AAS-Biographical memoirs-Hurley

Andrew Hurley was a distinguished theoretical chemist, noted for his clear insights, which he was always ready to share, and for his mathematical ingenuity. His career spanned what in many ways was the defining era of computational quantum chemistry.

Family background [1]

Andrew's ancestors, on both his father's and mother's side, were lured to Melbourne by the opportunities which the Victorian Gold Rush of the 1850s seemed to create.

John Hurley, Andrew's paternal great-grandfather, arrived in Melbourne from Devon, England in 1861, aged 27. Following a lack of success with gold mining, he started a small farm near Geelong, marrying Mary Margaret Quinn in 1863. Their son, Thomas, had an illustrious career with the Victorian Education Department, retiring as Chief Inspector of Schools in Melbourne. Thomas married Mary Elizabeth Scholes in 1887. (Thomas Ernest) Victor Hurley, the eldest of their seven children and Andrew's father, was born in 1888.

Andrew's maternal grandfather, George Henry Crowther, was the eldest son of English migrant parents who moved to Melbourne in 1856. George's father became a state school headmaster. George matriculated from Wesley College in Melbourne, graduating BA in 1875 and LLB in 1876. After teaching the senior classes at Hawthorn Grammar School for some years, he opened his own school, Brighton Grammar School, in 1882. Dr Crowther was widely recognised as an outstanding teacher and educational administrator [2]. He married Alice Armstrong in 1882, and their third child, Andrew's mother, Elsie May Crowther, was born in 1890.

Andrew's father, Victor Hurley, graduated from the University of Melbourne in 1909 with first class honours in medicine. In August 1914 he enlisted in the AIF as a Captain in the Australian Army Medical Corps, serving throughout WWI with great distinction and displaying valuable administrative skills.

Victor Hurley and Elsie May Crowther were married in London in June 1919. Upon returning to Australia, Victor became one of the most respected surgeons in Victoria, playing a prominent role in many aspects of medico-political affairs. With the advent of WWII, he was pressed to make his administrative skills available. He was appointed Director General of Medical Services for the RAAF, with the rank of Air Vice-Marshal. In 1950, he was created a Knight Commander of the Order of the British Empire, and in 1952 was given the rare honour for an Australian of election as an Honorary Fellow of the Association of Surgeons of Great Britain and Ireland. Sir Victor Hurley was such a straight-forward and friendly person that it was difficult for his family to understand what a famous man he had become. Those who had known him, referred to his impartiality and fairness; his excellent human relations; and complete absence of any trace of official arrogance. Many, if not all, of these attributes could be applied to Andrew.

There were six children in all. Ann was born in 1920, John in 1921, David in 1923, Tom in 1925, Andrew in 1926 and Barbara in 1930. All six became graduates of the University of Melbourne. Ann and Barbara both took Honours degrees in Arts, while John and Tom both studied medicine. John spent over thirty years with the Pathology Department of the University of Melbourne, retiring in 1986 as Professor and Chairman of that Department. Tom became a physician and, like his father, has used his considerable administrative skills on many committees, including President of the Royal Melbourne Hospital. David took Honours degrees in mathematics and physics and spent more than twenty years with the Mathematics Department of the University of Western Australia, retiring as Associate Professor in Applied Mathematics. Andrew also took Honours degrees in Mathematics and Physics before proceeding to higher degrees. All six children were highly talented, which is not surprising given the strong educational abilities of both of their grandfathers, but his brothers and sisters regarded Andrew's intellect as outstanding. In addition to Andrew, Ann, John and David have all died in recent years.

Early days

Andrew Crowther Hurley was born on 11 July 1926 and grew up at 16 Albany Road, Toorak. 'Wyuna' had almost an acre of garden, and was to be the family home for the next twenty-five years.

Both the Hurley home and their holiday home at Point Lonsdale had tennis courts, which enabled Andrew to develop as a tennis player. His father was a keen golfer and he and his sons formed a four at bridge.

Andrew's family soon recognised that he was unusually able. He was neither an avid reader nor a frequent questioner. He enjoyed reading books by Jane Austin, Agatha Christie and Dorothy Sayers, rather than technical reading. His ability to understand seemed to be innate, rather than acquired. As a boy, he would become absolutely engrossed in building 'incredible things' with a magnificent set of Meccano. He shared this hobby with a neighbour, who later became a Supreme Court Judge.

Andrew was admitted to Wadhurst Preparatory School, a junior component of Melbourne Church of England Grammar School (now Melbourne Grammar School), in 1934. He proceeded to the senior school in 1940 and Dr Graham Sargood, who retired from the University of Melbourne as Reader in Physics, has kindly recorded some of his memories of Andrew during this period, thus:

I was in the same form as Andrew for every subject in our last four years at school, 1940-43. I remember him as a quiet, undemonstrative, and very approachable boy who seemed to know the answer to every question that ever bothered the rest of us. I recall Andrew pointing out to me at the start of the 1941 school year that there was no need to do the first two assigned physics experiments because the third experiment included all of the measurements needed for the first two, so do the third experiment and then write up all three!

and

Andrew was the most innovative member of the class in the physics lab, and had a far greater insight into, and understanding of, the experiments we performed than anyone else. He was also the only one to try heating a beaker of kerosene with a Bunsen burner, thereby acquiring singed eyebrows!

Following his matriculation in 1942, Andrew completed Leaving Honours in 1943. He was top student in the state of Victoria in Mathematics I, III and IV, with First Class Honours in Chemistry and Physics.

Andrew enrolled as a student of the University of Melbourne in March 1944. At the end of that year, the first year of a Bachelor of Science degree course, he was top student in Pure Mathematics I, Applied Mathematics I and Physics I, with First Class Honours in Chemistry IA. His second year results were similarly spectacular, with first place in Pure Mathematics II and equal first in Applied Mathematics II and Physics II. In November 1946, he was awarded the degree of Bachelor of Arts with First Class Honours and equal first place. His subjects included Pure Mathematics III and Applied Mathematics III. In 1947, Andrew entered the third year of his BSc degree course and obtained Second Class Honours in Physics III, First Class Honours in Theoretical Physics and First Class Honours and first place in Theory of Statistics. He was admitted to the degree of Bachelor of Arts (Honours) on 19 April 1947 and to the degree of Bachelor of Science on 18 December 1948.

Andrew then undertook a research project in the School of Mathematics under the supervision of Dr Hans Schwerdtfeger and this resulted in a thesis entitled 'Finite Rotation Groups and Crystal Classes in Four Dimensions'. In March 1949, at the examination for the degree of Master or Arts, he was awarded First Class Honours and first place.

The honours that Andrew received at graduation included a CSIRO Studentship and a Dominion and Colonial Exhibition, awarded by the University of Cambridge. In addition, he was awarded a number of other scholarships and exhibitions in the course of his studies. For his golf he was awarded a Half Blue in 1948. However, Andrew's plans to proceed to Cambridge in 1949 were delayed due to ill health.

Cambridge 1950-1952

In July 1950 Andrew became a member of Trinity College, University of Cambridge, and commenced his research towards a PhD in theoretical physics under the supervision of Professor P. A. M. Dirac. Dirac is famous for his contributions to the fundamentals of quantum theory, but he was reputed to be discouraging in his initial contacts with prospective research students. Late in 1950, a paper based on Andrew's MA thesis was communicated by Dirac and accepted for publication in the Proceedings of the Cambridge Philosophical Society (1). However, after only one term, Andrew transferred to the Department of Theoretical Chemistry. This was the first Department of Theoretical Chemistry in the world, which was established in 1932. Its foundation Head, Professor Sir John Lennard-Jones, who was still in charge at the time, was a highly distinguished scientist and administrator. One reason for transferring to theoretical chemistry would have been Andrew's commitment, under the terms of his studentship, to return to Australia and to work with CSIRO for three years, with the expectation that he would be attached to the Section of Chemical Physics in the Division of Industrial Chemistry. Another reason for this choice may have been his recognition of the huge intellectual strength of the Department of Theoretical Chemistry at that time. Senior members included S.F. Boys, G.G. Hall and J.A. Pople. A 1952 photograph shows seventeen members in all, indicating the high regard of the research community for that department. Andrew would have had a close affinity with Hall, who was primarily a mathematician and who shared Andrew's interest in group theory. Boys had very recently outlined a new method for obtaining accurate atomic and molecular wave functions based on the use of Gaussian orbitals. Pople was awarded the Nobel Prize in Chemistry in 1998 for his contributions to theoretical chemistry over many years. R.K. Nesbet, who joined the department in 1951 and became a life-long friend of Andrew, comments as follows on the nature of the research at that time:

Several basic ideas essential for understanding interacting electrons and for developing quantitative theory for theoretical chemistry and atomic physics were formulated, possibly for the first time, within this group.

By December 1952, Andrew had qualified for his PhD and the work recorded in his thesis formed the basis of five substantial papers in the Proceedings of the Royal Society of London (2-6). Lennard-Jones was co-author of two of these papers. Both Lennard-Jones and Pople were co-authors of the last paper, which is widely recognised as having provided the precursor model of later methods that eventually achieved the practical goal of 'chemical accuracy' in variational calculations.

Also at Cambridge at that time was Angas Hurst, a contemporary and fellow student at the University of Melbourne of Andrew's elder brother, David. Angas later became Professor of Mathematical Physics at the University of Adelaide. He developed a very close friendship with Andrew and found him a very stimulating companion, 'being able to try my ideas out on him, knowing that I would always get perceptive and helpful comment'. Angas recalls that, at Cambridge, Andrew maintained his interest in quantum field theory and even gave one talk on that subject. They would usually go together to theoretical physics meetings such as the Ñ² Club to hear luminaries like Thomas Gold and Fred Hoyle. When they attended the first Rutherford Memorial Lecture, given by C.G. Darwin, they were late and had to sit out in front with the speaker! Angas and Andrew played together in the Trinity College table tennis and tennis teams. In 1951 they were members of the victorious Division I Trinity tennis team, and were awarded their First VI colours. They played regularly for the 'Grasshoppers', the Cambridge second division tennis team, with Andrew playing occasionally in the first division. Andrew was a frequent social visitor to the Hurst home in Cambridge where he enjoyed the company of other visitors, including some who have achieved greatness in fields as diverse as statistics, Australian history and geology.

George Hall did not collaborate closely with Andrew, but recognised him 'as a man of deep mathematical insight who could persist with new ideas until he had a satisfactory solution to his problem'.

Melbourne 1953-1954

Andrew returned to Melbourne early in January 1953 and commenced work with CSIRO's Division of Industrial Chemistry at Fishermens Bend, an industrial area of Melbourne about five km from the city centre. At that time, the Division consisted of six Sections namely, Minerals Utilisation, Cement and Ceramics, Chemical Physics, Physical Chemistry, Organic Chemistry and Chemical Engineering. The naming of the Sections was in accordance with the belief of the Chief, Dr I. W. (later Sir Ian) Wark, that his Division should carry out a considerable amount of fundamental work.

Andrew was assigned to the Chemical Physics Section, which was formally established in 1945 and whose head was Dr A. L. G. Rees. The initial emphasis was on the acquisition and development of modern physical instruments, both for the benefit of the whole Division, and for conducting independent research. The Section equipped itself to study and apply the techniques of electron microscopy and diffraction, X-ray diffraction and spectroscopy – including mass spectroscopy and infrared spectroscopy. Rees had a personal interest in the chemistry of defect solids and a conviction that the solution to many of the problems in this field would come with a thorough understanding of the quantum physics of those solids.

With a Chief convinced of the importance of fundamental research and a Section head convinced of the importance of theory, and with his own brilliant record, Andrew was warmly welcomed. He was free to pursue his own research, with the proviso that he should be available to provide theoretical support for the experimental work of the Section. However, Andrew had come from a department of perhaps fifteen theoreticians to a Section in which he was the only member classified as a theoretician and he may well have felt isolated. For Andrew, this would have been less of a problem than for most, because he was strongly self-motivated and he soon published a series of three papers on the electrostatic calculation of molecular energies (7-9). This method was more direct than the conventional one, where molecular energy was obtained as a difference between two very large quantities. During 1953, Andrew submitted a dissertation to Trinity College and later in the year was awarded a four-year Fellowship. Wark was so impressed with Andrew's summary of his dissertation and with his outline of the direction of research that he wished to pursue that he encouraged members of the CSIRO Executive to read them. After some consideration it was agreed that Andrew should not be required to complete his studentship commitment of three years with CSIRO before taking up the Fellowship. He was duly granted leave of absence from 31 December 1954 to accept the Fellowship for one year, with a possible extension to a second year. It was clear that CSIRO was keen not to lose such a talented scientist and also that Andrew's immediate superiors appreciated his isolation from the mainstream of theoretical chemistry. It is interesting to look briefly at the state of theoretical chemistry in Australia at that time in regard to this isolation.

Allan Maccoll, a lecturer in chemistry at the University of Sydney from the 1930s, was perhaps the first Australian to work primarily in theoretical chemistry. When D.P. Craig returned from WWII in mid-1944, Maccoll got him interested and together they worked through Dirac's Quantum Mechanics, a difficult book to absorb. At about that time, Eyring, Walter and Kimball's Quantum Chemistry appeared and they worked through that, too. They then tried, unsuccessfully, to apply non-empirical molecular orbital theory to a study of the ultraviolet spectrum of anthracene. Craig's first paper in theoretical chemistry was published in 1945. Maccoll, followed by Craig, then left for University College London (UCL), where they continued what they had started in Sydney. Meanwhile, in 1946 at the University of Melbourne, R.D. Brown, after reading a paper by C.A. Coulson and H.C. Longuet-Higgins on Hückel theory, applied molecular orbital theory to a study of azulene; work that was eventually published in 1948. Further publications followed. Brown also went to UCL in 1950, travelling on the same ship as Andrew. Brown obtained a lectureship in London and he found the intellectual environment very attractive, but for family reasons, returned late in 1953 to a position at the University of Melbourne. C.K. Ingold, Professor of Chemistry and Head of Department at UCL, saw this as a tragedy for his promising research career, believing that it would be impossible to continue it in Australia. At the University of Western Australia, N.S. Bayliss also had a strong interest in theoretical chemistry and published in 1948 a seminal paper on the free-electron theory of conjugated polyenes. In Sydney, I.G. Ross was active in theoretical chemistry from 1954. There was, however, no research with a very close connection to Andrew's field of accurate calculations for diatomic molecules.

On 19 September 1953, Andrew married Yvonne June Gallagher. Yvonne was a graduate in Arts from the University of Melbourne, specialising in French. Yvonne's first encounter with Andrew was as her tutor in a mathematics class. However, it was through Andrew's sister Barbara, that Andrew and Yvonne met socially. Barbara and Yvonne were both residents of Janet Clarke Hall, a residential college of the university. While Andrew was engaged in research for his PhD at Cambridge, Yvonne undertook higher studies in French literature at the Sorbonne in Paris.

Andrew followed his three papers on the electrostatic calculation of molecular energies by a very careful analysis of 'the method of atoms in molecules', which had been introduced by W. Moffitt in 1951 as another promising alternative to the traditional method (10).

Cambridge 1955-1956; MIT 1957

In March 1955 Andrew returned to Trinity College, Cambridge, as a Title 'A' Fellow. Yvonne and their baby son Victor later joined him. H.C. Longuet-Higgins had recently replaced Lennard-Jones as Head of the Department of Theoretical Chemistry.

At Cambridge, Andrew continued his study of Moffitt's method of atoms in molecules, focusing on how to overcome difficulties that he had identified in his first paper on this subject. He introduced his 'intra-atomic correlation correction' and obtained encouraging results for several molecular systems (11-14). Andrew's thorough investigations into the electrostatic method and the method of atoms in molecules were two parts of his overall effort to obtain molecular calculations with chemical accuracy. With the computational facilities then available, chiefly electromechanical calculators, quantitative calculations were limited to small molecules composed of light atoms.

While at Cambridge, Andrew received a flattering invitation to spend a year with J.C. Slater's Solid State and Molecular Theory Group at the Massachusetts Institute of Technology (MIT). This was a large group, with Slater and G.F. Koster as senior members, with many other visiting researchers whose interests covered both molecular and solid state physics. The group received generous funding from the US Air Force and Andrew was given a staff appointment. Commencing at MIT in about September 1956, he continued his work on the method of atoms in molecules and put his previously formulated intra-atomic correlation correction onto a more fundamental footing (16). Andrew benefited greatly from the broad range of interests at MIT. In particular, the strong interest of Slater in crystallographic space groups, together with the presence of Koster, an expert in group theory of both point groups and space groups, sharpened his interest in the application of group theory to problems of the solid state and of molecular physics and chemistry.

CSIRO 1957-1988; Ames 1963

When Andrew returned to CSIRO at Fishermens Bend on 1 October 1957, he was still the only theoretical chemist in the Chemical Physics Section. His outstanding research achievements during previous years were acknowledged by his almost immediate promotion to Principal Scientific Officer at the relatively early age of 31. Andrew would have found it an exciting time in the Section as the experimentalists, inspired by the leadership of Dr Rees and assisted by excellent technical support, strove to become world leaders in their various fields. As evidence of their success, six were to become Fellows of the Australian Academy of Science by 1973 and two also became Fellows of the Royal Society of London. Opportunities for overseas visits greatly helped Andrew to maintain important contacts and to keep abreast of his field.

Two substantial papers in 1958 and 1959 demonstrated that the intra-atomic correlation correction (ICC), which Andrew had introduced, could give molecular binding energies for the ground states and excitation energies of first row diatomic whose agreement with experimental data was almost an order of magnitude better than for self-consistent molecular orbital calculations (17, 18). At the 1959 Conference on Molecular Quantum Mechanics held at the University of Colorado, where he was an invited speaker, he presented his ICC results for CO. It was at this conference that C.A. Coulson gave his famous conference summary that included a warning of a possible split between 'the big computers' and those who used more qualitative approaches to the solution of molecular problems. Following the conference, Andrew spent several days with 'the big computers' at the University of Chicago and several more with Slater's group at MIT. His conference paper was published in Reviews of Modern Physics in an article that also summarised the ICC method (19). Andrew chuckled when reading the comments of the journal referee, who described his writing style as one of 'extreme compaction'. The reviewer's observation highlights one of Andrew's characteristics. His approach to any goal was always via the shortest route. Thus, his writing was clear but concise; seldom would he make a point twice, or elaborate on it.

I joined Andrew at the end of 1958 after completion of a DPhil at Oxford under Coulson. My arrival almost coincided with the Section of Chemical Physics being renamed a Division, with Rees as its Chief. Soon after my arrival, A.F. Beecham, the Division's only organic chemist, sought my help in obtaining a mathematical description of the counter-current separation of two chemical components, a request that gave me an early insight into Andrew's clear and lateral thinking. He observed that the mathematics required to describe this problem was remarkably similar to that which I had encountered earlier in a completely different context, namely when solving Hückel equations for conjugated hydrocarbons. Generally speaking, Andrew left me free to plot my course of research as he pursued his own goals. However, he was always ready and willing to discuss my queries and to make suggestions, which were invariably pertinent.

A major opportunity to give theoretical support to the Division's experimental activities arose in 1960 when the Mass Spectroscopy group, led by J.D. Morrison, measured some appearance potentials that they tentatively associated with the ground and excited states of a number of doubly positively-charged diatomic ions. To explore the correctness of this association, Andrew made use of his deep understanding of the quantum-mechanical virial theorem, which he had discussed in an early publication (7). Andrew and I computed theoretical estimates of the appearance potentials and these strongly supported the experimentalists' conjecture (23).

Early in 1962, Andrew received invitations to a conference and an associated workshop in Japan and also to a one-year appointment as Visiting Lecturer at the Institute for Atomic Research and Department of Chemistry at Iowa State University. This appointment would fill the vacancy created by the departure of K. Ruedenberg for the Johns Hopkins University at Baltimore in Maryland. In Japan he presented two papers, of which the one on dipositive diatomic ions generated particular interest, with a number of experimentalists expressing intentions to use emission spectra and low energy electron spectroscopy to search for some theoretically predicted molecular states. From Japan, he travelled direct to Ames in Iowa, where Yvonne, Victor, Catherine and Mark, who was born shortly before Andrew left for Japan, joined him.

In addition to carrying out his own research at Ames, Andrew was expected to deliver the lecture courses previously given by Ruedenberg, thus it was a very busy year. The lecture course was more time-consuming than anticipated. Nevertheless, Andrew completed a major paper on the elimination of atomic errors from molecular calculations, an early form of which he had presented in Japan, and also a chapter in a book honouring R.S. Mulliken on his retirement (29, 30). In addition, he worked with J.C. Browne on the construction of a program for computing diatomic molecular integrals. Finally, early in 1963, he tentatively accepted an invitation by D.P. Craig to write a monograph on the 'Electronic Theory of Small Molecules' for the series Theoretical Chemistry, to be edited by Craig and R. McWeeny and published by Academic Press.

Before returning to Australia in September 1963, Andrew spent six weeks at Johns Hopkins University with Ruedenberg and R.G. Parr and their research students. In 1964 he was invited to attend the Istanbul International Summer School in Quantum Chemistry, but in this instance, CSIRO declined to make a travel quota position available.

Early in 1965 the Division of Chemical Physics moved into new laboratories at Clayton adjacent to the newly established Monash University, and about 20 km southeast of the city centre. In the years that followed, Andrew frequently attended and occasionally spoke at university colloquia in mathematics, physics and chemistry. His questions and observations were infrequent but very penetrating and greatly valued.

Following Andrew's return to CSIRO, there was a slight slowing in his very high rate of publication. This may have been a consequence of early work towards the book that he had agreed to write, or from a change of focus. Andrew kept himself well informed of work being carried out by Slater's group at MIT through its quarterly reports, and he was especially interested in Slater's new technique for investigating irreducible representations of crystallographic space groups. Slater had used an unusual convention when describing his technique, and Andrew found certain inconsistencies that he was able to eliminate so that the technique could be incorporated into conventional theory.

At about this time, Andrew confirmed the correctness of a suggestion that, in the paper based on his MA thesis (1), he had overlooked 5 of a possible 227 four-dimensional crystal classes (31). When originally published, the work seemed to be a piece of pure mathematics, without physical application, but it had now become important in crystallography. He then continued to devote much of his attention to the solid-state area, with the publication of a major paper in 1966 (32). The obtaining of simpler and more direct means of using symmetry information in molecular and solid-state problems was to become a recurring theme in many subsequent papers.

In 1965, there arose another major opportunity for collaboration within the Division of Chemical Physics. B.T.M. Willis, of the Atomic Energy Research Establishment at Harwell, UK, had interpreted some neutron diffraction data for the fluorite structures UO₂ and CaF₂ in terms of anharmonic vibration of the crystal anions. This interpretation was controversial and he sought theoretical support from Barrie Dawson, an X-ray crystallographer in the Division. A very simple model, proposed by Andrew, resulted in good qualitative agreement with the experimental data (35). It gave strong support to Willis' interpretation and stimulated further work on anharmonicity within the Division.

In January 1967 Andrew was invited to attend an International Symposium on Atomic, Molecular and Solid State Physics at Sanibel Island, Florida, which was organised by P.O. Löwdin in honour of J.C. Slater. Andrew described the symposium as a great success and he evidently coped well with the daily program that commenced at 8.30 a.m. and frequently continued until after midnight. Spectacular progress was reported both by the ab initio (big computer) people and also by those using semi-empirical methods, with indications of co-operation between the two groups. This seemed to prove Coulson wrong in his prediction of a split. Andrew was pleased with the use by the ab initio people of ideas that he had helped to formulate in the early 1950s. The symposium turned out to be a meeting ground for atomic and molecular theorists with those whose areas of interest were solid-state physics and many-body theory. At about this time he was joint author of one publication and sole author of a second relating molecular calculations obtained by means of the Hellmann-Feynman theorem and the traditional energy-difference approach (34, 37). During 1967, Andrew was appointed a member of the Editorial Advisory Board of the newly founded International Journal of Quantum Chemistry, a position he held until 1984. In 1968, he was promoted in CSIRO to the level of Chief Research Scientist.

The Division's Annual Report for 1967-68 indicated that Andrew had completed the first five chapters of a book entitled The Electronic Theory of Smallish [3] Molecules and the Report for the subsequent year suggested that the whole of the proposed monograph was nearly complete. In 1969, he gave a course of sixteen lectures in group theory to the fourth year honours chemistry students at Monash University. From about this time, there was a marked increase in requests to serve as examiner for PhD and DSc degrees, and to provide courses for summer schools in theoretical chemistry. Particularly his Australian colleagues and their students were appreciating Andrew's qualities of insight more and more. Some recollections by Dr G.B. Bacskay and Professor P. R. Taylor illustrate this. George Bacskay was, at that time, a recent graduate of the University of Melbourne and the recipient of a CSIRO studentship. He visited Andrew in 1968, shortly before travelling to Cambridge to 'read' for a PhD and recalls:

...on that day at Clayton I met Andrew who told me about his research interests in quantum chemistry, but also about recent developments that made him optimistic about the future of computational quantum chemistry. Much of what he said went right over my head, but he patiently explained, while puffing on his pipe, what I did not understand, or at least admitted to not understanding. He somehow personified my mental image of a 'theoretician' that I had built up after reading about the Curies, Bohr and Einstein. That strong positive image stayed with me all my life.

George next met Andrew in February 1973 at the Second Australian Spectroscopy Summer School, which opened with a discussion forum in which early speakers were very pessimistic about the state and prospects of quantum chemistry:

And then Andrew stood up and spoke. He said that in his opinion the future of Quantum Chemistry never looked brighter or more promising. He talked of recent theoretical developments in the formulation of correlated wave functions in terms of pair natural orbitals; the application of Cizek's Coupled Pair Many Electron Theory to molecules; the use of Gaussian basis sets and the recent developments in computer hardware. All of these, he said, made the calculation of 'chemically accurate' properties by ab initio methods a reality not just for the hydrogen molecule, but also for small polyatomic molecules like water and nitrogen. These positive remarks made a strong impression on everyone, especially students who were about to decide what area of research to embark on.

Referring to Andrew's course of three lectures on electron correlation, George comments:

The course became something of a legend. It was a very thorough and rigorous course, with complete mathematical detail, with all the equations there on the blackboards. Andrew used to go into the lecture theatre at least 10 minutes early and put as much stuff on the blackboards as possible before he started lecturing. We, who attended, soon learnt to do likewise, feverishly copying it all down as fast as possible...For those of us who persevered, participating in those lectures proved to be a unique and remarkable experience, proving to be also incredibly valuable in our later work.

Peter Taylor was then an honours student in chemistry at the University of Sydney, who envisaged a future in inorganic chemistry with emphasis on experiment. He, too, attended the summer school and Andrew's lectures. He comments:

The lectures were extremely dense, with perhaps ten lectures-worth of material, at least, being covered in the three scheduled lectures...What struck everyone about Andrew's lectures (apart from the density) was his air of total confidence that THIS was the way calculations would ultimately be done, perhaps not in 1973, but eventually.

Peter was, in his words, 'mesmerised by the problem of electron correlation'. He decided within the next few months to pursue this as his PhD topic, preferably under Andrew's supervision. His determination was rewarded when Professor N.S. Hush, Head of the Department of Theoretical Chemistry, had Andrew elected an Honorary Research Associate of the Department and Peter's principal supervisor.

Andrew was elected a Fellow of the Australian Academy of Science in 1971. In 1973 he contributed a chapter to Advances in Quantum Chemistry in which he explored the circumstances under which Hartree-Fock and simpler calculations might be expected to give reliable estimates of molecular binding energies (41). He also collaborated with the Division's X-ray crystallographers and with A.F. Beecham to demonstrate the reliability of the Bijvoet method for determining the absolute configurations of molecules, following some doubts that had been raised in the literature (42, 43).

In 1976, Academic Press published Andrew's two books, Introduction to the Electron Theory of Small Molecules and Electron Correlation in Small Molecules (44, 45). One factor that contributed to the delay of seven years since Andrew's report that the 'monograph is almost complete' was the length of the original manuscript, which amounted to 750 pages and greatly exceeded the guidelines for books in the intended series. It was eventually agreed that the material should be published as two books; of which only the second and more advanced part would be a member of the Theoretical Chemistry series. This separation into two books required substantial changes, particularly in regard to cross-referencing. It occurred at a time when definite signs were emerging of ill health from emphysema, which steadily sapped Andrew's physical strength during the years that followed. One might also conjecture that the discipline of writing a book was contrary to his natural style of research. He seemed to enjoy switching between his several spheres of excellence. Both books received several very enthusiastic reviews, with comments on the unique insights that Andrew provided in areas notorious for misunderstandings. Some reviewers, while appreciating the merits of the books, criticised their failure to incorporate some very recent developments in the subject. Andrew was sensitive to this criticism, which he attributed to delays caused by the task of separating one intended book into two.

In 1975 Peter Taylor arrived to spend one year under Andrew's supervision. This was approximately the middle year of his PhD, which he completed in Sydney in 1977. The collaboration of Peter and Andrew with Bacskay and Hush from Sydney led to the publication of four substantial papers (46, 48, 49, 52).

Having largely achieved his early goal of molecular calculations with near chemical accuracy, Andrew seems to have shifted the emphasis of his research from that area. Perhaps he 'handed over the baton' for such work to Peter Taylor, who was proving a very talented researcher in the field of highly accurate molecular calculations and able to use to great effect the powerful computers and auxiliary software that were becoming available. Andrew maintained a close interest in Peter's work, but, from this point on, many of his publications resulted from collaboration with other Divisional projects. Thus, he was one of four authors of a paper, published in 1978, on the recasting of a standard formulation of forward scattering of fast electrons in crystals for cases where only a small number of beams is involved (50). This, together with further work with A.F. Moodie (55), led to a big advance on the information that could be provided by a two-beam model.

Andrew collaborated with A.F. Beecham and C.H.J. Johnson to resolve a question concerning hydrogen bonding (51, 53). Both Hurley and Beecham were keen golfers. This common interest led to a further collaboration that provided a clear graphical solution to a scheduling problem that had been of concern to the Victorian Golf Association for some years (54). It was a very challenging mathematical problem, during the solution of which Andrew consulted a number of eminent mathematicians. In another 'fun' publication, he demonstrated with delightful simplicity that there are only two ways in which the opposite faces of a dice can add up to a constant, for hyperdice of any dimension (56).

The year 1982 saw the publication of a superb demonstration of Andrew's mastery in applying the Hellmann-Feynman theorem. He used the simplest diatomic system H₂⁺ and a one-centre wave function to explain a paradox concerning the behaviour of electronic kinetic energy when a bond is broken (61).

Two papers in 1985 were perhaps the result of an abiding interest in the group theory of more than three dimensions. They both concerned the non-crystallographic symmetries that arose in studies of liquids and in solids exhibiting non-crystallographic long-range order (65, 66). In the same year, Andrew was able to catch up with several of his old Cambridge associates at a Symposium held in Canberra to mark the retirement of Professor D.P. Craig from the Foundation Chair of Physical and Theoretical Chemistry in the Research School of Chemistry at the Australian National University (Figure 1).

Figure 1

Reunion of former Cambridge colleagues at the 'D.P. Craig Symposium' (Canberra, Australia, February, 1985). Left to right: A.C. Hurley, G.G. Hall, A.D. Buckingham, J.N. Murrell and J.A. Pople.

Andrew had considerable interest in Galois theory. With the acquisition by the Division of an IBM personal computer and the availability of the symbolic algebraic program muMath, Andrew collaborated with A.K. Head in using Galois theory to answer the question of when a sextic equation, such as arises in crystal elasticity, is solvable. The resulting paper was published in a special issue of the International Journal of Quantum Chemistry honouring Andrew on the occasion of his sixtieth birthday (67). This was the first instance of a commemorative issue by that journal. Peter Taylor both proposed the special issue and put it together.

Andrew's final paper, except for a joint paper published posthumously in 1999, was published in 1988, shortly before his death (68).

Andrew was positively diagnosed as suffering from emphysema about ten years before his death. However, some of his close friends and colleagues were aware of the symptoms for several years before the official diagnosis. His deteriorating lung condition became increasingly limiting physically. Thus he made use of a mobile golf buggy on the golf course. Later, he avoided travelling to work on 'smog-alert ' days. He retired from full-time employment in August 1987 and continued bravely as an Honorary Fellow.

Andrew carried out his research in a Division where the policy of the foundation Chief was that scientists should concentrate on their research and should rely on the Chief to look after all other matters. He seemed very comfortable with this policy, which involved him in a minimum of administration. When the number of scientists nominally under his leadership grew, and it was briefly as high as five, he dealt with budgetary and reporting matters with that same efficiency which characterised his research. However, he did not relish administrative chores. Generally speaking, he tended to make very effective use of available computing and other facilities, but not to spend time and effort pressing for upgrading of those facilities.

Andrew retired at a time when the Division of Chemical Physics had recently merged with another Division. It was a time when the Division was 'shedding' a number of staff, including some long-standing, and the tradition of formal farewells was faltering. In this climate, Andrew declined the offer of a formal farewell for himself. It was only a few months later that he died on 18 October 1988. Many colleagues and former colleagues, from both the Division and from the academic world, attended his funeral.

In April 1989, The International Symposium on Quantum Chemistry, Solid State Theory and Molecular Dynamics dedicated one session to the memory of Andrew. Professor A.D. Buckingham introduced the session and Dr Peter Taylor delivered the first scientific paper.

Research

Most of Andrew's research was directed towards the pursuit of chemical accuracy in molecular calculations and the application of group theory to physical and chemical problems. A third group of papers resulted from the application of virial and electrostatic methods. Finally there is a variety of other papers, many stemming from collaborations within the Division of Chemical Physics.

The pursuit of chemical accuracy

Andrew's PhD research at Cambridge was part of a major project of the Department of Theoretical Chemistry entitled 'The molecular orbital theory of chemical valency' and Andrew was author or co-author of the final five of sixteen papers with that general title.

Earlier papers in the series were concerned with the transformation of a molecular orbital description of a wave function into a localised orbital description, which matched better the traditional picture of chemical bonds and lone pairs and in which the separation of electrons of parallel spin required by the exclusion principle was obvious. One paper, by J. E. Lennard-Jones and J.A. Pople, derived a pair wave function for one electron pair that accounted for a considerable fraction of the electron-electron repulsion between electrons of opposite spin. It was conjectured that the localised description was only applicable to ground states. Andrew's first paper extended the work of Lennard-Jones and Pople for an electron pair in the presence of two equal centres to all excited states (2). This was followed by a paper about wave functions of orbital type for the lowest states of symmetries ¹S⁺_u and ³S⁺_u of a homonuclear diatomic molecule (3). A third paper further generalised the description of an electron pair to the case of unequal centres (4), whilst a fourth provided illustrative calculations for polar bonds (5). The final paper of the series, co-authored by Lennard-Jones and Pople, incorporated the description of an electron pair into a wave function for a polyatomic molecule (6). Pople comments as follows:

After some time, he (Andrew) produced a long manuscript, giving the general theory and gave it to LJ, who passed it to me for comment. I found the theory complete and persuasive, but after some thought was able to reduce its length substantially. Andrew had made extensive use of permanents [4], which could be avoided, getting the final equation more directly. The manuscript was revised and my name was added to the paper submitted to the Royal Society. The ideas belonged to Andrew, however, and I was delighted when the work earned him a Trinity Fellowship shortly thereafter.

The theory outlined in that paper became known as the 'separated-pair approximation' and many regard it as the starting point for accurate incorporation of electron correlation into molecular calculations. R.K. Nesbet has provided the following description:

In the separated-pair model, the electronic distribution is represented by correlated localized-pair wave functions for each single bond, lone pair, or inner-shell electron pair. The advantage of such a model wave function is that an explicit variational expression can be derived for the total electronic energy, giving pair wave functions and energies when minimised. This model is formally exact for a sparse gas of He atoms or of H₂ molecules.

Accurate calculation for molecules more complex than H₂ was a daunting task in the mid-1950s. The two major obstacles were the integrals over six electronic co-ordinates resulting from electron repulsion terms, and the inaccuracies resulting from the indirect manner in which binding and excitation energies were derived. This might explain why, following a rather complete formulation of the separated-pair approximation, Andrew turned his attention to alternative approaches. Thus he considered the virial method introduced by C.A. Coulson and R.P. Bell and the electrostatic method, introduced independently by H. Hellmann and by R.P. Feynman. Simpler integrals were required and the electrostatic method was expressed primarily in terms of forces, with an appealing classical picture. The principal disadvantage of both methods was the lack of a principle such as the Ritz Variation Principle, which ensured that the molecular total energies calculated by the traditional method would not lie below the exact values. In a series of three papers, Andrew discussed these methods and their applications to simple molecular systems (7-9). He determined, more precisely than had been done previously, conditions that the wave functions must satisfy to ensure that results of the three methods agree. The number of published calculations that satisfied these criteria was small, but it did include the separated-pair approximation. Andrew showed that the standard Heitler-London model did not satisfy the criteria, but that this failure could be overcome by allowing the atomic orbital basis to be detached from the nuclear centres, forming 'floating functions'. E.F. Gurney and J.L. Magee had pointed out the satisfaction of the virial theorem by floating functions earlier. In a fourth paper, Andrew derived equations to determine the optimum form for separated-pair electron orbitals and he provided an electrostatic interpretation of chemical bonding using optimum paired-electron orbital functions (15). Time and again in subsequent research Andrew exploited his deep understanding of the virial and electrostatic methods to obtain meaningful results with a minimum of calculation.

While the electrostatic theorem enabled valuable physical insights into molecular bond formation to be obtained from comparatively simple calculations, it did not provide an alternative route to accurate a priori calculation of molecular energies because of the lack of a variation principle.

In 1951,W. Moffitt proposed his method of 'atoms in molecules', which used either accurate atomic wave functions or experimental data to provide an electron correlation energy correction to traditional molecular calculations. Moffitt and Scanlan applied this method to the relatively complex systems O₂, C₂H₄ and C₂H₆. To test the reliability of Moffitt's method, Andrew applied it to H₂, where all calculations could be carried out exactly. He identified two potential sources of error and found that the method was unreliable for estimating total molecular energies unless different atomic orbitals were used in describing atomic and ionic states of the molecule (10). This requirement, discovered independently by R. Pauncz, greatly complicated the calculations. Andrew also found the calculated energies to be too high and he suggested that atomic wave functions do not form a suitable basis for molecular calculations.

His next paper proposed a variation of Moffitt's method in which the approximate wave functions used to describe the products of molecular dissociation were required to match closely the electron densities of the exact wave functions, implying a close match in associated electron correlation energies (11). This requirement was a key assumption in what Andrew dubbed the 'intra-atomic correlation correction' (ICC) method. A trial calculation for H₂ gave a computed energy curve for the lowest energy state never deviating from the exact curve by more than 0.05 eV which was encouraging, as were calculated binding energies for HF and N₂ (12, 13). The results for N₂ led Andrew to favour the higher of two experimentally-deduced values for the binding energy, which later experiments confirmed.

sIn a further paper, a critical examination of traditional ab initio methods led to the conclusion that binding energies should be calculated relative to suitably defined generalised valence states of the dissociation products (16). At this time, in Japan, T. Arai was developing Moffitt's ideas along similar lines. Andrew's paper included a clearer derivation of the ICC method. His definition of a generalised valence state differed from that of Moffitt by taking into account the lack of orthogonality of atomic wave functions at the separation distances in a molecule and by removing those restrictions on parameters of the wave function at infinity which lead to misleading energy corrections.

The success of the ICC method was illustrated by a calculation for the ground states of LiH and BH and for the ground state of benzene. The method was then applied to the ground state and to some excited states of the first row diatomic hydrides, where the calculated binding energies generally exceeded the experimental values by 0.5-0.7 eV, with calculated excitation energies accurate to about 0.2 eV (17, 18).

A calculation for CO was used as a basis for supporting one of three experimentally-derived values for its dissociation energy (19). Another gave theoretical support for the existence of a hump in the potential energy curve of the A¹P state of BH and provided a theoretical value for its dissociation energy (22). A final paper identified potential sources of error in ICC calculations (29). Andrew showed that the ICC correction was substantial, even for Hartree-Fock calculations. On the other hand, results of chemical accuracy could be obtained for diatomic hydrides of the first row with relatively simple basis functions and the accuracy of excitation energies should generally lie within 0.2 eV of the correct values.

The paper 'Thermochemistry in the Hartree-Fock approximation' looked at the problem of obtaining accurate chemical calculations from a different perspective (41), aptly described by Peter Taylor:

Based again on his electron-pair models, he showed that reactions in which the numbers of electron pairs, or even better the number and type of electron pairs, were conserved between reactant and product and would be fairly well-described at the Hartree-Fock level, since the errors from electron correlation would tend to cancel. This is essentially the same as the 'isodesmic' schemes for calculating reaction energies used by Pople and co-workers.

Andrew's two books, Introduction to the Electron Theory of Small Molecules and Electron Correlation in Small Molecules, envisaged by him as one book provide a thorough foundation for those wishing to carry out molecular energy calculations of chemical accuracy (44, 45). In his foreword to Introduction to the Electron Theory of Small Molecules, Andrew expressed the hope that it would provide:

...a 'royal road' from basic quantum mechanics, as exemplified by Schrödinger's wave equation and elementary atomic structure to the various theories and techniques of calculation which today are yielding such detailed information on molecular interactions.

This book provides an account of the basic theory of potential energy curves and surfaces, an outline of the variational method for constructing approximate electronic wave functions and an account of the generalised virial and Hellmann-Feynman formulae and theorems. It also provides a brief but self-contained account of molecular symmetry and extended accounts of the determinantal approach and of molecular orbitals and the Hartree-Fock method. The practical aspects of applications of the theory scattered through the text enriches Andrew's presentation, and reviewers have remarked on the 'rich assortment of jewels'. The book includes separate chapters on the hydrogen molecule ion and the hydrogen molecule. Detailed comparisons of different approximate methods applied to those systems make these chapters very informative.

The second book has two chapters. The first chapter introduces theories that overcome the qualitative failures of Hartree-Fock theory; theories that are qualitatively correct for all molecular states and for all molecular geometries. This leads to an instructive comparison of molecular-orbital and valence-bond descriptions and it includes detailed discussions of multi-configuration self-consistent field methods and of the separated electron pair theory pioneered by Hurley, Lennard-Jones and Pople. The second chapter, 'The correlation problem', makes up the bulk of the book. Its emphasis is on the succession of pair theories that have taken progressively better account of electron correlation. The chapter includes a reformulation by Andrew of coupled-cluster theory, which was originally introduced to molecular problems by Paldus and Cizek, using diagram techniques. Coupled-cluster theory is regarded as the final step in the inclusion of electron correlation in an orbital-based theory, of which the separated-pair, independent-pair and configuration-interaction approximations were earlier steps. The reformulation proved to be particularly suitable for computation. J.A. Pople comments as follows:

At the time, we (Pople and colleagues) had completed programming Moller-Plesset (perturbation theory) up to third order and configuration interaction at the doubles level. We were contemplating going to higher orders and also implementing some form of coupled-cluster theory. However, my study of the original papers of Cizek and others left me puzzled about the connections with what we had done on MP2 and MP3. Andrew's clear presentation in his books and in his personal exposition completely clarified this and I could see the way forward with the inclusion of double substitutions up to fourth order.

Using the more powerful computers and computer programs available by the mid-1970s, Andrew, Peter Taylor, Noel Hush and George Bacskay used the coupled-cluster theory, in the form given by Andrew, to carry out accurate calculations for HCN, HNC and for the CN^– ion (46, 48, 49, 52). The target of accurate calculations for molecules of chemical interest had been reached.

Group theory and its applications

Andrew's first paper, 'Finite rotation groups and crystal classes in four dimensions', was a piece of pure mathematics, based on his MA thesis (1). In 1889, M.E. Goursat had identified the proper and improper rotation groups that included the element -I, I, being a four-rowed unit matrix. Andrew used the invariance of the trace and second invariant of a four-dimensional matrix to identify those of Goursat's groups that could be geometric crystal classes. Then, aided by the method of G. de B. Robinson and a new theorem derived in his paper, he eliminated those groups that are not crystal classes. He discovered one family of groups overlooked by Goursat and identified 222 crystal groups. This paper attracted the attention of crystallographers A. Niggli and H. Wondratschek and the latter found Andrew's list of crystal groups to be incomplete. Wondratschek and J. Neubüser, starting from results of Hermann and aided by electronic computation, discovered 227 crystal classes. This did not rely on Goursat's work. Andrew repeated the steps in his paper and discovered a more direct method. He independently confirmed the correctness and completeness of the results of Wondratschek and Neubüser and these results were published in 1966 (31).

In a second publication in 1966, he used ray representations, which were a generalisation of the normal vector representations, to provide a compact method for the rapid construction of matrix representations of space groups and double groups, thereby avoiding the need for huge tables (32). L.L. Boyle and K.F. Green criticised this work for considering only one set of projective representations. However, that set is exactly what is needed to construct consistent space group representations. Several groups engaged in major solid state physics calculations involving crystal symmetry have commented on the usefulness of this work.

Andrew's next paper devoted to group theory was published in 1977, following the publication of his two books. It follows a period during which he was in constant demand to provide courses on group theory for summer schools in theoretical chemistry. 'Group integration, projected basis functions and correlation rules for linear molecules' demonstrates the application of projectors to obtain projected basis functions and correlation rules for molecules of symmetry C_∞v and D_∞h, which are mixed discrete-continuous groups (47). Here he also generalised the famous Hund-Witmer-Wigner rules for diatomic molecules. In a related paper, co-authored by R.D. Harcourt and Peter Taylor, the generation of symmetry-adapted wave functions by means of projection operators was demonstrated for O₂ (60).

During the period 1982-84, Andrew published three papers on simply subducible groups, which cover most of the groups of interest in physics and chemistry. In the first, he showed that it is possible to derive complete sets of projectors for these groups using only their character tables (62). The paper demonstrates his ever-deepening knowledge of group theory and his ability to overcome previous limitations. In the second paper, he recast the theory of ray representations in terms of ordinary representations of a ray group, which enabled him to extend his earlier results to include space groups and double groups (63). In the third paper, Andrew showed that simple subducibility could be used to generate explicit matrix representations from character tables (64).

Andrew became interested in the helical structure built up as a column of face-sharing tetrahedra, sometimes called a tetrahelix. His attention had probably been drawn to its possible applications in structural crystallography. Andrew studied this structure and its analogues in other dimensions and he used matrix and other techniques to derive a number of results (65). In particular, all structures for dimensions higher than 2 are non-crystallographic. This work led to fruitful interaction with the great geometrician H.S.M. Coxeter, a recognised authority on the tetrahelix.

His last group theory paper, 'Pseudo-crystal classes: counterexamples to Lomont's conjecture', was published in 1985 (66). The three of Goursat's groups that failed to satisfy the requirements of a crystal class were shown to provide counter-examples to Lomont's conjecture. However, the conjecture may be preserved in dimensions up to four by introducing pseudo-crystal classes. Andrew postulated that these groups might describe the quasi-crystalline translations and rotations occurring in long-range order.

Further applications of virial and electrostatic methods

Andrew applied the virial and Hellmann-Feynman theorems to a number of problems that were not directly connected to his quest for highly accurate methods of molecular energy calculation. In 'Potential curves for doubly positive diatomic ions' he developed an integrated form of the quantum-mechanical virial theorem and used it, together with an assumption about scaling of the wave function, to derive potential energy curves of diatomic ions from those of isoelectronically related neutral molecules (23). The calculated appearance potentials for a number of ions showed satisfactory agreement with available electron impact data. However, insufficient data was available to enable a crucial test. In a subsequent note, this method was used to help in the identification of a recently observed electronic transition of N₂⁺⁺, an application that led Andrew to revise his scaling prescription (24). Then, in 'Potential curves for doubly positive diatomic ions II ', the method was used to predict potential energy curves and spectroscopic constants for a number of states of the ions N₂⁺⁺, O₂⁺⁺ and NO⁺⁺ (26). The calculations involved were simple but they were regarded as authoritative for many years and until replaced by very sophisticated calculations. They stimulated considerable experimental activity.

During 1962, Andrew published two short notes that would have resulted from his deep probing of the virial method during the above applications. In the first, he extended two derivations of the virial theorem by other authors to apply to polyatomic molecules and identified an erroneous conclusion and its source in one of those (27). The second note discussed a conflict between recent work by J.O. Hirschfelder and C.A. Coulson and earlier work by himself, among other controversies (28). This note highlighted the extreme care required when interpreting partial derivatives, a matter that Andrew returned to on a number of occasions.

In a volume issued as a tribute to R.S. Mulliken, Andrew contributed a chapter entitled 'The molecular orbital interpretation of bond-length changes following excitation and ionisation of diatomic molecules' (30). A highlight of the chapter is a thorough discussion of the applicability of the electrostatic and virial theorems to approximate wave functions. This was applied to Hartree-Fock wave functions, in conjunction with a 'rigid orbital approximation', to explain observed regularities in changes in bond length and other properties that followed from Mulliken's correlation diagram. Andrew extended the range of examples previously provided by Mulliken and G. Herzberg.

In 1967, Andrew collaborated with R.G. Parr and colleagues to investigate the relative merits of (a) the 'integral Hellmann-Feynman formula', which had recently been derived by Parr, (b) the traditional method of energy differences and (c) the established 'integrated Hellmann-Feynman formula' used for describing energy changes in an isoelectronic molecular process (34). The concept of 'superfloating functions' was introduced to describe wave functions that satisfy the integral Hellmann-Feynman theorem. A superfloating wave function arises from optimisation of several parameters rather than the single parameter that he had used earlier when defining a floating function. In a second paper, Andrew showed that superfloating wave functions could be obtained as solutions of a linear homogeneous integral equation that was closely related to the Fredholm equation and he solved this for a model system (37).

In a joint publication in 1968 with several CSIRO colleagues, Andrew adapted a method, previously used to discuss doubly-charged diatomic ions, to support the conjectured existence of the symmetric and linear entity (H₂O...H...OH₂)⁺, with d (O-O) @ 2.45 Å, both in crystals and possibly in solution (38). This was followed by an ingenious attempt to reconcile conflicting mass spectroscopic data for CO⁺⁺ and Auger data for CO, a system of considerable interest (39). However, the prevailing uncertainty in the correct value for the dissociation energy of BN led to uncertainty in the calculated curves and Andrew's results were eventually overtaken by the results of large ab initio calculations.

A paper published in 1982 put new light on the paradoxical role of kinetic energy in the formation of a chemical bond (61). This paradox had already been closely analysed by K. Ruedenberg and co-workers. However, by using one-centred wave functions to exclude questions of overlap and by the clever use of the virial theorem in particular, as well as the electrostatic theorem, Andrew was able to make many useful observations, some of them surprising. His last paper, other than a collaborative paper published posthumously, showed how standard computer programs for calculating the equilibrium geometry of a molecule could be adapted to yield floating wave functions and this was illustrated for a water molecule (68).

Other work

The short paper 'Improved molecular orbitals and the valence bond theory' used a simple transformation to display the valence bond equivalent of what had recently been proposed as an improved molecular orbital description of H₂ (20). This transformation enabled Andrew to correct a significant flaw in a previous theoretical description of the dissociation of the B¹S⁺_u state of H₂. In another short paper he proved the strict mathematical equivalence of the Rydberg-Klein-Rees and Dunham methods of deriving potential curves for diatomic molecules from spectroscopic data (25).

In 1967, Andrew collaborated with Dr B. Dawson and myself to investigate the likelihood of significant anharmonic vibration in fluorite structures. He provided the mathematical form, required by symmetry, of the potentials for the three distinct atomic sites and for the structure factors. He also proposed the use of an Einstein model. The model provided very good qualitative agreement with experimental data for UO₂ and CaF₂(35). This work was part of an ongoing collaboration with Dawson, who went on to develop a general structure factor formalism for interpreting accurate X-ray and neutron diffraction data.

In 1973, Andrew and others from CSIRO showed that consistent results were obtained for the structure of calycanthine by the Bijvoet X-ray analysis technique and by analysis of the circular dichroism spectrum (42, 43). This agreement was used to defend the reliability of the Bijvoet method, about which doubts had been raised. In 1978, Andrew, A.F. Moodie and others undertook an algebraic approach to N-Beam theory of fast electrons in crystals (50). Their aim was to produce a theory with a more intuitive link to the experimental results. Their success was limited, but did include a formal solution for the case of three beams. In a subsequent paper, Hurley and Moodie showed that, for a centrosymmetric crystal and in conditions where the approximation of three-beam scattering holds, both structure amplitudes and phases could be determined and they provided a technique for achieving this (55). Andrew's proposal to use the projection operator technique and his mathematical support greatly improved the presentation of Moodie's important discovery.

In 1979, A.F. Beecham sought Andrew's help in support of a reinterpretation of some circular dichroism spectra. In the first paper, they provided strong evidence that the solvent-induced 'blue-shift' in the c.d. spectrum of a,b-unsaturated ketones through the n® p* absorption region should not be interpreted primarily as a frequency shift but rather as the result of a redistribution of intensity among vibrational sub-bands (51). In the second paper, with C.H.J. Johnson as co-author, they proposed that redistribution was associated with changes in Franck-Condon factors (53). On the basis of a simple diatomic model, they attributed these changes to a small lengthening of the CO bond in the excited state. Sophisticated calculations later showed the model to be too simple, but confirmed the importance of the Franck-Condon factors.

Mathematical interests shared with Dr A.K. Head led to the publication 'Explicit Galois resolvents for sextic equations' (67). Head and Hurley sought to generalise the known conditions under which a sextic equation is analytically solvable. They chose to evaluate the Galois resolvents, which is straightforward in principle but almost impossibly tedious by hand calculation. The authors used the method of power sums in conjunction with the symbolic algebra program muMath and an IBM PC computer to carry out the computations. Considerable ingenuity was required, given the tiny computer memory available in 1986, and the calculation ran for eleven days. The results were applied to the sextic polynomial of crystal elasticity for crystals of cubic symmetry.

Epilogue

Andrew Hurley was a pure scientist in the fullest sense. He almost invariably followed the solution of a new problem by a search for applications and generalisations, but he never claimed what he could not prove. He deplored pretentiousness. He enjoyed the challenge of new ideas across a broad range of physics, chemistry and mathematics presented in lectures, books and scientific articles and he would sometimes spend extended periods in the library scribbling with pen and paper until he had mastered them. Once, when complimented on his ability to understand a difficult concept, he remarked that anybody could do it: it was just a matter of time! He was a willing 'tour guide' to his Division's experimental projects, in which he showed a keen interest. Andrew also maintained a keen interest in developments across a broad range of mathematics and was a member of the Australian Mathematical Association from 1957 until his death. Though described by some as quiet and as someone who worked alone, he had a very warm personality and friends and colleagues enjoyed his dry wit and penetrating analysis on almost any topic under discussion. He had a wonderful memory and his mental powers seemed to be largely unaffected by the deterioration in his physical health. Andrew and Yvonne were a very hospitable couple and Andrew was also a very active participant in the sporting activities in his Division such as golf, squash, table tennis and cricket.

Many scientific visitors found their way to Fishermens Bend or to Clayton to discuss their work with Andrew, and Professors K. Ruedenberg and R.G. Parr and Dr R.K. Nesbet chose to spend sabbatical periods with him. Many of his friends and colleagues would echo the following sentiments expressed by Peter Taylor:

He was never too busy for a discussion with a colleague and conducted all his discussions on a completely egalitarian basis, whether he was talking to a distinguished colleague or a student who had not even begun a research career. He loved a puzzle: a scientific one for choice, but he would happily settle for a chess or bridge problem, or a crossword puzzle. I will always remember him as a model theoretician.

Andrew is survived by Yvonne and by their children, Victor, Catherine and Mark. Victor and Mark are specialist medical practitioners and Catherine is an ABC journalist and program administrator.

Acknowledgments

I am very grateful to members of Andrew's family for information about his forebears and his early life. Dr J.K. Mackenzie and the archivists of Melbourne Grammar School, the University of Melbourne and Trinity College, Cambridge have kindly provided details of his achievements and awards. Mr M. Fergus and Dr L. Radom supplied photographs. When discussing Andrew's scientific career, I have had the benefit of comments and reminiscences of many friends and former colleagues, which I greatly appreciate. I have also enjoyed the assistance of the Information and Library Services of CSIRO and the Australian Science and Technology Heritage Centre at the University of Melbourne. Professors N.S. Hush, A.McL. Mathieson and P.R. Taylor and Drs P.E. Maslen and J.B. Willis contributed detailed comments on drafts of the memoir. I am especially indebted to Peter Taylor, who has given valuable advice, along with recollections of his own and of others. 'Sandy' Mathieson and Noel Hush have been constant sources of encouragement and John Willis has given much-needed editorial guidance. Would those who have helped me in any way, but whom I have not named, please accept my heartfelt thanks.

Notes

1. Details of family background have been extracted from J.V. Hurley, Sir Victor Hurley: Surgeon, Soldier and Administrator 1888-1953, published privately in 1989, (ISBN 0-731-66824-3). The late Professor J.V. Hurley was Andrew's eldest brother.

2. LLD, 1884.

3. 'Smallish' was chosen deliberately to emphasise an increase in size of molecules for which reliable theoretical calculations could be carried out.

4. The permanent of a matrix is similar to a determinant, but the coefficients of all terms in its expansion are positive.

Bibliography

(1) A.C. Hurley, 'Finite rotation groups and crystal classes in four dimensions', Proceedings of the Cambridge Philosophical Society, 47 (1951), 650-661.

(2) A.C. Hurley and J.E. Lennard-Jones, 'The molecular orbital theory of chemical valency. XII. The excited states of diatomic molecules', Proceedings of the Royal Society of London, A216 (1953), 1-10.

(3) A.C. Hurley, 'The molecular orbital theory of chemical valency. XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule', Proceedings of the Royal Society of London, A216 (1953), 424-433

(4) A.C. Hurley, and J.E. Lennard-Jones, 'The molecular orbital theory of chemical valency. XIV. Paired electrons in the presence of two unlike attracting centres', Proceedings of the Royal Society of London, A218 (1953), 327-333.

(5) A.C. Hurley, 'The molecular orbital theory of chemical valency. XV. Illustrative calculations of the properties of polar bonds', Proceedings of the Royal Society of London, A218 (1953), 333-344.

(6) A.C. Hurley, J.E. Lennard-Jones and J.A. Pople, 'The molecular orbital theory of chemical valency. XVI. A theory of paired-electrons in polyatomic molecules', Proceedings of the Royal Society of London, A220 (1953), 446-455.

(7) A.C. Hurley, 'The electrostatic calculation of molecular energies. I. Methods of calculating molecular energies', Proceedings of the Royal Society of London, A226 (1954), 170-178.

(8) A.C. Hurley, 'The electrostatic calculation of molecular energies. II. Approximate wave functions and the electrostatic method', Proceedings of the Royal Society of London , A226 (1954), 179-192.

(9) A.C. Hurley, 'The electrostatic calculation of molecular energies. III. The binding energies of saturated molecules', Proceedings of the Royal Society of London, A226 (1954), 193-205.

(10) A.C. Hurley, 'On the method of atoms in molecules', Proceedings of the Physical Society, A68 (1955), 149-155.

(11) A.C. Hurley, 'On the method of atoms in molecules. II. An intra-atomic correlation correction', Proceedings of the Physical Society, A69 (1956), 49-56.

(12) A. C. Hurley, 'On the method of atoms in molecules. III. The ground state of hydrogen fluoride', Proceedings of the Physical Society, A69 (1956), 301-309.

(13) A.C. Hurley, 'The binding energy of the nitrogen molecule', Proceedings of the Physical Society, A69 (1956), 767-776.

(14) A.C. Hurley, 'On the binding energy of the helium hydride ion', Proceedings of the Physical Society, A69 (1956), 868-870.

(15) A.C. Hurley, 'The electrostatic calculation of molecular energies. IV. Optimum paired-electron orbitals and the electrostatic method', Proceedings of the Royal Society of London , A235 (1956), 224-234.

(16) A.C. Hurley, 'Role of atomic valence states in molecular energy calculations', Journal of Chemical Physics, 28 (1958), 532-542.

(17) A.C. Hurley, 'Electronic structure of the first row hydrides BH, CH, NH, OH and FH. I. Ground states', Proceedings of the Royal Society of London, A248 (1958), 119-135.

(18) A.C. Hurley, 'The electronic structure of the first row hydrides BH, CH, NH, OH and FH. II. Excited states', Proceedings of the Royal Society of London, A249 (1959), 402-413.

(19) A.C. Hurley, 'Electronic structure and binding energy of carbon monoxide', Reviews of Modern Physics, 32 (1960), 400-411.

(20) A.C. Hurley, 'Improved molecular orbitals and the valence bond theory', Journal of Chemical Physics, 33 (1960), 301-302.

(21) A.C. Hurley, 'Erratum: improved molecular orbitals and the valence bond theory', Journal of Chemical Physics, 33 (1960), 1872-1873.

(22) A.C. Hurley, 'Electronic structure of the first row hydrides. III. Predissociation by rotation in the A¹ P state and the dissociation energy of BH', Proceedings of the Royal Society of London, A261 (1961), 237-245.

(23) A.C. Hurley, and V.W. Maslen, 'Potential curves for doubly positive diatomic ions', Journal of Chemical Physics, 34 (1961), 1919-1925.

(24) P.K. Carroll and A.C. Hurley, 'Identification of an electronic transition of N₂²⁺', Journal of Chemical Physics, 35 (1961), 2247-2248.

(25) A.C. Hurley, 'Equivalence of Rydberg-Klein-Rees and simplified Dunham potentials', Journal of Chemical Physics, 36 (1962), 1117-1118.

(26) A.C. Hurley, 'Potential energy curves for doubly positive diatomic ions. II. Predicted states and transitions of N₂²⁺, O₂²⁺ and NO²⁺', Journal of Molecular Spectroscopy, 9 (1962), 18-29.

(27) A.C. Hurley, 'Virial theorem for polyatomic molecules', Journal of Chemical Physics, 37(1962), 449-450.

(28) C.A. Coulson and A.C. Hurley, 'Comment on 'Hellmann-Feynman wave functions', Journal of Chemical Physics, 37 (1962), 448-449.

(29) A.C. Hurley, 'Elimination of atomic errors from molecular calculations', Reviews of Modern Physics, 35 (1963), 448-456.

(30) A.C. Hurley, 'The molecular orbital interpretation of bond-length changes following excitation and ionization of diatomic molecules', in Molecular Orbitals in Chemistry, Physics and Biology, eds P.O. Löwdin and B. Pullman, (Academic Press, New York, 1964), pp. 161-189.

(31) A.C. Hurley, 'Finite rotation groups and crystal classes in four dimensions. II. Revised tables and projection of groups of antisymmetry in three dimensions', in Quantum Theory of Atoms, Molecules and the Solid State, eD.P.-O. Löwdin (Academic Press, New York, 1966), pp. 571-586.

(32) A.C. Hurley, 'Ray representations of point groups and the irreducible representations of space groups and double space groups', Philosophical Transactions of the Royal Society of London, A260 (1966), 1-36.

(33) A.C. Hurley, 'Discussion on group theory', International Journal of Quantum Chemistry, 1S (1967), 716-717.

(34) S.T. Epstein, A.C. Hurley, R.E. Wyatt and R.G. Parr, 'Integrated and integral Hellmann-Feynman formulas', Journal of Chemical Physics, 47 (1967), 1275-1286.

(35) B. Dawson, A.C. Hurley, and V.W. Maslen, 'Anharmonic vibration in fluorite structures', Proceedings of the Royal Society of London, A298 (1967), 289-306.

(36) A.C. Hurley, J. Neubüser and H. Wondratschek, 'Crystal classes of four-dimensional space R4', Acta Cystallographica, 22(1967), 605.

(37) A.C. Hurley, 'Integrated and integral Hellmann-Feynman formulae. II. Construction of super-floating functions', International Journal of Quantum Chemistry, 1S (1967) 677-685.

(38) A.F. Beecham, A.C. Hurley, M.F. Mackay, V.W. Maslen and A.McL. Mathieson, 'Oxygen-proton-oxygen grouping and proton hydration', Journal of Chemical Physics, 49(1968), 3312-3313.

(39) A.C. Hurley, 'Auger spectra of CO and long-lived states of CO⁺⁺', Journal of Chemical Physics, 54 (1971) 3656-3657.

(40) A.C. Hurley, 'Dipositive diatomic ions', University of Queensland Chemical Society, (Brisbane, September, 1972).

(41) A.C. Hurley, 'Thermochemistry in the Hartree-Fock approximation', Advances in Quantum Chemistry, 7 (1973), 315-334.

(42) A.F. Beecham, A.C. Hurley, A.McL. Mathieson, and J.A. Lamberton, 'Absolute configuration by X-ray and circular dichroism methods of calycanthine', Nature Physical Science, 244 (1973), 30-32.

(43) A.F. Beecham, A.C. Hurley, A.McL. Mathieson and J.A. Lamberton, 'Addendum', Nature Physical Science, 245 (1973) 32.

(44) A.C. Hurley, Introduction to the Electron Theory of Small Molecules, (Academic Press, London, 1976).

(45) A.C. Hurley, Electron Correlation in Small Molecules, (Academic Press, London, 1976).

(46) P.R. Taylor, G.B. Bacskay, N.S. Hush and A.C. Hurley, 'The coupled-pair approximation in a basis of independent-pair natural orbitals', Chemical Physics Letters, 41 (1976), 444-449.

(47) A.C. Hurley, 'Group integration, projected basis functions, and correlation rules for linear molecules', International Journal of Quantum Chemistry, 11S (1977), 223-228.

(48) P.R. Taylor, G.B. Bacskay, N.S. Hush and A.C. Hurley, 'Unlinked cluster effects in molecular electronic structure. I. The HCN and HNC molecules', Journal of Chemical Physics, 69 (1978), 1971-1979.

(49) P.R. Taylor, G.B. Bacskay, N.S. Hush and A.C. Hurley, 'Unlinked cluster effects in molecular electronic structure. II. Pair correlations in the molecules HCN and HNC', Journal of Chemical Physics, 69 (1978), 4669-4677.

(50) A.C. Hurley, A.W.S. Johnson, A.F. Moodie, P. Rez and J.R. Sellar, 'Algebraic approaches to N-beam theory', Institute of Physics Conference Series, 41 (1978), 34-40.

(51) A.F. Beecham and A.C. Hurley, 'Hydrogen bonding and the n® p* blue shift in a,b-unsaturated ketones', Australian Journal of Chemistry, 32 (1979), 1643-1648.

(52) P.R. Taylor, G.B. Bacskay, N.S. Hush and A.C. Hurley, 'Unlinked cluster effects in molecular electronic structure. III. Potential curve for the CN^–ion and the adiabatic electron affinity of CN', Journal of Chemical Physics, 70 (1979), 4481-4490.

(53) A.F. Beecham, A.C. Hurley, and C.J.H. Johnson, 'Hydrogen bonding and the n® p* blue shift in a,b-unsaturated ketones. II. Franck-Condon factors and estimates of the effects of hydrogen bonding on CO bond lengths', Australian Journal of Chemistry, 33 (1980), 699-705.

(54) A.F. Beecham and A.C. Hurley, 'A scheduling problem with a simple graphical solution', Journal of the Australian Mathematical Society, B21 (1980), 486-495.

(55) A.C. Hurley and A.F. Moodie, 'The inversion of three-beam intensities for scalar scattering by a general centrosymmetric crystal', Acta Cystallographica, A36 (1980), 737-738.

(56) A.C. Hurley, 'Distinct hyperdice', Australian Physicist, 17 (1980), 129.

(57) A.C. Hurley, P.R. Taylor, G.B. Bacskay and N.S. Hush, 'Unlinked cluster effects in molecular electronic structure', Molecular Physics and Quantum Chemistry Conference, (Sydney, 1980).

(58) A.C. Hurley, A.F. Moodie and A.W.S. Johnson, 'The role of projection operators in the theory of N-beam diffraction. Application to the phase problem for centrosymmetric crystals', Molecular Physics and Quantum Chemistry Conference, (Sydney, 1980).

(59) A.C. Hurley, and A.F. Moodie, 'Problems in the inversion of three-beam convergent beam diffraction patterns', Sixth Australian Conference on Electron Microscopy, (Melbourne, 1980).

(60) A.C. Hurley, R.D. Harcourt and P.R. Taylor, 'Generation of symmetry-adapted wave functions for O₂ using group theoretical projection operators', Israel Journal of Chemistry, 19 (1980), 215-219.

(61) A.C. Hurley, 'Analysis of the covalent bond: one centre floating functions for the hydrogen molecule ion', International Journal of Quantum Chemistry, 22 (1982), 241-251.

(62) A.C. Hurley, 'Complete sets of orthogonal character projectors for simply subducible groups', Chemical Physics Letters, 91 (1982), 163-168.

(63) A.C. Hurley, 'Simply subducible groups. Ray groups and projectors for double groups and space groups', Chemical Physics Letters, 102 (1983), 203-212.

(64) A.C. Hurley, 'Simply subducible groups and ray groups. Explicit matrix representations and the group algebra', Chemical Physics Letters, 107 (1984), 155-161.

(65) A.C. Hurley, 'Some helical structures generated by reflexions', Australian Journal of Physics, 38 (1985), 299-310.

(66) A.C. Hurley, 'Pseudo-crystal classes: counterexamples to Lomont's conjecture', Journal of Physics A: Mathematical and General, 18 (1985), L907-L912.

(67) A.C. Hurley, and A. K. Head, 'Explicit Galois resolvents for sextic equations', International Journal of Quantum Chemistry, 31 (1987), 345-359.

(68) A.C. Hurley, 'The computation of floating functions and their use in force constant calculations', Journal of Computational Chemistry, 9 (1988), 75-79.

(69) A.C. Hurley, A.F. Moodie, A.W.S. Johnson and P.C. Abbott, 'The role of projection operators in the theory of N-beam diffraction and the inversion of three-beam elastic scattering intensities', Acta Cystallographica, A55 (1999), 216-219.

V.W. Maslen, Honorary Retirement Fellow, CSIRO Manufacturing and Infrastructure Technology, Melbourne.

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