Sigrid Peyerimhoff Article : The Development of Computational Chemistry in Germany Component of : Early Ideas in the History of Quantum Chemistry. (original) (raw)
INTRODUCTION
Computational chemistry was able to develop thanks to two major advances: first was the understanding and formulation of a mathematical description of the mkroscopic behavior of matter, and second was the technical development of computers much more powerful than mechanical desk calculators. A large part of the foundation of the mathematical theory was laid by the physics community in Europe in the 1920s. The University of Göttingen in Germany became a center of the new quantum mechanics.
Although various established chemists in Germany had become aware of the amazing explanatory power of the new quantum mechanics by Heisenberg and Schrödinger, they were not yet ready to make use of this tool for chemistry. Very likely they could not imagine that a mathematical theory would be able to describe data and processes that generations of experimentalists had collected and studied. Thus several young people were the first to apply the new theory to chemical problems. In early 1927, two Germans, Walter Heitler (from Karlsruhe) and Fritz London (who had received his Ph.D. degree in München), supported by a Rockefeller fellowship, spent some time in Zürich where Erwin Schrödinger was at that time. Both wanted to work in quantum mechanics. Apparently, Schrödinger was not fond of collaborations, so Heitler and London decided in Zürich to calculate the van der Waals force between two hydrogen atoms. According to the articleofGavroglu andSimoes 1 on the history of quantum chemistry, "nothing indicates that Schrödinger gave them the problem of the hydrogen molecule or that they talked with him about it." This work culminated in their famous Heitler - London paper 2 as basis for the valence bond approach of chemical binding. Later in 1927, Heitler became Max Born�s assistant in Göttingen, and London became the assistant to Schrödinger who had then moved to Berlin as the successor to Max Planck. Heitler and London had to resign their positions in 1933, and both emigrated to England.
Linus Pauling from the United States spent 1926 to 1927 (his postdoctoral year) with Arnold Sommerfeld in München. He was supported by a Guggenheim fellowship and made visits tO Göttingen. Pauling used the new quantum mechanics to study the electronic structure and physical properties of complex atoms and., atomic ions. 3 The young Robert S. Mulliken, also from the United States, spent 1927 - 1928 as a postdoctoral fellow in Göttingen where he met Friedrich Hund.They not only had intense scientific discussions with each other, but also became friends and even spent some vacation time hiking together in the Black Forest. Their approach to chemical binding, today referred to as the molecular orbital (MO) method, was derived from the study of molecular spectra 4,5. It was an exciting time, and Germany was an attractive place for scientific visits, especially for young people.
Still, skepticism remained as to the general power of quantum mechanics applied to complex chemical systems. The situation around 1930 is described by the well-known dictum of Paul Dirac 6 (the Nobel Prize winning physicist at Cambridge): "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation."
Indeed, approximate tnethods were quickly designed, and during the first years German scientists contributed their share. Erich Hückel 7 developed the very simple but highly successful Hückel method for aromatic pi-electron systems, and Hans G. A. Hellmann 8 made important contributions to the methodology of quantum chemistry. These two men may be considered the most prominent German representatives to apply quantum mechanics to chemistry in this era. Starting in 1933, the political influence of Nazi Germany forced many scientists to emigrate, including Hellmann, and Germany lost its lead in the field. It was probably the United States that became the strongest player due to the work and effort of Pauling, Mulliken, and John Slater. 9
COMPUTER DEVELOPMENT
The ZUSE Computers
The first fully automatic digital computer that could be programmed was developed by Konrad Zuse in Berlin during World War II. A description of the years of intense work under very difficult conditions is found in Zuse�s book appropriately entitled "Der Computer - Mein Lebenswerk." 11 The first working model was the Z3 introduced in May 1941. It was based on electromagnetic relays: 600 relays in the computing unit and 1400 in the storage unit. It used a binary number system, floating point operation, 22 bit word length and had a storage capacity of 64 words. It required a special keyboard to generate the input via an 8-channel punched tape (i.e., one instruction represented by 8 bits).
 Zuse Z3 - Photo and © from here. |
 Konrad Zuse |
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Most parts of the computer were constructed from used materials because new materials were hardly available during the war. This meant, for example, that the various relays required different voltage, and this had to be considered also. Nevertheless, the machine was apparently relatively stable in its performance. The speed was about 3 seconds for multiplication, division, or taking a square root. The Z3 was used to calculate determinants and, in particular, complex matrices that were important in optimizing the design of airplane wings. Part of the work on the Z3 was financially supported by the Deutsche Versuchsanstalt für Luftfahrt. This first model was completely destroyed in 1944 by Allied bombs, but a replica was reconstructed 1960 and can be seen in the Deutsches Museum in München.
Further development of the Z-series was seriously hampered by the war. The design of a much larger system Z4 started in 1942. The machine was transported in 1944 to Göttingen, which seemed a somewhat safer place than Berlin, but as Zuse writes 11 , it took two weeks for the transport, interrupted by heavy bombing of the trains.
 Konrad ZusePhoto, © and more info here. |
Work continued for a while in the building of the Aerodynamische Versuchsanstalt in Göttingen, which is near the center of Germany. From Göttingen, Zuse and some of his friends escaped in 1945 with the Z4 to Hinterstein, a small village close to Hindelang in the German Alps where other scientists such as Wernher von Braun had also found some shelter. In these years, they were entirely isolated from the rest of the world and heard only after the war the details of computer developments in the United States (MARK I, in operation 1944, and ENIAC, operating somewhat later) and in Britain (COLOSSUS, which was a stored program machine to break the code of the German forces in the war). There was no possibility of continuing work on the Z4 until the monetary reform of 1948. Zuse in Germany had been the first with an operational freely programmable digital computer but had lost the competition with other countries due to the war situation in Germany. |  The ENIAC Computer more here Photo and © Univ. Penn State |
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In 1949, Zuse started his companyZUSE KG (at Hünfeld in Hessen). The Z22 was his first computer with vacuum tubes (1955), followed by the Z23 with transistors. A small number of German universities was able to obtain such machines. Personally, I saw a Z22 for the first time in operation at the Technische Hochschule (TH) of Darmstadt (around 1960 in the Institute of Professor Atwin Walther) during an excursion organized by a course in applied mathematics from the University of Giessen, at which I was a student at that time.
Zuse Z22 -
Photo and © from here.
Zuse Z23 -
Photo and © from here, where there is more to be found on Zuse
As far as I know, there were no funding programs from the government to support computer development in Germany during the period before 1960. Unlike in the United States, it was impossible for the civilian technical sector to take advantage of products developed for the military. It was the Deutsche Forschungsgemeinschaft (German Science Foundation) that made it eventually possible for computers to be purchased at universities starting in the early 1960s. The ZUSE company was eventually taken over by Brown-Boveri (1964) and has belonged to Siemens AG since 1967.
The G1, G2, and G3 of Billing in Göttingen
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Heinz Billing, 2002born 1914 Photo and © Max-Planck-Gesellschaft | | Late in 1947 the building of the Aerodynamische Versuchsanstalt in Göttingen, which had housed the ZUSE Z4 for a short time during the war, became available for new institutions and institutes, including the Kaiser- Wilhelm-Gesellschaft (today called the Max Planck Gesellschaft) with Max Planck and Otto Hahn, and the Institute of Physics with Werner Heisenberg, Max von Laue, and Carl Friedrich von Weizsäcker. The experimental groups had to construct equipment since nearly all laboratory equipment had been destroyed in the war. Heinz Billing 12 started to build a small High-Frequency Lab in the "Institut für Instrumentenkunde" with a few instruments to measure electric currents and with some vacuum tubes left over from the German army. He was fascinated by a very short note on the existence of the ENIAC computer in the United States, a computer containing 18,000 vacuum tubes and with a weight of 30 tons. | | 
Heinz Billing, 1987 Photo and © here. |
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At this time, a group of British computer experts from Teddington, who, among others included Alan Turing, J. R. Womersley, and A. Porter, visited the British occupation zone of Germany. They intended to investigate whether there were new developments in Germany and met in Göttingen with selected German scientists, including Heinz Billing of Göttingen,Alwin Walther of the TH Darmstadt who had worked on Hollerith machines, and Konrad Zuse. Another pioneer in the computer development, Professor Friedrich Willers from Dresden was apparently not able to come to this visit because he was in the Soviet occupation zone. Womersley discussed with Billing computer plans in England that led in 1950 to the ACE (Automatic Computing Engine) machine, and Billing considers this discussion as the basis for his development of the G1 and G2 computers (G stands for Göttingen).
Magnetic tapes and magnetic recorders already had been used by him in 1943, and his first successful magnetic drum storage system was in 1948. The drum, which had magnetic tapes glued around, could store 192 dual (20-digit) numbers. The publication describing this device, submitted in July 1948 as "Numerische Rechenmaschinen mit Magnetophonspeicher" in Z_eitschrift für Angewandte Mathematik und Mechanik,_ showed, in addition, general aspects of how to construct a computer to solve the Schrödinger equation, Y" + F(x)Y + T(x) = 0.
| Billing�s development work was interrupted by the monetary reform of 1948, which caused heavy cuts in the Institute�s budget. Billing�s engineers took job offers from Argentina, and he himself accepted an offer from Australia in order to develop a computer including his magnetic drum at the University of Sydney. He left a detailed description of the design of his computer in Göttingen, however. Since the astrophysicist Ludwig Biermann in Göttingen was extremely interested in numerical calculations and believed in the future of digital computers, he convinced Heisenberg to bring Billing back. In June 1950, Billing was back in Göttingen and started to work on the computer, and Heisenberg was even able to obtain funds from the Marshall Plan to buy vaccum tubes and resistors. Since for Biermann the construction of the computer in its original concept would have taken too much time, a smaller model, the G1, was constructed and went into operation by the middle of 1952. This machine was the first programmable computer operating with vacuum tubes in Germany, and it was based on Zuse�s programmable relay computer. It made two operations per second, but was, as such, 10-20 times faster than a good mechanical desk calculator. In addition, it could be used 24 hours/day. The magnetic drum had a frequency of 50 revolutions per second; it had 9 tracks and could store four 32-bit numbers per track. Since 10 positions were required for transforming decimal numbers into binaries, only 26 of the 36 positions of the drum remained for the storage of numbers. | | 
Ludwig F.B. Biermann1907 - 1986Photo, © and further Biohere. |
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The larger model, the G2, with 30 operations per second and a magnetic drum storage of 2048 words at (50+1) bits fixed point, went into operation in the fall of 1954 in Göttingen, two years before the main German competitorPERM in München.
Billing�s third machine, the G3, used already existing ferrite kernels as main storage and floating point arithmetic. This storage device had been developed in 1952 in the United States. In 1953 a German company also started to produce such ferrite core storage for the G3. The storage of the G3 had 4096 words at (42+1) bits, that is, it needed 176,000 ferrite kernels, each costing 0.5 Deutsche Mark (DM), which amounted to the large sum of 90,000 DM. The main goal of the G3 was to have a very reliable machine - the speed was of second priority. So, the faster vacuum tubes were replaced as much as possible by more stable germanium diodes (1500 vacuum tubes, 6000 germanium diodes). This G3 model could then perform 5000 operations per second it was very robust and was inoperable only 1.1% of its entire life span from 1960 to 1972. Its operation ended in 1972, some time after it had been moved into the new buildings of the Max Planck Institut für Physik und Astrophysik in München. All three machines were eventually dismantled; only photographs are left of them today. {Note by this website: According to some internet link of around 2000, the G1-a is on display at the Deutsches Museum, Munich}
Computer Development at Universities
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Robert Piloty, 1989 Photo and © here. | | In the 1950s, the design of computers also started at various German universities. These efforts were supported by the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG), which initiated a special committee for this purpose (Kommission für Rechenanlagen). Main competitors to the machine in Göttingen were Professor Walther with Hans-Joachim Dreyer at the TH Darmstadt whose DERA machine went in operation in 1957, Robert Piloty at the Technical University (TU) of München with the PERM (1956), and Friedrich Willers with Joachim Lehmann in Dresden with D1 (1956) and D2 (1957). | | 
Alwin Walther1898-1967 Photo, CV and © here. |
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F.L. Bauer, 2003 Photo, some CV and © here. | | Even though PERM stands for "Programmgesteuerte Elektronische Rechenmaschine München," some people called it "Piloty�s erstes Rechen-Monster".{website:P.'s first monster calculator} This computer was later put under the guidance of Professor Friedrich L. Bauer at the TU München. More information can be found in Refs. 12 and 13. Looking back at these early developments at a research institution in Göttingen and at several universities, it is regrettable that the German industry was not able to take advantage of this knowledge and lost out in the internationally fast growing competition in computer technology. | |
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The Analog Computer in Chemistry
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The Kuhn analog computer from a 1961 paper (ref.16, photo and ©).The rackheight was about 3 meters. | | Hans Kuhn at the University of Marburg was interested in the spectra of dyes 14. Based on the electron gas model, he could understand the quantum mechanical states involved in such light absorption processes in a qualitative way, but he wanted to have quantitative results. So he developed an analog computer to determine stationary wave functions and corresponding energies of a particle (it electron) in a one- and two-dimensional (1D and 2D) potential field as given by the Schrödinger equation. The basic idea was put forth 15 in 1951 when he experimentally determined the vibrational frequencies of membranes whose form represented that of certain (planar) molecules. The transition from the mechanical system described by masses and springs to the analogous electrical system replaces masses by self-induction (coils) and springs by capacitances. The potential acting on the site of an atom could be changed by an adjustable capacitor. The entire network was driven by high-frequency voltage that was varied to obtain stationary electric waves. Hence, the actual computer was based on the analogy between oscillatory states of a network of electric circuits and the stationary waves of a corresponding quantum mechanical system. | |
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| The energies of the stationary states were given by the applied frequencies and the corresponding wave functions by the voltage at each mesh point of the network. The entire network had 4000 resonators; a picture of the size of the installation can be found in Ref. 16 and details to the installation in Ref. 17. In this way, Kuhn and his co-workers calculated it electron distributions in effective potentials of the molecular skeletons of many organic dyes 18 and found that in long polyene chains the alternating bond lengths had analogous values as the C-C single and C=C double bond in butadiene. The treatment of benzene showed equal bond length in such "calculations." Later on, Kuhn was also able to obtain from this analog computer transition moments, and in this way he could determine and explain the location, intensity, and form of absorption bands and even the shift of a phosphorescence band of a dye relative to its fluorescence location. With the introduction of digital computers to German universities and research institutions in the mid-1960s and ab initio programs for larger polyatomic molecules in the 1970s, the Marburg analog computer reached the end of its service. It should not be forgotten, however, that it was a considerable technical achievement and a very valuable tool during its time, at which the calculational alternatives were very simple Hückel type (without the possibility of taking into account different nuclear potentials) and semiempirical Pariser-Parr-Pople (PPP) 19 MO treatments. | | 
Another Kuhn analog computer.Photo and © ref 17. |
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QUANTUM CHEMISTRY, A NEW START
After the important work of Heitler and London 2 in 1927 as well as that of Hund 4 and Mulliken 5, a great interest arose among scientists to apply the new quantum theory to problems in chemistry, particularly to molecular structure and spectra and to the study of the chemical bond. According to Schwarz et al. 8, the word "Quantenchemie" was probably used first in 1929 by Arthur Haas in his presentations at the Chemisch-Physikalische Gesellschaft in Vienna. One of the young Germans in this field was Hans G. A. Hellmann in Hannover, close to the center of development of this new theory (Göttingen). His scientific achievements to the further development of quantum chemistry are summarized in a recent article that also contains details of his life. 8 He left Germany in 1934, being married to a Jewish wife and in opposition to the Nazi regime, and found an attractive position at the Karpov Institute in Moscow. Under the Stalin regime, he was arrested and executed in 1938. His heritage is the excellent textbook "Einführung in die Quantenchemie," 20which appeared in the German language in 1937 and served as a basis to introduce German scientists to this field after World War II.
The first activity after the war seems to have started at Göttingen, again at the Max Planck Institut für Physik, where the G1 computer was also designed. Various publications by H.-J. Kopineck 21 derive analytical expressions for Coulomb and exchange two-center integrals over 2s and 2p Slater-type functions (e — ζ r ) required for the quantum chemical calculations of diatomic molecules and give extensive tables of numerical values of such integrals as a function of internuclear separation.
| Kopineck based some of this work on the tables of auxiliary functions published in 1938 by Kotany, Ameniya, and Simose 22, but was careful enough to recalculate all those that he specifically needed and found that the Japanese tables were very reliable. Apparently, these latter tables had been overlooked when other work started on the evaluation of integrals for selected applications 23. In Kopineck�s papers, **21, 24, 25,**acknowledgment is expressed to Professor K. Wirtz for suggesting the work, to Professor L. Biermann for support, and to a group of people of the astrophysical section of the institute (director Biermann) for carrying out all the tedious numerical computations. This happened all before the electronic computer G1 became available. A very interesting work on the potential energy curve of N2 as a 6- and 10-electron problem based on the Heitler-London method as described by Hellmann 20 made use of the previous tables of integrals and is among the first German publications in this area. This 1952 paper was dedicated to the 50th birthday of Heisenberg. | | 
Masao Kotani, 1955 Photo © Austin Conf. 1955 |
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While work on the computation of two-center two-electron molecular integrals continued in Göttingen, it became known 25 that Clemens C. J. Roothaan 26 and Klaus Ruedenberg 27 at the University of Chicago had also started a program to evaluate molecular integrals, obviously in connection with the seminal Roothaan article on the self-consistent field (SCF) procedure 28.
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Heinzwerner PreußPhoto and © here,where some additional CV may be found. | | In 1952, Heinzwerner Preuß came to the Institute in Göttingen as successor to Kopineck. He already had experience in H2 calculations and integral approximations 29 performed while at Hamburg, and was the ideal person to continue the work on integral evaluation in Göttingen. He first extended the studies to heteronuclear diatomics, and later on, with the use of the G1 and G2 electronic computers, this work culminated in four books Integraltafeln zur Quantenchemie. 30 These volumes give an excellent introduction to the general problem of quantum chemical calculations and contain many references to historical work in this connection. They are also an excellent dictionary to look up details of the analytical derivations of molecular two-center integrals over Slater functions and their necessary auxiliary functions. The numerical values are tabulated for a small grid so that intermediate values could easily be obtained by interpolation. These tables were used for quantum chemical calculations 31 of diatomics until the beginning of the 1960s.I used these tables of Preuß for the first part of my doctoral work. The computation of integrals for a valence bond treatment of the H-F molecule on a mechanical desk calculator was greatly simplified by the fact that I could look up values for the required auxiliary functions in these tables. Toward the end of this work (1962-1963), I got access to the electronic computer Z23, which of course could perform the calculations in a much shorter time with much higher accuracy. |
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Other numerical tables were apparently also produced in 1954-1956 by a Japanese group 32. One must conclude that at that time it was not widely forseeable that such numerical tables of functions, similar to tables of logarithms, would become obsolete so soon due to the rapid progress in electronic computers.
Parallel to the work on molecular integrals, Preuß also worked on conceptual developments. Boys had introduced Cartesian Gaussian functions 33 as a possible basis for molecular calculations. Preuß was the first to discuss what he called "reine Gaußfunktionen" 34 and what is known today as "floating Gaussians." It is interesting that in Vol. IV of his Tables of Integrals 30 Preuß already had a chapter of numerical examples comparing integrals over Gaussians with those over exponential (Slater) functions and concluded that numerical tables for integrals involving pure Gaussians with different origins are not required because integrals over Gaussians are so easy to compute. Calculations with such basis sets were started later on by J. L. Whitten 35 without the knowledge of this part of the work of Preuß.
Even though the incentive to perform quantum chemical ab initio calculations came from the Max Planck Institute at Göttingen, quantum chemistry ideas were also used in other physical chemistry departments of German universities. The work of Hans Kuhn on large pi-electron systems with the use of his analog computer has already been mentioned in the previous section.Hermann Hartmann in Frankfurt published his textbook Theorie der chemischen Bindung 37 in 1954 and had a great influence for the next 10 years on advertising theoretical chemistry to the chemistry community. Theodor Förster in Stuttgart was also open to quantum chemistry ideas in his investigations of molecular excited states and energy transfer. Bernhard Kockel from the Institute of Theoretical Physics at Leipzig used his book Darstellungstheoretische Behandlung einfacher wellenmechanischer Probleme 38 to present numerous examples of how to apply algebraic concepts to the quantum theory of atoms and molecules. As a result of this, he began actual quantum chemical calculations himself. Finally, the textbook by P. Gombas from Budapest Theorie und Lösungsmethoden des Mehrteilchenproblems der Wellenmechanik 39should also be mentioned since it is an excellent introduction to the quantum theory of many-body problems, oriented especially toward experimental physicists and chemists, and which has an appendix with analytical formulas for important molecular one- and two-center integrals.
THEORETICAL CHEMISTRY 1960 - 1970
Meetings to publicize theoretical chemistry methods and their results were organized and a special priority program to support theoretical chemistry was created by the Deutsche Forschungsgemeinschaft in 1966. At least part of the German organizational support was due to the influence of Professor Hermann Hartmannin Frankfurt. He was also the first (in 1963) to establish a journal devoted specifically to the subject of theoretical and computational chemistry: Theoretica Chimica Acta. I personally remember this era as having an atmosphere of great fascination and competition.
On the other hand, one should not forget that at the beginning of this period the Wall went up on August 13, 1961 and separated Germany into two parts. The travel of colleagues from the East (Deutsche Demokratische Republik, DDR) to the West (Bundesrepublik Deutschland, BRD) was severely restricted, and only a very small percentage of the Eastern colleagues received permission to visit institutes or to attend meetings in the BRD. Likewise travel from the BRD to the DDR became more difficult, and even the exchange of letters was controlled. While scientists from the BRD could freely move to almost all countries, the flow of information between the two parts of Germany became very much restricted. Scientists in the DDR became increasingly isolated internationally.
The Deutsche Rechenzentrum at Darmstadt
The building for this central German computer center had 85 rooms, altogether 2150 m2, and the part of the computer installation plus tape units required air conditioning of 570 m2. The total area of the entire site was 8700 m2. In 1966 the DRZ had a staff of 50 scientific and technical persons, in addition to a number of operators, people to punch cards and handle the program libraries, secretaries, and others. 40 Three technicians from IBM were on site. Details of the installation can be found in Ref. 40. In short, the equipment consisted of a main memory of 32,768 words, 13 magnetic tapes, 1 disk, 1 cardreader, 1 automatic punch, 1 plotter, 1 reader for punched paper tape, 1 sorting machine, 10 card punches for users, 8 card punches for internal use, and 2 teletypes. The cost of one hour of computer time was 240 DM. Starting at the end of 1965, the trade unions did not allow any work on Sunday any more, so that this computer center was shut down on Sundays and on holidays. Office hours were from 8.00 to 17.30 from Monday to Friday.
Looking back from today�s standard, where a workstation or a laptop personal computer is more powerful and has more memory than the entire DRZ in 1966, it is almost unbelievable that method developments and actual calculations could have been performed under the circumstances given. Access to the DRZ was in three ways: either one traveled to Darmstadt by train or car with one or several boxes of punched cards - in case one had a card punch at the home university. This way was probably the "normal" situation. One tried to compile the programs, correct errors and, if fortunate, stored the program somewhere on tape in binary code for further use at the DRZ. Such a procedure worked quite well as long as a friendly person of the DRZ staff took care of the programs and was available for further telephone instructions. We had such a person who had worked at our university for a while, and so we were lucky people. The second way was to send cards by mail to the DRZ, but to debug programs or to run them using this approach was a very slow process. If one was very fortunate, one could use the third way: a teletype (which was the exception at universities), via which one could send input data for programs already stored in binary somewhere in the DRZ and administered by the DRZ personnel. The output was always sent back by regular mail.
The preferred symbolic languages were FORTRAN II and IV, ALGOL (developed in Germany) and COBOL; FAP, MAP, and LISP were also heavily used to optimize computer codes. In 1965, the DRZ had acquired programs from the Quantum Chemistry Program Exchange (QCPE) at Indiana University and was proud that by 1965-1966 they had distributed 65 such programs to researchers outside of Germany such as Great Britain (15), France (13), Sweden (2), Spain (2), Switzerland (3), Italy (1), Denmark (11), Finland (1), Belgium (1), and Romania (1), demonstrating their international visibility.
Formation of Theoretical Chemistry Groups
Most experimental chemists in Germany in those times did not believe that quantum theory beyond the simple Hückel model had any use for chemistry in the foreseeable future. 42,43 So quantum chemistry had to get its main support from the more optimistic international community. Per-Olov Löwdin's summer schools held in Uppsala (Sweden) were instrumental in getting young researchers interested in quantum molecular science. Since these schools (lasting 4—5 weeks) had international participation from both teachers and students, they were also a very attractive place to start international contacts. Heinzwerner Preuß was the first German to spend a postdoctoral year in Löwdin's quantum chemistry group in 1958-1959. Werner Kutzelnigg and Martin Klessinger participated in Löwdin�s summer school in 1960. My turn came in 1962, together with four other Germans, all of whom later became professors of physical or theoretical chemistry at German universities. Raphael Levine (Jerusalem) was one of the most eager students in my class.
Access to international publications also improved in West Germany. The Technical Reports of the Laboratory of Molecular Science and Spectra in Chicago, which contained reprints and preprints of the work done around Mulliken and Roothaan, got distributed to some of the German scientists 44(e.g., L. Biermann, G. Briegleb, Th. Förster, H. Hartmann, F. Hund, H. Kuhn, R. Mecke, and Georg Maria Schwab). The results of the 1959 Conference on Molecular Quantum Mechanics held in Boulder, Colorado, were published in_Reviews in Modern Physics_ 45 and were extremely exciting. This conference is also discussed in connection with the history of computational chemistry in the United States9 and the United Kingdom. 10 All of this work offered encouragement, especially for young people.
Hartmann had his group at the University of Frankfurt, but believed more in models than in ab initio calculations. Nevertheless he tried hard to get students interested in theoretical chemistry and held extra summer courses at Konstanz. Bernhard Kockel, from the University of Leipzig, had been vacationing together with his wife in West Germany (canoeing on the Danube) when the Wall was built (1961); he remained in the BRD upon receiving an offer for the theoretical physics chair at the University of Giessen. He started a small computational group to which I belonged. W.A. Bingel, who was the only German of his generation whose doctoral advisor had been a pioneer in theoretical chemistry (E. Hückel), became professor at the University of Göttingen in 1963. Werner Kutzelnigg joined him in 1964 after his postdoctoral years from 1960 to 1963 (with a NATO fellowship) first in Paris with Bernard Pullman and Gaston Berthier and later on with Per-Olov Löwdin at Uppsala. Kutzelnigg had received his doctorate with Reinhard Mecke in Freiburg and had been so impressed by Bernard Pullman's invited talk in Freiburg that he decided to move into the field of quantum chemistry. Bingel and Kutzelnigg soon attracted the excellent students Reinhart Ahlrichs and Volker Staemmler, most probably because at that time the chair in theoretical physics at Göttingen was vacant and also because theoretical chemistry seemed to be the closest to the original intention of these two students.
I myself was fascinated from what I heard from Chicago and in 1963 went with a fellowship of the Volkswagen Foundation administered by the Cusanuswerk to join the group of Clemens Roothaan and Robert Mulliken. Then in 1964 I spent several months in the laboratory of Ernest R. Davidson in Seattle. In Chicago, I realized for the first time how important it was to have access to a reasonably-sized computer (IBM 7090) on campus, even if runs could be performed only during the night. And furthermore that a turnaround time of a day or two for computer jobs made all the difference compared to the German situation using a Z23 or sending programs and outputs back and forth to the DRZ in Darmstadt by regular mail. After a short visit back to Germany, I spent another postdoctoral period (1965-1966) with Leland C. Allen at Princeton, where we could use the Gaussian-lobe function SCF program for polyatomics, which was due to J.L. Whitten, 35 also a postdoc at that time in Allen�s group. To compute realistic molecular structures and properties, based solely on the Schrödinger equation, was a great challenge to us. I seriously considered staying in the United States. But then the situation for such kind of work had improved drastically in Germany because it had been realized that other countries were far ahead, and for this reason special programs were initiated in Germany to produce top-quality researchers in this field. It was finally realized that state-of-the-art computers were needed at research institutions in addition to the central DRZ and that special support for research in theoretical chemistry was needed.
Deutsche Forschungsgemeinschaft-Schwerpunktprogramm Theoretische Chemie
In 1966, the DFG decided to initiate a special priority program for theoretical chemistry for the next 5 years in order to support this field on a broad basis. 46 The intention was to support primarily new ideas and the development of methods in theoretical chemistry and to a lesser extent computations.
The DFG had been reestablished after World War II on January 11, 1949, under the name of "Notgemeinschaft der Deutschen Wissenschaft". Its present name came into existence after merging with the Deutsche Forschungsrat in 1951. The DFG is legally registered as a private association based in Bonn. Its members are universities, some research institutions, and academies of science. Member institutions delegate one representative each to a general assembly that meets annually.
All research supported by the DFG is investigator initiated. It is the "bottom-up" principle. Funds can be granted only on the basis of applications, and the responsibility for all projects for which funds are granted lies with the principal investigator. All applications are subject to peer review, and in all DFG programs the reviewers� evaluation is the basis for the decision on funding. The DFG's peer reviewers work in an honorary capacity. They are elected every four years by direct, secret ballot. Active voting rights are accorded to all scientists who have held a doctorate for at least three years and are working in a university or other publicly funded research institution. In the year 2000, there were 524 elected members of 37 review committees responsible for 186 disciplines.
There are basically two forms of research support under the DFG system: financing of individual research projects ("Normalverfahren" is the largest in this category) and coordinated, cooperative funding programs with structural effects, among which the most important are the Schwerpunktprogramm (special priority program) and Sonderforschungsbereich (collaborative research centers). Again the initiative for such programs comes from the scientific community. To establish a Schwerpunktprogramm, researchers draft a program, submit it to the DFG Senate, which decides once a year on the adoption of new programs. Within a given scope, participants in such a priority program are free to choose their project, research plan, and methods. Coordination is ensured through a coordinator - generally one of the initiators of the application for such research program - and through annual colloquia.
Looking back, this theoretical chemistry program turned out to be one of the most successful priority programs of the DFG. It was adopted immediately and welcome to all researchers in the field. In the first year, there were 29 project proposals, 13 of which were applications to participate in summer schools. The total budget in this first year was 350,000 DM, that is, 0.64% of the total priority program budget. These funds were used primarily to pay students (60%), but also to pay for computer time at the DRZ or at some other installation (such as the research institution at Julich), or for short-term visitors. These funds were vital for the work of young scientists, most of whom bad become Privatdozent without - or with very little - budget from their own university institution. In the last year of this priority program (1970), the number of accepted research proposals was increased to 45 for which a total sum of 720,000 DM was granted. Fifteen of these proposals were applications to participate in summer schools in Uppsala or in Oxford. This increase in the number of proposals in the course of the program showed the growing acceptance and interest in the field, but also that there was a special need for teaching theoretical chemistry, which at that time had not been introduced into the standard curriculum of chemistry studies in Germany.
And finally, the list of applicants in this program includes many names whose carreer in this field is now well known (Werner A. Bingel, Jürgen Brickmann, Gerd Diercksen, Hermann Hartmann, Georg Hohlneicher, Martin Klessinger, Edgar König, Hans Georg Kuball, Werner Kutzelnigg, Jörn Manz, Sigrid Peyerimhoff, Heinzwerner Preuß, Ernst Ruch, and Armin Schweig).
Theoretical Chemistry Symposia
Professor Hartmann, who had been among the initiators of the DFG special priority program, also organized the first "Symposium für Theoretische Chemie" in Frankfurt in 1965. His goal was to bring experimentalists together with theoreticians in this new field. About 60 scientists participated in this first event 48 coming from the German speaking countries: Germany, Austria, and Switzerland.
The main emphasis of the 1965 symposium 48 was on ligand-field theory, a topic close to Hartmann�s interests at that time, and on Kuhn�s electron gas model. The organization committee, consisting of Hartmann (Frankfurt), H. Labhart (Zürich), and 0.E. Polansky (Vienna) - to which at a later time W.A. Bingel (Göttingen), E. Ruch (Berlin), G. Wagniere (Zürich), and P. Schuster (Vienna) were added - suggested holding an annual symposium with the location rotating between the three countries. These meetings not only provided the opportunity to exchange ideas between experimentalists and theoreticians and to meet with colleagues in a similar field, but were primarily a platform for diploma or doctoral students to present their own results for the first time to a larger audience in the scientific community without language difficulties.
To some extent, these symposia reflect the state of the art in the field of theoretical quantum chemistry in Germany at a given time. The meetings continue. For many years, W.A. Bingel was the person who selected the next organizer, and this procedure worked quite well. Today, the symposium organizer is selected by the Arbeitsgemeinschaft Theoretische Chemie (AGTC), which was founded in 1992 to give this field a more official status in concert with the established professional organizations of chemistry (Gesellschaft Deutscher Chemiker, GDCh), physical chemistry (Deutsche Bunsengesellschaft für Physikalische Chemie, DBG), and physics (Deutsche Physikalische Gesellschaft, DPG). Initially, experimentalists and theoreticians had about equal weight among the participants, but gradually the theoreticians took the lead. Today the symposium is the annual meeting for German speaking theoretical chemists, even though an increasing number of talks and posters are presented in the English language. For many students, these symposia are still the first opportunity to present their results and to learn about the scientific work and atmosphere in other groups from personal contacts. These contacts on the student level are also very important for the exchange of computer programs or computer information. The location of these meetings varies in the series between Germany-Switzerland-Germany-Austria.
Scientific Developments
The period of diatomic SCF calculations using Slater functions, which were extensively pursued in the Laboratory of Molecular Structure and Spectra in Chicago, 9 passed by the German scientists. I think I was one of the few Germans who got a glimpse of this fascinating work during my stay at Chicago 49 and less so during my doctoral work on valence bond (VB) calculations of the hydrogen fluoride molecule. 50 Starting in 1966, a large number of polyatomic molecules were treated by the newly written SCF-MO-LC(LCGO) program of Preuß and Diercksen. 51 This program constructed MOs as a linear combination (LC) of another linear combination of Gaussian orbitals (LCGO). Preuß called this group of pure Gaussians with fixed linear coefficients "LCGO"; these could consist of atom-centered Gaussians or a group of functions representing molecular fragments. Numerous applications including molecules such as C6H6, C5H5 -, C3H6, C2H4, CH4, CH3 + and so on 52 were published side by side in the International Journal of Quantum Chemistry.
At about the same time, SCF calculations for a series of polyatomic molecules 53 such as AH2 (A = first-row atom) C2H6, B2H6, F20, CH2, C2H4, C2H6, and ozone 54were carried out in dependently at Princeton, employing the same type of Gaussian functions. In this approach, various Gaussian (lobe) functions were also grouped together in a linear combination with fixed coeffcients, referred to as "atomic group orbitals". Later on, the name "contracted Gaussian orbitals" for such groupings or LCGO became more popular. This was the early exciting time of polyatomic ab initio treatments. Relatively soon however, it became clear that SCF treatments have serious drawbacks if one is interested in relative stabilities, dissociation energies, or electronically excited states. Configuration interaction (CI) calculations, carried out at whatever computer was available in the United States or Germany, started on formate anion and cyclobutadiene, 55 and even systems as large as C10H8were treated by ab initio methods. 56 Such work was only possible by a combined use of computers in Germany and at various sites in the United States.
In 1962, the newly established journal Theoretica Chimica Acta (TCA; edited by H. Hartmann in Frankfurt) contributed also to the visibility of theoretical chemistry in the German scientific community. It preceded the International Journal of Quantum Chemistry (founded in 1967 by Per-Olov Löwdin) by 5 years. TCA welcomed manuscripts from the entire field of theoretical 4llpmistry, and special emphasis was placed on the application of quantum Theory and problems of chemical physics. According to Hartmann's philosophy, general and analytical work in the field of quantum chemistry was preferred, and computational work was considered if it concerned new methods and questions of special chemical interest. Articles could be published in English, German, and French, and even articles in the Latin language were allowed, presumably to point to the common background of European languages and the language of erudition for many centuries in Europe. The first volume 1962-1963 had 25 articles in English (from many European countries, the United States, and Canada), 19 in German, and 5 in the French language. All abstracts - at least for many years to come - appeared trilingually (English, German, French), translated into the corresponding two other languages by the editorial office. This journal showed very distinctly the growth of the field of theoretical chemistry within Europe; but it also made clear that there were still language barriers in international communication. In 1984, the sentence "Papers will preferably be published in English" was added to the stated editorial policy. Shortly before his death (1984), Hartmann turned the editor- ship of TCA over to an editorial team headed by Klaus Ruedenberg at the Iowa State University in the United States. After Ruedenberg's retirement 1997, the name of Theoretica Chimica Acta TCA was broadened to Theoretical Chemistry Accounts: Theory, Computation, and Modeling, still keeping its initials TCA, with the new editor Donald G. Truhlar, at the University of Minnesota in the United States.
Before concluding the decade 1960-1970, it should be mentioned that theoretical chemistry started to influence not only chemical research in Germany but slowly became an independent field for which professorships were created at universities. H. Preuß moved from the MPI in Munich to a chair of theoretical chemistry at the University of Stuttgart in 1969, while Diercksen remained at the MPI at Munchen. Ludwig Hofacker, coming from Northwestern University near Chicago, took the chair at the Technical University of Munich, E. Ruch was appointed professor of theoretical chemistry at the Freie Universitat of Berlin, and Karl Heinz Hansen became professor of theoretical chemistry at the University of Bonn.
COMPUTATIONAL CHEMISTRY 1970 - 1980
Theoretical chemistry, whose major part in the 1960s was quantum chemistry of molecular structure, was now ready to propagate into other areas of chemistry. Work started on the dynamics of chemical reactions, on spectroscopy, on database and expert systems in chemistry, and on synthesis planning. During the 1970s, about 15 chairs in theoretical chemistry at German universities became available in addition to five positions for associate professors. International conferences were organized by Germans and took place in Germany. Germans participated in the design of the European Centre for Atomic and Molecular Calculations (CECAM), which is described later. However, computer time was still a bottleneck since the demand for computer power was much greater than could be financed by the universities or the DFG.
Again, it should be stressed that it was the initiative of the potential scientific users that was the driving force to obtain a computer installation at their university; the proper choice of the director of the computer center and its advisory committee was of great importance. The Kommission für Rechenanlagen (KfR) of the DFG had given general recommendations to the government about the necessity of computational resources, but the negotiation with the various computer companies and the formal application for the computer installation had to be submitted from the universities with a very detailed justification for every item, generally based on the research requirements of the faculty. The KfR reviewed the application, oftentimes made visits to the site, and then gave final recommendation to the Science Council. Because an application had to include comparable offers from three different computer companies, the KfR recommendation (considering a variety of arguments) sometimes took precedence over the specification outlined in the application.
For users, there was always the problem of computer program compatibility between different machines. An IBM 7094 had a word length of 36 bit, a CDC 3300 generally 24 bit, the TR machines 48 bit, and the IBM 360 series had 4 bit. A large problem for quantum chemical calculations was the small main memory. Our CDC 3300 at Mainz had 5 modules at 16 K word memory, which were separated so that one array of floating point numbers (e.g., a matrix) had to fit in a single module; this meant that we could have only symmetric CI matrices up to dimension 178 in core storage. External storage on magnetic tape with 800 bits/inch was extremely slow.
The reason for my accepting a professorship from the University of Bonn (1972) (over that of Berlin and Bochum) was primarily the much better computer installation compared to the other places. With our atomic orbital (AO) integral program (floating point number crunching), the four-index transformation routine (integer arithmetic), SCF program (input/output oriented), and a special integral program testing double precision arithmetic, I compared the running time on the CDC 3300 (Mainz), Siemens S4004/55 (Berlin), TR440 (Bochum) and IBM 370/165 (Bonn). In all cases, the IBM at Bonn was ahead of the others. For number crunching, the relative times were 1.0:1.64:0.43:0.086, for integer arithmetic 1.0:1.15:0.37:0.08, for I/0 1.0:1.5:0.35:0.1, and for double-precision (DP) arithmetic 1.0:0.24:0.08:0.036. This txample also shows that, in spite of commercial benchmarks, computer performance could depend very much on the individual program requirements.
European Efforts
At the end of the 1960s, the idea arose to create a European Centre for Atomic and Molecular Calculations 61 (Centre Européen pour des Calculs Atomiques et Moléculaires). CECAM opened in Orsay, France, in October 1969 with IBM 360-50-75, CDC, and UNIVAC computers. The main aim of CECAM was not to offer computer time, and simply "cranking away" was not permitted. It was expected that the most original and creative uses of computers must be developed. The lag behind the United States in this field was clearly evident, and it is stated 61 "that the level in many laboratories could be raised by bringing together for short periods of time from these several laboratories scientists who are interested in the same or related problems, so that they could benefit from a mutual stimulation which would lead to a much more rapid development of ideas in the employment of computers". The general hope was expressed that this center would become a driving force for progress in atomic and molecular physics. Carl Moser (France) was the first director, and W.A. Bingel and W. Kutzelnigg from Germany were in the governing body.
Computer-Aided Synthesis
The first internationally available computer programs for planning organic syntheses 63 were primarily based on the retrieval and manipulations of filed data on known reactions (reaction library as databases).64 This approach led to programs such as LHASA, 65 SECS, 66 or SYNCHEM, 67 and Ugi had also his own version for peptide syntheses. 68 These programs are typical expert systems with a large database and a set of rules, and are based on a retrosynthetic approach from which one does not expect totally novel synthetic reactions. A completely different approach to the use of computers in chemistry came from the organic chemist Ivar Ugi at the Technical University of München and the mathematician J. Dugundji. 69
Ugi, Dugundji, and co-workers conceived a novel mathematical model of constitutional chemistry. 69 It is based on an algebraic model and logical connectivity. It represents reactants with B and R matrices resulting in E matrices for the products. The "chemical distance" between B and E is an important metric and represents something as the minimum number of valence electrons which must be shifted to convert reactants into products. In this approach, it is possible in principle to find entirely novel synthesis routes not based on prior experience stored in databases. The hard part is to cut the branches of the enormous tree of possible reactions. The approach was implemented in a series of computer programs such as CICLOPS, 70 EROS, and IGOR. A detailed discussion of this work is contained in a summarizing article, 64 which presents examples of true novel syntheses and simplifications of syntheses designed earlier by empirical approaches.
Progress in Quantum Chemical Methods
Even though computers were an essential tool in quantum chemical calculations, the main challenge was the further development of methods and concepts to describe even more facets of chemistry and with higher accuracy. Methods that account for electron correlation were extended to be able to describe energy surfaces more reliably. Several variants of the CEPA Ansatz (CIW41, CEPA-2) were developed as well as the method of self-consistent electron pairs (SCEP). 71 Formulations using canonical or localized orbitals (e.g., pair natural orbitals, 72 PNO, as a kind of optimized virtual orbitals) were put forth. These methods were extensively used for two decades, primarily in Germany, until coupled cluster formulations became more popular.73
The computation of electronically excited states and hence the interpretation of ultraviolet-visible (UV-vis) spectra saw much activity outside Germany in the postwar years by semiempirical methods such as the Platt primeter model, the PPP,19 and the complete neglect of differential overlap (CNDO) 74 approaches. Thus after more than a decade of dealing primarily with ground-state properties of molecular systems, the stage was now set to attack this problem by ab initio methods. The first international discussion meeting, under the auspices of the DFG, was held at Schlo1ß Reisensburg in 1974. The book of abstracts 75 contains many of the ideas that were extended technically to much higher proficiency at a later time. Multireference - configuration interaction (MR-Cl) was presented for excited states of a number of small diatomic and polyatomic molecules (by Robert J. Buenker and Sigrid D. Peyerimhoff and by Jerry L. Whitten), different ways of configuration selection discussed (by Isaiah Shavitt and by Buenker and Peyerimhoff), and the choice of orbitals for CI, that is, natural orbitals (Charles F. Bender) and MC-SCF orbitals (Fritz Grein) to improve CI convergence was treated. Ruedenberg presented advantages of the even-tempered orbital basis. Enrico Clementi showed that adjoined basis sets, used to evaluate less important integrals and matrix elements, could reduce the computation time for 450 primitive Gaussians from 4 h to 35 min without loss of accuracy in the results. The mixing of Rydberg states with valence states was discussed from experimental (Camille Sandorfy) and theoretical (by Robert S. Mulliken, by Helene Lefebvre-Brion, and by Eugen Schwarz) perspectives in great detail. The role of negative ions as interstellar molecules (Jurgen Barsuhn) and responsible for Feshbach resonances (Lefebvre-Brion) was discussed, and suggestions were given for how to compute nonadiabatic couplings in predissociation processes due to avoided crossing of states (Jean-Claude Lorquet). Studies using equation of motion (EOM) methods for excited states and data on photoionization cross sections based on a discrete orbital basis (Vincent McKoy) were shown. Even first results for transition metal compounds (Alain Veillard) were presented. This meeting was remembered by many of the participants for its scientific content, but also because of the beautiful site of this castle, which serves as the guest house of the University of Ulm.
In 1976, Paul von Ragué Schleyer moved from Princeton to the University of Erlangen-Nürnberg to accept a professorship in organic chemistry, after he had spent 1974—1975 at the Technical University of München as Senior U.S. Scientist Awardee of the Alexander von Humboldt Stiftung. Trained as an experimental organic chemist, he had become aware of the great potential of computational quantum chemistry for the study of new chemical compounds and reactions. Coming from the same background as other organic chemists, he spoke their language and - after a number of years 76 - was able to convince them of the practicability of this new theoretical tool. In particular, his work on organolithium compounds 77 and carbonium ions, carbanions, and reactive intermediates was essential in this respect. His work certainly had a great impact on the acceptance of computational chemistry within the community of German (experimental) organic chemists.
IBM in Germany organized a symposium on "Computational Methods in Chemistry" 78 at Bad Neuenahr in 1979 with the preface: "According to Graham Richards 79 the 'Third Age of Quantum Chemistry' has started, where the results of quantum chemical calculation can guide the experimentalists in their search for the unknown". One of the examples chosen to underline this statement was the acetylene molecule. In 1970 Kammer 80 had made qualitatively correct predictions for the first cis (3B2, 3A2) and trans (3Bu, 3Au) bent electronically excited states of this molecule. In 1975 Demoulin 81 had calculated the corresponding potential energy curves, and in 1978 Wetmore and SSchaefer 82 reliably determined the geometry of C2H2 in these states. With the help of this guidance, Wendt, Hunziker, and Hippler 83 took up the search and succeeded in finding the theoretically predicted near infrared (IR) absorption for the cis conformer. The measured spectrum confirmed all theoretical predictions quantitatively.
This symposium showed very convincingly how theoretical methods had taken up a large variety of different problems and had influenced experimental studies. At the symposium, W. Meyer with co-workers P. Botschwina, P. Rosmus, and H.-J. Werner reported on their work on molecular properties. This group discussed results on spectroscopic data (Re, omegae, omegaekappae, alphae ), ionization energies, electron and proton affinities, dipole moment functions, and static dipole polarizabilities, and even showed results on polarizability anisotropies. In all caIculations, they included electron correlation (PNO-CI or PNO- CEPA) and showed the importance of going beyond simple Hartree-Fock calculations. W. von Niessen, L. S. Cederbaum, W. Domcke, and J. Schirmer showed how the Greens function approach, 84,85 which computes energy differences directly, can be used to analyze vibrational structure and vibronic coupling effects in photoelectron spectra (PES). They also discussed complications in inner-shell ionization spectra due to the breakdown of the one-particle picture. Inner-shell phenomena were also discussed by MR-Cl methods (Buenker and Peyerimhoff), and it was shown that such methods can reliably predict details of molecular spectra in small polyatomic molecules including vibrational features and intensities. The use of computer chemistry for the study of organic reactions (in particular the Wolff rearrangement which involves isomerization of alpha-carbonyl carbenes into ketenes) presented by the IBM crew was an excellent example of how quantum chemistry had joined experimental organic chemistry to study chemical reactions. First calculations on silicon clusters prepared the way to investigate problems in surface chemistry. 86 One section of this symposium was devoted to the analysis of molecular spectra (NMR, IR) and the problem of data storage and man-machine communication, and another section was held on computer-aided synthesis, as discussed before. This symposium not only treated quantum chemical methods, but demonstrated further uses of computers in chemistry; its title "Computational Methods in Chemistry" was thus fully justified.
Toward the end of the 1970s, the challenge of Ch. Schlier to describe atom-molecular collisions by quantum chemical methods was met by two young Germans, Jörn Manz and Joachim Römelt for a three-body A + BC reaction. Traditionally, chemical reactions had been treated using the coordinates leading from the reactants to the product, 87 according to chemist�s intuition. In accurate quantum calculations, such a scheme excludes the description of branching ratios, dissociative processes, or heavy-light-heavy reactions associated with small skewing angles. The polar Delves or hyperspherical coordinates, on the other hand, allow the treatment of all such processes (elastic, inelastic, reactive, and dissociative) for all mass combinations. In 1980, Hauke, Manz and Römelt, using such coordinates, published their theory and a first numerical example for a quantum mechanically exact treatment 88of a collinear reaction, which was followed by applications to H + HI, H + H2, and dissociative collinear reactions. 89 When Römelt saw his third paper in print, he realized that A. Kuppermann and co-workers had thought very much along the same lines. 90
Finally, the ground was almost ready for the ab initio calculation of NMR chemical shifts. Kutzelnigg 94 designed the IGLO (individual gauge for localized orbitals) method, and Schindler 95 presented the first systematic application of this method to compute 13C chemical shifts of carbocations. The computation of NMR chemical shifts 96 is an ideal link between theory and experiment because calculated shifts can be used in combination with the NMR measurements to differentiate between various structural possibilities of the species under investigation. Hence, IGLO calculations are an ideal tool to give fingerprints to identify transient species with unusual structures.
BEYOND 1980
The field of computational chemistry found itself in good times by the 1980s, and many young students were fascinated by the combination of computer usage and chemical research. At the 1981 Theoretical Chemistry Symposium, about 160 people participated. Henry Fritz Schaefer III talked about the third age of quantum chemistry. He stated that the Americans had been proud to have the center of gravity of quantum chemical or computational research after World War II. He had to admit that this center had moved - seen from a geographical point of view - at least toward the middle of the Atlantic Ocean, and that German scientists had a heavy weight in this change.
International cooperation had become the rule in universities and research institutions. Computers became cheaper so that it became possible to purchase "minicomputers" such as VAX 11/780 (Digital Equipment Corporation), Perkin-Elmer 8/32, or Convex C220 for dedicated purposes. For a number of theoretical chemistry groups, this helped them to become independent of the long queue of users at their university central computer. In addition, access over a network to machines at a remote site became realistic, even if it was only via a 1200-baud special telephone line. For these reasons the development of computational chemistry seems to have become very similar in various countries. Applications rather than method development became dominant and many inorganic and organic chemists as well as scientists in molecular physics and pharmaceutical research were no longer hesitant to use the new computational methods. Computer programs for molecular modeling based on quantum chemistry, on classical mechanics, or on empirical force fields became available in international exchange. Monte Carlo simulations became feasable on vector computers and parallel machines, and access to large databases was made possible. The quantum chemistry tools were extended to include relativistic effects, 97 which play an important role in transition metal and heavy-element chemistry. Such efforts were later on supported by a program from the European Science Foundation 98 which gave financial support to a number of European groups working in this field. The possibility to include relativistic effects, either directly or by effective potentials 93 made quantum chemical calculations also interesting for many inorganic chemists and organometallic chemists. Today, theoretical and computational chemists participate in many of the collaborative research centers (Sonderforschungsbereich) at German universities, which are created to support interdisciplinary work in areas expected to have great impact for our future.
At this point, a look at computational chemistry in German industry is appropriate. An evaluation is somewhat difficult, however, because generally only a few of the industrial computational chemists attend the annual chemistry conferences in Germany, and in addition, these chemists are generally reluctant to talk about details of their work. The main topic in the era 1970-1980 was presumably computer-aided synthesis. It was a joint endeavor of seven companies in Germany and Switzerland (BASF, Bayer, Ciba—Geigy, Hoffmann-LaRoche, Merck, Hoechst, and Sandoz). Pattern recognition was also an important tool to find structurally related compounds that show similar or better molecular properties. Computer programs for the automatic recognition of the maximal common substructures among drug molecules, or computerized systems with graphical and topological information for handling and analysis of large databases were topics at special conferences. 99Quantum chemistry played a minor role in these investigations; in industry it was used at most on the semiempirical level in this era.
In the middle of the 1980s, molecular modeling, molecular mechanics (MM), molecular dynamics (MD), and some ab initio quantum chemistry became important tools in industry to study quantitative structure-activity relationships (QSAR). The necessary computer programs were purchased from academic or commercial institutions. A number of young German theoretical chemists accepted job offers from chemical industry in the 1980s in the hope to build up a computational chemistry nucleus within the companies, doing applied but also some basic research. At a special symposium on "Scientific Computing and Modeling in Chemical Industry" at the annual meeting 1994 of the Physical Chemistry Society (Bunsentagung), young computational chemists from seven chemical and pharmaceutical companies in Germany presented already 13 talks. The main topics were QSAR, enzymes, polymers, and databases, and the studies were clearly dominated by applications. The restructuring of chemical companies that took place in the second half of the 1990s under new managements left little room for the development of computational chemistry methods in industry. Invitations for consultants were seldom. The future will show whether the cooperation between German universities and industry in the area of computational chemistry will strengthen.
Fast expansion of the German university system in the 1970s had brought a considerable number of new positions in theoretical and computational chemistry to universities. However, this positive side was turned around in the following 20 years. Financial restrictions lead to a decrease in budgets, and salary lines of postdoctoral positions at universities were often simply cut off. Since many of the professors, who came into office toward the end of the 1970s, were quite young, there was essentially no university post open for young people until the mid 1990s when retirement of this first generation of professors started. In other words, the generation of young scientists who were all well trained in the field could not really use their talents for research at German universities or research centers. Many of those people went into (computer-oriented) industry or took their talents to other countries.
Looking back, I find it truly amazing with what intensity science in Germany recuperated after the total vacuum caused by the Nazi regime and World War II. If I ask myself what were the main influences on the positive development of computational chemistry in Germany, I see it in our "bottom-up" principle of support. Contrary to some other countries, in which the "top-down" principle is favored, that is, in which research topics that are thought to deserve funding are earmarked from a centralized body, West German support of science wanted to be far away from dictating any route - especially after considering Germany�s recent history. Hence, a small number of young energetic people, in competition with each other, fascinated by new tools and methods, were the hard core to develop the field. The first generation was generally trained in physics or mathematics; the second generation originated mostly from chemistry. The foresight of a few senior scientists that digital computers would become an extremely useful tool and should be made available to researchers (recommended by a committee of the DFG) and that it was worthwhile to bring the young German researchers together within a special priority program gave important support to the field. The advance of quantum chemistry and computational chemistry and its introduction into the education of chemistry students occurred without the support of large government contracts from the ministry of education or ministry of research and technology and largely without the support of dedicated research institutions such as the Max Planck Institutes or industry.
It is gratifying to observe that computational chemistry in Germany is again strongly visible internationally. This remarkable development should be kept in mind in the present tendency to favor the support of large scientific centers over modest proposals from young individuals.
ACKNOWLEDGMENTS
I would like to gratefully acknowledge the help I received from various colleagues. In particular, I want to thank W. Kutzelnigg for information on the Theoretical Chemistry Symposia and for various articles in which he looks back on the history of quantum chemistry. I want to thank H.-W. Preuß for annotated reprints of his early work and H. Kuhn for information on his work with the analog computer. I am also grateful to Frank-Dieter Kuchta who helped to search for essential data in DFG reports.
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Rechnende Maschinen, Technikgeschichte in Einzeldarstellungen.
VDI-Verlag, Düsseldorf, Band 41, 1985.
14. H. Kuhn,
Fascination in Modeling Motifs.
in: Selected Topics in the History of Biochemistry: Personal Recollections VI
(Comprehensive Biochemistry, G. Semenza and R. Jaenicke, Eds.,
Elsevier Science, Amsterdam, The Netherlands, 2000, Vol. 41), pp. 301-362.
15. H. Kuhn,
Analogieversuche mit schwingenden Membranen zur Ermittlung von Elektronenzuständen in
Farbstoffmolekülen mit verzweigtem Elektronengas.
Z. Elektrochem., 55, 220 (1951).
16. H. Kuhn,
Analogiebetrachtungen und Analogrechner zur quantenchemischen
Behandlung der Lichtabsorption der Farbstoffe.
Chimica, 15, 53 (1961).
17. F.P. Schäfer,
"Analogrechner und Registrierautomat zur Ermittlung der
stationären Wellenfunktionen und Energieniveaus eines Teilchens in einem zweidimensionalen Potentialfeld".
Doctoral Thesis, Marburg, Germany, 1960.
18. H. Kuhn,
Neuere Untersuchungen uber das Elektronengasmodell organischer Farbstoffe.
Angew. Chem., 71, 93 (1959).
19a. R. Pariser and R. Parr,
A Semi-Empirical Theory of the Electronic Spectra
and Electronic Structure of Complex Unsaturated Molecules. I.
J. Chem. Phys., 21, 466 (1953).
See also,
19b. R. Pariser and R. Parr,
A Semi-Empirical Theory of the Electronic Spectra and
Electronic Structure of Complex Unsaturated Molecules. II.
J. Chem. Phys., 21, 767 (1953).
19c. J.A. Pople,
Electron Interactions in Unsaturated Hydrocarbons.
Trans. Faraday Soc., 49, 1375 (1953).
19d. J.A. Pople,
Application of Self-Consistent Molecular Orbital Methods to pi Electrons.
J. Phys. Chem., 61, 6 (1957).
20. H. Hellmann,
Einführung in die Quantenchemie.
Franz Deuticke, Leipzig und Wien, 1937.
21a. H.-J. Kopineck,
Austausch- und andere Zweizentrenintegrale mit 2s- und 2p-Funktionen.
Z. Naturforsch. 6a, 420 (1950).
21b. H.-J. Kopineck,
Zweizentrenintegrale mit 2s- und 2p-Funktionen. II. Ionenintegrale.
Z. Naturforsch., 6a, 177 (1951).
22. M. Kotani, A. Ameniya, and T. Simose,
Proc. Physico-Math. Soc. Jpn., 20, Extra Nr. 1(1938); 22, Extra Nr. 1 (1940).
23a. P.J. Wheatley and J.W. Linnett,
Molecular Force Fields. Part XI. A Wave Mechanical Treatment of the Change with Distortion
of the Interaction Energy of Carbon 2ppi Orbitals.
Trans. Faraday Soc., 45, 897(1949).
23b. R.G. Parr and B.L. Crawford,
On Certain Integrals Useful in Molecular Orbital Calculations.
J. Chem. Phys., 16, 1049 (1948).
23c. J.0. Hirschfelder and J.W. Linnett,
The Energy of Interaction between Two Hydrogen Atoms.
J. Chem. Phys., 18, 130 (1950).
24a. H.-J. Kopineck,
Quantentheorie des N2-Moleküls. I. Problemstellung und Grundlagen
der durchzuführenden Untersuchungen. Das N2-Molekül als Sechselektronenproblem.
Z. Naturforsch., 7a, 22 (1952).
24b. H.-J. Kopineck,
Quantentheorie des N2-Moleküls. II. Behandlung des N2-Moleküls als Zehnelektronenproblem.
Z. Naturforsch., 7a, 314 (1952).
25 H.-J. Kopineck,
Zweizentrenintegrale. III. Integrale mit 2p- und wasserstoffähnlichen 2s-Funktionen.
Z. Naturforsch., 7a, 785 (1952).
26. C.C.J. Roothaan,
A Study of Two-Center Integrals Useful in Calculations on Molecular Structure. I.
J. Chem. Phys., 19, 1445 (1951).
27. K. Ruedenberg,
A Study of Two-Center Integrals Useful in Calculations on Molecular Structure. II. The Two-Center Exchange Integrals.
J. Chem. Phys., 19, 1459 (1951).
28. C.C.J. Roothaan,
New Developments in Molecular Orbital Theory.
Rev. Mod. Phys., 23, 69 (1951).
29. H. Preuß,
Berechnung des H2-Molekül-Grundzustandes.
Z. Phys., 130, 239 (1951).
29. H. Preuß,
Abschätzung für Zweizentrenintegrale.
Z. Naturforsch., 8a, 270 (1953).
30. H. Preuß,
Integraltafeln zur Quantenchemie.
Springer-Verlag Berlin, Göttingen, Heidelberg,
Vol. I, 1956; Vol. II, 1957; Vol. III, 1961; Vol. IV, 1960.
31. See, for example,
B. Kockel,
Zustandsfunktionen für die Atome Li bis Ne.
Z. Naturforsch., 16a, 1021 (1961).
32a. M. Kotani, A. Amemiya, E. Ishiguro, and T. Kimura,
Tables for Molecular Integrals.
Maruzen, Tokyo, 1955.
See also:
32b. E. Ishiguro, S. Yuasa, M. Sakamoto, and T. Arai, Nat. Sci. Rep., 5, 33 (1954).
33. S.F. Boys,
Electronic Wave Functions. I. A General Method of Calculation for the Stationary States of Any Molecular System.
Proc. Roy. Soc. London, A 200, 542 (1950).
34. H. Preuß,
Bemerkungen zum Self-consistent-field-Verfahren und zur Methode der Konfigurationswechselwirkung in der Quantenchemie.
Z. Naturforsch., 11a, 823 (1956).
35. J.L. Whitten,
Gaussian Lobe Function Expansions of Hartree-Fock Solutions for the First-Row Atoms and Ethylene.
J. Chem. Phys., 44, 359 (1966).
36.a H. Preuß,
Untersuchungen zum kombinienten Näherungsverfahren.
Z. Naturforsch., 10a, 365 (1955).
36.b H. Preuß,
Die Güte von Näherungslösungen der Schrödingergleichung
und die Genauigkeit der Erwartungswerte und Übergangselemente.
Fortschritte Phys., 10, 271 (1962).
36.c H. Preuß,
Die Bestimmung der Energiehyperflächen mehratomiger Systeme nach einer Interpolationsmethode
mit Hilfe der Vorstellung der Atomassoziationen. Dreizentrensysteme.
Theor. Chim. Acta, 6, 413 (1966).
37. H. Hartmann,
Theorie der chemischen Bindung auf quantentheoretischer Grundlage.
Springer-Verlag, Berlin, 1954.
38. B. Kockel,
Darstellungstheoretische Behandlung einfacher wellenmechanischer Probleme.
Teubner Verlagsgesellschaft, Leipzig, 1955.
39. P. Gombas,
Theorie und Losungsmethoden des Mehrteilchenproblems der Wellenmechanik.
Verlag Binkhäuser, Basel, Switzerland, 1950.
40. Deutsches Rechenzentrum,
Allgemeine Information.
Darmstadt, November 1966.
41. Jahresbericht 1966 des Deutschen Rechenzentrums, Darmstadt, 1967.
42. H. Preuß,
Die gegenwärtige Situation der Quantenchemie.
Naturwissenschaften, 11, 21 (1960).
43. W. Kutzelnigg,
Theoretische Chemie in Deutschland.
Nachr. Chem. Techn., 13, 351 (1965).
44. Laboratory of Molecular Structure and Spectra,
Technical Report,
Department of Physics, University of Chicago, Chicago, IL, 1961.
45. Reviews Modern Physics, 32, No. 2, 169-476 (1960).
(S. A. Goudsmit and E. U. London, Eds.
with an introduction by R. G. Parr.
The Conference was held at the University of Colorado, June 21-27, 1959.)
46. DFG - Jahresberichte 1966-1970.
(Annual Reports of the German Science Foundation, 1966-1970,
Kennedyallee 40, D-53 170 Bonn, Germany).
47. There were three more in chemistry:
analytical chemistry, crystal structure research, and physics and chemistry of interfaces.
48. W. Kutzelnigg, private communication and a preprint
"30 Jahre Symposium Theoretische Chemie",
presented at the 31st Theoretical Chemistry Symposium, Loccum, Germany, 1995.
49. S.D. Peyerimhoff,
Hartree-Fock Roothaan Wavefunctions, Potential Curves and Charge-Density Contours for the HeH- (X1Su+) and NeH+ (X1Su+) Molecule Ions.
J. Chem. Phys., 43, 998 (1965).
50. S.D. Peyerimhoff,
Berechnungen am HF-Molekül.
Z. Naturforsch., 18a, 1197 (1963).
51a. H. Preuß,
Das SCF-LCGO-MO-Verfahren.
Z. Naturforsch., 19a, 1335 (1964).
51b. G. Diercksen and H. Preuß,
Erste Mitteilung über Absolutrechnungen nach der neuen SCF-MO-LC(LCGO)-Methode
am Benzol und Cyclopentadienylanion.
Z. Naturforsch., 21a, 863 (1966).
52a. H. Preuß and G. Diercksen,
Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF-MO-LC(LCGO)-Methode. I. Das Cyclopentadienylanion (C5H5 -).
Int. J. Quantum Chem., 1, 349 (1967).
52b. H. Preuß and G. Diercksen,
II. Das Benzol (C6H6).
Int. J. Quantum Chem., 1, 357 (1967).
52c. H. Preuß and G. Diercksen,
III. Das Cyclopropan (C3H6).
Int. J. Quantum Chem., 1, 361 (1967).
52d. H. Preuß and G. Diercksen,
IV. Das Athylen (C2H4, and following articles.
Int. J. Quantum Chem., 1, 369 (1967).
53a. S.D. Peyerimhoff, R.J. Buenker, and L.C. Allen,
Geometry and Molecules. I. Wavefunctions for Some Six- and Eight-Electron Polyhydrides.
J. Chem. Phys., 45, 734 (1966).
53b. R. J. Buenker, S.D. Peyerimhoff, L.C. Allen, and J.L. Whitten,
Geometry of Molecules. II. Diborane and Ethane.
J. Chem. Phys., 45, 2835 (1966).
53c. R.J. Buenker and S.D. Peyerimhoff,
Geometry of Molecules. III. F20, Li20, FOH, LiOH.
J. Chem. Phys., 45, 3682 (1966).
54a. R.J. Buenker, S.D. Peyerimhoff, and J.L. Whitten,
Theoretical Analysis of the Effects of Hydrogenation in Hydrocarbons:
Accurate SCF MO Wavefunctions for C2H2, C2H4, and C2H6.
J. Chem. Phys., 46, 2029 (1967).
54b. S.D. Peyerimhoff and R.J. Buenker,
Geometry of Ozone and Azide Ion in Ground and Certain Excited States.
J. Chem. Phys., 47, 1953 (1967).
55a. S.D. Peyerimhoff,
Relationships Between AB2 and HnAB2 Molecular Spectra and Geometry:
Accurate SCF MO and CI Calculations for Various States of HCOO -.
J. Chem. Phys., 47, 349 (1967).
55b. R.J. Buenker and S.D. Peyerimhoff,
Ab Initio Study on the Stability and Geometry of Cyclobutadiene.
J. Chem. Phys., 48, 354 (1968).
56. R.J. Buenker and S.D. Peyerimhoff,
Ab Initio SCF Calculations for Azulene and Naphthalene.
Chem. Phys. Lett., 3, 37 (1969).
57a. R. Ahlrichs and W. Kutzelnigg,
Direct Calculation of Approximate Natural Orbitals and Natural
Expansion Coefficients of Atomic and Molecular Electronic Wavefunctions.
II. Decoupling of the Pair Equations and Calculation of the Pair Correlation
Energies for the Be and LiH Ground States.
J. Chem. Phys., 48, 1819 (1968).
57b. R. Ahlrichs and W. Kutzelnigg,
Ab initio Calculations on Small Hydrides Including Electron Correlation.
I. The BeH2 Molecule in Its Ground State.
Theor. Chim. Acta, 10, 377 (1968).
58a. W. Meyer,
Ionization Energies of Water from PNO-CI Calculations.
Int. J. Quantum Chem., Symp. No. 5, 5, 341 (1971).
58a. W. Meyer,
PNO-CI Studies of Electron Correlation Effects. I. Configuration Expansion by Means of
the Nonorthogonal Orbitals, and Application to the Ground State and Ionized States of Methane.
J. Chem. Phys., 58, 1017 (1973).
59. R. Ahlrichs, H. Lischka, V. Staemmler, and W. Kutzelnigg,
PNO-CI (Pair Natural Orbital Configuration Interaction) and CEPA-PNO
(Coupled Electron Pair Approximation with Pair Natural Orbitals)
Calculations of Molecular Systems. I. Outline of the Method for Closed-Shell States.
J. Chem. Phys., 62, 1225 (1975).
60. W. Kutzelnigg and P. v. Herigonte,
Electron Correlation at the Dawn of the 21st Century.
Adv. Quantum Chem., 36, 185 (2000).
61. Centre de Calcul du C.N.R.S., Facultê des Sciences, Orsay, France.
A description of the centre to open October 1969; a booklet of 13 pages.
62.
CECAM Annual Report.
C. Moser Ed.,
CECAM, Batiment 506, 91-Campus Orsay, France, 1973.
63a. E.J. Corey and W.T. Wipke,
Computer-Assisted Design of Complex Organic Syntheses.
Science, 166, 178 (1969).
63b. E.J. Corey, W.T. Wipke, R.D. Cramer, and W.J. Howe,
Computer-Assisted Synthetic Analysis.
Facile Man-Machine Communication of Chemical Structure by Interactive Computer Graphics.
J. Am. Chem. Soc., 94, 421 (1972).
63c. E.J. Corey, W.T. Wipke, R.D. Cramer, and H.J. Howe,
Techniques for Perception by a Computer of Synthetically Significant Structural Features in Complex Molecules.
J. Am. Chem. Soc., 94, 431 (1972).
64. I. Ugi, J. Bauer, K. Bley, A. Dengler, A. Dietz,
E. Fontain, B. Gruber, R. Herges, M. Knauer, K. Reitsam, and N. Stein,
Die Computerunterstützte Lösung Chemischer Probleme -
Eine neue Disziplin der Chemie.
Angew. Chem., 105, 210 (1993).
65. E.J. Corey and X.-M. Cheng,
The Logic of Chemical Synthesis.
Wiley, New York, 1989.
66. W.T. Wipke and D. Rogers,
Artificial Intelligence in Organic Synthesis. SST: Starting Material Selection Strategies.
An Application of Superstructure Search.
J. Chem. Inf. Comput. Sci., 24, 71 (1984).
67a. H. Gelernter, N.S. Sridharan, A.J. Hart, S.-C. Yen, F.W. Fowler, and H.-J. Shue,
The Discovery of Organic Synthetic Routes by Computer.
Top. Curr. Chem., 41, 113 (1973).
67b. H. Gelernter, J.R. Rose, and C. Chen.
Building and Refining a Knowledge Base for Synthetic Organic Chemistry
via the Methodology of Inductive and Deductive Machine Learning.
J. Chem. Inf. Comput. Sci., 30, 492 (1990).
68. I. Ugi,
A Novel Synthetic Approach to Peptides by Computer Planned Stereoselective Four Component Condensations of alpha-Ferrocenyl Alkylamine and Related Reactions.
Record of Chemical Progress, 30, 289 (1969).
69a. J. Dugundji and I. Ugi,
An Algebraic Model of Constitutional Chemistry as a Basis for Chemical Computer Programs.
Top. Curr. Chem., 39, 19 (1973).
69a. I. Ugi,
The Potential of Four Component Condensations for Peptide Syntheses -
A Study in Isonitrile and Ferrocene Chemistry as well as Stereochemistry and Logics of Syntheses.
Intra-Sci. Chem. Rep., 5, 229 (1971).
70. J. Blair, J. Gasteiger, C. Gillespie, P.D. Gillespie, and I. Ugi,
CICLOPS - A Computer Program for the Design of Synthesis on the Basis of a Mathematical Model.
in: Computer Representations and Manipulation of Chemical Information,
W. T. Wipke, S. R. Heller, R. J. Feldmann, and E. Hyde, Eds.,
Wiley, New York, 1974, pp. 129-145.
71. W. Meyer,
Theory of Self-Consistent Electron Pairs.
An Iterative Method or Correlated Many-Electron Wavefunctions.
J. Chem. Phys., 64, 2901 (1976).
72. W. Meyer,
Configuration Expansion by Means of Pseudonatural Orbitals.
Modern Theoretical Chemistry, Vol. 3, H. F. Schaefer III, Ed.,
Plenum Press, New York, 1977.
73. T.D. Crawford and H.F. Schaefer III,
An Introduction to Coupled Cluster Theory for Computational Chemists.
in: Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds.,
Wiley-VCH, New York, 2000, Vol. 14, pp. 33-136.
74. For details, see:
J.A. Pople and D.L. Beveridge,
Approximate Molecular Orbital Theory.
McGraw-Hill, New York, 1970.
75. Abstracts,
Symposium on Calculation of Electronically Excited States of Molecules by Ab Initio Methods,
Schloß Reisensburg, Ulm, Germany, July 2-5, 1974.
76a. K. Krogh-Jespersen, D. Cremer, D. Poppinger, J. A. Pople, P. v. R. Schleyer, and J. Chandrasekhar,
Molecular Orbital Theory of the Electronic Structure of Molecules.
39. Highly Unusual Structures of Electron-DeficientCarbon Compounds.
Reversal of van�t Hoff Stereochemistry in BBC Ring Systems.
J. Am. Chem. Soc., 101, 4843 (1979).
76b. K. Raghavachari, R.A. Whiteside, J.A. Pople, and P. v. R. Schleyer,
Molecular Orbital Theory of the Electronic Structure of Organic Molecules.
40. Structures and Energies of C1-C3 Carbocations, Including Effects of Electron Correlation.
J. Am. Chem. Soc., 103, 5649 (1981).
77a. E.D. Jemmis, J. Chandrasekhar, and P. v. R. Schleyer,
The Unusual Structures, Energies, and Bonding of Lithium-Substituted
Allenes, Propynes, and Cyclopropenes.
J. Am. Chem. Soc., 101, 2848 (1979).
77b. A.J. Kos, I. Clark, and P. v. R. Schleyer,
Die ab initio Berechnung der Struktur von 1,3-Dilithioaceton.
Angew. Chem., 96, 622, (1984).
78. J. Bargon, Ed.,
Computational Methods in Chemistry.
The IBM Research Symposia Series.
Plenum Press, New York, 1980.
79. G. Richards,
Third Age of Quantum Chemistry.
Nature (London), 278, 507 (1979).
80. W.E. Kammer,
Ab Initio SCF and CI Calculations of Linear and Bent Acetylene.
Chem. Phys. Lett., 6, 529 (1970).
81. D. Demoulin,
The Shapes of Some Excited States of Acetylene.
J. Chem. Phys., 11, 329 (1975).
82. R.W. Wetmore and H.F. Schaefer III,
Triplet Electronic States of Acetylene:
Cis and Trans Structures and Energetics.
J. Chem. Phys., 69, 1648 (1978).
83. H.R. Wendt, H. Hippler, and H.E. Hunziker,
Triplet Acetylene: Near Infrared Electronic Absorption
Spectrum of the Cis Isomer and Formation from Methylene.
J. Chem. Phys., 70, 4044 (1979).
84a. L.S. Cederbaum,
Direct Calculation of Ionization Potentials of Closed-Shell Atoms and Molecules.
Theor. Chim. Acta, 31, 239 (1973).
8b. L.S. Cederbaum
One-Body Green�s Function for Atoms and Molecules: Theory and Application.
J. Phys. B, 8, 290 (1975).
85. L.S. Cederbaum and W. Domcke,
Outer-Valence Greens� Functions (OVGF).
Adv. Chem. Phys., 36, 205 (1977).
86. P.S. Bagus, B. Liu, A.D. McLean, and M. Yoshimine,
The Application of Ab Initio Quantum Chemistry to Problems of Current Interest Raised by Experimentalists.
in: Computational Methods in Chemistry, J. Bargon, Ed.,
Plenum Press, New York, 1980, pp. 203-237.
87a. G.L. Hofacker,
Quantentheorie chemischer Reaktionen.
Z. Naturforsch. A18, 607 (1963).
87b. R.A. Marcus,
On the Analytical Mechanics of Chemical Reactions.
Quantum Mechanics of Linear Collisions.
J. Chem. Phys., 45, 4493 (1966).
87c. R.A. Marcus,
On the Analytical Mechanics of Chemical Reactions.
Classical Mechanics of Linear Collisions.
J. Chem. Phys., 45, 4500 (1966).
88. G. Hauke, J. Manz, and J. Römelt,
Collinear Triatomic Reactions Described by Polar Delves� Coordinates.
J. Chem. Phys., 78, 5040 (1980).
89a. J. Römelt,
The Collinear H+H2 Reaction Evaluated by S-Matrix Propagation along Delves� Radial Coordinate.
Chem. Phys. Lett., 74, 263 (1980).
89b. J. Manz and J. Römelt,
Dissociative Collinear Reactions Evaluated by S-Matrix Propagation along Delves� Radial Coordinate.
Chem. Phys. Lett., 77, 172 (1981).
89c. J. Manz and J. Römelt,
On the Collinear I + HI and I + MuI Reactions.
(Here Mu represents a muonium isotopic variant.)
Chem. Phys. Lett. 81, 179 (1981).
90. A. Kuppermann, J.A. Kaye, and J.P. Dwyer,
Hyperspherical Coordinates in Quantum Mechanical Collinear Reactive Scattering.
Chem. Phys. Lett., 74, 257 (1980).
91. J. Flad, H. Stoll, and H. Preuß,
Calculation of Equilibrium Geometries and Ionization Energies of Sodium Clusters Up to Na8.
J. Chem. Phys., 71, 3042 (1979).
92. H.-O. Beckmann, J. Koutecký and V. Bonacić-Koutecký,
Electronic and Geometric Structure of Li4 and Na4 Clusters.
J. Chem. Phys., 73, 5182 (1980).
93a. H. Stoll, L. v. Szentpály, P. Fuentealba, J. Flad,
M. Dolg, F.-X. Fraschio, P. Schwerdtfeger, G. Igel, and H. Preuß,
Pseudopotential Calculations Including Core-Valence Correlation:
Alkali and Noble-Metal Compounds.
Int.J. Quantum Chem., 26, 725 (1984).
93b. M. Dolg, U. Wedig, H. Stoll, and H. Preuß,
Energy-Adjusted Ab Initio Pseudopotentials for the First Row Transition Elements.
J. Chem. Phys., 86, 866 (1987).
93c. M. Dolg, H. Stoll, A. Savin, and H. Preuß,
Energy-Adjusted Pseudopotentials for the Rare Earth Elements.
Theor. Chim. Acta, 75, 173 (1989).
94. W. Kutzelnigg,
Theories of Magnetic Susceptibilities and NMR Chemical Shifts in
Terms of Localized Quantities.
Isr. J. Chem., 19, 193 (1980).
95a. M. Schindler and W. Kutzelnigg,
Part II.Applications to Some Simple Molecules.
J. Chem. Phys., 76,1919(1982).
95b. M. Schindler,
Magnetic Properties in Terms of Localized Quantities. 5. Carbocations.
J. Am. Chem. Soc., 109, 1020 (1987).
96. See, e.g.,
D.B. Chesnut,
The Ab Initio Computation of Nuclear Magnetic Resonance Chemical Shielding.
in: Reviews in Computational Chemistry.
K. B. Lipkowitz and D. B. Boyd, Eds.,
VCH Publishers, New York, 1996, Vol. 8, pp. 245-297.
97. B.A. Heß,
Relativistic Electronic Structure Calculations
Employing a Two-Component No-Pair Formalism with External Field Projection Operators.
Phys. Rev., A 33, 3742 (1986).
98. Program of the European Science Foundation,
"Relativistic Effects in Heavy-Element Chemistry and Physics", 1992-1998.
See : http://www.chemie.uni-erlangen.de/hess/html/esf/nl.html
{this website:link ok 7-2003}
99. Abstracts of Papers,
VIIth International Conference on Computers in Chemical Research and Education.
Garmisch-Partenkirchen, Germany, June 10-14, 1985.