Early ... Intro Picture

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Per-Olov Löwdin

Lwdin in 1999           Born 1916 in Uppsala, Sweden. Ph.D. in Physics 1948. From 1960-1983 professor at the University of Uppsala, in parallel professor at Gainesville, Florida until 1993.

Lowdin was a member of the Swedish Nobel Committee in Physics for many years. He was the founder of the International Journal of Quantum Chemistry and of the series Advances in Quantum Chemistry.

He started the very famous Sommer Schools of Quantum Chemistry at Uppsala around 1958.

In 1955 he came out with what is now known as Löwdin Orthogonalisation ( 1 ).

In 1998 he obtained a honorary doctor's degree at the University of Constance, one of many others ( 2 ). Löwdin died in 2000.

Please note : The following download zip-file 'Lowdin starts a lecture' is a testfile only. It covers the start of a lecture given by Löwdin on the occasion of a Dr. h.c. given to him by the University of Konstanz (Germany) on July 3, 1998. Length 30 sec., 5 MB in AVI format, it runs directly on Win 9x, ME,NT4. The Codec used is Indeo 5.04 or better, its download(2MB) may be obtained free of charge from Ligos, USA. (As stated elsewhere the shortness is due to my presently limited web site.

Video clip Löwdin talks briefly about the orthonormalization procedure (40 sec) MPEG4; 5 MB Just in case, for Win9x,ME,NT4(?): Get the free download codec DivX4FullInstaller.exe V.4.02 (710 KB) (or better).
Or you may obtain presently (11/2001) from Microsoft the Windows Media Player 7.1 / 10MB, www.microsoft.com, in Europe from : http://www.eu.microsoft.com/germany/ms/windowsmedia/.
It will work. If they are too busy or too advanced get it from this site.
in English
Video clip download Löwdin talks briefly about the orthonormalization procedure (40 sec) ZIP/AVI, Indeo 5.04; 5 MB Just in case: You might want to install presently (11/2001) from Microsoft the aboveWindows Media Player 7.1 /10MB. It will work. An other alternative might be : Free plugin download codec Indeo 5.04 (2 MB) in English
Sound clip Löwdin in a brief chat about Summer School, orthonorm. etc. (3 min) WAV; 1.5 MB - in English
Sound clip Löwdin in a brief chat about Summer School, orthonorm. etc. (3 min) MP3; 350 KB Also here, among others, the Windows Media Player 7.1 will do the job. in English

For the feel of the times you may be interested in what Ohno tells us about Löwdin and a bit also about himself :

K. Ohno : Per-Olov Löwdin, Conqueror of Scientific, Educational and Rocky Mountains.

in : Quantum Science - Methods and Structure. A Tribute to Per-Olov Löwdin.

Edited by Jean-Louis Calais, Osvaldo Goscinski, Jan Linderberg and Yngve Öhrn.
Plenum Press, New York, 1976, pages 1-11.

In 2002 Jan Linderberg gave a Löwdin memorial talk, including some older photographs, at the Sanibel 2002 meeting. Have a look at it right here.

Interview with Professor Per-Olov Löwdin (Lowdin)

Uppsala, Uppsala University, June 2, 1999; 15:00

A: Prof. Löwdin, you have many degrees, many honorary degrees, one of the University of Constance, then I know of at least three others. And you are well known, and I don't want to repeat it, one finds you on the Internet. Everywhere I go, I hear about the Summer School, whether it is in Italy, in France or in Germany, everybody still likes to talk about it. Now of course it is interesting to know how you got that idea.

L: I had Harrison Shull, ( 3 ) who is now at Indiana working with me, and he said it's remarkable how all these discoveries are forgotten. And I said, what can we do about it? So we agreed that we would start a summer school, a small summer school and go through the original literature up to the present day.

A: Shull - is that the person who also started the Quantum Chemistry Program Exchange?

L: Yes.

A: About what time was that?

L: That was in 1958. He was here at Uppsala and was actually doing postdocs with me. And several periods, I think, he spent a total of three of four years with me. It was a very nice collaboration and he had many ideas.

A: That must have come out of the discussion with you?

L: Yes, that's true (laughs).

A: And then, when the idea first occurred to you, whom did you want to reach?

L: We wanted to reach the people in theoretical chemistry, who wanted to learn what quantum chemistry is. And also ordinary chemists. But the difficult point was, that there was no literature and no text books and so on. So, the idea was, that perhaps we could go up somewhere in the mountains for five weeks and keep them isolated and then to teach quantum chemistry (laughs).

A: The summer school did not occur in Uppsala here but in the mountains?

L: Actually it occurred in the mountains. Karin, was the first summer school up in Vålådalen {east of the town of Östersund, middle Sweden, website note} ? I think it was.

Karin Löwdin, his wife: Yes, in '58.

L: That was up in Vålådalen in the Swedish mountains. And then we moved down to Uppsala. So part of it was always in Uppsala, but part of it was in some isolated place, where they couldn't escape (laughs with a slightly sarcastic undertone).

A: How did you feel about the mathematics of the chemists?

L: One had to give a special course in linear algebra to them, and this was very useful then when later the computers came in. So they could use linear algebra (laughs).

A: How many people did you have each year in your Summer School, approximately?

L: Actually, the biggest one was 120, because that filled the chemistry lecture room here in Uppsala, and the smallest ones were around 25.

A: And with how many persons did it start?

L: It probably started with 25/ 30 people in '58.

A: And how did you do it now practically? Did you hand out sheets or did you let them work? I heard later on you gave them a little problem and let them work on it, while they were here.

L: Yes, that's right. And there was no text book you could refer to. So we had to give them the material by writing and they had to copy it and then we could discuss it. That went rather slowly. It was a tremendous amount of mathematical material. A lot of linear algebra and similar things and we had also to include a lot of quantum theory.

A: Prof. Löwdin, I may change the subject now. In your early papers you took up the methods of Landshoff and Wannier. Landshoff has had a development of an expansion with two terms and where the third term was only approximate. How did that idea occur to you working with those ionic crystals. How do you remember this?

L: I can tell you, because actually I was interested in field theory, in the structure of the elementary particles and so on. And I went to Wolfgang Pauli in Zurich, he was a very nice man, but rather tough to work with. So I asked him one day if there would not be another part of physics which will be easier then field theory. And he said: "Why don't you try solid state physics? And you have an excellent teacher in Uppsala, Ivar Waller and you go back to him and ask him if the problem is still available." So I had studied previously for Waller and I went back and Waller said "Yes, there is a wonderful problem from 1927 that has not been solved: The failure of the Cauchy relations for the elastic constants in crystals." And he said that no one had applied quantum chemistry to it yet. And if you can solve that it might be a very, very good starting program. So, I started studying the elastic constants and particularly the failure of the Cauchy relations, there are six Cauchy relations for all crystals. And in alkali halides there is only one because of the symmetry, and I found one day that there were many ion forces, because the ions overlapped. And it turned out that this was the explanation of the failure of Cauchy's relations. And not only that, but I had to work out from ab initio the elastic constants for some of the alkali halides and it worked very very well, they agreed with experiments within about 10 %, except for one case, Lithiumfluorid, but there were right on three features. And I was very surprised about this and then I met the man who made the experiments, that was a fellow named Huntington. And met him in Texas and I said "Dr. Huntington, I have a problem with the elastic constants because I have found that I have the elastic constants with some of the alkali halides right on the nose, and they ought to be 10% off." And he said: "You are probably right, I used the wrong density (laughs)."

A: That was a positive response. And how did you come about to have that idea about orthonormalisation when you used Landshoff's functions?

L: I had in some way to solve this norm orthogonality problem. And I looked through the literature and learned about Wannier's work of course, and of Landshoff and all the others. And then probably wrote a paper which was about 100 pages. Then one day I got the idea - and it could be derived on one page (laughs).

A: And how did that idea of orthonormalisation happen? Did it just occur to you? What was the mental process, thinking back 50 years, how did that pop into your mind?

L: That was rather interesting because the problem was not solved by itself so to say, and I worked on it and wrote hundreds and hundreds of pages and one day it hit me that I could derive it in three, four lines (laughs).

A: But as a physicist you had learned your mathematics, of course.

L: Yes, so it was a symmetric orthonormalisation which came out at this time. Then a little bit later the canonical orthonormalisation came out which is really leading to topological orbitals. And I was very happy of course, because it was enough to (laughs) give me the doctor's degree here at Uppsala University.

A: The ideas of molecular orbitals and their functions were just starting at the time you did your work on crystals, and I think it was Mulliken who had coined the word orbital. How did this idea appeal to you? How did the idea of orbitals strike you when you first encountered them?

L: Actually it was very natural for me to have the orbitals and have them extended over the entire molecule so to say, and it was very appealing and I remember, when Mulliken finally got the Nobel prize for it. He said: "I am very happy because now I know that I will share it with Hund ." And I said: "Robert, you are not going. It's final, it's already out officially, you are alone." And he said: "That's a great pity, because I feel that Friedrich Hund contributed as much as I ever did." So Mulliken was very sorry, but then of course he had to accept it, because there is no way you can claim that it is wrong, so to say.

A: And then the Löwdin atomic orbitals are another thing which played an important role in the semiempirical days in the 60th.

L: And don't even recognize the name Löwdin atomic orbitals (laughs heartily).

A: Didn't you coin the word natural orbital?

L: Yes, natural orbital, that I coined.

A: So, when did you come out with these orbitals?

L: Probably in 1955 ( 4 ).

A: How did you feel that chemistry accepted the ideas you gave to quantum chemistry?

L: As a general rule, they didn't accept it at all (laughs heartily). They thought these things were useless. And actually quantum chemistry had no standing in chemistry at that time.

But finally it got its way in, and here in Uppsala something remarkable happened. The chemists wanted to learn about quantum chemistry! So I was invited to give a double lecture every morning five days the week, for one full semester. It was between 8 and 10 in the morning and they came, all of them, including the professors and including some of the very old guys, and they were interested in it. And they wanted to finish by 10 o'clock so they could go to the laboratories, so we started at 8 o'clock with that double lecture, five times the week. That was about between '55 and '58.

A: The physicists on their part also took up for crystals. How did you feel from your point of view, was this a better uptake of ideas and the use of your methods as compared to the chemists?

L: It was probably easier in physics than in chemistry, they were better mathematicians, there was so much mathematics involved.

A: About these natural orbitals, how did you come to them.

L: Oh, Slater, John C. Slater, posed a problem. And he said there should be - everything can be expressed, every wave function, in terms of CI-configuration interaction, superposition of configurations. And he said: "Don't you think there ought to be one which has the quickest convergence, the best conversion properties." So I started looking for it. He was looking for it, and I was looking for it, and I found the natural orbitals. And he was very pleased (laughs).

A: Now, Hückel Theory. The term "Hückel Theory" didn't occur much in your publications. How did you, as a theoretician, view the Hückel approach? Some chemists at this time liked to use it.

L: Oh, I liked it very, very much. But the point was that I wanted it derived from first principles and connected, associated, with first principles and that was much tougher than anyone expected.

A: Freed worked on it in Chicago. Karl Freed. Did they ever succeed really? Could one be content with their formal derivation of the Hückel Theory from basic principles?

L: Yes. Actually everything there is fine, except for one thing. The effective the Hamiltonian they are finally using is not selfadjoint. Otherwise everything is perfect (laughs).

A: Fischer-Hjalmars had also worked on this.

L: She came out with a long article in Advances in Quantum Chemistry.

A: For many years you were an editor of this famous row of books. Did you read it all when they send you the articles.

L: I don't know if they were famous but they were very, very comprehensive, Advances in Quantum Chemistry. And actually since they were not too long, these papers, I read them and I had two independent referees. So I would never edit or suggest any changes, this would have killed these series, but the referees were anonymous and they could make the comments and so on. And it worked out, but I had to read it all. When it came to Advances in Quantum Chemistry, I think I read every paper carefully, when it comes to the International Journal of Quantum Chemistry, it was all delegated. There were many different directions and actually I have been the editor of about 5000 pages a year and I had to delegate most of it (laughs thoughtfully). I am still in for the International Journal of Quantum Chemistry and for Advances in Quantum Chemistry.

A: So, if you got a paper using the Hückel method what did you think about it? Did you think they should have used a better method?

L: No, the molecules were too big to use a better method. On the other hand the Hückel approach had semiempirical parameters which could be adjusted on one set of molecules and then used on all the molecules in this set, and it worked. If you calculated these parameters ab initio they can be completely differently, but that didn't worry me.

A: And later on the NDO methods, was that the same story concerning the multitude of parameters? Would you say the same thing about their parameters as in the Hückel method?

L: If you have one parameter you can describe an elephant, and if you have two you can say if he's drunk (laughs).

A: And later on you went to biological molecules. Can you explain a little bit this field of your work?

L: Yes, it was mostly the structure of DNA and the question how the molecule could be stable at our body temperature, which is 310 K, so this was a great mystery to me. But the calculations we could do at these times confirmed that the molecule was stable even at this very high temperature. But you also looked at tunnel effects, rotations through tunneling, proton tunneling, and a few other things, and so on. Very much interesting was the structure of memory function for some time and the structure of our thinking process, but we were of course not too successful but we got some insight, but not too much (laughs).

A: Do you think there is any progress still to be made in this direction?

L: Of course. A tremendous amount of progress has to be made and it will be made sooner or later, including quantum chemistry and ordinary thermodynamics. They have to come in at the same time since we are living at the high temperature (laughs).

A: Presently, you are not doing quantum theoretical work - you are going back to the roots, so to speak?

L: Yes, so I have written a little pamphlet about the foundations of physics - I don't know if I have a copy available - and so what I have done is to derive the Lorentz transformations without any assumptions about light. And then derived quantum mechanics from the point of view of Schrödinger as a mathematical eigenvalue problem, really independent or Planck's constant h. And the third one has to do with gravitation. Black holes and so on, without using the general theory of relativity. So it is a fairly broad interest and from there it is rather shallow (laughs).

A: I wouldn't think so. Now you are also thinking about some philosophical problems. You are thinking about philosophy of science and natural science and thinking.

L: Yes, I have written some paper about the connection between philosophy and the natural sciences and then to find out also what is really truth from the point of view of science. And how much you can really derive and so on.

A: If you have a reprint of this, this might be very interesting. I want to bring this in as well. Del Re is doing some similar work.

L: You know, Del Re was a student at my very first summer school in 1958 in Vålådalen.

A: In the summer school you rented a house or a hotel there and cook and so on?

L: No, we actually rented a hotel. The first one was in Vålådalen and then we went to other places, we went to Lidingö and so on and we always had some hotel manager helping us.

A: As a physicist you started with ionic crystals and so on, but then you had to learn about molecules. Is it the same thing working with either ionic crystals or the covalent bonding? That didn't pose any serious problems to you?

L: No, it wasn't. Actually as a physicist I started with a structure of elementary particles. And that problem is not solved, even today. So I struggled and struggled and struggled. And then I worked with Wolfgang Pauli at Zürich and I said: "Dr. Pauli is there any field which is real physics today?" And he said: "Why don't you go to solid state physics and try it out, you have a good teacher in Uppsala, Ivar Waller, so why don't you try that." And I did.

A: About Pauli, it is now said that he, at least during some span of his life, was considered an alcoholic and that he has had an analysis with C. G. Jung. Was he an unstable person?

L: Oh, that was not my feeling. My feeling was that he was a very stable scientist but very opinionated. And if he didn't like what you were doing he would tell you. And he would sit into the lectures and when he didn't like what the lecturer said he would just shake his head all the time. And that was of course very horrifying for many lecturers who didn't know him. But I got to know him fairly well and he was kind enough. I asked him once if I could come to a seminar in Zurich and he said: "Löwdin, if you don't ask any questions you couldn't do any harm." But then he invited me back to speak about progressing the correlation energies and so on. And actually I found him bizarre but very kind (laughs).

A: One more question to the paper of Landshoff. How did you come to it? Just by literature search?

L: No, I went from elementary particle physics theory over to solid state physics. And I asked Ivar Waller about, so to say, where I could find a program. And he said: "There is paper by Landshoff. He has tried to solve the orthogonality problem and this solution is incomplete, so could you please start on it." And I started on it and wrote probably 100 pages and I found another derivation which was only three or four lines.

A: What anecdotes do you still recall out of your long work?

L: (Thinking) Yes - I don't know, I haven't thought about it in this way for a long time. So give me a little bit of time and some hints, I may be able to get something (laughs).

I don't remember the name of the guy who worked with me, probably at an American University. And he had gotten his thesis problem by his professor and he solved it at the summer school. So he gained certainly two or three years of his life (laughs). And then some of the professors said: "From now on you can do anything what you want but you cannot use material from the Summer Schools, because it is too good help."

A: And is it true, that when you had thought of a problem, you then presented this at the summer and that you gave them this problem together with hints as to the solution? And that then they would go and finish the problem on their own?

L: I don't recall any practical examples right know, but I think it is true.

A: You had two professorships, one at Uppsala and one in the States. How could you remain so creative?

L: I don't know if I ever was creative, but I must have had creative students (laughs). I do have ideas but actually the interaction with the students was very important.

A: Which good student do you recall? Maybe at the Summer Schools?

L: At the Summer Schools, someone calculated this, we had about 5000 participants over the years, in the Summer Schools including the symposia which followed. So it was a big contact so to say, and there were some people who were absolutely brilliant. I take no credit for Roald Hoffmann, he was at the '59 Summer School were he met his first Swedish wife - but let us see - he is one of the few who has got the Nobel prize, of these people.

A: In Sweden, is there a quantum chemistry group which you influenced? Fischer-Hjalmars for instance also participated in your Summer Schools.

L: Yes, I have a small one, and Fischer-Hjalmars had another one, and then of course the young people came up, Björn Roos, Per Siegbahn (5), whose father Kai M. Siegbahn was the one with photoelectron spectroscopies and got a Nobel prize for that. Per Siegbahn is doing more quantum chemistry, so to say. And then there was a new development, namely computational quantum chemistry, with the big computers, at Uppsala, too.

A: And in the States, did you have a research group as well? And was that mainly mathematical or applied to chemistry?

L: It was theoretical. Quantum theory applied to chemistry. And I got an offer from the National Science Foundation to start a Winter Institute, a five week winter institute of the same type as Summer Institutes here. And I could put it up anywhere in the States. So I went around, and I went around to all the famous schools. And then I fell in love with a very nice university down in Florida, in Gainesville, Florida. And put up this school now and a Quantum Theory Project which I started from scratch of course. And then we had the Sanibel Symposia ( 6 ) plus the Winter Schools. And I had very good coworkers, I always have been blessed with good coworkers, so it happened very easy to have to projects going. And the Florida Project started back in, I believe, 1958, and it is still going on. So I am going over there every year.

A: And do you have doctoral students in the States as well?

L: No, no longer. I am emeritus and I don't think it is fair to them, particularly since I am in two places. In the old days I stayed in contact with them through mail and then came the electronic mail the whole thing has been very easy.

Let me tell you what has been very important in my early days so to say, because I had good contacts with Robert S. Mulliken at Chicago and with John C. Slater, at MIT. He had something called the SSMTG, Solid State and Molecular Theory Group at MIT. And I could be there for half a year at that time. I had a rather loose position as a docent here in Uppsala so I could travel a lot. And Slater was fantastic, he should have been awarded the Nobel prize too, but unfortunately he died too young. And he was pretty tough to work for, but also very human. We went to Japan together in '53 and the Japanese International Congress in Theoretical Physics had about 50 western scientists, this was very interesting little group.

A: In one of your books you came out with a long and interesting article on John Slater. I will reread it and then there might be some more questions by me.

L: Yes, OK.

A: Whom else of the old founders of quantum chemistry would you remember? Mulliken, Hoffmann we talked already about. When Ruedenberg came out with his work, how did you view this? It was fairly complicated and never used very much.

L: I thought it was a very interesting idea. Because he put the atoms in specific states before they join into molecules or in the molecules they were in various specific states and so on. I thought it very important but it hasn't been of great importance in the development of our science. In contrast to many of Roothaan's ideas. I have a volume being credited to Klaus Ruedenberg coming out in the International Journal of Quantum Chemistry in the near future.

A: What about Dewar? How do you remember Dewar? He was an organic chemists and yet he went quite far in applied theory. How do you view his work?

L: I remember Michael Dewar , yes. I think, his work was very interesting and very important. But I am more at the ab initio side, so from this point of view... . He came to Gainesville, Florida, in the last few years he had to live and I had a volume in his honor in the International Journal of Quantum Chemistry and I asked Dewar to write an introduction. So I read it and I went back and said: "Michael, the fight is over, you have won. You don't have to fight any longer (laughs). You can just enjoy your victories." And he said: "You mean what you've said?" And I said: "Yes." He: "And I have to rewrite the introduction?" and he did, in a much more friendlier way, so to say. It was rather funny, he was a very fighting fellow. He worked with us in Gainesville and he died there also. It was nice to have him there and the fact that he would join a theoretical group was very interesting to me, and he did most of the ab initio things there, he felt at home.

A: Professor Löwdin, thank you very much for the interview.


References and Notes

    Please note:
    Since P.-O. Löwdin did not live to make the corrections to this interview, this website gratefully acknowledges the help of Prof. J. Linderberg and who also contributed these 'References and Notes'.

    (1) Per-Olov Löwdin, On the Non-Orthogonality Problem Connected with the use of Atomic Wave Functions in the Theory of Molecules and Crystals, J. Chem. Phys. 18, 367-370 (1950).            ... return ...

    (2) Lwdin was also promoted Jubeldoktor at Uppsala, May 29, 1998 on the 50th anniversary of receiving his doctorate there, this being a Swedish tradition. There were 5 "survivors" in 1998, 4 were present and Lwdin gave a brilliant speech to the students on behalf of the Jubeldoktors. Priv. communication J. Linderberg.             ... return ...

    (3) Shull was on leave from Indiana Feb 58 thru Aug 59 and returned there. He went into administration at Rensselaer Polytechnic, Colorado and The Naval Postgraduate School at Monterey, California. He lives in Monterey as retired. Priv. communication J. Linderberg. {Note from this website: Shull was approached via letter at his home, yet unfortunately without results.}             ... return ...

    (4) Per-Olov Lödin, Quantum Theory of Many-Particle Systems I. Physical Interpretations by means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction. Phys. Rev. 97, 1474-1489 (1955).             ... return ...

    (5) Per Siegbahn's father is Kai Siegbahn, Nobel Laureate 1981 for ESCA, Electron Spectroscopy for Chemical Analysis. Kai's father was Manne Siegbahn, Nobel Laureate for X-ray work 1924.             ... return ...

    (6) The Symposia are called Sanibel Symposia after the Sanibel Island where they were held 1961-1977, the location has since then been on the Florida East Coast. Palm Coast was the place for a few years as was Marineland. Then St. Augustine and one year, 1994, at PonteVedra, then back at St. Augustine where the 42nd was held 2002. {Priv. commun. J. Linderberg.}             ... return ...

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