This text was taken from:
C. Reinhardt (ed.)
Chemical Sciences in the 20th Century
Wiley-VCH, Weinheim, 2001
More info about this book here.
Issues in the History of Theoretical and Quantum Chemistry,
Ana Simões and Kostas Gavroglu
Contrary to what is sometimes supposed, the theoretical chemist is not a mathematician,
thinking mathematically, but a chemist, thinking chemically.
In this paper we discuss a number of issues which manifest the theoretical
particularity of quanfum chemistry and which are usually not discussed in an
explicit manner either in the historical or in the phiosophical studies related to
quantum chemistry. We shall focus on five issues: the re-thinking of the problem of
reductionism, the discourse of quantum chemistry as a confluence of the traditions
of physics, cheniistry, and mathematics, the role of textbooks in consolidating this
discourse, the ontological status of resonance, and the more general problem of the
status of the chemical bond. Finally, we shall briefly discuss the impact of large scale
Re-thinking Reductionism or the Chemists' Uneasy Relation with Mathematics
The question of reductionism has been reigning supreme in any discussions
concerning the philosophical, theoretical, methodological and many times historical
aspects of chemistry. In 1929, Paul A. M. Dirac, after he had successfuliy incorporated the spin quantum number into the newly developing quantum mechanics,
expressed what every physicist felt to be true and what every chemist was afraid that
it might be true.
The underlying physical laws necessary for the mathematical theory of a large part
of physics and the whole of chemistry are [now] completely known, and the
difficulty is only that the exact application of these laws leads to equations much
too complicated to be soluble.
The interesting aspect of this dictum was that although it was trivially true, it was, at
the time, of no practical help nor of any consequence for the chemists. In fact the
very success of the Heitler-London paper — which could be taken as the first
instantiation of Dirac's program — was a strong indication that what prevented
chemistry from being reduced to physics was mathematics — or rather, the lack of it.
Dirac's 1929 pronouncement encapsulated what was already part of the physicists'
culture for many decades. And, with Dirac's specific contributions to the development of quantum mechanics, it became possible to articulate this reductionist
program. After the Heitler-London paper, chemistry could be perceived as being
different manifestations of spin, and spin, after all, was under the jurisdiction of the
physicists. And though physicists felt that the new quantum mechanics had also
taken care of chemistry, the chemists themselves did not appear to have panicked
that their identity was being transformed and they were being turned into
physicists. Nor did they feel that their very existence was being threatened, though it
appeared that what they had been doing could now be done much better by the
physicists. The appropriation of quantum mechanics, the aftempts to overcome
cultural resistances within the chemical community on how to appropriate
quantum mechanics, and the different views on how to form the appropriate discourse
are some of the issues related to the problematic of reductionism which we have
Here we want to raise a different issue and investigate whether reductionism may
be a misplaced category if one wants to discuss a number of questions for chemistry.
Perhaps reductionism is a physicist's analytical tool and not a chemist's. Might it be
the case that the whole notion of reductionism expresses a trend that is dear to the
physicist's own culture rather than that ofthe chemists? Though physicists took for
granted the reduction of chemistry to physics and did little about it, the chemists did
not have the luxury of waiting for history to fulfill such an agenda. For reductionism
may have been a program, but it was nearly impossible to realize it because, as
became evident right at the beginning, one could not deal analytically with any of
the other elements except hydrogen and helium, even in grossly approximate
Are there any other dimensions to reductionism, whose discussion may be
considered more fruitfull in addressing the same set of problems? What we would
like to discuss is the (uneasy) relationship of chemists and mathematics and argue
that the chemists' relationship with the appropriation of mathematics into their
culture was far more complex and difficult than their appropriation of physics. And
though the two cannot be considered as totally independent of each other, it can in
fact be argued that chemists were more resistant in accepting the use of
mathematics rather than the physical concepts, and the physical techniques.
Like all forms and expressions of appropriation, opinions differed among the
members of the chemical community. Some pushed quite strongly for introducing
mathematics into chemistry. The chemist Edward Frankland predicted that the
future of chemistry was to lay in its alliance with mathematics. The chemist Paul
Schützenberger believed that mathematics would become an instrument as useful
to the chemist as the balance. Jacobus H. Van't Hoff could not have been more
mathematical in his systematic study of chemical therrnodynamics. Wilhelm
Ostwald's extensive use of mathematics would have been much more influential had it
been not undermined by his insistence on energetics. Gilbert N. Lewis was not less
skilled in mathematics. Even Joseph Larmor and Joseph J. Thomson before him
tried to propose a mathematical framework for dealing with chemical problems. But
resistance to such programs came from different quarters.
As early as 1884, one of the pillars of the British chemical establishment and a
person who was very sympathetic to the physicists meddling into the chemists'
affairs, Henry E. Roscoe was still not sure how successftil mathematics would be for
One of the noteworthy features of chemical progress is the interest taken by
physicists in fundamental questions of our science. We all remember Sir William
Thomson's interesting speculations, founded upon physical phenomena,
respecting the probable size of the atom. Also Helmholtz's about the relation between
electricity and chemical energy. A further subject of interest to chemists is the
theory of vortex-ring constitution of matter first proposed by WT and lately
worked out from a chemical point of view by J. J. Thomson ... How far this
mathemcstical expression of chemical theory may prove consistent with thefacts remains
to be seen.
In 1906, Ostwald had indicated that he was having second thoughts about his denial
of the existence of atoms. The British chemists did not waste any time to settle their
accounts with the person who — when he gave the Faraday Lecture in London two years
earlier — had put them in such a difficult situation, trying to convince them to
abandon the atomic notions and lure them into the vague promises of energetics.
Without even waiting for Ostwald's official declaration that he did, indeed, believe in
atoms, Arthur Smithells, the forceful spokesman of British chemistry at the 1907
meeting of the British Association for the Advancement of Science, took it upon
himself to deliver the pangeric of the victorious.
Smithells, initially, expressed bis excitement about the state of chemistry. Though
the discovery of radioactivity did mark a new epoch in the history of chemistry, and
radium was in a way an embarrassment, since it was elementary and it also broke
into elementary substances, there was not enough evidence to warrant any
unsettlement of "the scientific articles of the chemists' faith."
The perplexities of the chemists are not due to the new ideas being presented, but
to the invasion of chemistry by mathematics ... With radioactivity, in relation to
the ponderable, we seem almost to be creating a chemistry of phantoms ... this
reduction in the amount of experimental materials, associated as it is with the
exuberance of mathematical speculation of the most bewildering kind concerning
the nature, or perhaps I should say the want of nature, of matter, is calculated to
perturb a solid and earthly philosopher whose business has hitherto been
confined to comparatively gross quantities of materials and to a restricted number
of crude mechanical ideas.
He said that as a representative of the chemists he wanted to make some points,
because in recent times, even before the advent of radium, a good deal had
happened which had given chemists occasion to ask themselves whether chemistry
was not beginning to drift away from them. In the past years, the most important
developments had been on the physical side, and one great chemist remarked to
him that he was feeling "submerged and perishing in the great tide of physical
chemistry, which was rolling up into our laboratories."
It is precisely such men who should be preserved to chemistry. Though chemistry
and physics meet and blend there is an essential difference between the genius of
physics and the genius ofchemisiiy. Äpart from his manipulative skills, the latter
is not given to elaborate theories and is usually averse to speculation; nor has he
usually an aptitude in mathematics. Such the normal chemist is, or was, and I
hope he always may be — naked perhaps in some respects, but unashamed. There
seems to be a solicitude in some quarters to make a chemist more than a chemist,
a solicitude which, if granted will make him something less than one .... The
most important undertaking in the education of the chemists is to be trained in
the act of exact experiment and that his experimental conscience should acquire a
finer edge. Chemistry should not be invaded by mathematical theorists.
Smithells's conservative backlash was complemented in two years by Henry
Armstrong's aggressive stand. Obviously to prepare his audience about the spirit of the
things to come, Armstrong started by quoting a professor of world-wide reputation
— whom he preferred to be anonymous — who had said that a "man's opinions are of
much more value than his arguments." And in the longest address to the chemical
section of the BAAS for over 30 years, the audience was, indeed, treated to the man's
opinion, induding a long tirade of why women should not be made Fellows of the
Chemical Society since to encourage such a move will "inevitably lead women to
neglect their womanhood". Concerning his views about the energeticists,
Armstrong boasted that, even though his attitude was one of "complete antagonism
towards the speculations of the Ostwald school", he was nevertheless the first
English chemist to publicly remark that Ostwald's investigations were of the highest
importance. But now Ostwald had changed his mind, and Armstrong warned his
fellow chemists in a most dogmatic manner about the dangers of dogmatism. He
reminded his audience how Ostwald had:
charged his test tubes with ink instead of chemical agents and by means of a too
facile pen he has enticed chemists the world over into becoming adherents of the
cult [of his school] — a cult the advance of which may well be ranked with that of
Christian science, so implicit has been the faith of its adherents in the doctrines
laid down for them, so extreme and narrow the views of its advocates ... The
lesson we shall have learnt will be of no slight import ... if it serve to bring home
to us the danger of uncontrolled literary propagandism in science, if it but cause
us always to be on our guard against the intrusion of authority and of dogmatism
in our speculations.
But that was not the end. There was one more account to be settled. Armstrong
appealed to the physicists to make themselves more acquainted with the methods of
the chemists and to stop speculating unnecessarily.
Now that physical inquiry is largely chemical, now that physicists are regular
excursionists into our territory; it is essential that our methods and our criteria be
understood by them. I make this rernark advisedly, as it appears to me that, of late
years, while affecting almost to dictate a policy to us, physicists have taken less
and less pain to make themselves acquainted with the subject matter of chemistry
especialiy with our methods of arriving at the root conceptions of structure and
the properties as conditioned by structure. It is a serious matter that chemistry
should be so neglected by physicists.
Though Armstrong's views may be taken to express the chemists' assertiveness, it is
interesting to note the following. When Arrnstrong died in 1937, Ernest Rutherford
wrote to Nevil V. Sidgwick and said that he had been told that "Armstrong had never
got beyond arithmetic, and that even algebraic symbols were Greek to him. This
may account for his attitude to all mathernatical theory
This uneasy relationship between chemists and mathematics can, also, be traced
during the emergence of quantum chemistry. All those who were directly involved
in the development of quantum mechanics were conftonted with the evaluation of
the relations of chemistry to physics and by extension to mathematics. In 1928, in a
review paper written for Chemical Reviews, John Van Vleck outlined the problems
faced by the new science of a "mathematical chemistry". Most were eager to point to
the subsidiary role of mathematics. Linus Pauling managed to present a coherent
treatment of the chemical bond which was appealing to the chemists because of its
frequent reliance on the "chemists' intuition" and the use of a lot of existing
experimental data to be able to explain or predict other experimental data. Though it
was repeatedly stressed that the understanding of the nature of the chemical bond
was possible only because of the developments due to quantum mechanics, his use
of detailed mathematical formulations was reduced to a bare minimum.
Some years later, Charles A. Coulson argued that the "splenclid and elegant
elucidation" of so large a part of chemistry by quantum mechanics forbade chemists
to be happy with an electronic theory of valence couched in pre-quantum mechan-
ical terms. In 1952, he was careful to stress in his book Valence that quantum
chemistry should be understandable by a chemist with no mathematical training.
The presentation of the principles of quantum mechanics was reduced to two
introductory chapters, and in many instances mathematical results were illustrated
or complemented by the extensive use of visual representations, an implicit
acknowledgment that visualizability, instead of elaborate mathernatics, still re-
mained one of the constitutive features of chemistry.
Hugh C. Longuet-Higgins, one of Coulson's students, went even further in
assessing the complex relation of quantum chemistry to mathematics. He turned
the whole argument upside down. He did not consider that there was a danger that
quantum chemistry might be subsurned under mathematics, and boasted that the
time had come for chemists to teach mathematics to the mathematicians. He
introduced the paper "An application of chemistry to mathematics" with the bold
I imagine that the title of this paper will shock many of the readers of this Journal.
It is generally taken for granted, at least by mathematicians, that in the hierarchy
of the exact sciences mathematics holds first place, with physics second and
chemistry an insignificant third. Organic chemistry is considered at best a
practical necessity and at worst a rather noisome branch of cookery. In this paper
I hope to show that pure mathematics is occasionally enriched not only by the
fruits of physics, but also by those of chemistry and to establish this thesis by
proving a mathematical theorem of some intrinsic interest which was, in fact,
suggested by an empirical generalization in organic chemistry.
The problem was the solution of Schrödinger's equation under certain simplifying
assumptions, and specifically the task of obtaining expressions for the electronic
energy and electron densities by recourse to the theory of complex variables for
benzenoid hydrocarbons, a rather special but very important dass of molecules.
Such is the case of naphthalene, which Coulson and his group had defined as an
alternant hydrocarbon, and for which experiment suggested that the effect on the
electron density around atom r due to the effect of a perturbation at atom s is of one
sense if r and s belonged to the same system and of the opposite sense if they
belonged to different systems. It was this experimental result that Longuet-Higgins
showed to imply the validity of a certain mathemafical theorem. He concluded by
pointing that the discovery of many other theorems, with an intrinsic interest from
the purely mathematical point of view, was prompted by chemical laws. He hoped
then that "the more trained mathematicians will come to recognize theoretical
chemistry as a subject not altogether unworthy of their professional attention." 
We have noted these cases not in order to make any condusive argument about
the relationship of chemists to mathematics, but rather as indicative instances of a
trend among chemists which has not been properly discussed up to now: as
chemists were discussing the appropriation of physics into their own culture, there
was a parallel and relatively independent discussion among them concerning their
appropriation of mathematics.
Convergence of Diverging Traditions: Physics, Chemistry, and Mathematics
When referring to the different approaches to the question of atomic bonding,
nearly all textbooks and research papers project two such methods: the Heitler-
London-Slater-Pauling valence bond method and the Hund-Mulliken method of
molecular orbitals. Elsewhere we have argued that the views of these protagonists
about theory building and the role of theory in chemistry form a set of criteria that
justifies a different classification: the Heitler-London approach versus the Pauling-Mulliken approach. Walter Heitler and Fritz London shared, in effect, Dirac's
reductionist view: the underlying laws governing the behavior of electrons were
known; and hence to do chemistry meant to deal with equations which were in
principle soluble, even though in practice they may only produce approximate
solutions. Pauling and Robert S. Mulliken thought differently on how the newly
developed quantum mechanics could, in practice, be applied to problems of
chemistry and, more specifically, to the problem of the chemical bond. They felt that
a reductionist agenda was, in practice, useless to the chemist, and by making ample
use of semi-empirical methods they developed their respective approaches, whose
only criterion for acceptability was their practical success. And, most signiflcantly,
they both shared a common outlook on how to construct their theoretical schemata,
on the character of the constitutive features of their theories, on what the relation of
physics to chemistry should be and on the discourse they developed to legitimize
their respective theories.
Let us now turn to a number of issues associated with the theoretical outlook
shared by Pauling and Mulliken. Pauling's valence bond and Mulliken's molecular
orbital approaches were not simply two practical methods to solve valence problems.
They were part of two different conceptual schemata, which can be explained in
terms of two different legacies — that of physics in the case of Mulliken and that of
chemistry in the case of Pauling. Their contributions were simultaneously the
culmination of two different research traditions and the beginning of a new
discipline and a new practice. Their research programs evolved from two different
research programs developed in the context of the old quantum theory. Pauling was
eager to establish a continuity between his contributions and Lewis's program for
the explanation of the covalent bond developed in the context of the work of the
community of physical chemists. In contrast, Mulliken's work on band spectra
structure can be seen as an instantiation of the research agenda carried out by the
American molecular physics community. Pauling's research program was presented
as an extension of the classical structure theory whereas Mulliken's agenda was
presented in sharp contrast with them. 
Extending Heitler and London's work but demarcating himself from their
methodological orientation, Pauling outlined a chemical theory based on the
concept of resonance. The appropriation of resonance from the quantum
mechanical context in which it was used by the physicists Heitler and London, to a new
context in which it served a strictly chemical end, played a fundamental role in the
formulation of a number of new concepts, from the hybridization of bond orbitals,
to one-electron and three-electron bonds, the discussion of the partial ionic character of covalent bonds in heteropolar molecules, and the idea of resonance among
several hypothetical bond structures. In certain aromatic compounds such as
benzene, Pauling suggested that the wave function should be written as a
superposition of wave functions associated with the different valence bond structures
which chemists had introduced to represent all its properties. The new concept
explained in "an almost magical way"  the many puzzles that had plagued
organic chemistry, establishing the connecting link between Pauling's new valence
theory and the classical structural theory developed throughout the second half of
the nineteenth century.
The most characteristic feature of Pauling's approach, which became known as
the valence bond approach (VB) is that it considers the combining atoms as units.
The molecule is therefore supposed to be formed by bringing together two or more
atoms that are then allowed to interact. Pauling's ontological commitments were
associated from the start to a number of rules enabling him to get numerical values
of bond energies and bond angles. This quantitative dimension of the VB approach
was not matched for a while by the molecular orbital approach (MO), developed by
Mulliken and others, in which the molecules are taken as the main building blocks.
It is assumed that only nuclei (or nuclei plus inner electrons) are brought together
into their positions, and only afterwards are the remaining electrons — the valence
electrons — allowed to be fed into what were called molecular orbitals. According to
Mulliken, the first method followed the "ideology of chemistry"  whereas the
latter departed from it.
The clarification of the relations between electronic states and band spectra
structure led Mulliken to dispense altogether with classical valence theory and to
propose an entirely different approach to the question of molecule formation and
chemical bonding. Mulliken rejected the accepted notion of chemical structure and
proposed to analyze the phenomena of molecule formation in terms of the
electronic structure of molecules. Reasoning by analogy with Bohr's building-up
principle for atoms, Mulliken considered that molecules were formed by feeding
electrons into molecular orbitals, that is, into orbitals that encircled two or more
nuclei. Electrons were delocalized in the sense that there was a non-zero probabiity
of finding them near more than one nucleus. The assignment of quantum numbers
to electrons in molecules, and the classiflcation of molecular orbitals, was achieved
by exploring the relations to the united-atom description and the separated atom
description. New auxiliary concepts were introduced such as promoted and un-
promoted electrons, bonding, non-bonding, and anti-bonding electrons, and varying
bonding power of electrons. In 1929, John Lennard-Jones introduced the physical
simplification of representing molecular orbitals as linear combination of atomic
orbitals (LCAO), a step that was fundamental to the mathematical development of
Many reasons contributed to the successful way in which quantum chemistry
developed in the United States. Mulliken summarized them well when he called
himseff a middleman between theory and experiment, and between physics and
chemistry. A particular kind of institutional atmosphere accounted for the
appearance of this new type of scientist, whose definition as a chemist or physicist was in
many instances a matter of chance, personal preferences, or institutional affiliation.
The institutional ties between chemistry and physics were stronger in the United
States than in Europe. At universities like Berkeley and Caltech, chemistry students
were often learning as much physics as chemistry and thus were more apt to learn
and accept quantum mechanics than their European counterparts. Pauling's
knowledge of physics was impressive and Mulliken was an expert on the quantum theory
of molecules. Besides Berkeley, Caltech, Harvard, and MIT, more universities were
promoting the cooperation between their physics and chemistry departments.
Examples were Princeton, Chicago, Michigan, Minnesota, and Wisconsin. But
before Mulliken, Pauling, John Slater, and Van Vleck, the preceding generation of
chemists and physicists — chemists like Lewis and Arthur A. Noyes, Richard C.
Tolman, and Wiiliam Harkins, and physicists like Edwin C. Kemble and Raymond T.
Birge — planted the seeds which blossomed into quantum chemistry.
The abilty of the particular scientists to be at ease with both theory and
experiment might well account for the successful development of quantum
chemistry. Mulliken started as an experimentalist but shifted into theory owing to the
delay in getting the high-resolution spectrograph he had been promised when he
moved to Chicago in 1928. Pauling's determinations of crystal structures were
instrumental as a source of practical information on bond angles and bond lengths
to be used in his ftiture, more theoretical endeavors.
An altogether different situation occurred in Europe, specifica]ly in Germany.
There was a sharp division between theory and experiment in the German physical
community. As to the German chemists, they were in general ill-prepared to cope
with the challenges of quantum mechanics. One example was Kasimir Fajans, a
professor of Physical Chemistry in Munich when the young Pauling was there in
1925—1927. Fajans was already one of the leading physical chemists. Many years
later, in 1987, Pauling remembered that Fajans' inabiity to get a good grasp of
quantum mechanics was a problem that bothered him for the rest of his life.
In Germany, by the early 1930s, chemistry and physics were well established
disciplines, entertaining few disciplinary, methodological, or institutional ties to
each other. Therefore, scientists whose profile could favor an attack on chemical
problems using the tools of the newly developed quantum mechanics were hard to
flnd. Several German physicists, but not chemists, were interested in applications to
chemistry and contributed initially to the fleld; but they were unable in the long run
to carry out their research programs. Such were the cases of Heitler, London,
Friedrich Hund, and Max Born. An exceptional case in the German context was the
physicist Erich Hückel. He was able to overcome his deficient chemical background
by taking advantage of his brother Walter Hückel's expertise in organic chemistry,
which probably helped him in asking the pertinent questions in organic chemistry
to be answered in the framework of quantum mechanics.  Erich Hückel developed a reductionist program in which the facts of organic chemistry were to be
interpreted by taking seriously the peculiar theoretical features ofquantam mechan-
ics. Its non-visualizabiity was seen as forbidding Pauling's description of the
structure of benzene by means of resonance among several fictitious valence bond
structures. By 1937, Hückel abandoned the field, unable to challenge a scientfflc
establishment in which German physicists were not yet ready to accept research on
the quantum mechanical properties of the chemical bond as a topic of research for
physicists, and German chemists did not consider quantum chemistry a field of
The genesis and development of quantum chemistry as an autonomous sub-
discipline owed much to those scientists who were able to realize that "what had
started as an extra bit of physics was going to become a central part of chemistry".
Those that manage to escape successfully from the "thought forms of the phys-
icist"  by implicitly or explicitly addressing issues such as the role of theory in
chemistry, and the methodological status of empirical observations helped to create
a new space for chemists to go about practicing their discipline. The ability to "cross
boundaries" between disciplines was perhaps the most striking and permanent
characteristic of those who consistently contributed to the development of quantum
chemistry. Moving at ease between physics, chemistry, and mathematics became a
prerequisite to be successful in borrowing techniques, appropriating concepts,
devising new calculational methods, and developing legitimizing strategies.
In the mid- and late 1930s when quantum chemistry was already delineated as a
distinct sub-discipline, there was in Britain a group of people whose contributions to
the further entrenchment of the disciplinary boundaries of quantum chemistry
proved rather decisive. Lennard-Jones, Douglas R. Hartree, and Coulson were the
best known members of this group. Coulson was the most vocal and the person in
whose work we find all those trends that have characterized the "British approach"
to quantum chemistry. If the "German approach" inaugurated by London, Heitler,
Hund, and E. Hückel was emphasizing the application of first principles of
quantum mechanics to chemistry and if the "American approach" of Pauling,
Mullliken, Van Vleck, and Slater was characterized by a pragmatism combined with
a creative disregard towards the strict obeisance to the first principles of quantum
mechanics, the British succeeded in enlarging the domain of applied mathematics
so as to include techniques derived from their discussion of problems of quantum
Both Cambridge, where Coulson studied and completed his doctorate, and
Oxford, where Coulson became professor of Applied Mathematics and then
professor of Theoretical Chemistry, had researchers who were particularly receptive to
the new possibiities offered by the new quantum mechanics for chemistry. Two in
particular, Ralph H. Fowler at Cambridge and Sidgwick at Oxford, were quite
decisive in creating a milieu where these possibiities were actively sought. When
the new quantum mechanics was first formulated, Fowler was 37 and Sidgwick was
53 years old, and they immediately became enthusiastic converts to the new ideas.
Their subsequent work was not directly related to the developments of quantum
mechanics, hut Sidgwick through his book Some Physical Properties of the Covalent
Link in Chemistry (1933), his annual reports, and his presidential addresses became
one of the most effective propagandists of the immense usefulness of resonance for
chemistry. Fowler, on the other hand, was himself one of the very expressions of the
Cambridge tradition of mathematical physics. Two of the students Fowler su-
pervised became professors at Cambridge in 1932, the same year he himself was
appointed professor of Mathematical Physics. Dirac became the Lucasian Professor
in Natural Philosophy and Lennard-Jones the first Professor in Theoretical
Furthermore, the supervisor and his two students appeared to share similar views
on the relations of the new quantum mechanics to chemistry. At the end of 1929
Fowler, who was one of the editors for Cambridge University Press, asked London
whether he would be interested to write a book on "the foundations of chemistry in
quantum mechanics".  Dirac during the same year had, as we saw, expressed bis
view about chemistry, which would permanently mark the physicists' culture. By
1931, Fowler was already expressing a subtler view of the whole problem. In a report
delivered at the Centenary Meeting of the British Association for the Advancement
of Science, he expressed the view that now the chemical theory of valence had
shown that it was no longer independent from physical theory but just a beautiful
part of a simple self-consistent whole, that of non-relativistic quantum mechanics.
He felt that he had sufficient chemical appreciation to claim that quantum mechan-
ics is glorified by the successes in theoretical chemistry rather than saying that the
recent developments had shown that "there is some sense in valencies."  He still
believed, though, that a full quantum mechanical explanation of the valence rules of
the quantum chemist was to be reached in the near future.
Lennard-Jones in an artide in Nature in 1931 which also echoed the views he
expressed in lectures at the Physical and also Mathematical Societies in London,
considered the connection between the pairing of electrons with the "valency rules
ofthe chemist" as a consequence of the same "mathematical and physical principles
which have been formulated for other branches of physics."  He was convinced
that the general principles behind the different forces were understood and that
such insights may come to be regarded as one of the greatest achievements of the
present formulation of quantum mechanics. What was now required were mathe-
matical techniques capable of applying them to particular cases.
The year 1932, when they were all appointed professors, was also the year Coulson
started his doctorate, first as a student of Fowler, and then he was nominally
supervised by Lennard-Jones. But Coulson's researches, though they were deeply
grounded in this Cambridge tradition, showed a characteristic resistance against
being lured by the excesses of this program. Coulson, the mathematical physicist,
would "refuse" to become the long hand of physics in chemistry. His works and the
evidence in the archival material show that Coulson was progressively displaying an
increased sensitivity to the needs of the chemists rather than taking a physicist's
patronizing view. It was he who legitimized the use of such heavy — by the chemists'
criteria — mathematics in chemistry and managed to have a rather wide recognition
by the chemical community.
The British quantum chemists perceived the problems of quantum chemistry first
and foremost as calculational problems and, by devising novel calculational
methods, they tried to bring quantum chemistry within the realm of applied
mathematics. It may not have been as exciting an undertaking as the Germans' or the
Americans', but it was surely a particularly effective one. In that specific context, the
demand for more rigor was not primarily a demand for a rethinking of the
conceptual framework, but rather it was a demand for developing as well as
legitimizing formal (mathematical) techniques and methods to be used in chemical
problems. For the members of this group, and for Coulson in particular, the
demand to make a discipline more rigorous meant to have more mathematical
techniques that will be inimical to the discipline itself, and that meant to get
involved with (applied) mathematics.
One of the most intriguing aspects of the initial phase of quantum chemistry was
the formulation of a host of concepts devised to conceal the impotence of
mathematics to produce exact solutions and to cater to a community for whom visualization was one of the necessary ingredients of their practice. Exchange integral,
hybridization, directed valence, bonding, and antibonding orbitals, and, above all,
resonance were attempts to mellow the blow felt when chemists realized that,
perhaps, chemistry is a purely quantum phenomenon, since it is so dependent on
spin. And we know that the explanatory strength of quantum theory has been a
factor undermining the perennially difficult process of pictorial representation.
For a long tixne, it appeared that in quantum chemistry the four procedures —
conceptual, mathematical, experimental, and pictorial — were complementary to
each other, each having a relative autonomy and at the same time each coming to
the rescue of the whole enterprise whenever the other(s) were reaching their limits.
With the extensive development of numerical techniques, one gets the feeling that
something had been changing. It is rather intriguing to pursue the question
whether the development of calculational techniques progressively
"de-conceptualized" quantum chemistry. This is not to imply that the work of the British was
devoid of any new and novel concepts. The question to be discussed is to understand
the characteristics of their work as they were developing the mathematical
techniques for chemistry. Or to put it another way, understanding the particularities of
the British quantum chemists entails the understanding of their overall outlook to
reformulate the problems of quantum chemistry as problems of applied
mathematics.  Is it the case that in their attempts to build theoretical schemata, their
specific methodological choices and ontological commitments led to their becoming
less dependent on concepts and more on mathematics — and then more dependent
on calculating machines?
The Role of Textbooks in Building a Discourse for Quantum Chemistry
Textbooks have always played a rather dominant role in the early stages of the
formation of sub-disciplines: by formalizing the "principles" of the sub-discipline,
making explicit the solutions to hitherto unsolved problems, reviewing the state of
the field, codifying what there is to be taught, and giving background information
for non-experts to learn about the field, the early textbooks in a sub-discipline's
history contribute to the legitimation and institutionalization of the field.
The development of quantum chemistry has been no exception. Is quantum
chemistry an application or use of quantum mechanics for chemical problems? Is
quantum chemistry the totality of chemical problems formulated in the language of
physics and which could be dealt by a straightforward application of quantum
mechanics with, of course, the ensuing conceptual readjustments? Or is it the case
that chemical problems could be dealt with only through an intricate process of
appropriation of quantum mechanics by the chemists' culture? By attempting to
provide an answer to these seemingly pedantic questions and oflen implicitly posed
questions, various textbooks attempted to define the status of quantum chemistry,
that is, to define its degree of autonomy with respect to both physics and chemistry
as well as the extent of its non-reducibiity to physics. And even though these issues
were being discussed in the reseaxch papers, the meetings, and the conferences, the
early textbooks of quantum chemistry became equally decisive in articulating the
constitutive aspects of quantum chemistry.
Textbooks in general are — necessarily — a-historical and only in a very few
instances do we find a mention and, in even fewer cases, a discussion of some of the
disputes in a discipline's early history. Interestingly, the early textbooks of quantum
chemistry could also be read as polemic or partisan texts: by proposing and arguing
in favor of particular (ontological) hypotheses and approximation methods, each one
of them adopts a particular viewpoint on how to answer the question of whether
quantum chemistry is an application or use of quantum mechanics for chemical
Early textbooks in a discipline's history could also be viewed as a genre for
consolidating a consensus as to the language to be used and the practice to be
adopted. In the case of quantum chemistry, such an agenda revolved around the
question of whether chemists should start diverging from the accepted norms of
their disciplinary culture where chemistry is not thought of as a mathematical
science, or whether they should continue to be faithftil to such a culture and
appropriate the right dose of quantum mechanics for their own purposes. The
dilemma, then, of whether chemists should apply quantum mechanics to chemical
problems or use quantum mechanics in chemistry, and the ensuing issues as to the
extent of mathematics to be introduced, was really a dilemma concerning the status
of quantum chemistry: the question, that is, about the extent of its relative autonomy
with respect to physics.
We will now give a few examples. The Electronic Theorg of Valence, the book the
English chemist Sidgwick published in 1927, the year often considered to be the
birth date of quantum chemistry, announced a new era, sensing the promises that
lay in the road ahead. His next textböok Some Physical Properties ofthe Covalent Link
in Chemistiy (1933), born out of a series of lectures delivered in the USA, went
further in assessing the methodological guidelines to be followed by the new
discipline. By 1939, the Americans had imposed their agenda. Coincidentally, this
was the year of the publication of two textbooks — Pauling's The Nature of the
Chemical Bond, and John Slater's Introduction to Chemical Physics. These two
articulate writers aimed — by adopting different viewpoints — at educating an
audience of both students and professionals in the ways of the new discipline.
Pauling, the chemist, proceeded to a reform of the whole of chemistry from the
standpoint of quantum chemistry. Slater, the physicist, saw the beginnings of
quantum chemistry, which he christened chemical physics, as heralding the unification of physics and chemistry. Both books reflected the tendency to impose a new
(sub)discipline by establishing a new language, a new practice, a new theoretical
agenda, and a concomitant methodology, and flnally by securing an audience. That
was no longer the case with two other textbooks. The organic chemist George W.
Wheland, one of Pauling's former students, contributed more than any other
chemist towards the extension of the scope of the theory of resonance to organic
chemistry. He adopted Pauling's research agenda and pushed it ahead by arguing
that it is possible for organic chemists to use quantum chemistry without having to
turn their discipline into a fully mathematized science. In fact, his book The Theory
of Resonance and its Applicatian to Organic Chemistry published in 1944 was to play a
prominent role in the education of organic chemists. In 1952, the textbook Valence
written by Coulson reflected a growing awareness an the part ofsome chemists that
Pauling's viewpoint had been strongly overrated. Coulson's book was the first
serious and successful attempt to replace The Nature of the Chemical Bond, with
important repercussions in the teaching of quantum chemistry.
Whether we look at textbooks written during the 1930s, the 1940s, or even later
on, we condude that many of the textbooks dealt with the implications of quantum
mechanics to chemistry, however, taking different views an the matter. In some
cases, they provided qualitative discussions of the applications ofquantum theory to
chemistry, particularly to chemical bonds, avoiding as much as possible the mathematical structure of the theory. In other cases, they presented quantum mechanics
with full consideration of its mathematical methods and different degrees of
emphasis an topics of chemical interest. In still other cases, they attempted to
combine the advantages of both approaches. In same instances, these different
strategies reflect implicit or even explicit views about the autonomy of quantum
chemistry that is, about the hypothetical reduction of chemistry to physics and,
interestingly, textbooks written in later years continued to display a similar ambivalence towards the kind of mathematical details to be introduced in quantum
It is, thus, interesting to note that from the very first days when it became possible
to expand the domain of quantum mechanics to chemical problems until the period
when there was a consensus among the chemists of the relative merits and
shortcomings of a number of approaches, the problem of reductionism was at the
forefront ofpressing questions for many chemists. A number of leaders in the field
had no qualms in declaring that quantum chemistry was a branch of physics, others,
by emphasizing the qualitative arguments so prevalent in chemical thinking, were
attempting to define a framework where quantum chemistry will develop a relatively
autonomous status with respect to physics. In many textbooks this problematic was
expressed by the authors' dilemmas as to whether quantum chemistry will be an
application of quantum mechanics to chemical problems or whether quantum
chemistry would be able to articulate its languagely the successful appropriation of
quantum mechanics by chemistry. It is this subtle differentiation between the
approaches which led to the writing of a number of pedagogically effective and
ideologically diverse textbooks in quantum chemistry.
3.5 The Ontological Status of Resonance
Pauling's resonance theory raised questions as to the ontological status of theoretical entities very similar to the problématique associated with discussions about
scientific realism. Differences in the assessment of the methodological and ontological status of resonance were the object of a dispute between Pauling and
Wheland, who worked towards the extension of resonance theory to organic
molecules. Wheland, in his book The Theory of Resonance and Its Applications to
Organic Molecules dedicated to Pauling, argued that resonance was 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,» which he classified as one example ofthe nonsense
organic chemists were prone to.
What I had in mind was, rather, that resonance is not an intrinsic property of a
molecule that is described as a resonance hybrid, but is instead something
deliberately added by the chemist or the physicist who is talking about the
molecule. In anthropomorphic terms, I might say that the molecule does not
know about resonance in the same sense in which it knows about its weight,
energy, size, shape, and other properties that have what I call real physical
significance. Similarly... a hybrid molecule does not know how its total energy is
divided between bond energy and resonance energy. Even the double bond in
ethylene seems to me less "man-made" than the resonance in benzene. The
statement that the ethylene contains a double bond can be regarded as an indirect
and approximate description of such real properties as interatomic distance, force
constant, charge distribution, chemical reactivity and the like; on the other hand,
the statement that benzene is a hybrid of the two Kekulé structures does not
describe the properties of the molecule so much as the mental processes of the
person who makes the statement. Consequently, an ethylene molecule could be
said to know about its double bond, whereas a benzene molecule cannot be said,
with the same justification, to know about its resonance ... Resonance is not
something that the hybrid does, or that could be "seen" with sufficiently sensitive
apparatus, but is instead a description of the way that the physicist or chemist has
arbitrarily chosen for the approximate specification of the true state of
Pauling could not disagree more. For him, the double bond in ethylene was as
"man-made" as resonance in benzene. Pauling summarized their divergent
viewpoints by saying that Wheland seemed to believe that there was a "quantitative
difference" in the man-made character of resonance theory when compared to
ordinary structure theory — but he could not find such a difference. He asserted that
Wheland made a disservice to resonance theory by overemphasizing its "man-made
character."  Wheland conceded that resonance theory and classical structural
theory were qualitatively alike, but he still defended, contrary to Pauling, that there
was a "quantitative difference" between the two. He viewed his disagreement with
Pauling as a result of different value-judgements on what he dassified as philosophical, rather than scientific matters.
Nevertheless, acknowledging or denying the existence of differences between
resonance theory and classical structural theory was dependent on their different
assessments of the role of alternative methods to study molecular structure.
Wheland equated resonance theory to the valence bond method and viewed them as
alternatives to the molecular orbital method. Pauling conceded that the valence
bond method could be compared with the molecular orbital method, but not with
the resonance theory that was largely independent of the valence bond method. For
Pauling the theory of resonance was not merely a computational scheme. It was an
extension of the classical structure theory, and as such it shared with its predecessor
the same conceptual framework. If one accepted the concepts and ideas of dassical
structure theory one had to accept the theory of resonance. And, how could one
reject their common conceptual base if they had been largely induced from
I think that the theory of resonance is independent ofthe valence-bond method of
approximate solution of the Schrödinger wave equation for molecules. I think that
it was an accident in the development of the sciences of physics and chemistry
that resonance theory was not completely formulated before quantum mechanics.
It was, of course, partially formulated before quantum mechanics was discovered;
and the aspects of resonance theory that were introduced after quantum
mechanics, and as a result of quantum mechanical argument, might well have been
induced from chemical facts a number of years earlier. 
This discussion with Wheland prompted Pauling to make his position about these
issues public. More than the question of the artificiality of the resonance concept, to
which he alluded briefly in his Nobel lecture,  he wanted once and for all to state
as dearly as possible his views on theory building. A new version of the arguments
brought about in the discussion with Wheland appeared in Perspectives in Organic
Chemistry  and later on in the third edition of The Nature of th€ Chemical
Bond.  In the preface, Pauling pointed out that the theory of resonance involves
"the same amounts of idealization and arbitrariness as the classical valence-bond
theory". Pauling added a whole section in the new edition to discuss this question.
His manifesto was called "The Nature of the Theory of Resonance." There, he
argued that the objection concerning the artificiality of concepts applied equally to
resonance theory as to classical structure theory. To abandon the resonance theory
was tantamount to abandoning the classical structure theory of organic chemistry.
Were chemists willing to do that? According to Pauling, chemists should keep both
theories because they were chemical theories and as such possessed "an essentially
empirical (inductive) basis".
I feel that the greatest advantage of the theory of resonance, as compared with
other ways (such as the molecular-orbital method) of discussing the structure of
molecules for which a single valence-bond structure is not enough, is that it
makes use of structural elements with which the chemist is famiiar. The theory
should not be assessed as inadequate because of its occasional unskillful applica-
tion. It becomes more and more powerful, just as does classical structure theory,
as the chemist develops a better and better chemical intuition about it... The
theory of resonance in chemistry is an essentially qualitative theory which, like
the classical structure theory, depends for its successful application largely upon a
chemical feeling that is developed through practice. 
In 1947, Coulson wrote an artide in a semi-popular magazine on what he thought
Is resonance a real phenomenon? The answer is quite definitely no. We cannot say
that the molecule has either one or the other structure or even that it oscillates
between them ... Putting it in mathematical terms, there is just one full,
complete and proper solution of the Schrödinger wave equation which describes
the motion of the electrons. Resonance is merely a way of dissecting this solution:
or, indeed, since the full solution is too complicated to work out in detail,
resonance is one way — and then not the only way — of describing the approximate
solution. It 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. 
The question as to the ontological status of resonance was not an issue that was
confined to this exchange between Pauling and Wheland. Pauling's theory of
resonance was viciously attacked in 1951 by a group of chemists in the Soviet Union
in their Report of the Commission of the Institute of Organic Chemistry of the
Academy of Sciences.  They themselves, stressed that their main objection was
methodological. They could not accept that by starting from conditions and
structures that did not correspond to reality one could be led to meaningful results. Of
course, they discussed analytically the work of Aleksandr M. Butlerov who in 1861
had proposed a materialist conception of chemical structure: this was the distribu-
tion of the action of the chemical force, known as affinity, by which atoms are united
into molecules. He insisted that any derived formula should express a real sub-
stance, a real situation. According to the report, Pauling was moving along different
directions. For him a chemical bond between atoms existed if the forces acting
between them were such as to lead to the formation of an aggregate with sufficient
stability to make it convenient for the chemist to consider it as an independent
molecular species. To these chemists Pauling's operational definition was totally
In this treatment the objective criterion of reality of the molecule and of the
chemical bond vanishes. Since the definition of the molecule and the chemical
bond given by Pauling is methodologically incorrect, it naturaJly leads, when
logically developed, to absurd results. 
It is interesting to note the initiative of the New York Chapter of the National
Council of Arts, Sciences and Professions to organize a meeting on the subject. It
was proposed that the meeting have the form of a debate where N. D. Sokolov from
Moscow, Coulson, and Pauling would each contribute a paper and there would
follow a discussion of the points raised in the communications. Coulson felt that the
best way would be for Sokolov and Pauling to present their viewpoints and that he
would make a series of comments. Each party would be asked to provide answers to
the following questions: What is the resonance theory? What is the evidence in
proof or disproof of the resonance theory? Is the convenience of the theory a proof
or a corroboration of the theory? Is the resonance theory essentially a theory with
physical nleaning, or a mathematical technique or both? Has the resonance theory a
basis in related sciences, such as physics? Is the resonance theory applicable in all
aspects of chemical valence or is it in conflict?  The meeting did not take place
basically because of the unwillingness of the Soviets, but the points that each party
would have had to address were indicative of the uncertainties involved as to the
methodological significance and ontological status of resonance in quantun
3.6 The Status of the Chemical Bond
Coulson called the chemical bond a "concept of the imagination", and used it to
illustrate the role and status of concepts within quantum chemistry. According to
Coulson, all chemistry rests on the idea of a chemical bond, and every generation of
chemists has tried, in its own way, to describe what is a bond. The different
descriptions that have been given show how greatly our understanding of the "real
essence of chemistry"  has developed in the past since Frankland or Kekulé. For
nearly one hundred years chemists noticed the characteristic affinities of one
substance for another. Lewis had suggested that this affinity is related to the
disposition of two electrons, but "remember, no one has ever seen an electron". 
Since 1927, applied mathematicians have been able to handle the differential
equations of wave mechanics, although they soon faced the embarrassment of not
being ahle to solve exactly Schrödinger's wave equation, which describes the
behavior of the wave function that carries the answer to every chemical question we
can ask. The quantum mechanical underpinning of Lewis's description showed next
that the shared electrons have their spins pointing in opposite, or anti-parallel,
directions, but "remember, no one can ever measure the spin of a particular
electron!"  However, everyone was captivated by "the simpliciy of the idea 
Then the distribution in space of these electrons is described analytically with closer
and closer degrees of precision, but "remember, there is no way of distinguishing
experimentally the density distribution of one electron ftom another!" 
Concepts like hybridization, covalent and ionic structures, resonance, and fractional bond orders have been introduced in the process, and Coulson was rather
uneasy that none of these concepts could be linked to a directly measurable quantity.
Nevertheless, "chemical knowledge and, perhaps even more, chemical intuition,
find their full expression and their proper setting within the mathematical frame-
work that has now been devised."  The importance of conceptual insightfulness
together with the usefulness and truthfulness of concepts is stressed again and
again in Coulson's writings. As "concepts of the imagination" they have not
necessarily to be real.
It does not require our friends the logical positivists to give us pause. (...) I
described a bond, a normal simple chemical bond; and I gave many details of its
character (and could have given many more). Sometimes it seems to me that a
bond between two atoms has become so real, so tangible, so friendly that I can
almost see it. And then I awake with a little shock: for a chemical bond is not a
real thing: it does not exist: no-one has ever seen it, no-one ever can. It is a
figment of our own imagination. 
In the inaugural lecture as professor of Applied Mathematics, Coulson had already
made the same point, perhaps even with more poise:
Dare we make a lesser claim than this for the modern description of a chemical
bond? For all these concepts of the imagination give us such understanding and
feeling for the thing that sometimes it seems to me that a chemical bond is so
real, so huge, so life-like that I can almost see it. Then I wake with a shock to the
realization that neither I nor anyone else will ever see one: a chemical bond does
not exist: it is a figment of imagination which we have invented — it is most useful,
most satisfying, but (though perhaps in this building [the Physical Chemistry
Laboratory, Oxford] I should be careful with what I say) no more real than the
square root of —1! 
What is going to happen in the future to the idea of a bond? Coulson gave two
possible answers to this interesting question. The work of the next years will have to
be more concerned with refining and perhaps simplifying the sort of description
already worked out.  In a symposium commemorating the 50 years of valence
theory which took place in 1970, Coulson went much further.
So to the question: has the chemical bond now done its job? Have we grown to
that degree of knowledge and that power of calculation that we do not need it?
Certainly in the more elaborate of the calculations that I have referred to, the
authors seldom if ever use the word "bond." This a tantalizing question. And only
a little can be said by way of comment. Chemistry is concerned to explain, to give
us insight, and a sense of understanding. Its concepts operate at an appropriate
depth, and are designed for the kind of explanation required and given. If the level
of enquiry deepens, as a result of our better understanding, then some of the
older concepts no longer keep their relevance. No one talks much now about the
polarization of non-bonding electrons, of dynamic oscillation, or of bond fixation.
From its very nature a bond is a statement about two electrons, so that if the
behavior of these two electrons is signiflcantly dependent upon, or correlated
with, other electrons, our idea of a bond separate from, and independent of, other
bonds must be modified. In the beautiful density diagrams of today the simple
bond has got lost. It is as if we had outgrown the early clothes in which, as
children, we could be dressed, and now needed something bigger. But whether
that 'something bigger' that should replace the chemical bond, will come to us or
not is a subject, not for this Symposium, but for another one to be held in another
50 years time, and bearing for its title: The Changing Role of Chemical
3.7 The Impact of Computers in Quantum Chemistry: the Split of the Community
Let us now come to our last point. Since we want to talk until about the end of the
1960s when it was still possible to go a long way in both physics and chemistry
without the use of computers, we shall be pointing out to the beginnings of the
diverging trends among the chemists and the effects they had in the community,
rather than discussing the totally new practice which was consolidated when
computers started more or less to dictate to the theoretical chemists the kinds of
problems they would work on and the ways to deal with these problems.
The introduction and growing dissemination of digital computers in quantum
chemistry opened the way for the calculation of ever more difficult molecular
integrals and made it possible to seriously consider the delineation of an extensive
program of "completely theoretical" (ab initio) calculations. It was, in a way, an old
dream come true. These calculations contrasted with those "semi-empirical" calculations, in which the impossible analytical calculation of certain parameters was
substituted by the introduction of their values as given by experimental determinations. Semi-empirical calculations had become one of the constitutive aspects of
quantum chemistry since its early days, and had contributed decisively to the
articulation of its partial autonomy in relation to physics. What were the implications of ab initio calculations for quantum chemistry? It soon became clear that
quantum chemists gave different answers to the former question, and that there was
the danger of an irreversible splitting of the quantum chemical community reflecting divergent and irreconcilable attitudes towards the outcome of the use of
The Conference on Molecular Quantum Mechanics held at Boulder, Colorado, in
June 1960, was the first major meeting of its kind since the 1951 Shelter Island
Conference. It was also the first meeting where the many theoretical chemists
started realizing that there were deep — and perhaps irreconcilable — divisions in the
community of quantum chemists among those who continued the semi-empirical
calculations with the use of computers and the ab initio-ists. Coulson, again,
emerges as one of the more perceptive observers of this situation and in the after
dinner speech he delivered one finds Coulson not preaching tolerance but advocating partisanship. 
In discussing the major condusions from the Conference he noted that "the
whole group of theoretical chemists is on the point of splitting into parts ... almost
alien to each other."  The splitting was the result of the different views concern-
ing the large-scale use of electronic computers — but there could even be a deeper
reason than that. During the week of the conference, he had heard more than once
the phase "Oh, but you're not doing quantum chemistry." The occasions which
gave rise to such assessments were the computational techniques presented for
calculating energy values for atomic helium and molecular hydrogen, the calculations of a "highly empirical" kind to estimate energy levels and charge distributions
of heteronudear aromatic molecules and, the tabulation and interpretation of
barriers to internal rotation in substituted ethane type molecules. His view was that
these three situations represented quite distinct aspects of what used to be called
quantum chemistry, since they differed considerably in their underlying a
ssumptions. But each group thought that what the others did was not quantum chemistry.
"The situation is indeed serious. For my own part, I am very far from laughing at it,
and I want us to look at as openly and as dispassionately as possible. The questions
that we are really asking concern the very nature of quantum chemistry, what
relation it 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 
The splitting, he thought, in the community resulted ftom the antagonism of two
extreme groups. The first group possessed great computational skills and advocated
that there are a number of problems that a dispute can only settle by computation
since experiments are too difficuit. To many people, this group of chemists appeared
to be moving away from the conventional concepts of chemistry, such as bonds,
orbitals, and overlapping hybrids "as to carry the work itself out of the sphere of real
quantum chemistry."  On the other extreme were calculations with very rough
approximations for biological molecules. These calculations give quite interesting
results, but the approximations put forward would be greatly upsetting to the people
who extensively used computers.
"Where, in all this, does 'real' quantum chemistry lie?" Coulson wondered. The
possibilities offered by the electronic computers enabled one to distinguish three
levels of activity — a distinction with which most of the exponents of computing at
the conference agreed.
Firstly, there are the molecules or atomic systems of 1 - 6 electrons, for which one
could effectively calculate energies as accurately as they can be measured. Secondly,
the all too realistic prospects for faster computers allowed to extend the range of
molecules for which it would become possible to have effectively exact solutions to
those with 6 - 20 electrons. Nevertheless, accurate results for these cases were
achieved at the expense of visualizabiity. Coulson thought it was not very probable
— and also not particularly desirable — to deal in such a manner with molecules of
more than 20 electrons. There was such a deep distinction between those chemists
whose main interest laid in the 1 - 20 range, and consequently thought in terms of
full electronic computatlon, and those who did not think in these terms that the two
groups deserved distinct names — Group I (the eledronic computors or ab initio-ists
as some would call them) and Group II the non-electonic computors or a posterior-
But he thought that it would be an oversimplification to think that the difference
is only a difference having to do with the use of electronic computers. In their desire
for complete accuracy, Group I appeared to be prepared to "abandon all conventional
chemical concepts and simple pictorial quality in their results." Against this, the
exponents of Group II argued that chemistry is an experimental subject, whose
results are built into a pattern around quite elementary concepts. He did not make
any effort to conceal that his sympathies lay with the latter and re-emphasized that
the role of quantum chemistry is to understand these concepts and show what are
the essential features in chemical behavior. Nevertheless, he was also aware that
none of these concepts Could be made rigorous.
Chemistry itself operates at a particular level of depth. At that depth certain
concepts have significance and — if the word may be allowed — reality. To go
deeper than this is to be led to physics and elaborate calculation. To go less deep
is to be in a field akin to biology. Once this is recognized, it is not difflcult to see
that there is a perfectly sound basis for all three comments about "not doing
quantum chemistry" that I reported earlier. 
Coulson felt that it would be a great disaster if quantum chemistry were limited to
either the "very deep" or the "shallow" level. And certainly it would be a serious loss
if it did not maintain a close link with experiment and with conventional thought
forms of chemistry. He felt strongly that there was a danger that Group I people will
forget that chemistry is associated with the real world. He ended in a pessimistic
Mathematically a bond is an impossible concept for Group I. It is not surprising
that it is practically never used by them. Yet the existence of bond properties is
basic to all chemistry... It is not surprising that the orientations of these two
groups of quantum chemists are so different that cross fertilization has now
become much less frequent than in earlier days... Many members of Group I do
not realize what is happening to them; and members of both groups display an
undesirable lack of sympathy for each other's work. 
In a way Coulson's work contributed decisively in making the chemists' nightmare
come true: Dirac's pronouncement of 1929 could, in fact, be realized and chemistry
was, in fact, physics. Though his work accelerated the ab initio-ist culture of
theoretical chemistry, Coulson himself appears to be entrenched in the more
traditional culture. He was deeply committed to the view that theoretical chemistry
was first and foremost an enterprise whereby mathematical notions, numerical
methods, experimental measurements, pictorial representations and, above all,
chemical concepts, constituted an undivided whole. There was a fine balance among
all these aspects, a balance that could not be articulated in any distinct way and yet,
Coulson felt, it was the distinctive feature of theoretical chemistry itself.
References and Notes
The following abbreviations are used:
LP — Fritz London Papers, Duke University
PP — Ava Helen and Linus Pauling Papers,
Kerr Library Special Collections, Oregon
SP — Nevil V. Sidgwick Papers, Lincoln College, Oxford University
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2 P.A.M. Dirac, "Quantum mechanics of
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4 H. Roscoe, "Presidenfial address to Section
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5 A. Smithells, "Presidential address to Section B-Chemistry" Proceedings of the British
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6 Ibid., 478. Italics ours.......... return ....
7 H. Armstrong, "Presidential address to
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8 Ibid., 424.......... return ....
9 SP. V-Correspondence. Item 71. Rutherford. Letter Rutherford to Sidgwick, 26 July
1937.......... return ....
10 H. C. Longuet-Higgins, "An application of
chemistry to mathematics," Scientific Journal ofthe Royal College of Science 23 (1953):
99—106, on 99.......... return ....
11 Longuet-Higgins, "An application of chemistry to mathematics," 106.......... return ....
12 A. Assmus, "The molecular tradition in
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(1992): 209—231; A. Assmus, The americanization of molecular physics," Historical Studies in the Physical and Biological
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Gavroglu, "Different legacies and common
aims: Robert Mulliken, Linus Pauling and
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Calais and E. S. Kryacbko (eds.), Conceptual
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13 PP, Box 242, Popular Scientific Lectures
1925 —1955, "Resonance and organic chemistry" 1941.......... return ....
14 R. S. Mulliken, "Electronic structures of
polyatomic molecules and valence. VI. On
the method of molecular orbitals," Journal
of Chemical Physics 3 (1935): 375—378.......... return ....
15 Letter Pauling to Reymond Holmen, March
1987, as quoted in R. Holmen "Kasimir
Fajans" Bulletin for the History of Chemistry
6 (1990): 7—15.......... return ....
16 Walter Hückel's Theoretische Grundlagen der
organischen Chemie (1931) induded quantum interpretations and was very influential when eventually translated into English. H. Kragh, "The young Erich Hückel:
His scientffic work until 1925," invited paper given at the Erich Hückel Festkolloquium at the Philipps-Universität, Marburg, 28 October 1996; J. A. Berson, "Erich
Hückel, pioneer oforganic quantum chemistry: Reflections an theory and experi-
ment," Angewandte Chemie International
Edition in English 35 (1996): 2750-2764; A.
Karachalios, "Die Entstehung und Entwicklung der Quantenchemie in Deutschland,"
Mitteilungen der Gesellschaft Deutscher
Chemiker Fachgruppe Geschichte der Chemie
13 (1997): 163—179.......... return ....
17 C.A. Coulson, "Recent developments in valence theory," Pure and Applied Chemistry
24 (1970): 257—287, an 259.......... return ....
18 LP, Letter D. Whyte to London, 14 December 1929; Letter Fowler to London, 14 January 1930.......... return ....
19 R. H. Fowler, "A report an homopolar valency and its mechanical interpretation," in
Chemistry at the Centennary Meeting of the
British Association for the Advancement of
Science (Cambridge: W. Heffer and Sons
Ltd, 1932), 226—246, on 226 return ....
20 J. E. Lennard-Jones, "The nature of cohesion," Nature 128 (1931): 462—463, on 462.......... return ....
21 A. Simões, K. Gavroglu, "Quantum chemistry qua applied mathematics. The work of
Charles Coulson (1910—1974)," Historical
Studies in the Physical and Biological Sciences 29 (1999): 363—406. return ....
22 G.W Wheland, The Theory of Resonance
and Its Applications to Organic Molecules
(New York John Wiley & Sons, 1944). return ....
23 PP, Box 115, Letter Wheland to Pauling, 20
January 1956. return ....
24 PP, Box 115, Letter Pauling to Wheland, 26
January 1956. return ....
25 PP, Box 115, Letter Pauling to Wheland, 8
February 1956. return ....
26 L. Pauling, "Modern structural chemistry.
Nobel lecture, December 11, 1954," in Nobel Lectures in Chemistry 1942—1962 (Amsterdam: Elsevier Publishing Company,
1964), 134—148. return ....
27 L Pauling, "The nature of the theory of
resonance," in A. Todd (ed.), Perspectives in
Organic Chemistry, Dedicated to Sir Robert
Robinson (New York: Interscience publishers, 1956), 1—8. return ....
28 L. Pauling, The Nature of the Chemical Bond
and the Structure of Molecules and Crystals.
An Introduction to Modern Structural Chemistry (New York: Cornell University Press,
1967), third edition, 215—220. return ....
29 L. Pauling, "The nature of the theory of
resonance," in Perspectives in Organic
Chcmistry, 6-7; L Pauling, The Nature of
thc Chemical Bond, 219—220. return ....
30 C. A.Coulson, "The meaning of resonance
in quantum chemistry," Endeavour 6
(1947): 42—47, on 47. ..... return ....
31 D. N. Kursanov, M. G. Gonikberg, B. Dubinin, M.I. Kabachnik, E.D. Kaveraneva,
E. N. Prilezhaeva, N. D. Sokolov, R.Kh.
Freidlina, "The present state of the chemical structural theory." Translation in English by I. S. Bengelsdorf; published in Journal of Chemical Education (January 1952): 2—13; V. M. Tatevskii, M. I. Shakhparanov,
"About a machistic theory in chemistry and
its propagandists." Translation by I. S. Bengelsdorf in Journal ofChcmical Education (January 1952): 13—14. lt was not, of
course, the case that such sentiments were
shared by all the chemists of the community. Characteristic of the differences is the
editorial note to the first article where it is
stressed that any particular way of dealing
with chemical phenomena should not be
excluded on a priori grounds, but should
be first closely studied. In the same article
Ya. Syrkin and M. Dyatkina were also attacked. They were the authors of the
excellent book The Chemical Bond and the
Structure of Molecules and had translated
Pauling's book into Russian. See also I.
Moyer Hunsberger, "Theoretical chemistry
in Russia," Journal of Chemical Education
(October 1954): 504—514. ..... return ....
32 D. N. Kursanov et al., "The present state of
the chemical structural theory." Translation
in English by I.S. Bengelsdorf published in
Journal ofChemical Education (January
1952): 2—13, on 5. ..... return ....
33 PP, Box 261. Letter M.V. King to Pauling,
23 January 1953; letter Coulson to Pauling,
7 October 1953; letter Coulson to King, 18
January 1954; letter King to Pauling, 9 Feb-
ruary 1954. ..... return ....
34 C.A. Coulson, "What is a chemical bond?"
Scientific Journal of the Royal College of Science 21 (1952): 11—29, on 11. ..... return ....
35 C.A. Coulson, The Spirit of Applied Mathematics (Oxford: Clarendon Press, 1953),
20—21. ..... return ....
36 Ibid. ..... return ....
37 C. A. Coulson, "Recent developments in valence theory," Symposium: Fifty Years of
Valence Theory, Pure and Applied Chemistry
24 (1970): 257—287, on 287. ..... return ....
38 Coulson, The Spirit of Applied Mathematics,
20-21. ..... return ....
39 Coulson, What is a Chemical Bond?" 13. ..... return ....
40 C.A. Coulson, "The contributions of wave
mechanics to chemistry," Journal of the
Chemical Society (1955): 2069—2084, on
2084. ..... return ....
41 Coulson, The Spirit ofApplied Mathematics,
20-21. Italics ours. ..... return ....
42 Coulson, What is a chemical bond?" 12. ..... return ....
43 Coulson, "Recent developments in valence
theory," 287. ..... return ....
44 C. A. Coulson, "Present state of molecular
structure calculations," Conference on Molecular Quantum Mechanics, University of Colorado at Boulder, June 21—27, 1960, Reviews of Modern Physics 32 (1960): 170—177. ..... return ....
45 Ibid., on 172. ..... return ....
46 Ibid. ..... return ....
47 IbicL< ..... return ....
48 Ibid., on 174 ..... return ....
49 Ibid.< ..... return ....
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