P.-O. Löwdin and the International Journal of Quantum Chemistry: A kaleidoscopic agenda for quantum chemistry



This is a article about P.-O. Löwdin's life, his work in shaping quantum chemistry into a mature discipline at the intersection of mathematics, physics, chemistry, and biology, and his founding of the International Journal of Quantum Chemistry in 1967. Unavoidably, it is, also, a article reflecting our views about the history of quantum chemistry. We attempt to convey the complexities in the becoming of a subdiscipline, like quantum chemistry, where a variety of factors will have to be taken into consideration for a comprehensive understanding of its historical developments: the relations of chemists to the Heisenberg-Schrödinger formulation of quantum mechanics after 1926, the institutional dynamics centered around the establishment of new courses and chairs, the research agendas and the vying for dominance within the community of quantum chemists, the methodological, and philosophical issues that have never left the quantum chemists indifferent, and, of course, the dramatic role of the computer in transforming the culture for actually practicing quantum chemistry. Furthermore, attracted by American history, culture, and ways of life, Löwdin suggested in the late 1970s that the post-WWII character of quantum chemistry was dependent on its ability to hub a “scientific melting pot,” much like the United States of America which he viewed as a fusion of people from diverse provenances and cultures. In this article, we attempt to investigate another metaphor, that of the “kaleidoscope.” Löwdin believed that quantum chemistry's strength arose from its ability to nurture a multiplicity of heterogeneous cultural elements/subcultures and practices, interacting with each other, exchanging perspectives and modes of action, which circulated in an increasingly extended network of actors and institutional frameworks. © 2013 Wiley Periodicals, Inc.


The International Journal of Quantum Chemistry was founded in 1967 after a series of initiatives by the Swedish quantum chemist Per-Olov Löwdin (1916–2000). He was, then, 50-years old, and probably one of the most influential quantum chemists of the “second generation,” having been born about two decades later than most of the protagonists of the discipline: Walter Heitler (1904–1981), Fritz London (1900–1956), Friedrich Hund (1896–1997), Eric Hückel (1896–1980), Linus Pauling (1901–1994), John Clarke Slater (1900–1976), and Robert Sanderson Mulliken (1896–1986). He was someone for whom quantum chemistry became a “lifestyle,”[1] according to his junior colleagues, but also someone whose contributions to quantum chemistry in the post-WWII era, helped to shape a mature discipline—born at the intersection of various historical disciplines, such as mathematics, physics, chemistry, and biology. The International Journal of Quantum Chemistry played a pivotal role in materializing such a vision, and its great success bears witness to Löwdin's decisive role as one of the most articulate defenders of quantum chemistry in a mature stage of its development.

Eager to establish quantum chemistry in secure foundations within quantum mechanics, and exploring at the same time its connections with solid-state physics and materials science, Löwdin sought inspiration in the work of the pioneers of the “first generation,” and especially in Slater, with whom he developed a strong intellectual affinity. He created the Quantum Chemistry Group in Uppsala, inspired by Slater's group at M.I.T., (The correspondence between Slater and Löwdin, held at Slater Papers at the American Philosophical Society is particularly telling. See citations from the correspondence in Ref. [ [2]) and then proceeded to duplicate it with the Florida Quantum Chemistry Group. He, also, founded summer and winter schools, in order to reinforce, quickly and efficiently, the training and interaction of scientists from different places and cultural upbringings. Much like Charles Alfred Coulson (1910–1974), Löwdin was an indefatigable and captivating speaker who addressed different audiences. Besides strictly technical talks, he liked to reflect on issues which expressed the importance of quasi-philosophical problems of quantum chemistry, such as the relation of theory and experiment, merits and shortcomings of the semiempirical versus the ab-initio approaches, and the role of numerical and computational inputs.

In the post-1970s era marked by the foreseeable dominance of the computer in quantum chemical calculations, Löwdin became a community builder, whose activities and initiatives for quantum chemistry became imprinted at every level of the subdiscipline: epistemic, institutional, organizational, and computational. He referred metaphorically to quantum chemistry as a “scientific melting pot,” choosing this same expression for the title of the meeting he organized to celebrate both the 500th anniversary of the University of Uppsala (1477) and the 50th anniversary of Heitler and London's 1927 paper heralding the beginning of quantum chemistry.[3] Attracted by American history, culture and ways of life, Löwdin suggested in the late 1970s that the post-WWII character of quantum chemistry was dependent on its ability to hub a “scientific melting pot,” much like the United States of America were then depicted as being a “melting pot” in which a fusion of people from diverse provenances and cultures took place giving way to a homogeneous and harmonious whole sharing a common culture.

This is a article about Löwdin's life, work, and his founding of the International Journal of Quantum Chemistry. Unavoidably, it is, also, a article reflecting our views about the history of quantum chemistry—this most intriguing discipline. We feel that Löwdin's own metaphor concerning the melting pot, can be further elaborated and, to a certain extent, complemented by another metaphor, that of the “kaleidoscope.” In our opinion, the strength and dynamism of quantum chemistry arose from its ability to nurture a multiplicity of heterogeneous cultural elements/subcultures and practices, interacting with each other, exchanging perspectives and modes of action, which circulated in an increasingly extended network of actors and institutional frameworks. It was this kaleidoscope of cultural elements/subcultures, which came to constitute the various interlaced strands of views and practices shared by practitioners of quantum chemistry.

As someone fully committed to shape quantum chemistry as an “in-between” discipline, born and developed at the intersection of physics, chemistry, applied mathematics, and biology, Löwdin was not divisive but open-minded about diverse and plural approaches. Like in a kaleidoscope set in motion, the history of quantum chemistry is a complex and varied change of forms, patterns, and colors, continuously shifting from one set of relations to another. In quantum chemistry, different groups with different methodological commitments, interacting with each other on an equal footing, forged its associated scientific multiculturalism.

This was precisely the rationale behind the invitation sent to Slater to attend the meeting “Quantum chemistry. A scientific melting pot,” “devoted primarily to discussions of the nature of our branch of science, as seen both by professional philosophers and by quantum chemists”:

  • Quantum chemistry has contact areas with pure and applied mathematics, physics, chemistry, and biology. There is conflicting emphasis both on a sound epistemological basis and successful applications: differences in aims, language, economic or interdisciplinary relevance of the results, and so forth. This makes a confrontation of methods, purposes, and norms of interest not only for our subject itself but also as a living model of the development of science.
  • Quantum mechanics is an order of magnitude younger than the University of Uppsala. Yet it has influenced the world around us, materially and in the domain of ideas in a profound and shattering way. Unlike previous scientific revolutions it experienced an almost instant feedback and demands: computerized data systems, material sciences applications, molecular biology, to name a few of the driving forces, and poles of attraction. This is why foundation research is necessary for chartering the future in a transcendental fashion. The principal role of the universities throughout the centuries has been and should be to provide a fertile atmosphere for the confrontation of ideas, leading on some rare but incomparably important occasions to the birth of new ideas and concepts. It is only in this spirit that the continuity of 500 years endeavor of learning and research can be celebrated properly.[4]

Framing the discussion of foundational issues in the context of the mission of universities as they were conceived since their creation, Löwdin not only stressed the importance of “confrontation of ideas” to the birth of novel concepts within the general framework provided by quantum mechanics, but pointed to the salutary practice of methodological pluralism, and its in-built confrontations, as an identity trait of quantum chemistry, which endowed it with a privileged role as a “living model of the development of science.”

Despite his belief in reductionism and his penchant for ab initio calculations, Löwdin envisioned the future of quantum chemistry as dependent on its ability to accommodate different approaches and yet having a rigorous set of common grounds. His many initiatives, including the organization of meetings and schools, the launching of a series of books and a journal, negotiations with governmental agencies, industries and philanthropic institutions to promote the use of high speed computing facilities, are exemplarily mirrored in the plurality of fields and approaches which the International Journal of Quantum Chemistry was to accommodate.

A Historians' Interlude

Löwdin appeared on the “scene” when quantum chemistry had already a very rich history and with his work as well as his initiatives gave it a further dynamism. Rather than reiterate some of the landmarks of the history of quantum chemistry prior to Löwdin, which are more or less well known to the readers of this journal, we would like to present these developments in a different manner. The following reflects ways historians approach their subject matter and, more specifically, our own approach, which attempts to articulate a framework where the history of quantum chemistry can be narrated not in a strict chronological order.[5] It appears that a host of interesting developments concerning the development of quantum chemistry—a classic case of an “in-between” discipline—can be narrated through six interrelated clusters of issues that manifest the particularities of its evolving (re)articulations with chemistry, physics, mathematics, and biology, as well as its institutional positioning. We, thus, hope the readers of this Journal will get a feeling of the history of quantum chemistry not in strictly chronological terms, but in ways that are closer to the historians' mode of thinking.

The first cluster involves issues related to the historical becoming of the epistemic aspects, the knowledge content, of quantum chemistry: the multiple contexts that prepared the ground for its appearance; the ever present dilemmas of the initial practitioners such as Hund, London, Heitler, Hückel, Mulliken, and Pauling as to the “most” appropriate course to choose between the rigorous mathematical treatment, its dead ends, and the semiempirical approaches with their many promises; the novel concepts introduced and the intricate processes of their legitimization. The source of these dilemmas lies in what appeared from the very beginning to be a doomed prospect: the Schrödinger equation, used in any manner for the explanation of a chemical bond, could not provide analytical solutions except for the case of hydrogen. Quantum chemistry appears to have been formed through the confluence of a number of distinct trends: the relatively straightforward quantum mechanical calculations of London and Heitler in 1927; the rules proposed by Mulliken to formulate an aufbau principle for molecules; Pauling's reappropriation of structural chemistry within a quantum mechanical context; Charles Alfred Coulson's and Douglas Rayner Hartree's systematic but at times cumbersome numerical approximations; or later Löwdin's bid on conceptual clarification, mathematical rigor and numerical computational tools—by themselves and in a manner isolated from each other—all these gave quantum chemistry its particular characteristics. And although it may appear that there is a consensus that quantum chemistry had always been a “branch” of chemistry, this was not so during its history, and different (sub)cultures (physics, applied mathematics) attempted to appropriate it. The historical development of quantum chemistry has been the articulation of its relative autonomy both with respect to physics as well as with respect to chemistry, and we argue for the historicity of this relative autonomy.

The second cluster of issues is related to disciplinary emergence: the naming of chairs, the writing of textbooks, the organization of meetings, the intense networking, as well as alliances quantum chemists sought to build with the practitioners of other disciplines were quite decisive in the formation of the character of quantum chemistry. We know that many of the protagonists have spent a substantial amount of time in specific activities as community builders. Academic politics, tensions, and consensus in the various scientific societies and the work of individuals were all entangled. The emergence of quantum chemistry in the institutional settings of Germany, the United States, and Britain, and later on in France and Sweden, and a number of conferences and meetings of a programmatic character helped to mold its character: a marginal activity at the beginning, it had the good luck to have gifted propagandists and able negotiators among its practitioners. The strong pleas of Heitler, London, and Hund for chemical problems to yield to quantum mechanics, Mulliken's tirelessness in familiarizing physicists and chemists with the attractiveness of the molecular orbital approach, Pauling's aggressiveness to project resonance theory as the only way to do quantum chemistry, Coulson's incessant attempts to popularize his views in order to explain the character of valence, the research of Raymond Daudel and of Bernard and Alberte Pullman into molecules with biological interest, and Löwdin's incessant organizational and networking activities geared toward effective internationalization together with the founding of the International Journal of Quantum Chemistry, all these contributed toward the gradual coagulation of the language of the emerging subdiscipline and of its social presence as well.

The third cluster of issues is related to a hitherto totally neglected aspect of quantum chemistry; that is, its contingent character. Quantum chemistry could have developed differently, and the particular form it took was historically situated, at times being the result of not only technical but also of cultural and philosophical considerations. “In-between” (sub)disciplines provide a privileged context in which to investigate the interpretative possibilities provided by the notion of contingency. Contingency is not an invitation to do hypothetical history. It is not an invitation to ruminate about meaningless “what if” situations, but rather to realize that at every juncture of its development, quantum chemistry had a number of paths along which it could have developed. What is important to understand is not what different forms quantum chemistry could or might have taken, but rather the different possibilities open for developments, and the set of difficulties that at each particular historical juncture formed those barriers that dissuaded practitioners from pursuing these possibilities. Throughout this 50-year period, the criteria for assessing the “appropriateness” of the approaches being developed gravitated among a rigorous commitment to quantum mechanics, a pledge toward the development of a theoretical framework where quasi-empirical outlooks played a rather decisive role in theory building, and a vow to develop approximate techniques for dealing with the equations. Such criteria were not, strictly speaking, solely of technical character, and the choices adopted by the various practitioners at different times had been conditioned by the methodological, philosophical, and ontological commitments, and even by institutional considerations.

The fourth cluster of issues is related to a rather unique development in the history of this subdiscipline: the rearticulation of the practices of the community after the early 1960s, which was brought about by the electronic computer. The fundamental liability of quantum chemistry, the impossibility to perform analytical calculations, was, all of a sudden, turned into an invaluable asset that also contributed to the further legitimization of electronic computers. In the early 1960s, it appeared that a whole subject depended on this particular instrument in order to produce trustworthy results. In 1929, Dirac had announced that “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.[6] It appeared that quantum chemistry came to be regarded as a success story of quantum mechanics. Although it took some time for physicists to realize that Dirac's statement was a theoretically correct but a practically meaningless dictum, the first attempts to solve chemical problems in the “proper way”—that is, in the physicists' way—by, say, Heitler and London appeared to be rather promising. These attempts started before the publication of Dirac's paper, and they may have provided some kind of justification for such a generalized statement. Dirac's statement was a true statement, but helped no one because it was impossible to perform analytical calculations, and new concepts and numerical techniques had to be continuously devised in order to circumvent the difficulty of performing exact calculations. However, in a very short while, a particular instrument undermined most of the fundamental criteria with respect to which the practitioners were making their choices since the late 1920s. All of a sudden, ever more scientists started to realize that “quantum chemistry is no longer simply a curiosity but is contributing to the mainstream of chemistry.”[7] The prospect of ab initio calculations, which did not use experimental data built in the equations in any way, seemed to offer the promise of new and reliable results, and apt to reach a sophistication and accuracy dependent on the needs of each quantum chemist. The members of a whole disciplinary community, who, through a historically complicated process had attained a consensus about the coexistence of different approaches for doing quantum chemistry, became in a relatively short time subservient to the limitless possibilities of computations provided by a particular instrument. Fostered by the use of computers, applied to ab initio but also to semiempirical calculations, members of the community of quantum chemists recognized that a new culture of doing quantum chemistry was asserting itself and vying for hegemony among the more traditional ones. The increasing complexity of molecular problems was dealt with by means of mathematical modeling and a burst of activities in relation to the writing and dissemination of computer programs. There were even cases where it became unnecessary to perform expensive experiments because calculations would provide the required information. Of course, such a dramatic development was often a pretense for serious soul-searching. Despite Coulson's own contributions and those of his research associates to the calculation of molecular integrals using ever more elaborate computer programs, Coulson was never oblivious to the dangers of their indiscriminate use. He was among the very first to realize that the extensive use of the computer was heralding deep changes within the community of quantum chemists. In an impassioned speech at the Boulder Conference of 1959, he expressed his fear that “the whole group of theoretical chemists is on the point of splitting into parts (…) almost alien to each other.” The extensive use of computers has obliged the community of theoretical chemists to ask questions related to the “very nature of quantum chemistry, what relation [the computer] has to experiment, what function we expect it to fulfill, what kind of questions we would like it to answer. I believe we are divided in our own answers to these questions (.). Where, in all this, does ‘real' quantum chemistry lie?” Coulson wondered.[8] He was right. Nothing was really the same after the advent of the computers. Among members of the “second generation” who had no qualms in appropriating computers into their culture, Löwdin excelled in addressing in his practice and reflections all those questions premonitoriously posed by Coulson at the Boulder conference.

The fifth cluster of issues is related to philosophy of science. It is undoubtedly the case that in recent years there has been an upsurge of scholarship in the philosophy of chemistry. The issues that have been raised throughout the history of quantum chemistry played a prominent role in these philosophical elaborations and discussions: reductionism, scientific realism, the role of theory, including its descriptive or predictive character, the role of pictorial representations, and mathematics, the role of semiempirical versus ab initio approaches, and the status of theoretical entities and of empirical observations.[9] Throughout the development of quantum chemistry, it appears that almost all its practitioners were aware that apart from the technical problems they had to deal with, they were also encountering a host of “other” problems as well. These problems were, in fact, philosophical problems. But almost none of these practitioners were thinking of formulating the answers in philosophical terms, as no one, really, thought of these problems as philosophical problems. Yet, they all considered the answers to these thorny issues as a necessary procedure toward the establishment of quantum chemistry. In discussing these issues, many quantum chemists were, in effect, negotiating the ways to “escape the thought forms of the physicists.”[10] Notably, most of the first generation of quantum chemists became strong allies to the philosophers of science, who, long after these people were gone, attempted to establish the subdiscipline of philosophy of chemistry. Coulson, and later Löwdin, were among those who spent much effort in elaborating various issues in the interpretation of quantum chemistry. Of specific importance was the question concerning the “artificiality” of resonance. And although Coulson considered resonance to be something very useful, he insisted that it would “be a pity if anyone ever came to believe that resonance was real.”[11] For Coulson resonance remained not a well defined molecular property, but just a heuristic device. He repeated that resonance “is a ‘calculus' if by calculus we mean a method of calculation; but it has no physical reality. It has grown up because chemists have become used to the idea of localized electron pair bonds that they are loath to abandon it, and prefer to speak of a superposition of definite structures, each of which contains familiar single or double bonds and can be easily visualizable.”[12] George W. Wheland, a close collaborator of Pauling, was, also, not sharing the latter's view about the reality of resonance. Wheland in a series of letters to Pauling tried to no avail to convince him that resonance was, indeed, a “man-made-concept” in a more fundamental way than in most other physical theories. This was his way to counter the widespread view that resonance was “a real phenomenon with real physical significance.”[13] Löwdin was particularly concerned with the nature of quantum chemistry, often discussing the role of theory, experiment, numerical calculations, and computations, as well as the role of explanations by contrast to that of predictions. We will discuss these issues more analytically later in this article.

The sixth cluster is of a quasi-methodological and quasi-cultural character. The history of quantum chemistry displays instances that we suggest to discuss in terms of “styles of reasoning.” The types of styles are introduced as categories of possibilities, the range of possibilities depending upon that style. What Heitler and London did by introducing group theory for the study of valence, what Mulliken did by extending Bohr's aufbau principle to molecules and by the articulation of molecular orbitals, and what Pauling did with his resonance theory, all these could be considered as different discourses, each characteristic of a different style. The crucial point to have in mind is that our suggestion is not to substitute “theory” or “models” for “style.” It is to consider the developments within a variety of theoretical frameworks so that we can have as many multifaceted insights into the developments as possible.

These six clusters of issues—the epistemic content of quantum chemistry, the social issues involved in disciplinary emergence, the contingent character of its various developments, the dramatic changes brought about by the digital computer, the philosophical issues related to the work of almost all the protagonists, and the importance of styles of reasoning in assessing different approaches to quantum chemistry—form the narrative strands of our history. Such an approach may be a useful way to deal with the development of in-between subdisciplines—atmospheric chemistry, biogeochemistry, chemical oceanography, chemical physics, colloid chemistry, electrochemistry, environment chemistry, geochemistry, nuclear chemistry, photochemistry, physical chemistry, radiation chemistry, and so forth. It is, however, certainly the case that these clusters of issues appear to be indispensable for understanding how quantum chemistry developed during its first 50 years.

Let us now return to Löwdin and unfold his own contributions to the further developments of quantum chemistry.

From Peripheral Youngster to Central Networking Actor

Born on 28 October 1916, Löwdin's life and career unfolded in the city of Uppsala, renowned for its old cathedral and university, both built in the 15th century. His attachment to the city and the country was further strengthened in his adulthood despite his constant wanderings abroad, in the United States of America and the world at large, so that Uppsala became a central node in an extended network of quantum chemists.

Having received an education in the sciences and the humanities, he completed his undergraduate degree in 1939 at the University of Uppsala, and decided to continue to study theoretical physics, including thermodynamics, relativity, and quantum mechanics. Löwdin obtained his Swedish degree of “Filosofie licenciat,” roughly equivalent to having passed the qualifying examinations for the Ph.D., in 1942, and became an assistant lecturer in Mechanics and Mathematical Physics at the University of Uppsala. His scientific tours abroad began at this stage. He visited Wolfgang Pauli's group in Zürich, in 1946, and continued the work he had started for his doctorate by concentrating on the strong-coupling meson theory of nuclear forces. He was not particularly happy with the results he got and decided to move from particle physics to molecules and solids. He was awarded a Ph.D. (degree of “Filosofie Doktor”) in solid-state physics, in 1948. It was a very original piece of work, which dealt with a calculation from first principles of the cohesive energy and elastic constants of ionic crystals, and specifically of the alkali halides. He developed a number of mathematical techniques to deal with the overlap and nonorthogonality problem which involved the calculation of molecular integrals carried out on FACIT desk-calculators. Calculations were performed with the help of two or three assistants who were assigned the same task in order that their results could be checked against each other. “Parallel processing” secured the validity of results. These were the first successful ab-initio calculations on crystals (Biographical information and assessments of Löwdin's career by participants can be found in Ref. [ [14]).

After he became “Docent” at the University of Uppsala, he alternated his duties in the university with regular travelling abroad, whenever possible taking advantage of a year off for every 3 years of teaching, granted by the Swedish Government to university docents. In 1949, he paid a short visit to Nevill Mott's group in Bristol and Coulson's group in University College, London, and spent the whole academic year 1950–51 in the USA, visiting Hertha Sponer's Molecular Spectroscopy Group at Duke University, Mulliken's Laboratory of Molecular Structure and Spectra in Chicago, and Slater's Solid-State and Molecular Structure Group at M.I.T. This American sojourn was also associated with his initiation as a young and active participant in important international forums. He attended the 1951 March meeting of the American Physical Society, held in Pittsburgh, in which he delivered a talk in a joint symposium organized by the Division of Solid-State Physics and the newly created Division of Chemical Physics, in which Mulliken and Slater also participated [Löwdin talked about “Overlap Integrals of Many-Orbital Effects in the Theory of Molecules and Crystals.”].[15] In September, he was among a small group of well-known scientists who gathered at Shelter Island, Long Island, to discuss calculational questions in quantum chemistry. [From the United States came T.H. Berlin, B.L. Crawford, H. Eyring, J.O. Hirschfelder, G.E. Kimball, D.A. MacInnes, H. Margenau, J.E. Mayer, R.S. Mulliken, R.G. Parr, K.S.Pitzer, C.C.J. Roothaan, K. Rüdenberg, H. Shull, J.C. Slater, C.W. Ufford, J.H. van Vleck, and G.W. Wheland. From Great Britain M.P. Barnett, C.A. Coulson, J.E. Lennard-Jones, W. Moffitt, and L.E. Sutton.][16] This conference marked a turning point in the development of quantum chemistry, by gearing its agenda toward calculations,[17] together with the understanding that such a complex job could only be accomplished by splitting tasks in an articulated network of people and machines. Löwdin became a central player in this new way of doing quantum chemistry. After the Shelter Island meeting he would visit the USA. every year, spending half the year at various American universities, but mostly at Slater's group at M.I.T.

In 1953, he attended the Nikko Symposium, which followed the International Conference of Theoretical Physics, which took place in Tokyo and Kyoto, and, according to Kotani, was the first big international forum to be organized in Japan.[18] At Nikko, presentations and discussions centred on the refinement of approximations used in molecular problems, the extension of methods to deal with larger molecules, crystals and solids, and the assessment of the state of calculations of molecular integrals after the Shelter Island Conference. Nikko turned to be a privileged forum for assessing progress in the calculations of molecular integrals. Two informal meetings were held during and after the Symposium in which contributions from well-known groups being specialized in numerical calculations (Kotani's Tokyo-Kyoto group, Mulliken's Chicago group, Coulson's Oxford and King's College, London group, and Löwdin's Uppsala group) were discussed.[19] The importance of progress reports and standardization of nomenclature was emphasized, and a collective strategy for handling future calculations was delineated.

Having in mind the developing intellectual affinities between Löwdin and Slater, and Löwdin's regular sojourns at M.I.T., it is no wonder that it was during one such stay that Löwdin worked and published his well-known trilogy on the “Quantum theory of many-particle systems.”[20] He advocated the use of reduced density matrices in the analysis of general wave-functions, provided detailed formulas for nonorthogonalized orbitals, introduced the notion of natural spin orbitals conducive to a configuration interaction expansion of more rapid convergence, and proposed extensions of the Hartree-Fock method. This series illustrated his concern for introducing and discussing novel concepts and methods to be applied to the many-body problem underlying the study of atoms, molecules, and crystals.

Creating the Quantum Chemistry Group in Uppsala and the Quantum Theory Project in Florida

Löwdin's emphasis on mathematical rigor, and search for methods conducive to numerical calculations, became at the core of his contributions to quantum chemistry. Simultaneously, Löwdin's ability to establish and strengthen an extensive network of connections became also central to his role as a leader in discipline building. It is no surprise that his agenda encompassed an articulate plan to create an active research group at Uppsala, mirroring those of Mulliken and especially Slater's Solid-State and Molecular Structure Group.

By 1955, Löwdin was rather well established within the community of quantum chemists. He started his efforts to form his group, which in the coming 5 years shared many characteristics with similar initiatives in the post-WWII period of Big Science, including the connections with military and private agencies, the centrality of digital computers, and the international dimension, all interwoven with the role of the King of Sweden's patronage. The Quantum Chemistry Group was officially founded on July 1, 1955, and Löwdin became its first director, with a position paid by the Swedish Natural Science Research Council. The Group was an autonomous unit within the university, administratively independent and pursuing its own research goals. It was a truly international group from the very beginning. Besides Swedish scientists and staff members, which included Löwdin, Anders Fröman, Klaus Appel, Jan Linderberg, and Jean-Louis Calais, the group received from the beginning foreign scientists who came for more or less extended visits. Hall, Shull, J.O. Hirschfelder, Bernard Pullman, Joseph and Maria-Goeppert Mayer, K. Ohno, were among those who visited the Quantum Chemistry Group for extended periods of time. Among others, the group counted on the support of the Texas-Swedish Cultural Foundation to cover subsistence expenses for foreign visitors in Uppsala, and starting in 1957, the US Air Force through its European Office of Air Research and Development Command, located in Brussels, became a major sponsor, keen on supporting research of potential interest to materials science irrespective of immediate military applications.

With the acquisition of a computer ALWAC IIIE, built with vacuum tube technology, and the construction of an appropriate laboratory to house the big machine and a tightly structured group of collaborators, the Quantum Chemistry Group became one of the best equipped centers in the world. It was formally inaugurated on April 23, 1958, the centenary anniversary of Planck's birth.[22b], pp.[24-27] The group's long term research program was very ambitious, reflecting the leader's aim to embrace most of the field of quantum chemistry and solid-state physics, from basic theoretical tools and research in quantum theory to its applications to atoms, molecules, and crystals.[22b], pp.[28-30]

In the meantime, Löwdin's tenure as Docent was coming to an end, and the process of finding a permanent position was unexpectedly tortuous, due to a combination of the paralyzing effects of academic politics and Löwdin's own long term strategy. Many at the University of Uppsala did not want to loose him to an American university and were willing to proceed with the creation of a personal chair, with privileged conditions concerning his long stays abroad. This was opposed by Ivan Waller, his former PhD supervisor and a professor of Mechanics and Mathematical Physics at Uppsala, who preferred an ordinary, but permanent, chair on quantum chemistry which would continue to exist even after the retirement or death of whoever held it. The situation became even more complicated, as Löwdin was strongly attracted by the USA. university system, academic mores, and life, but at the same time he felt the moral responsibility toward his country, which had supported his education all along. Finally, in 1959, the University of Uppsala included in its budget the funding for a new chair, and by May 1960, Löwdin succeeded in becoming the first professor of quantum chemistry at the University of Uppsala and possibly in the world.

The Swedish-American connections, which were so aptly boosted by Löwdin, were not restricted to the inspiration by Mulliken's and Slater's groups on the creation of the Uppsala group, the sponsorship of American agencies, or the unfaltering support and friendship of Slater. While the process leading to the establishment of the Chair of Quantum Chemistry was slowly taking place, negotiations with the University of Florida at Gainesville, involving the Dean of the Graduate School and the Heads of the Departments of Chemistry and Physics led to the official creation of the Florida Quantum Theory Project in 1960, very much like the one in Uppsala.[21] This group acted as a bridge between quantum chemistry on both sides of the Atlantic, as a bridge between the Department of Chemistry and the Department of Physics at Florida, and finally as an institution to attract students from Latin America. It was agreed that Löwdin would spend one third of the year at Florida and bring with him some Swedish collaborators for 1–2-year stays in order to run the program during his absence.[22] The Florida group included a graduate program; a team pursuing research in quantum chemistry and solid-state physics, as in Uppsala; a winter school for the training of newcomers to the field mirroring the summer school instituted in Sweden (which we discuss in the next section); an international exchange program; and finally a computational unit dedicated to numerical analysis and electronic computing.[23] A few years later, in 1964, Mulliken joined Michael Kasha's group at Florida State University at Tallahassee and then Slater also moved to Florida to join Löwdin's group. Already retired, but both still active, they were eager to continue to accompany, support, and collaborate with their younger colleague.

Summer and Winter Schools

The first international conference organized by Löwdin in Sweden, took place in March 1955. Jointly organized with the energetic Inga Fischer-Hjalmars, Coulson's former student, it took place in Stockholm and Uppsala, and its success reflected the recognition bestowed on Löwdin as one of the prime movers in the discipline in the post-WWII years. Although, it was planned as a small-scale meeting, it accommodated 70 scholars from 12 countries,[24] among them well-known stars such as Mulliken and Coulson, but also Harrison Shull, S.F. Boys, and H.C. Longuet-Higgins. Two memorial lectures were part of the meeting. Heitler delivered a lecture on London and G.G. Hall spoke about J.E. Lennard-Jones. They respectively addressed “The theory of the chemical bond” and “The molecular orbital theory of chemical valency,” in this way paying homage to two “pioneers” and recalling the parallel development of valence bond and molecular orbital theories. Revisiting the past was an unusual move in such forums, but one typical of what became central to Löwdin's agenda for quantum chemistry. It is our contention that for him the further development of disciplinary avenues should be concomitant to a knowledge of its history, as no plans for the future were to succeed if not enlightened by the understanding of past events. No wonder that history made also its appearance in the various summer and winter schools which became Löwdin's hallmark, and a fundamental way to shape the training of successive generations of quantum chemists.

Eager to strengthen relations between chemists and quantum chemists, enlarge and consolidate the community of quantum chemists, and participate in the training of young students from diverse places, Löwdin built on Coulson's experience of organizing summer schools in Oxford since 1955, and put forward the idea of summer schools especially devoted to the discussion of methods, concepts and results in quantum chemistry. They became famous for their contribution to “the removal of both national and scientific language barriers.” [25]

The first such initiative took place in Vålådalen in the Swedish mountains during the summer of 1958, from 26 July to 30 August.[26] The next summer schools (Uppsala Summer Institutes) became a meeting point for senior and junior scholars, and a must for newcomers. In the first one, an intensive program of lectures, problem solving sessions, and informal discussions was interlaced with mountain hiking, soccer games, and swimming in chilly waters. Participants were supposed to have read the first half of Pauling and Wilson's Introduction to Quantum Mechanics and encouraged to bring with them textbooks such as Eyring, Walter and Kimball's Quantum Chemistry.[27] The summer school was capped with a week-long symposium on “Correspondence between concepts in chemistry and quantum chemistry” for which well-known quantum chemists were invited, including Pauling and Mulliken as guests of honour. Presentations were followed by lively discussions, highlighted by the known conflicting viewpoints and styles of both pioneers of quantum chemistry. (They were recorded and summarized by Hall. A rather complete version of the proceedings came out in the Technical Note 16, issued by the Quantum Chemistry Group, and known unofficially as Acta Vålådalensia. A selection of the discussions was published in Ref. [ [28]).

Löwdin chose to reflect on the state and nature of quantum chemistry, along the directions explored not long before in “Present situation of quantum chemistry” in the Journal of Physical Chemistry (1957). (For methodological reflections by Löwdin on the state of quantum chemistry see Ref. [ [29]) He summarized the basic principles of quantum mechanics, in order to address the development of quantum chemistry and its goals. He offered diagrammatic representations of the various methods used in quantum chemistry for the solution of Schrödinger's equation as well as the various mathematical steps needed in solving the many-electron Schrödinger equation for a molecular system. They depicted four different ways to connect quantum chemistry to quantum mechanics, which were discussed again before the audience at Vålådalen. In one of the methods, chemists themselves translated and adapted ordinary chemical concepts to the language and ideas of quantum science. Pauling's resonance theory was the epitome of this approach. In another, the unification of chemical and quantum-mechanical ideas was accomplished by means of semiempirical approximations, which offered the advantage of simplicity, and could lead to quantitative predictions if not pushed too far. The other two methods of establishing connecting links between chemistry and quantum science started by the quantum theory of many-electron systems and attempted to derive solutions of Schrödinger's equation, either approximate or of high accuracy. If one was only looking for strictly quantitative results, the connection between chemistry and Schrödinger's equation remained very weak. To overcome such state of things, one should work on an ever more reliable basis for the theory itself, and look for approaches built by analogy and based on the exploration of mathematical and numerical techniques, to be handled by electronic computers in the case of small molecules. Looking back at the various paths traversed to arrive at the “present situation” enabled Löwdin to pinpoint the plurality of trends and approaches, which jointly came to constitute the identity of quantum chemistry.

As to the goals of quantum chemistry, Löwdin used once again a visual representation to describe them, and underline their utilitarian role. It was a simple little diagram.

The horizontal axis represented the refinement of theory and the vertical axis indicated agreement between theory and experiment. The wave-like curve approaching an asymptotic limit was meant to show that “an elementary theory may often be brought to give excellent agreement with the experimental results, whereas most refinements of the theory will disturb the nice situation and cause disagreements.” He called the first peak “Pauling point” and the first minimum the “Ph.D. point” to call attention to the sort of problems given to Ph.D. students. Electronic computers enabled the theory of small systems to overcome the first maxima and minima on the agreement curve, but in the case of more complex systems it was not even clear where theory stood at the time. The diagram purported to show that agreement between theory and experiment was a necessary but not a sufficient condition for the validity of theory. On the short term, quantum chemists should aim to go beyond the Pauling point in order to test the final outcome of theory. On the long term, they should strive to turn quantum chemistry into an exact and predictive discipline established on secure quantum mechanical foundations, to such an extent that the accurate prediction of the properties of a hypothetical polyatomic molecule by laboratory synthesis would become a reality.

Starting in December 1960, winter schools were also established in Florida (Florida Winter Institutes). They were planned to last from 4 to 5 weeks, and planned to be sponsored by the National Science Foundation. Exactly as the summer institutes, they were followed by 1-week international symposia, which came to be known as the Sanibel Symposia since the first 16 years 17 symposia were organized in the Sanibel Island, in the Gulf of Mexico outside Fort Myers, Florida. Mulliken reminisced in his autobiography that the site of the conference was particularly attractive, due to the great variety of sea shells populating its wonderful beaches.[30] Exactly like the summer schools, the idea behind the winter schools was to organize forums for the discussion among young researchers, graduate students and researchers from other areas of the main lines of research, methods, and problems dominating the discipline. [The Sanibel Symposia were supported by the US Air Force Office of Scientific Research, and, later on, those devoted to computational quantum chemistry were supported by IBM.]

The odd year Sanibel symposia were dedicated to honor founding figures in the development of “Quantum Theory of Atoms, Molecules and Solid-state,” including events and practices associated with their contributions, not only for their intrinsic interest but also for their role in guiding future developments. Those honored were successively E. Hylleraas (1963), Mulliken (1965), Slater (1967), H. Eyring (1969), J.H. van Vleck (1971), E.U. Condon (1973), and L. Thomas (1975), just to name the first of a long series. The proceedings of the two first Sanibel meetings commemorating the contributions of Hylleraas (1963) and Mulliken (1965) appeared in the Reviews of Modern Physics and in the Journal of Chemical Physics, respectively, both published by the American Institute of Physics, which became increasingly unhappy with the space these activities were taking in its publication outlets. The proceedings of the third Sanibel meeting organized in Slater's honor (1967) were published as a supplement to the first volume of the International Journal of Quantum Chemistry, founded precisely in that very year. From then on, subsequent Sanibel meetings used the new journal as an outlet for their communications.

The International Journal of Quantum Chemistry. When History Becomes Part of the Future of Quantum Chemistry

In 1933, the Journal of Chemical Physics was founded in order to publish those papers which were “too mathematical for the Journal of Physical Chemistry, too physical for the Journal of the American Chemical Society or too chemical for the Physical Review,” according to the suggestive expression used in a letter written by K.T. Compton to G.N. Lewis announcing the future venture.[31] In 1967, roughly 30 years later, the International Journal of Quantum Chemistry, published by Interscience Publishers, a division of John Wiley and Sons, was created, among other things, to provide an outlet for the proceedings of the Sanibel meetings. But this is certainly just part of the story. Three years earlier, in 1964, together with the various scientific and educational activities in which Löwdin was deeply involved at the two sister institutions on both sides of the Atlantic, he had launched a series of books called Advances in Quantum Chemistry published by Academic Press in order to help experts and nonexperts to follow the rapid developments in quantum chemistry, “a borderline area,” “a rapidly developing field” which “falls between the historically established areas of mathematics, physics, chemistry, and biology.”[32] The series was meant to offer a survey of the recent developments in quantum chemistry as seen by a number of its internationally leading research workers in various countries. Authors were invited to give their personal points of view on the current state of selected parts of quantum chemistry, freely and without space limitations, in order that a plurality of voices, including those of the “pioneers,” could be heard. Two pioneers in the field, Hylleraas and Slater, “as active as ever,”[33] gave their views on two fundamental problems, the Schrödinger two-electron atomic problem, and energy band calculations by the augmented plane wave method, respectively.[34] In line with this venture, but offering extra possibilities, emerged the International Journal of Quantum Chemistry. That there was continuity in change is clear from the striking similarity between the two initial paragraphs of the journal's “Program” and two paragraphs of the “Preface” to Advances in Quantum Chemistry. They both were concise but sharp editorial manifestos setting Löwdin's agenda for quantum chemistry in no uncertain terms. We cite them fully from the “Program”:

  • Quantum chemistry deals with the theory of the electronic structure of matter: atoms, molecules, and crystals. It describes this structure in terms of wave patterns, and it uses physical and chemical experience, deep-going mathematical analysis, and high-speed electronic computers to achieve its results. Quantum mechanics has rendered a new conceptual framework for physics and chemistry, and it has led to a unification of the natural sciences which was previously unconceivable; the recent development of molecular biology shows also that the life sciences are now approaching the same basis.
  • Quantum chemistry is a young field which falls between the historically developed areas of mathematics, physics, chemistry, and biology. As a result the research workers in this field have published their results in periodicals of many different types. Today quantum chemistry is undergoing such a fast development that many scientists feel that it deserves its own journal on an international basis. The purpose of such a journal would not be to compete with the existing periodicals but to provide a special means of communication for quantum chemists all over the world.[35]

Written at a time in which quantum chemistry was experiencing intense networking and growing internationalization, and was exploring the possibilities provided by the electronic digital computer while at the same time extending its domain to molecules of biological interest, Löwdin's programmatic declaration called attention to a number of specific features of the subject-matter of quantum chemistry—the elucidation of the electronic make-up of atoms, molecules, and aggregates of molecules; the interplay of theory, experiment, mathematics, and computational algorithms in forming the methodological framework of quantum chemistry; its relationship with chemistry, physics, mathematics, and biology; and finally the assessment of the role of quantum mechanics in providing a unifying framework for the natural sciences, and eventually for the life sciences.

Paying heed to his belief that the past of quantum chemistry should be an integral part of its future developments, Löwdin chose as honorary editors “three great pioneers,” Heitler, Mulliken, and Slater. The editorial board included Coulson, Raymond Daudel, Kotani, Roy McWeeny, C.J.J. Roothaan, Shull, J.O. Hirschfelder, L. Jansen, and R. Pauncz, who were in charge of formulating the scientific policy of the journal together with Löwdin himself. Calais and Y. Öhrn were assistant editors and composed the editorial office. The advisory editorial board included 35 members from 24 countries and 4 continents (17 in Europe, 3 in Asia, 1 in Oceania, and 3 in America), representing various aspects of quantum chemistry, and materializing Löwdin's bid on ever growing internationalization.

Furthermore and since for Löwdin the strength of quantum chemistry resulted from a diversity of interlocking constitutive elements and approaches, the main fields to be addressed in the journal were: fundamental concepts and mathematical structure of quantum chemistry; applications to atoms; to molecules; to crystals; and to molecular biology; and finally, computational methods in quantum chemistry. They all dealt with the application of quantum mechanics to the theory of atoms, molecules, and crystals.

However, the journal was not envisioned as a mere outlet for original contributions to quantum chemistry, but as an extra means of enhancing communication between a geographically dispersed community of practitioners. For that reason, it was meant to include short notes about papers published elsewhere, progress reports of major research centers, besides housing the proceedings of the Sanibel conferences, successor associated meetings, 1 and many other conferences, as well as various announcements.

The view of the past as a clue to the future emerged from the editorial program, and came to be reflected in the journal's organization. It was revealed by the inclusion of proceedings of meetings honoring “pioneers,” recollections by participants, obituary notices or whole special issues dedicated to selected participants, reproduction of classical papers in the area, and papers of a more historical bent. But even in what relates to scientific papers themselves, history played a role. According to the guidelines expressed in the “Program” in the first issue, some “basic rules” should be followed: “a fairly extensive historical review of the field” should be included as an introduction to the presentation of major new results, whereas “a very short introduction” should precede the presentation of minor results.

Furthermore, in the first issue, history was part and parcel of the reflection on the “Nature of quantum chemistry” offered by the editor. Disguised as straightforward guidelines to journal's contributors, it really offered Löwdin's perceptive considerations on the nature, methods and tools of his discipline Figure 2. In delineating the “ideal form of a theoretical paper,” Löwdin called attention to the interplay of experiment and theory in any “science,” presented the role of interpretations as rules to go from one to the other, and considered at the time that quantum chemistry “could boast more of its conceptual framework than of its numerical achievements.” He used his knowledge of the history of quantum chemistry to emphasize that its future was tied to numerical computations and analysis with the recourse to potent and fast computers, but he was also adamant that “various types of theories are constructed for different purposes,” so that ab-initio, semiempirical theories or any other sort of theory had a role to play in any phase of disciplinary development, to such an extent that they should be explored in parallel having always in mind their respective domains of applicability. So, for him, the construction of “meaningful semiempirical theories” continued to be one of the most important future goals for applied quantum theory. Despite Pauling's estrangement from the discipline's postwar developments, and his absence from the list of honorary editors chosen by Löwdin, his legacy continued to play a role in disciplinary inroads. But contrary to Pauling who had always defended a monolithic view to quantum chemistry, Löwdin wholeheartedly embraced a pluralistic view of quantum chemistry in which different approaches contributed consistently to forge the evolving identity of quantum chemistry.

Concluding Remarks

The hybrid conception of the International Journal of Quantum Chemistry, and its function as a privileged communication outlet for experts and newcomers alike, continued to shape the journal's evolving identity. When one compares the two paragraphs we quoted from the “Program,” announced in 1967, with how the journal is presented nowadays, similarities are striking while adaptation to new trends is accommodated:

  • Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules, and the condensed matter. Over the past decades, synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology, and materials science.[36]

For the new editor, it is clear that in the past 50 years, quantum chemistry has certainly succeeded in providing an explanatory framework for the electronic structure of matter, be it in atoms, molecules, crystals or generally condensed matter. Exploring computational possibilities has turned it into a “truly interdisciplinary science” able to accommodate new and diverse techno-scientific fields. As such the journal continues to respond efficiently to the needs of the quantum chemistry research community, “providing a dedicated forum for rapidly reporting breakthroughs in the development and application of quantum mechanical concepts in chemistry, physics, biology, and materials science.”

Interestingly, it does so through the introduction of some novelties, materialized in the publication of “an exciting mix of comprehensive reviews, instructive tutorials, visionary perspectives,” together with more traditional “high-impact rapid communications and full papers that represent the gamut of the field of quantum chemistry, from theory to simulations to applications (see Figure 3).”

Reviews, tutorials, and perspectives are new ways found to manifest Löwdin's old belief in the power of a journal playing multiple functions beyond those of a strictly scientific one. Training newcomers with the help of tutorials and reviews, guiding them into new problem research areas, continuing to publish proceedings of many conferences, pays certainly heed to Löwdin's kaleidoscopic view of quantum chemistry, illustrated by a happy coincidence in the journal's menu by a kaleidoscope-like diagram.

In this article, we tried to highlight some of the events in the history of quantum chemistry associated with Löwdin, the most committed advocate of quantum chemistry of the “next generation,” and to show that for him a kaleidoscope of cultural elements/subcultures came to constitute the various interlaced strands of views and practices shared by quantum chemists. Surely, he was a larger than life character, an indefatigable practitioner of a subdiscipline in a particularly critical juncture of its history. We very much hope that this necessarily sketchy article, may underline the need for a full-fledged biography of Per-Olov Löwdin.

Figure 1.

In P-O Löwdin, “Twenty-five years of Sanibel Symposia: a brief historic and scientific survey”, Int. J. Quantum Chem. 28, S19, 19–37 (1985).

Figure 2.

Connection between theory and experiment in science. In “Nature of Quantum Chemistry”, Int. J. Quantum Chem. 1, 1, 7–12 (1967).

Figure 3.

From the journal's website (http://q-chem.org). Retrieved August 12, 2013.


The authors thank Matteo Cavalleri for the invitation to contribute to the reviews section of the International Journal of Quantum Chemistry and for his perceptive comments on our article. We also extend our thanks to the referees for their remarks and suggestions.


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    Ana Simões is associate professor at the Faculty of Sciences of the University of Lisbon. She is presently the head of its Unit for the History and Philosophy of Science and of the Interuniversity Research Center of History of Science and Technology, which includes historians and graduate students from the University of Lisbon and the New University of Lisbon. Her research has centered on the history of quantum chemistry and the history of science in the European Periphery, both from a historical and historiographical viewpoint. She is a founding member of the international group STEP — Science and Technology in the European Periphery and of the online journal of history of science and technology HoST. She is the author and editor of more than 90 national and international publications. Her most recent book, co-authored with Kostas Gavroglu, is titled Neither physics nor chemistry. A history of quantum chemistry (2012). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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    Kostas Gavroglu is professor of history of science at the Department of History and Philosophy of Science of the University of Athens. He is, also, the Director of the University Historical Archives. His research interests are the history of low temperature physics, the history of quantum chemistry and the issues related to the appropriation of scientific ideas and practices in the regions of the European Periphery since the 18th century. He is co-editor (with Professors Jurgen Renn and Robert Cohen) of the Boston Series in Philosophy and History of Science of Springer Publishers and editor of the series on history of science of University of Crete Publishers. His most recent books are with Ana Simões Neither physics nor chemistry. A history of quantum chemistry (MIT Press, 2012) and the edited volume of History of Artificial Cold, Scientific, Technological and Social Issues (Springer 2013). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]


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    They have assumed diferent titles in time, adapting to new trends: Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory (since 1967); Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory and Quantum Biology (since 1968); Proceedings of the International Symposium on Quantum Biology and Quantum Pharmacology (since 1969); Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory and Quantum Statistics (since 1974); Proceedings of the International Symposium on Atomic, Molecular, and Solid-state Theory, Collision Phenomena, and Computational Methods (after 1978); Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory, Collision Phenomena, and Computational Quantum Chemistry (after 1981); Proceedings of the International Symposium on Quantum Chemistry, Theory of Condensed Matter, and Propagator Methods in the Quantum Theory of Matter (after 1982); Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory, Scattering Problems, Many Body Phenomena, and Computational Quantum Chemistry (after 1986).]