broglie waves along each branch), I was happy to see that the spectroscopic behavior of many dyes can be very well described [36]. I assumed that the electron waves are like the waves along a branched string (Fig. 6). This was intuitively obvious, but I had no rigorous proof for the proposed branching condition. I extended the model to systems with circular electron gas such as bacterio-chlorophyll [37] and systems in which CH in the chain was replaced by N which served as a probe for the pi electron distribution and its change when exciting by light [38] (Fig. 7).



Niels Bohr and the branched pi electron systems


In 1950 I had the marvelous opportunity to stay in Niels Bohr's institute for a couple of months. Bohr impressed me deeply; getting in touch with this profound thinker was a fascinating experience. Listening to his remarks at the end of seminars was a particular excitement. The seminars were usually highly theoretical, and I did not understand a word. But then



Fig. 7. Cyanine and aza-cyanine. Highest occupied and lowest unoccupied molecular orbitals. Wave functions and energy levels. Replacing CH by N: level of lowest unoccupied molecular orbital lowered, excitation energy decreased, shift of absorption toward longer waves.

Niels Bohr used to give a kind of summary on what the speaker had reported, which was very clear and simple. His flair for extracting the essence was a great lesson to me.

I had to give a seminar on my work on the free electron model. Niels Bohr joined my seminar and expressed his appreciation. Of course I was extremely happy about this and mentioned to him my problem with the branching condition. He suggested that I should explicitly solve the Schrödinger equation for a branched box. His advice was exactly the impact I needed. But at that time, without a computer, this was quite a difficult job. I got around the difficulty by making use of the analogy between the quantum mechanical problem and the problem of finding the stationary states of a vibrating membrane of corresponding shape.




Tests and refinements of the free electron model


Back in Basel, I made such membranes and excited them with sound. The result supported the branching condition [39]. The sound was in the high frequency region, and the experiments were accordingly noisy. This caused a lot of trouble, i.e. complaints by neighbors and a visit by the police.

Testing the free electron model by absorption and fluorescence spectroscopy and refining the model kept me busy during the 1950s. I became associate professor in Basel in 1951. Giving lectures on the chemical bond was fun. I approached chemical bonding from the free electron point of view using the box model as a tool to understand the principles in forming atoms and molecules. There was no gap between research and teaching, and the lecture was an excellent possibility to test ways to transmit to the student the message resulting from the recent research [40].

Consider the simplest case - the hydrogen molecule ion [41]. Being formed from an 11-atom and a proton, what leads to bonding? The electron attracted by both nuclei keeps the nuclei together. In forming the bond, the electron cloud becomes narrower around the axis connecting the nuclei because of the increasing Coulomb field between both nuclei, resulting in a decrease of the potential energy (Coulomb attraction of the nuclei toward the oppositely charged electron cloud accumulated in between) and an increase in kinetic energy due to the narrowing of the electron cloud; half of the Coulomb energy gained in forming the bond is used to speed up the electron. This is considered in the box model. In the approximations based on combinations of the orbitals of the atoms forming the bond, the compression effect of the electron cloud is not taken into account and this results in a decrease in kinetic energy in bonding instead of an increase. In considering this problem, I still feel that the box model is a useful tool to approach an understanding of chemical bonds. We have written a textbook on physical chemistry using this approach [8].

In spring 1953 I became Professor and Head of the Institute of Physical Chemistry at the University of Marburg in Germany. My institute was an old villa and I had to plan for a new building. Students working for their diploma to become a chemist or a physicist and for their PhD joined me and shared my excitement for pi electrons.

Our goal was a better understanding ofthe branching condi- tion and of the basic assumptions of the electron gas model [42], and checking specific features of the model by absorption and fluorescence measurements [43].

We considered a pi electron in the more realistic potential given by the atomic potentials of the atoms constituting the molecular skeleton and taking account of the shielding by the residual pi electrons. In this way the reliability of the simplifying free electron model assumptions was confirmed and the model was established.

A reinvestigation of the polyenes was part of our focus. Polyenes with up to 15 conjugated double bonds were known and the absorption wave lengths were in agreement with the theory when assuming a bond length alternating between 135 and 146 pm. This supported the proposed considerations on the instability of equal bonds. A quantitative theory on bond lengths in polyenes was our goal. It had been generally assumed in those days that long polyenes have equal bonds [44], so a detailed theoretical approach seemed important to clarify the situation.

Computers did not exist, so we developed an analogue computer to solve the Schrödinger equation for complicated potentials. I was particularly glad that one of my first students turned out to be an outstanding experimentalist and a profound thinker, Fritz Peter Schäfer. Fritz Schäfer was strongly involved in that development [45]. The computer was based on the analogy between the oscillatory states of a network of electric circuits and the states of a corresponding quantum mechanical system. This analogy made the calculation immediately transparent. The energies of the stationary states were given by the applied frequencies and the corresponding wave functions were given by the voltage at each mesh point in the network [46].

In this way we calculated the pi electron distribution in the effective potential of the molecular skeletons of polyenes, assuming distinct bond lengths, varied the proposed geometry and compared the electron densities in each bond with the assumed bond length. Self-consistency between bond lengths and pi electron densities was only obtained when assuming the same bond lengths as in butadiene, 135 and 146 pm [47]. The treatment of benzene resulted in equal bond lengths [48]. We were very happy to have reached these results without introducing adjustable parameters (we simply used the values of the CC-single bond length and the CC-double bond iength of butadiene (135 and 146 pm) to consider the elasticity of the skeleton of the sigma-bonded atoms of a polyene; the values were experimentally weil established).




Coupled oscillator approach


It became clear in those years that the correlation between pi electrons is important in cases where several transitions play a role, e.g. porphyrins. But how to find a simple and lucid way to achieve this goal?

Having in mind the message from my teachers, I felt that refinements must be introduced in a step-by-step process in order to see what was important and what added unnecessary complications. It appeared to me that the way to go was to consider each pi electron as an electron in the field of the molecular skeleton, the alternating electric field ofthe incident light wave and the time dependent field of all other electrons in the system, neglecting the tremendous complications caused by the antisymmetry of the total wave function of the pi electron system for electron exchange. The equations resulting from this quantum mechanical treatment correspond to the equations for coupled classical oscillators, and in this way the problem becomes lucid [49]. The shift of the phosphorescence band relative to the fiuorescence band of a dye could be described by considering the ground state and the singlet and triplet excited states by electron pair wave functions obtained with the analogue computer [46].

We checked the results of the model by measuring the dichroism of dyes in stretched polymer films and the p olarization of the fiuorescence giving account of the direction of the transition moments, and studied the vibronic structure of the absorption bands to check the change in bond lengths predicted by the model [43].

In this situation in the late 1950s I felt that we had achieved a useful approach to treat pi electron systems including correlation effects [50]. The consideration was simple and lucid. The model accounted for the relevant experimental facts.




The 1950s and today


Discussions on pi electrons were full of excitement. The scientific community was open to new ideas and I was very happy to find a good response from the people engaged in the field. I am particularly grateful to Robert Mulliken for many interesting discussions, and to Herzberg, Slater, Charles Coulson, Erich Hückel and Joe Hirschfelder for their interest and encouragement in those days. I enjoyed exciting conversations with John Platt who had been in Marburg for a few months as a visiting professor. Lively discussions with Theodor Förster and Günter Scheibe stimulated my thinking on interactions between molecules with pi electron systems.

The situation is very different today and it is useful to reflect on this. I mentioned the failure of the Hückel method in treating the absorption of cyanine dyes. By adjusting the beta value to spectroscopic data (an unacceptable ambiguity in my view at that time), the discrepancy disappeared. An LCAO confirmation of our result that polyenes have alternating bonds was given by an approach depending on adjustable parameters. Adjustment of parameters became customary. Semi-empirical methods were developed. Today LCAO-based approaches are a kind of dogma in treating pi electrons. Things are considered to be settled.

In my opinion, this change is unfortunate. The usefulness of the free electron model as a counterpart of advanced semi-empirical methods should be seen. Let me illustrate this in the case of the two dye molecules 1 and 2 [51].



Surprisingly, 1 absorbs at longer wavelengths than 2 in spite of the smaller size of the pi electron system. The effect was explained by performing a standard quantum mechanical calculation considering the interaction of 50 configurations, using the usual values of the adjusted parameters. A reasonable agreement of the shift of the absorption band with the experiment was found, but the oscillator strength of the band of dye I was four times larger in the experiment than according to the theory [51]. Using the simple free electron model approximation - de Broglie waves extending over the molecular skeleton considering heteroatoms by potential wells - the position and oscillator strength ofthe absorption band is found to be in agreement with the experiment in both dyes [52].

This shows the power of simple models. The possibility that important features can be neglected even in sophisticated approaches (being hidden in a complicated formalism) should be kept in mind. Attempts to attain an understanding of pi electrons by using lucid models are still valuable; pi electrons are a marvelous example of the use of simple approaches to keep the tradition of seeing and appreciating the beauty of lucidity and simplicity in the motif used to understand experimental facts. In a recent textbook by Horst-Dieter Försterling and myself, we emphasize the importance of viewing the free electron model and LCAO as complementary approaches [53].

A 'forbidden' transition was observed in polyenes below the allowed transition from the highest occupied to the lowest unoccupied molecular orbital [54]. This strongly supported the suspicion against simple models. However, the result can be easily understood on the basis of the coupling model discussed above [55]. The problem of finding self-consistency of pi electron density in bonds and bond lengths can be simplified by using a step potential. This allows the easy treatment of solitons in polyacetylene and non-linear properties of pi electron systems [56].

I enjoyed my stay in Marburg in the 1950s. There was a Meerwein, already in his eighties and still very active, Sieg- fried Hünig, Karl Dimroth and Klaus Hafner). I was particu- larly impressed by Hans Kautsky who at this time was Head of the Institute of Inorganic Chemistry; his research activities were much broader and he was of an extremely creative personality. He had started as an artist before becoming a chemist and his enthusiasm in attempting to grasp the beauty of nature in his paintings stayed unchanged, and as a chemist he was interested in elucidating color phenomena, fluorescence and phosphorescence. By investigating the fluorescence of plants as a function of intermitting illumination he (and independently, at the same time, Hill) came to the conclusion that two photosystems cooperate in series (Z-scheme) [57,58].

A most remarkable early experiment by Hans Kautsky, which certainly stimulated my own work, was the transfer of the excitation energy of a dye molecule to a molecule of another kind of dye at short distance. The first (excited) molecule activates oxygen which reaches the second molecule by diffusion and disposes its activation energy, so that the second dye molecule becomes excited [59].


Supramolecular machines

An unforeseen event in 1961 shifted my interest from pi electrons to supramolecular machines. An Israeli, Moshe Zwick, wrote to me saying that he would like to stay with me for 3 months to do work on polymers. No polymer work was going on in my lab, but we were studying the interaction between dye molecules in relation to the free electron model. I thought that Dr. Zwick, as a compromise, might measure the energy transfer between dyes through a thin polymer film used as spacer, but then it appeared to me that this should be made easier by using fatty acid as spacer layers. Langmuir and Blodgett [60] had demonstrated in the 1930s how to make and superimpose fatty acid monolayers. So when Dr. Zwick actually arrived I suggested that he use monolayers instead of polymers. He agreed and worked with great enthusiasm [61]. I was fascinated to see a fatty-acid-dye monolayer being used as a tool to manipulate single dye molecules and to build organized arrangements of individual molecules by superimposing, in a programmed sequence, fatty acid monolayers doped with dyes.

It was a very exciting time in chemistry in the early 1960s. On the one hand, classical organic chemistry, developing the basic reactions of synthesis, had reached the goal; on the other hand, molecular biology had just started, showing that organisms are highly organized at the molecular level. New playgrounds for physical chemists became visible. Both biosystems and machines are complex functional entities, but biosystems, in contrast to machines, are composed of functional units of molecular size. I thought why not try to build machines consisting of interacting molecules forming functional units, i.e. trying to realize 'molecular engineering' as a complement of molecular biology. I was convinced that chemists should start with a new task, constructing molecular functional units, i.e. synthesizing mutually interlocking molecules, purposely designed to form functional entities by self-organization under appropriate environmental conditions. In other words, chemistry appeared to me to enter a tremendous renaissance by moving into this new direction, changing its paradigm from the isolated molecular species, the pure substance, toward functional systems, with the machine of molecular size as the goal of synthesis.

Thus, the question was how to try to catalyze such a development. Trying to build a prototype of a machine of molecular size appeared to be the way forward, and I was very excited to see a possibility in this direction by assembling monolayers. Obviously, the energy transfer arrangement that we had experimentally realized already constituted such a molecular machine, with the dye molecules acting as solid parts and the light quanta as movable parts ......
.............



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------------------- electron gas model related

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         [30] L.G.S. Brooker, xxxxxxx. Rev. Mod. Phys. 14, 275 (1942).


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         [34] R.E. Peierls, Quantum Theory of Solids, p.l08. Oxford, Clar-
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               die Wellenfunktion des Elektrons im Wasserstoffatom und Wasser-
               stoffmolekülion. Helv. Chim. Acta 35, 1155 (1952).


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               symmetric polymethines. J. Chem. Phys. 32, 467 (1960).


         [43a] R. Eckert and H. Kuhn, Richtungen der Ubergangsmomente
               der Absorptionsbanden von Polyenen, Cyaninen und Vitamin B12 aus
               Dichroismus und Fluoreszenz-polarisation. Z. Elektrochem. 64, 356 (1960).


         [43b] F. Bär, W. Huber and H. Kuhn, Ueber die Schwingungsstruk-
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         [43c] F. Bär, H. Lang, E. Schnabel and H. Kuhn, Richtungen
               der Ubergangsmomente der Absorptionsbanden von Phthalocyaninen
               und Porphyrinen aus Fluoreszenzpolarisationsmessungen. Z. Elek-
               trochem. 65, 346 (1961).


         [43d] H. Jakobi and H. Kuhn, Richtungen der
               Übergangsmomente der Absorptionsbanden von Acridin-, Phenazin-,
               Phenoxazin-, und Xanthenfarbstoffen aus Dichroismus und Fluores-
               zenz-polarisation. Z. Elektrochem. 66, 46 (1962).


         [43e] H. Jakobi, A. Novak and H. Kuhn, 
               IR-Dichroismus länglicher Moleküle in gestreckten
               Polyäthylen- und Polyvinylalkoholfolien. Z. Elektrochem. 66, 863 (1962).


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        [54]  B.E. Kohler, O. Spangler and C. Westerfield, C.  The 21A5 state in
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        [55] H. Kuhn and O. Kuhn, xxxxxxxxxxx. Chem. Phys. Lett. 204, 206 (1993).


        [56] O. Kuhn, The dynamics of solitons in trans-polyacetylene. In:
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             baumer, R.L. and Reynolds, J.R., eds.). New York, Marcel Dekker (1998).


               O. Kuhn, Solitons, polarons, and excitons in polyacetylene:
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             C. Kuhn, Step-potential
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             Synthetic Metals 41-43, 3618 (1991).


        [57] H. Kautsky, W. Appel and H. Amann, xxxxxxxxxxx. Biochem. Z. 332, 277 (1960).


        [58] R. Hill and F. Bendall,  Function of the two cytochrome components in chloroplasts: a working hypothesis. Nature 186, 136 (1960).


        [59] H. Kautsky, H. de Bruijn, R. Neuwirth and W. Baumeister, 
             Photosensibilisierte Oxydation als Wirkung eines aktiven metasta-
             bilen Zustandes des Sauerstoffmoleküls. Berichte Deutsch. Chem.
             Ges. 66, 1588 (1933).


        [60]     Blodgett, K.B. (1935) xxxxxxx.J. Am. Chem. Soc. 57, 1007; Langmuir, 1. (1939)
             Proc. R. Soc. London, Ser. A 170, 15.



-------------------


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             systems. J. Chem. Phys. 53, 101.


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          [78]     Seefeld, K.P., Möbius, D. and Kuhn, H. (1977) Electron transfer in
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          [79]     Deisenhofer, J., Epp, 0., Miki, K., Huber, R. and Michel, H. (1984) J.
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          [80]     Kuhn, H. (1986) Electron transfer mechanism in the reaction center of
             photosynthetic bacteria. Phys. Rev. A 34, 3409.


          [81] Haupts, U., Titor, J. and Oesterhelt, D. (1997) Biochemistry 36, 2.


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             On the mechanism of proton pumping. Chem. Phys. Lett. 253, 61. lt
             has been shown (Vonck, J. (2000) EMBO J. 19, 2152) that no signifi-
             cant change in conformation occurs during the M-stage. This supports
             the model which assumes no change in proton-accessibility during
             that stage.


          [83]     Lehn, J.-M. (1995) Supramolecular Chemistry, Concepts and Perspec-
             tives. Weinheim, VCH.


          [84]     Kuhn, H. (1968) Modellbetrachtung an Beispielen aus der physika-
             lischen Chemie. Nova Acta Leopoldina 33, 89.


          [85] Kuhn, H. (1972) Selforganization of molecular systems and evolution
             of the genetic apparatus. Angew. Chem. Int. Ed. Engl. 11, 798.


          [86]     Kuhn, H. and Waser, J. (1981) Molecular selforganization and origin
             of life. Angew. Chem. Int. Ed. Engl. 20, 500.


          [87] Bolli, M., Micura, R. and Eschenmoser, A. (1997) Pyranosyl-RNA:
             chiroselective self-assembly. Chem. Biol. 4, 309; Eschenmoser, A.
             (1999) Chemical etiology of nucleic acids structure. Science 284,
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          [88] Luther, A., Brandsch, R. and Kiedrowski, G.v. (1998) Nature 396, 245.


          [89] Eigen, M. (1972) Molekulare Selbstorganisation und Evolution. Nova
             Acta Leopoldina 37, 171; Eigen, M. (1971) Self-organization of matter
             and the evolution ofbiological macromolecules. Naturwissenschaften
             58, 4365.


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