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«Hans G.A. Hellmann (1903-1938) 1) Part I. A Pioneer of Quantum Chemistry W.H.E. Schwarz*** and D. Andraea), S.R. Arnoldb), J. Heidbergc), H. Hellmann ...»

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Translated from Bunsen - Magazin 1999 (1) 10-21, (2) 60-70

by Mark Smith* and W.H.E. Schwarz**, with revisions by J. Hinzea) and A. Karachaliose)

Hans G.A. Hellmann (1903-1938) 1)

Part I. A Pioneer of Quantum Chemistry

W.H.E. Schwarz*** and D. Andraea), S.R. Arnoldb), J. Heidbergc), H. Hellmann jr.d), J. Hinzea),

A. Karachalios e), M.A. Kovner f), P.C. Schmidt g), L. Zülickeh)

The history of great scientific discovery is the story

of the disappearance of human prejudice under the weight of experimental evidence [...] The incorruptible guardian of the progress of our knowledge is testing our experience against statements established by mathematical theory.

Hans Hellmann [H30] Hellmann was a theoretical physicist with an excellent knowledge of chemistry.

His most important, lasting achievements are:

1. Pioneering contributions to the physical significance of covalent bonding

2. The molecular virial theorem and description of its consequences

3. The quantum mechanical force theorem (Hellmann-Feynman Theorem)

4. The "combined approximation method", today's pseudopotential or effective core potential method

5. The formalism of diabatic and adiabatic elementary reactions

6. The textbooks on "Quantum Chemistry" 1) A "Hellmann-Archive" was created in Siegen in commemoration of Hans Hellmann. This is where documents on the biographical details can be found. Correspondence with further details and materials are welcome at the correspondence address below. We should be most grateful to receive comments from our readers, especially with regard to Hellmann's scientific effect, and also for additions to our Hellmann archives, particularly as we are presently engaged in a complete biography incorporating also historic and socio-political details.

The Hellmann-Archive contains also copies of all papers of Hellmann. They are listed in the Appendix.

*Mark Smith, B.Sc., 68 Osborne Street, Swindon SN2 1DA, GB (Hellmann's great nephew) **Correspondence address: Theoretische Chemie, Universität, D-57068 Siegen; Fax 0049(0)271-740-2851; email: schwarz@chemie.uni-siegen.de

a) Prof. J. Hinze, Dr. D. Andrae, Theoretische Chemie, Universität, D-33594 Bielefeld

b) Dr. S.R. Arnold, Journalist, Bismarckstr. 21, D-80803 München, and Moscow

c) Prof. J. Heidberg, Physikalische Chemie, Universität, D-30167 Hannover

d) Dipl.Ing. H. Hellmann, Paul-Fickeler-Weg 24, D-57072 Siegen (son of Hans G.A. Hellmann)

e) Dott. A. Karachalios, History of Natural Sciences, Universität, D-55099 Mainz

f) Prof. M.A. Kovner, History of Natural Sciences, Academy of Science, RUS-11551 Moscow, Kashirskoje Chaussee 98-2-286 (a former student of Hellmann)

g) Prof. P.C. Schmidt, Physikalische Chemie, Technische Universität, D-64287 Darmstadt

h) Prof. L. Zülicke, Theoretische Chemie, Universität, D-14467 Potsdam Hans Hellmann and His Fate For more than half a century the fate of one of the great pioneers of quantum chemistry lay hidden in darkness. The political upheavals in socialist states in the late 1980s have enabled some light to be shed on this matter. We can now give a preliminary summary of our scientific and historical researches in order to maintain the memory of Hans Hellmann's achievements for the scientific community. He was born in Wilhelmshaven (north-west Germany), and his publications were mainly in German, but later also in Russian. After he had had no choice but to emigrate from National Socialist Germany to the Soviet Union, he was finally liquidated in 1938 by the "Real-Socialists" and then passed over in silence for a long time.

1. Grounding in Wilhelmshaven, Kiel and Stuttgart (1903-1929)

1.1 Childhood, School and Basic Studies Hans Gustav Adolf Hellmann was born on the 14th of October 1903 in the seaport town of Wilhelmshaven in nothwest Germany as the first of two children. His parents were a non-commissioned officer in the navy, Gustav Diedrich Hellmann, and Hermine Anna Bernhardine Hellmann, née Hasse.

The background of the family was in smallholdings and manufacturing work in north-west Germany.

While Hans was still at elementary school, his father died in a traffic accident. His mother eked out her meagre pension with earnings from midday meals served to working men in her own home. Thus Hans was able to attend the classical grammar school in Wilhelmshaven and obtained the higher leaving certificate at Easter 1922. He earned his own pocket money as a local tourist guide.

At this economically difficult time after the first World War it seemed sensible for Hellmann to learn something "practical". After the appropriate manual training he enrolled for the winter term 1922/23 at the Institute of Technology in Stuttgart for electrical engineering. However, by the next summer term, following his inclinations, he changed to the more theoretically aligned »technical physics« department.

He financed his studies partly through work at the workshops and laboratories of the wharves in his home town. Nevertheless he found time, as was then common, to join a students' association (see Fig. 1). After a total of four semesters he took one semester's leave of absence to work as a private tutor. During this period he had the leisure to prepare himself for the preliminary physics diploma.

Figure 1: Hellmann as a student 2)

1.2. Applied Physical Chemistry for a Livelihood: Experiments on Electrolytic Solutions In the following summer semester 1925 we find Hellmann at the University of Kiel. Among other lectures he heard Professor Walther Kossel, no doubt for the first time about the electronic theory of valency. The main purpose of the Kiel semester was, however, to work as a student assistant in the laboratory of experimental physics, run by Professor Hermann Zahn, on a topic from the field of physical chemistry.

This research was supported financially and with equipment by the Reich Navy and the "Emergency Association of German Science" (a forerunner of the "German Research Foundation", DFG). It concerned the measurement of the frequency dependent dielectric constants of conducting hydrous salt solutions (see info-box below). Hellmann's original ideas in his contributions between 1925 and 1934 [H1-H7, H15, HC15] occurred during the turbulent period of the theory of strong electrolytes developed by Peter Debye, Erich Hückel, Lars Onsager and Hans Falkenhagen in the years from 1923 to 1932.[1] The details of charge distributions of ionic clouds in solutions, and their relaxation processes determining the permittivity as a function of electrolytic concentration and frequency of the electric field, were to be tested.

Hellmann's experimental work was characterized by extremely careful execution of difficult procedures.

He continued this work later at Hannover (see below sect. 2.9), when his research was already concentrated on quantum chemistry. He also set an example by his work on the theory of electrochemical measurement techniques. His far-reaching research into all sources of error allowed him, even then, to obtain measured results of the correct sign and order of magnitude (even to one-percent accuracy, see Fig.

2), which not all pioneers of the time were fortunate enough to achieve (cf. Walden, Ulich, Werner [2] and [H5, H6]). This high precision enabled scrutiny and confirmation of an important kinetic aspect of the theory of strong electrolytic solutions. Later research [3] confirmed the earlier findings by Hellmann and Röver [H15, HC15]. It is only recently and thanks to the development of microwave spectroscopy that these properties can be measured reliably and accurately in the corresponding frequency region and that important knowledge about structure and dynamics of electrolytic solutions can be established.[3a] Hellmann's Procedure to Determine the Frequency Dependency of Dielectric Constants Hellmann's method was to measure the intensity I of a standing radio wave on a "Lecherparalleldrahtsystem". The standing wave was formed between the surface of the electrolytic solution and the short-circuited end of the "Lechersystem" after which, through raising or lowering the level of the liquid, it was tuned into the resonance frequency. I, at the fixed position of maximum

intensity, depends only on the reflexion coefficient R of the electrolytic solution:

I = const · {(1 + R)/(1 – R)}2 where R2 = (η – 1)/(η + 1) is given by the complex permittivity η(λ) = ε(λ) – iκ(λ) /2π cε0.

ε is the dielectric constant or dielectric dispersion of the electrolytic solution at wavelength λ, κ denotes its specific conductivity and c the speed of light. (The dielectric loss plays a significant role only when the wave lengths λ are shorter than those applied here.)

1.3. Graduation in Physics: Experimental Atmospheric Chemistry For the next seven semesters Hellmann again studied at Stuttgart, under Professors Ewald, Regener, Fues and others. One may suppose that those named, who later, for instance, tried to obtain a lectureship for Erich Hückel at Stuttgart, would have informed their students about the exciting results of the newly created quantum mechanics and its application to molecules and crystals. This must have made an impression on Hellmann. First, however, after a short time training under Otto Hahn and Lise Meitner at the Berlin "Radioactive Laboratory", he passed his physics graduation examination with distinction. It included experimental work on the "synthesis of radioactive preparations for physical research". Shortly before that, Hellmann was one of the first to be admitted to the "Württemberg Regional Association of German Physicists", founded by Erich Regener.

2) [n] The citations refer to the general list of references, and [Hn] and [HCn] to Hellmann's bibliography in the Appendix.

After graduation Hellmann became practical assistant to the experimental physicist Erich Regener, who had many and varied interests.[4] In May 1929 he obtained his doctorate under the auspices of Regener, his thesis being "On the Occurrence of Ions from the Decomposition of Ozone, and the Ionization of the Stratosphere". At that time there was speculation about the origin of charge carriers in the stratosphere. In particular it was suspected that pairs of ions appeared when ozone decomposed. Hellmann was able to show, however, that markedly fewer than one pair of ions were formed per 1015 molecules of ozone. This work also showed special care in carrying out and interpreting difficult laboratory experiments, so that despite the limitations of measurement technology at that time, it was possible to obtain admirably accurate results. Hellmann also helped his professor with the analysis of critical data in other projects [H8].

1.4. Marriage with Political Consequences The relationship of Professor Regener with his students was decidedly friendly.[4] After invitations to Regener's home, Hans Hellmann became acquainted and fell in love with the Regeners' charming foster daughter Viktoria Bernstein (see Fig. 3), a distant relative of Regener's wife Viktoria, née Minchina.

(Both Viktorias came from Ukrainian Jewish families, a fact which was later to have dangerous consequences for both men, particularly for Hans Hellmann). Viktoria Bernstein's parents had both died early, and she was finally able to leave the Soviet Union in 1922 after the First World War and the Revolution and seek shelter with her aunt in Stuttgart. There she was trained as a children's teacher.

Shortly after Hellmann's doctorate, at the beginning of January 1929, he and Viktoria were married.

Figure 2: Percentage increase ∆ε of the Dielectric Constant (i.e. the real part of the permittivity) of hydrous salt solutions (MgSO4, CuSO4) at 270 MHz, versus the root of the equivalent concentration γ* in Mol/l. (+, ∆,  ): measured by Röver, a candidate for a doctor's degree studying under Hellmann, at a wavelength of 1.1m, and (------): calculated according to the Debye-Falkenhagen theory for a stationary field (λ = ∞) and for 1m waves (λ= 1m). Some data of other authors were omitted from the original diagram [HC15, Fig.11] for clarity.

2. Lectureship in Hannover (1929-1934)

2.1. The Change to the Newly Developing Discipline of "Quantum Chemistry" At this time, Professor of theoretical physics Erwin Fues, mentioned above, was called from Stuttgart to the Institute of Technology (TH) in Hannover. He offered Hans Hellmann an assistant's post, and thus the latter could finally carry out his intention to apply quantum mechanics to the problems of theoretical chemistry. Hellmann started work on the still new area of "Quantum Chemistry", whose birth[5,6] was marked by the work of Heitler and London in 1927.[7] In 1928 this area was still called "mathematical chemistry"[8] or "sub-atomic theoretical chemistry",[9] later also "chemical physics".[10] The phrase "quantum chemistry" seems to have been used for the first time in 1929 in Arthur Haas' lecture to the Viennese Chemical-Physical Association.[11] The fact that quantum chemistry at that time was a particularly topical subject is confirmed by the Annual General Meeting 1928 of the German Bunsen Association ("Types of Chemical Bonding and the Structure of Atoms"),[12] further by the "Leipziger Woche" initiated by Debye ("On Problems of Quantum Theory and Chemistry");[13] it was also topical at meetings of the English Faraday Society ("Molecular Spectra and Molecular Structure")[14] and of the American Chemical Society in the same year ("Symposium on Atomic Structure and Valence").[15]

2.2. Problems with Principles of Quantum Mechanics: Does Spin exist?

At first, however, Hellmann devoted himself to a burning question of current interest, posed by Prof.

Fues, which was then controversial: were there spin-polarized electron waves, that is, have free electrons in space four or only three degrees of freedom? Shortly before, Bohr and Mott had suspected and reliably proved the impossibility of a Stern-Gerlach experiment for free electrons.[16] Does spin perhaps only exist as an additional and two-valued degree of freedom for atoms and molecules? Fues and Hellmann [H10] were able to solve the problem through a thorough discussion of Dirac's equation: there are spin polarized free electrons. In particular they proposed experiments to test this.

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