Eigen

Eigen s office in Gottingen on December 10, 1997. The following narrative is based on parts of this conversation. 

Arnold Eucken (courtesy of William B. Jensen and the Oesper Collection, University of Cincinnati). 

Eucken wanted him to go to as high temperatures as possible. They had a sealed Jenaer glass vessel to protect their sample from impurities. Its volume was half a liter in order to have a big heat capacity. They did not know what temperature the glass vessel would stand. Eucken thought that even 200°C would be possible, but Eigen wanted to go only as high as 175°C in the first experiment. However, there was a big explosion at 169°C, and the whole apparatus landed on the ceiling. 

Heavy water at that time was very much at premium so Eucken was very unhappy and thought that the explosion blew up Eigen s project. Although Eigen promised him to build a new calorimeter in three weeks, the heavy water would have been impossible to replace. Fortunately, however. 

Eigen did not risk their heavy water in the very first experiment. When Eucken learned about this, from that point on he let Eigen do whatever he pleased. Eigen received his doctorate at the age of 23. 

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Eigen function In wave mechanics, the Schrodinger equation may be written using the Hamiltonian operator H as... 

Only certain energy values ( ) will lead to solutions of this equation. The corresponding values of the wave functions are called Eigen functions or characteristic wave functions. 

Eigen M 1996 Die unmessbar schnellen Reaktionen (Ostwalds Klassiker der exakten Naturwissenschaften) vol 281 (Thun und Frankfurt Harri Deutsch)... 

Eigen M and de Maeyer L 1963 Relaxation methods Technique of Organic Chemistry o 8, ed S L Friess, E S Lewis and A Weissberger (New York Wiley) pp 895-1054... 

Eigen M and Rigler R 1994 Sorting single molecules application to diagnostics and evolutionary biotechnology Proc. Natl Acad. Sc/. USA 91 5740-7... 

Eigen M 1954 Methods for investigation of ionio reaotions in aqueous solutions with half-times as short as 10 sec Discuss. Faraday Soc. 17 194-205... 

Molecular aspects of geometric phase are associated with conical intersections between electronic energy surfaces, W(Q), where Q denotes the set of say k vibrational coordinates. In the simplest two-state case, the W Q) are eigen-surfaces of the nuclear coordinate dependent Hermitian electronic Hamiltonian... 

Porschke, D., Eigen, M. Cooperative nonenzymic base recognition. HI. Kinetics of the helix-coil transition of the oligoribouridylic oligoriboadenylic acid system and of oligoriboadenylic acid alone at acidic pH. J. Mol. Biol. 62 (1971) 361-381... 

Edsall, J. T. George Scatchard, John G. Kirkwood, and the electrical interactions of amino acids and proteins. Trends Biochem. Sci. 7 (1982) 414-416. Eigen, M. Proton transfer, acid-base catalysis, and enzymatic hydrolysis. Angew. Chem. Int. Ed. Engl. 3 (1964) 1-19. 

V.L. Druskin and L.A. Knizhnerman Krylov subspace approximation of eigen-pairs and matrix functions in exact and computer arithmetics. Num. Lin. Alg. Appl., 2 (1995) 205-217... 

If a tran sition state has notheen reach ed after a certain niiinherof steps, th e user may n eed to upgrade th e Hessian an d repeat th e calculation. It may be necessary if many calculation steps have been don e, and the curren t geo in etry differs con siderably from th e starting poin t. fh e Hessian calculated at th e starting poin t an d updated at each n e v poin t m ay n ot be appropriate at the geo in etry reach ed by th e search. fh is procedure can also h elp to get to a good startin g point where the Hessian has a correct structure with only one negative eigen value. 

Th c eigen value of ih is Sch riidiri gcr equation. the electron ie energy deperi ds parametrically, as sh own, on the coord in ales of th e nuclei (assumed to he fixed for the purposes of calcti lali ri g each Heie.lK), bin variable in general), I h e electronic energy, combined with y, (K,K) is the total energy of Single Point semi-em pirical calculation s. 

Theexact eigenfunctions and eigen values can now be expanded in a Taylor series in A. 

The energies. Ip and hp of the initial and final slates of transitions in eq 11 ation s (T 78 i an d (1791are tlelerminetl by the Cl eigen values and the Iran sition tlipole moment dp is obtained by n sing the Cl eigen vectors, Lh at is. 

For example, after the drum head has been hit, its shape will evolve spatially and in time in a manner that depends on how it was prepared by the initial blow. However, if one carries out an experiment to detect and frequency-analyze the sound that emanates from this drum, thereby measuring differences in the eigen-energies of the system, one finds a... 

The 1967 Nobel Prize in chemistry was shared by Manfred Eigen a German chemist who developed novel methods for measur ing the rates of very fast re actions such as proton transfers... 

M. Eigen, ia S. Claesson, ed.. Fast Reactions and Prima Processes in Chemical Kinetics, 5th ed., Wiley-Interscience, New York, 1967, pp. 333—369. 

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