Charles A. Coulson

1910-1974

Photo : Courtesy of K. Ohno; © R. McWeeny

Charles Alfred Coulson, (1910-1974), English theoretical chemist who developed a molecular orbital theory and the concept of partial valency. He developed many mathematical techniques for solving chemical and physical problems. Coulson was born in Dudley, Yorkshire, and studied at Cambridge. He became professor of theoretical physics at King's College, London, 1947, professor of mathematics at Oxford 1952, and later Oxford's first Professor of Theoretical Chemistry. He was chair of the charity Oxfam 1965-71.        ... [more CV details]

Photo : Courtesy of K. Ohno; © R. McWeeny	C.A. Coulson, Valence. Oxford University Press, New York & Oxford, 1952.
Something historic of time-dependent importance : C.A. Coulson : The Present State of Molecular Structure Calculations.     Read it here. Revs. Mod. Phys. 32, 171-177 (1960).

Of historical interest, from the archive of K. and A. Ohno © : Some personal notes from C. A. Coulson to K. Ohno : Letters 1/2    Letters 2/2

Here at this 5th Canadian Symposium on Theoretical Chemistry, we meet to honour the name and the memory of Charles Coulson, not just as a scientist — who presided for so long over the growth of a new discipline — but as a great and remarkable man. Already, many eloquent tributes have been paid : in churches and chapels, in the daily press, in School and College magazines, in the journals of learned societies, and at a more personal level, in countless letters to Eileen his wife. I am deeply conscious of my privilege in being allowed to add my own reflections on "Coulson, the man and the scientist". In doing so I must admit many gaps in my personal knowledge which reaches back uncertainly to my days as a student with him some 28 years ago — and my indebtedness to many of his contemporaries for the things they too have written or said about him.

Charles Coulson was born at Dudley in Worcestershire in 1910. His forebears had been farmers, but his father was then Principal of the local Technical College. It was his father who implanted in him as a child the deep religious faith which throughout his life was to make every scientific achievement an act of service; in the dedication of one of his books be refers to his father who "first showed me the unity of science and faith". This belief in the unity of human aspirations, particularly in science and religion — where many others experience conflict — was to permeate his whole life; thousands who would never know him as a scientist were to hear him as a lay preacher or as a lecturer on the great religious and moral issues of our time. He was a schoolboy at Clifton College, Bristol, where Holmyard — the prolific writer of elementary textbooks — apparently met with no success in attracting him towards Chemistry; indeed, he chose quite firmly the Classics. What appears to have influenced his later development most deeply was a lecture by Brodetsky, the applied mathematician and astronomer, an experience about which he had this to say: "I was specializing in Latin and Greek. But I had a wise and cunning mathematics master H. C. Beaven. One day he said to me "Coulson, there's a talk at the University tonight, would you like to come?" Of course I was flattered for at that time the ways of universities were not within my ken. Professor Brodetsky of Leeds was talking and by the time I left that University lecture room I'd said "I'm going to be a mathematician." The spell it cast remains to this day." He did of course, characteristically, do as he resolved, proceeding to Trinity College Cambridge and achieving 1st Class Honours in the Mathematical Tripos. But he did more, again characteristically, following this performance by studying physics for a year and then achieving a similar distinction in the Natural Sciences Tripos!

At that time he had a serious interest in the mathematics of meteorology (I stress the "mathematics" because he never had a taste for wbat were to him the excruciatingly dull periods in the physics laboratory). In a precocious first paper in 1931, on geostrophic winds, he attempted to demolish some work by Harold Jeffreys — an incident which underlies another aspect of his character, namely the courage with which he would pursue truth (scientific or otherwise) relentlessly and without regard to personalities or to conflict with the establishment. He was elected to a Fellowship of Trinity and became absorbed in the work of two other Fellows — Gray and Lea — who were studying the actions of ionizing radiations on living systems, a highly original enquiry in those early days and one wbich Lea, in particular, was to press to great lengths.


PIONEER WORK

Coulson was not to stay in that area: he was at the same time attracted by the blossoming field of wave mechanics, heralded as the key to an understanding of chemistry — following the work of Heitler and London, on the one hand, and of Mulliken and Lennard-Jones (using their entirely different approach), on the other. Lennard-Jones was then already at Cambridge, where he was to remain for many years and it was with him that Coulson finally elected to work for his Ph.D. His thesis work — completed, remember, forty years ago — included the first ab initio calculation (published in 1935) on a polyatomic molecule, the ion H ₃ ⁺! One can only marvel at the patience and sheer determination of a man who could sit down to perform such a calculation on a Brunsviga calculator {note by McWeeny : The old "barrel-type" machine, with a handle to turn and a bank of small levers for setting the numbers — quite painful to the fingertips after hours of non-stop activity!} — how many times must he have turned the handle in evaluating the three-centre two-electron integrals! At that time, one feels, he was still an applied mathematician, in the narrower sense of the word, believing this to be a field in which numerical analysis could solve the basic problems of chemistry. He believed the Mulliken-Lennard-Jones approach, using "molecular orbitals", offered a mathematically more convenient framework than that provided by the valence bond or "resonance" theories; and he supported this view by reaching what is nowadays called the "Hartree-Fock limit" in a calculation on the hydrogen molecule — publishing the results in 1938. Many years later, however, he gave me another reason. Molecular orbital theory was not getting a fair deal, it was not well accepted by chemists, who were — by and large — uncritical in their adoption of "resonance" theory; and he set out to champion what most at the time have seemed something of a lost cause. He never hesitated to swim against the tide of orthodoxy, and would always go to great lengths to see the other point of view, whatever the issue might be.

During the decade before I knew him, 1936-46, he laid the foundations for many other developments in theoretical chemistry, producing more than forty significant papers. (in over half of which he was sole author). To many of you this may seem like the stone age of theoretical chemistry, so perhaps I may remind you of how much progress was made in Coulson's early papers, written first from Cambridge, where he was a graduate student, then from Dundee (where he became lecturer in Mathematics), and finally from Oxford where he took a Lecturership at University College and an ICI Fellowship at the Physical Chemistry Laboratory — the "PCL". In 1937 he made a molecular orbital calculation on methane, in which he removed the chemist's main objection to MO theory by means of a unitary transformation from MO's to localized "bond orbitals" — an idea which anticipated by more than 10 years the famous series of papers by Lennard-Jones and his collaborators, and which is now a familiar corner-stone in molecular theory. In the course of that work he developed what later came to be known as the zeta-function method for calculating many-centre integrals over Slater orbitals. In the semiempirical MO theory of conjugated systems, as formulated by Hükel, he and his co-workers made a whole series of major contributions; he defined the charges and bond orders (in 1939), which provided the key to so many correlations between electronic structure and molecular properties, and was at the same time a pointer to future developments in density matrix theory and the more systematic use of "population analysis". He showed how both the total electronic energy and the density matrix elements could be obtained, without solving the secular equations, by means of an elegant contour integral method. This was a remarkable anticipation of current work using Green's functions, in which the "Coulson contour" is still used to enclose singularities corresponding to "ionization poles"; in the Hüekel approximation, as used by Coulson, these poles occur at the energies of the occupied MO's.

With Rushbrooke, he first recognised and characterised mathematically the peculiar properties of alternant hydrocarbons, paving the way for more excursions into organic chemistry than I can begin to enumerate. And during this period he also developed, with his old Cambridge friend Duncanson, a rather complete theory of the momentum distribution in molecules and its connection with the Compton profiles observed in scattering experiments — work which is again highly topical as a result of recent improvements in experimental techniques.



"THINGS HAD TO BE DONE"

The period I have just referred to (up to about 1945) was indeed so rich that no graduate student in theoretical chemistry, even today, can fail to benefit from a careful reading of the many classic papers it contained — all the more so because they were written with a freshness and lucidity characteristic of all that Couison wrote. But then he had a great love of teaching and may well be remembered by many as a teacher above all else. He had the rare gift of making difficult things seem easy; he was certainiy well aware of the difficulties and pitfalls — but he was a brilliant expositor and skilfully led his students round them. By this time he had written his weil known book on "Waves", as well as a D.Sc. thesis which was later expanded into his book on "Valence"; both were to become "best-sellers", running to many editions and translated into many languages, and "Valence" in par- ticular must have had a colossal impact on the teaching of chemistry.

I have spoken so far only of academic activities: but his life during those years was equally full and fruitful in other respects. He had always been a convinced and deeply committed Christian: and from his College days, when he had been in great demand as a lay preacher in the country vihlages around Cambridge, he had worked unceasingly for Methodism and Christian fellowship. He was neither bigoted nor "stuffy"; his Christianity was always intensely practical and he would give himself unsparingly to help a friend or acquaintance with any kind of difficulty.

Charles Coulson with his wife Eileen . Photo : Courtesy of K. Ohno; © R. McWeeny

There are countless stories of his generosity in helping other students and colleagues, and later in life such activities were to consume more and more of his time. He had also embarked on what was to be a long and happy family life, marrying Eileen in the summer of 1938 before taking up his first lecturing position, at Dundee. Like the wives of so many great men, she was to give him, throughout his hife, the selfless and untiring support which enabled him to devote himself so freely to so many things. Andrew, the first of their four children, was born just before they moved to Oxford.

Some years ago I came across some old letters, written to me when, as a physics student at Leeds, I first had aspirations to do research in quantum mechanics. As always, they were typed with a good sprinkling of errors, on paper of any size, colour and shape that happened to be handy, and invariabiy enclosed in a much used envelope re-sealed with an economy label. I was struck by how little he had changed in so many years. He was always helpful, always constructive, and would always reply within a day or two of receiving a letter: I remember his remarking that he tried to deal with the day's mail, however large, the same morning he received it, and that he expected to work a 70-hour week in order to do the things that had to be done. In my case, on the strength of a note representing my first steps in research, he persuaded a Govemment Department and an Educational Foundation (after much correspondence) to award the grants which took me to Oxford. This — or something very like it — must have happened to so many of the peo- ple he helped.



"AUSTERE AND SPARTAN"

I had, of course, done some homework before arriving in Oxford. Coulson had written a lot about molecular orbitals, often at a semi- popular level and for chemists — who at that time couldn't be expected to know any quantum mechanics! But what had impressed me much more was his book on "Waves" which was one of my principal guide books during my final year as a physics undergraduate; so many aspects of physics — from ripples 00 water to radiation from dipoles — were drawn together with such elegance and clarity in terms of a few partial differential equations. I was naturally apprehensive about meeting the aothor. I was relieved, and a little surprised, to find a man of such simplicity and warmth; tall, slightly dishevelled, at home with his charming and equally friendly wife, and their two-year old son. He had no "edge" of any kind and was down-to-earth and direct; if you wanted to find lodgings in Oxford at that time you just had to set off along Walton Street, knocking on every door!

Bill Moffitt and others had done that and I followed suit. Once established I fell quickly into the normal routine, meeting Charles perhaps once a week in his room at the PCL (in those days Hinshelwood's Department) and working the rest of the time pretty independently. I'd been given a thesis to read; by Svartholm, on "The Binding Energies of the Lightest Atomic Nuclei" — which both flattered and frightened me. I could understand hardly a word of it; and my ignorance was so shameful (especially for a physicist in a chemistry department) that I couldn't ask for help — the only acceptable remedy was to follow the instructions — read the books by Pauling & Wilson, and by Dirac, and go to Maurice Pryce's lectures on quantum mechanics. I don't think Charles ever taught his graduate students the things they could find in books; he pointed them in the right direction and expected them to find the way themselves, just as he had done. He was always ready to give a helping hand on some specific difficulty; but in his view the function of a research supervisor was "mainly to prevent one making a fool of oneself". It seemed a hard school at the time, but on looking round at those who were shaped by it there is no doubt that it encouraged independence and originality of thought.

In those days Charles Coulson was, it seemed to us, a mildly revolutionary character — certainly not a pillar of the establishment. His tall gaunt figure was adorned at the top end by a shock of overlong dark hair, with a boyish face beneath it (often with a day's growth of stubble); and at the other end by those familiar (and apparently everlasting) walking shoes — dusty, battered and comfortable; in the summer he sometimes came to the PCL in shorts and on one occasion received a curt note from Hinshelwood who said "I would not lecture in shorts" (a statement which, on reflection, was not altogether surprising). He always loved to walk in the hills and to take camping holidays with his family or friends; camping holidays of the more Spartan variety, bug before the days of organized camps with their metal- and-canvas bungalows and plastie furniture, with only a ground-sheet between himself and the earth. His great personal simplicity had more than a touch of frugality, and this made his generosity and hospitality to others shine all the more brightly. I remember debating with a fellow student whether we could ask him to go walking with us at the weekend; that we wanted to, indicates our affection for him; that we didn't ask, indicates the slight awe with which we regarded him across a generation gap of a mere 15 years.

Some found him aloof but one of his close friends has said: "This was a mistaken judgment but It was provoked partly by his austere and spartan approach to life and partly by his distaste of those things which were trivial or tawdry. In other words he was a man of character." He seemed always shy of worldly pleasures, and reluctant to expose himself to extravagance, to luxuries, or to special treatment of any kind.



"WITH RIGOUR AND ELEGANCE"

Coulson's time at the PCL was short, but immensely fruitful. It seems to me that his transition from mathematician to theoretical chemist was completed during that period, mathematical rigour being tempered more and more by the insight and intuitions of the chemist. In the introduction to a long review article on the "Representation of Simple Molecules by Molecular Orbitals" it was stated that "we have avoided all mathematics, and have insisted everywhere upon the pictorial character of each step in the argument. It is the visual character of these steps that makes the method of molecular orbitals so fundamentally simple ..." When mathematics was used it was less and less at the level of the many-electron Schrödinger equation; it was nearly always at the level of a well-defined mathematical model, such as the Hückel model, in which physico-chemical intuition was employed in the systematic simplification of the "real world" by means of approximations. Coulson was a genius at model building. The broadening of his philosophy is summed up in a sentence be himself used only a few years ago, in a lecture on mathematical models, given at Dar es Salaam: he said "It is likely that one cannot be a good applied mathematician unless one has the ability to simplify to the point of absurdity!" — recalling at the same time a remark by Eddington that "If the model is right, the rest is easy".

During most of his work from 1945 onwards, Coulson's scientific activity was concerned more with the building of simplified theories than with direct attempts at solution of the many-electron Scbrödinger equation. He was never wholly convinced that large computers could provide answers to the real problems of theoretical cbemistry. The beautiful series of papers on "The Electronic Structure of Conjugated Systems", written in collaboration with Longuet-Higgins, seems to me to be the epitome of this philosopby; the model to be used is carefully defined and all its implications are theo worked out with rigour and elegance. Most of the chemically important concepts developed in these papers have, in fact, survived the passage of time; the charges and bond orders are the elements of density matrices; the atom and bond polarizabilities are related to response functions; and the whole mathematical framework is strong enough to allow a complete generalization from the Hückel model to ab initio many-electron theory without significant modification of the underlying concepts.

In 1947 Coulson moved to London, to the Chair of Theoretical Physics at King's College, where he built up a new department and greatly expanded his research group. He was prolific in the application of simple MO theory to problems in organic chemistry; particularly to large condensed ring systems, to theories of reactivity and carcinogenesis, to strained molecules, and to free radicals. But, along with Craig and others, he was also among the pioneers in the systematic use of configuration interaction as a means of calculating ab initio wave functions; and with Barnett he completed the development of the necessary methods of integral evaluation. He continued his work on momentum distribution in molecules; I used to visit him at King's and we were able to complete our work on the direct calculation of wave functions in momentum space.

And he broke into new fields; long range forces between large molecules; the solid state, with band theory calculations on graphite and related compounds, and with some of the earliest work on surface states — now so important in theories of catalysis. At the same time he was able to write and lecture extensively on such topics as "The Christian religion and contemporary science", "The place of science as a cohesive force in modern society", "Some reflections on the significance of the new cosmology", and "Atomic energy: the moral issue". He was elected to Fellowship of the Royal Society in 1950, and in the years that followed was the recipient of many prizes and distinctions. He travelled a great deal and broadcast often; in 1952 he spoke here, for the Canadian Broadcasting Corporation, on one of his favourite themes — Christianity in an age of science. That same summer he returned to Oxford, to the Rouse Ball Chair of Mathematics and to a Fellowship of Wadham College, leaving behind in London an established and flourishing Department of Theoretical Physics.



A SEEKER FOR SIMPLICITY

Oxford had broken with classical tradition in Applied Mathematics by appointing E. A. Milne, an expert in general relativity theory, as first Rouse Ball Professor; to appoint as his successor a Theoretical Chemist, who openly affirmed that he would go on doing Theoretical Chemistry, must have seemed, to some, outrageous. But it was a wise appointment; for twenty years Charles Coulson played a double role supremely well — he was Professor of Applied Mathematics and simultaneously (except in title) of Theoretical Chemistry! One of his first actions was to organize a weekly colloquium, again in the PCL, to which he attracted a steady stream of theoretical chemists. His guests often had to play a similar double role, giving one specialist (and mathematically "high - powered") colloquium in the Mathematical Institute, and another, with a more general and "chemical" flavour, at the PCL. He also atracted large numbers of graduate students, research fellows, and visiting professors from all over the world : Oxford became a cross roads, and to meet any theoretical chemist one might want to see it was only necessary to stand at the corner of South Parks Road until he appeared!



Coulson lecturing Photo :© Brookhaven National Laboratories.

Coulson's contributions to theoretical chemistry during the ensuing 20 years are well known to this audience and there is no need to recite them; but I would like to single out just a few which seem to me unusually significant. He was always looking for simplicity and had realised from the early days that the concept of hybridization had an important role to play in the discussion of localized chemical bonds and of the shapes of molecules; he developed such ideas in two fields. In the solid state, he gave a comprehensive discussion of the electronic structure of diamond and, with Mary Kearsley, produced the most ambitious theory so far of colour centres arising from vacancies; with Altmann, Hume-Rothery, and others, he explored the connection between bond hybrids and the metallic structures, with special reference to tetrahedral semiconductors; and he was among the first to make theoretical studies of hydrogen honding, and a detailed study of the structure of ice. As for free molecules, he used the idea of hybridization extensively in the interpretation of properties (eg. electric moments); and he helped to open up the field of conformational analysis, with many papers on "strained" molecules and intemally overcrowded condensed ring systems such as the helicenes.

At the same time, however, be never lost his taste for more formal mathematics — the use of commutator relationships, the hypervirial theorems which he and Joe Hirschfelder established, the saddle-point character of the Hartree- Fock stationary value, or spheroidal wave functions for the hydrogen atom — and in 1967 he and Levine made an important contribution to the theory of absolute reaction rates, using the methods of multi- channel collision theory. He even found time for the occasional purely academic problem — "the minimum dipole moment required to bind an electron to a finite electric dipole". The breadth of his interests was enormous, and whatever he did he did with a thoroughness and passionate enthusiasm which never failed to infect his students and collaborators. Nor did be subscribe to the view that pure and applied science belonged in different compartments; searching through his publications list (with some 400 titles) was a revelation — he fully appreciated, for example, the down-to-earth practical implications. of hydrogen bonding and accordingly wrote on the subject at considerable length for the British Gelatine & Glue Research Association!



THE GOSPEL AND OXFAM

What more can be said of his twenty years at the Mathematical Institute? I think one might say that above all else he devoted himself to "spreading the gospel" with the widest possible interpretation — whether in the orthodox religious sense, or in the scientific sense of promoting the acceptance of theoretical chemistry, or in the dissemination of any of the beliefs, views and attitudes to which he was deeply committed — and always on the grandest scale. The Summer Schools which he founded are known the world over, and over a period of 20 years undoubtedly had a uniquely powerful influence on the development of chemistry in at least a dozen countries. He also exercised his considerable organizing and administrative abilities by accepting in large measure the responsibility for the creation of a new Mathematical Institute in the fine modern building it has occupied since 1966. His other activities are better known in other circles but may have touched the lives of a vastly greater number of ordinary people and no tribute to Charles Coulson would be complete without some reference to them. They were essentially humanitarian, religious, and educational.

From the early fifties he was probably as much in demand as a lecturer on religious and moral issues as he was in scientific circles. I first heard him speak on a religious theme in 1953, at Newcastle-on-Tyne, where he gave the Riddell Memorial Lectures on "Christianitv in an Age of Science", and confess I was amazed that his convictions were so deep and unshakable, when the arguments on which they were based seemed to me so slender and insubstantial: but his faith was strong enough for five hundred and he would invariabiy carry his audience with him in the strength of his own fervour. I met him the following year in the U.S.A., delivering lectures almost daily on purelv nonscientific subjects. In 1959 he became Vice-President of the British Methodist Conference, and during his year of office delivered well over 100 lectures or sermons.

His humanitarian activities were no doubt a natural consequence of his Christianity, which found a practical expression in the resolution with which he sought to help the underprivileged, the poor, the hungry, the uneducated. He threw himself with great vigour into educational programmes based on the universities of Africa and India — at some of which he was a frequent visitor. And in 1965 he became Chairman — and an extremely hard-working Chairman — of OXFAM, the Oxford Committee for Famine Relief, which, from its small heginnings in Oxford, rose to become perhaps the greatest and most universally respected international charity of our time.



A WISH TO SHARE

In the educational field, his particular concern was with the teaching of mathematics, about which he spoke with missionary zeal. He was excited by mathematics and its beauty, and wanted to share this excitement with others. He spoke in Malaya on "Likes and dislikes in mathematics" and on "Mathematics and the real world"; in Calcutta on "What makes a beautiful proof?"; in Dar es Salaam on "Mathematical models"; and to the Mathematical Association (Lon- don), whose President he was in 1969, with the title "On liking Mathematics". He was as happy to talk to an association of school teachers as to an intemational congress, and equally diligent in prepar- ing his talks for publication — not, one feels, for personal glory but because, having something pleasurable to communicate, he wished to share it with the largest possible audience.

Towards the end of this period one particularly happy event took place. In April 1971 some 70 or 80 of his old students and collaborators, from at least 14 countries, came together in Oxford to celebrate his 6Oth birthday with a conference. It was a moving reunion, one which gave him, I believe, deep satisfaction and pleasure, and one which all those present will always remember.

It was not until 1972 that Charles Coulson became Oxford's first Professor of Theoretical Chemistry; as he said in his Inaugural Lecture "Theoretical Chemistry has not been offlcially recognised here until this time. But now it is!" It seemed that with five years or so before retirement he could hope to establish his subject, at last, as an independent discipline within the Chemistry Sub-Faculty of the University, and that he would have time to build the new school up to full strength. In spite of ill health, he had the courage to take on all the necessary planning and to supervise personally the conversion of the large old house in Sooth Parks Road which is now the Department of Theoretical Chemistry. Back from hospital, with apparently undiminished enthusiasm, he would be seen helping with the unloading of newly delivered desks, or carrying books to the library. He had always appeared to be temperamentally incapable of resting. When for any reason he was confined to his bed he regarded his indisposition as an excuse for an excursion into some less familiar part of the literature, an intellectual tonic. On one such occasion, I remember, he produced an elegant note on the random walk problem for slugs and snails, which in the presence of non-isotropic lighting adjust their motion so as to avoid facing the light. During his last illness, however, his disinclination to rest was a worry to all of us. It seemed that his inner drive was at last burning him out.



A WARNING HEEDED

Charles Coulson gave a few important review lectures, in addition to his Inaugural, during the last years of his life; and I think these, along with other things he wrote, help to give a fairly clear picture of what might be called his "scientific philosophy". I have remarked on the fact that he was never convinced that computers held the key to a golden age in chemistry when all would be predicted by direct solution of the Schrödinger equation. Many of you will remember his famous after-dinner speech at the Boulder Conference in 1960, when he introduced the classification into "Group 1" theoretical chemists, concerned with very accurate calculations on molecules with fewer than, say, 20 electrons; and "Group 2", concerned with what he called (with a characteristically apt and emotive turn of phrase) "the establishment of correlations and primitive pattems of understanding". After starting life himself in Group 1, I think he put himself fairly firmly, by 1960, into "Group 2"; but he was passionately concerned by the fact that communication between the two Groups, seemed to be breaking down — or had already broken down. For he said on that occasion "I cannot help feeling that the gap between the two groups is so large that there is now little point in bringing them together.

This is probably the last conference of the old kind. In future we should either have two distinct conferences, or else be prepared to plan parallel sessions for Group 1 and Group 2 enthusiasts." His own feelings were disclosed, I believe, in a reference to the Group 2 philosophy, which I quote: "Chemistry is an experimental subject, whose results are built into a pattem around quite elementary concepts. The role of quantum chemistry is to understand these concepts and show what are the essential features of chemical behaviour. [To say] that the electronic computer shows that D(H-F)»D(F-F) ... is not an explanation at all, but merely a confirmation of experiment. Any acceptable explanation most be in terms of repulsions hetween non-bonding electrons, dispersion forces between atomic eures, etc This belief, that "explanation" most he pictorial and conceptual, rather than numerical — a re-affirmation of the views he put forward in his molecular orbital review article in 1947 — was absolutely fundamental to all his scientific work. In retrospect, it is ironical that a future Professor of Mathematics should ever have said, with evident satisfaction, "we have avoided all mathematics and have insisted everywhere upon the pictorial character of each step... but for him the framing and linking of concepts was the supreme creative activity, to which mathematical manipulation, however indispensable, was always subservient.

Coulson's expression of concern about an impending Group 1/Group 2 split, which he viewed as an approaching disaster, was time- ly and received wide publicity. The disaster has, I believe, been averted; there seems now to be a more continuous gradation between Group I and Group 2 activities, with everyone making some use of computers and with an increasing emphasis on exploratory work and use of the results in developing new concepts. Many individuals belong in some respects to both Groups and the polarization has tumed out to be much less severe than was anticipated. He would, I think, have been greatly reassured by the programme of this Symposium.



NO LOOSE ENDS

Towards the end of his life, Coulson himself became an avid collector of computer output — and in his review articles proclaimed that "These calculations have been tremendously enriched by the widespread use of electronic computers and package programmes . In his Inaugural Lecture in 1973 he could say "But computers are admirable servants: and they grow steadily more rapid in their working. I want to stress the power of the modem computer. " He had, in fact, achieved his own Group 1/Group 2 reconciliation. What was important was to put together what was good and to throw out what was bad; and for him "what was bad" meant "Bastard Mathematics" — which could all too easily be employed by those with nothing to say, aided by large computers, to produce mountains of illegitimate output! Let me quote a few passages from that Lecture: "The computer is a tool, just like a spectroscope or a calorimeter. But this does not mean it should always be used — the laboratory instruments will often be mure appropriate. And if we use a computer without a clear idea of why we do it, we are really wasting time and money — doing Bastard Mathematics as I have sometimes called it." And on turning to more approximate calculations he had this to say "So much for the business of trying to rival Nature and get the numerical answer absolutely right. As I have said, this is unly one part of the role of theoretical chemistry. Often, without such accuracy and with only just sufficient numerical agreement to satisfy ourselves that we have really gut the right model, we can acquire a profound and deeply satisfying insight into some particular phenomenon." Charles Coulson was indeed a great builder of mathematical models; he knew when to simplify and when to stop simplifying; in short, how to find the right model.

It was sadly ironic that one who did so much fur theoretical chemistry should live for less than a year after his Inaugural Lecture as Professur of Theoretical Chemistry. His time at the new Department, where I visited him quite often, was overshadowed by declining health, but in spite of frequent physical disability, pain and frustration, his spirit was unquenchable. He knew that his time was running short, and early in January of this year was told he could hope unly for a few days. He used those days in clearing outstanding correspondence (over 80 letters in the last three days), making arrangements and generally tying up loose ends. All this done, by 6th January, he went to bed and died quietly in his sleep in the early hours of 7th January. We shall miss his presence at Conferences such as this; we shall miss his comments and questions, always kind and sincere; and his scholarly contributions to the literature; but thousands more will miss the help he gave them as a human being — his concern, his compassiun and his humanity.

Charles Coulson with his family. Photo : Courtesy of K. Ohno; © R. McWeeny