This text originates from:
Molecular Pysics, 88, 309-314 (1996).
© 1996 Taylor and Francis Ltd.
Samuel Francis Boys - 1911-1972
George G. Hall
Shell Centre, School of Education,
University of Nottingham,
Nottingham, NG7 2RD United Kingdom
(Received 11 December 1995)
A contribution to the international conference,
held in Cambridge in September 1995,
in memory of S. F. Boys and in honour of I. Shavitt,
remembering their paper reporting the
calculated structure of H3.
It is difficult to overestimate how much quantum chemistry owes to Frank
Boys. He was a pioneer, an individualist, a dedicated scientist and a great man.
We start with a look back at the state of Quantum Chemistry before the war in
1939. The subject had developed in a quiet way from the work of spectroscopists
such as Mulliken and Herzberg, chemists such as Pauling and Eyring, physicists such as
Slater and Kotani, and mathematicians such as Lennard-Jones and Coulson. It was a
research area with very little influence on degree courses. It had, at its
centre, a small nucleus of hard information, based on group theory and qualitative molecular orbital theory, which was used widely to interpret molecular structure and spectra. In the hands of an expert it aided experimentalists in several different ways. It
provided a qualitative understanding of valence leading to approximate bond angles and
lengths. It could often describe a ground state structure in terms of the occupied orbitals and identify an excited state in a similar way. Even when it could not solve an experimental problem it could often rule out some possible solutions and so simplify further investigations. Into this limited subject Boys was first introduced as an outsider.
Frank Boys was born in 1911 in Pudsey. After attending the Grammar School
there he went to Imperial College, London where he graduated as a chemist in 1932.
During his first year doing research with Professor Baker, he attended the mathematics
degree courses and acquired a working knowledge of quantum theory. His first
research topic was optical rotatory power and his first papers , in 1934, deal with this
using a simple classical model. It is interesting to note that his treatment is
semi-empirical in terms of the parachor. He moved to Cambridge in 1935 to continue
research in this subject for his Ph.D., but now using quantum mechanics. His
supervisor was Professor T. M. Lowry, a leading physical chemist who specialized in
this field, but he transferred to Professor J. E. Lennard-Jones when Lowry died.
Unfortunately for Boys, others working in the same field published their work before
he could do so, and the only record of his theory is in his thesis. The Cambridge
theoretical chemistry group was then, as now, one of the leading theoretical groups in
Europe. Lennard-Jones himself was working with Devonshire on liquids but the group
also included Coulson, who was developing his theory of bond order and its relation
to bond length, and Penney, who applied valence bond theory to the valence shells of
diatomics. Boys must have been an outsider even then because his topic was so far
from their interests and his entry to the group so indirect.
2. War-time research
Boys’ first academic appointment was in Queen’s University, Belfast, in 1938, as an
Assistant Lecturer in Mathematical Physics under Massey, who later moved to
University College and was then interested in negative ions as detected in a mass
spectrometer. This was my own first University and I first came across Boys' name in
1943 when looking at some old examination papers on classical mechanics which he
had set. I also found him cited in our chemistry textbook  as the source for the
absolute configurations of several sets of stereoisomers.
Early in the war, in 1939, he was recruited for research with the Ministry of Supply
at Woolwich Arsenal - Lennard-Jones was one of his superiors. His war work was on
explosives. First he had to study the burning of the propellant explosive during the
acceleration phase of the shell along the barrel. This is related to the problems of
shaped charges and the development of armour piercing shells. Then he moved to
rocket fuels where the burning process is quite different. His research group, during
this time, was both theoretical and experimental. I remember him telling me with some
glee how they refurbished a couch in their common room with springs made from
cordite explosive. Every important visitor was made to sit there and gently told what
was below him. The practical results of this effort are largely buried in official reports
though a few were issued in modified form . His personal contribution included
designing experimental apparatus as well as producing theoretical analysis.
At the close of the war, in 1945, Boys accepted an ICI fellowship at Imperial
College as a transition towards returning to an academic position. His principal aim
was, even then, to produce wavefunctions that were accurate enough to predict some
of the important molecular quantities. He started with atoms, where self-consistent
field theory had done a good qualitative job but had very limited accuracy when
compared with spectroscopic results.
I would like now to look at the subject as I think Boys approached it then. His
experience of optical rotation had shown him the need to develop the subject with
mathematical rigour and care if major errors are to be avoided. Anyone who has
experience of the theory of the refractive index will know how critical this is. The old
molecular orbital theory of pre-war days was of very limited quantitative value. Its
foundation was vague and imprecise. Its attempts at calculating wavefunctions
foundered over the problem of evaluating integrals over Slater orbitals. Its semi-
empirical theories, at best, relied on suggestive and plausible arguments rather than
rigour. Boys needed something better. His war-time experience proved to him that the
really interesting species, from the theoretical chemical point of view, were the short-
lived ones that entered fundamentally into reactions and flames but were beyond the
reach of conventional experiment. They were equally beyond the reach of the
contemporary theories, which used empirical rules derived from ground states of
stable molecules. His aim was to predict the structure and properties of radicals, ions
and unstable molecular fragments and then to trace their reaction paths with enough
detail to feed into the theories of molecular reaction rates.
4. Calculations at Cambridge
Cambridge is fortunate in having had since 1935 a Mathematics Laboratory,
which was founded and initially directed by Lennard-Jones. When Boys arrived in
Cambridge, in 1949, to take up a Lectureship in Theoretical Chemistry he was
accompanied by two computers. No, these were not electronic, they were two young
ladies who spent-their time in the Maths Lab on electric calculators churning out
integrals! With their help he managed to produce analytical wavefunctions  for the
B and C atoms which were more accurate than Hartree had achieved by numerical
integration. He could, for example, give a better ratio for the splitting of the lowest
excited states. His method of attack was what we call 'superposition of configurations'.
This idea had been introduced many years earlier to explain results in experimental
spectroscopy and he adapted it, in a much more general way, as a theoretical tool. In
principle this technique could be extended to even higher accuracy but the hand
calculations were expensive and slow.
When electronic computing first became available in Cambridge Boys was one of
the first to see its advantages and exploit it. EDSAC was a modest machine by present
standards with a memory of 1/2 K. Inevitably the paper tape external memory had to
be skilfully exploited to achieve anything of significance, and Boys became expert in
optimizing many operations on the machine. His students acquired a competence in
producing results under near impossible odds and at least three of them, Price, Reeves
and Cook, later moved to chairs of computing. I often used part of their precious
ration of computing time - all night once a week - to do my own rather different
calculations, and I then learned much from his comments and advice.
Boys saw that the computer could be used to do many types of calculation. His
programs and those of his students for symbolic manipulation of the data structures
representing configurations and their vector coupling were forerunners of many
algebraic programs. He even tried to design a new computer language which he called
CALBRA. The local computer experts, whom he consulted, were not encouraging.
When I first saw APL (A Programming Language), with its use of mathematical
notation integrated with computer language, I realized how advanced he had been in
his CALBRA ideas. Before Cambridge moved to EDSAC2 he realized the need to
learn to program this in advance so that he could exploit its power and speed before
others flooded in to take the computer time. He profited greatly from such planning.
I would like to remind you that computers then were not as reliable as they are
now. Every calculation that Boys or his students published had to be checked. This
usually meant running the entire calculation again at a different time and with no cross
connection so that exact agreement became a good guide to accuracy. Often the first
calculation was done long before the second so that the chance of suffering the same
computer fault was minimal.
I suppose Boys is best known now for his 1950 paper  on Gaussians. This started
accidentally. He wanted to prove that a wavefunction could be found with accuracy as
good as may be desired by superimposing a sufficient number of configurations. To do
this he had to show that there were no theoretical or practical problems other than the
labour of calculation. As part of this proof he showed that all the four-centre integral
problems could be solved by using Gaussians. The idea that the product of two
Gaussians is a Gaussian, which is the essence of this solution, is not really new: it lies
at the heart of the theory of normal errors in probability theory. The main purpose of
the paper was to establish an existence theorem rather than to propose a practical
method. It succeeded in doing both because of the electronic computer.
The high spot of his work at this time is the calculation , along with Isaiah
Shavitt, on H3. It established the fact that there is not a lake at the top of the activation
barrier as earlier semi-empirical theory had suggested. It also highlighted the ability of
quantum theory to explore areas of chemistry that experiment could touch only by
indirect inference. He achieved his aim of contributing to our understanding of
chemical reactions as well as to molecular structure.
Boys felt that his approach to quantum chemistry could be extended to other areas
of science. Indeed his first work with Shavitt  was on the use of Gaussian-like
expansions of the intermolecular potential to compute virial coefficients. He even tried
to bring Gaussians into quantum field theory. He knew that the subject was plagued
by infinities which were sometimes the result of poor technique and sometimes of poor
modelling. His Gaussian-based treatment could get rid of some of these but, when he
talked to the local experts about his proposed starting point, they indicated that one
infinity remained in the operators which he could not remove, so the entire treatment
fell down. Nothing came of it but he was not disheartened.
One of Boys’ greatest interests, outside his science, was the welfare of foreign
students. His keen interest in and chairmanship of the International Club in
Cambridge is one example of this. Since he himself had come to Cambridge as an
outsider he knew how daunting it could be and how restricting were the rules and
practices that the University applied. He refused to enter the College system more than
he could help, being repelled by its luxury and its formal procedures. Since he did not
drink or smoke and had no deep interest in food the usual delights of a College
Fellowship did not attract him. Nevertheless, he did eventually accept a Fellowship in
I was fortunate enough to spend some time in 1961 with Frank Boys and Bob Parr
at the Institute for Theoretical Physics at Naples. I believe this was the longest time he
had spent outside the UK though he did pay an extended visit to the USA after the
Boulder Conference  in 1959. We had the opportunity to compare our theoretical
ideas at length and to talk with the people in the Institute, including Guiseppe Del Re
who organized our visit. This Institute is placed inside a Zoo and we had the chance,
every day, to wander around and survey the other exhibits. I wonder what the visitors
thought of us! One of our excursions was to the Isle of Capri. I remember it as a stormy
journey where everyone in the boat became sick. This made the island even more
attractive - ;because it was in a stationary state.
Another example of his wider citizenship was the project which Frank started in his
last years. He felt that a key to the development of the poorer countries of the world
lay in organizing them to exploit science in an international way. He studied
economics and econometrics with this aim in view. One felt that he was looking for a
more accurate theory of how wealth is created so that he could calculate a better
economic system for the world. Unfortunately his ideas were never fully worked out
and we can only guess at what they might have achieved. It can be assumed that they
would have aroused maximum resistance and opposition from the establishment!
Frank was a quiet man with a nice sense of humour. He was completely dedicated
to his work and allowed few other things to interfere with it. In particular, he came to
believe that most big conferences were a waste of time since he could not work during
them nor even propagate his ideas with Banda spirit-stencil sheets as he usually did.
This attitude may have been induced by the Oxford Conference of 1961, where he was
hit by a gastric upset and, after his own paper had been given, spent most of the
conference time confined to bed in College. Earlier, in 1955, he attended the
Conference organized by Löwdin and Fischer-Hjalmars in Sweden and then many of
the much smaller Quantum Theory Conferences held in England. I am reminded also
of the Faraday Symposium of 1968 where Boys presented his transcorrelated ideas 
for the first time. The Faraday format is very restricting, because the author, since his
paper has been circulated in advance, is given only a very limited time to present it.
Boys had hardly reached the core of his talk when the chairman stopped him and asked
for questions. I had the cheek to ask what he had been about to say when he was
stopped and that gave him another ten minutes to explain his very new ideas.
Frank retained an experimental attitude to theory in that he was determined to
make things work regardless of difficulties. So he would try things out repeatedly till
he found something that worked. This could be wasteful of his time but he seemed to
relish the challenge and to rejoice in cheating the snags as they came along. The use [6,
10] of fixed sets of Gaussians to simulate Slater functions in the two-electron integrals
while using the Slater functions elsewhere is one example of this determination. The
result is not neat. It is not even very accurate nor consistent with the variation
principle. It falls short of modern techniques of using optimized sets of Gaussians as
basis orbitals. But it did give answers and we all learned from it.
Frank tried to give sensible names and notations for all the important entities in the
theory. His advice, unfortunately, has been ignored. The attempt to use the words
detor and codetor, for example, seemed to make his work more remote from readers
and made the chemical community suspicious of him and his work. This became one
of the factors which made the recognition of his work slow to mature . His mistrust
of semi-empirical theories and his refusal to guess at results also isolated him from
many colleagues. From time to time he was the object of biting attacks. He was
promoted to a Readership but he never became a Professor.
Frank Boys has to be one of the great names of our subject. He set standards for
himself and his students which brought a new rigour and, hence, a new utility to
quantum calculations. He harnessed computer power and showed the importance of
integrating computing and numerical techniques with quantum equations and ideas.
He brought into the subject techniques which have proved their usefulness many times
over. He trained students who themselves have enriched the subject. We owe him
 Boys, S. F., 1934, Proc. R. Soc. [London], A 144, 656, 675.
 Lowry, T. M., and Cavell, A. C., 1942, Intermediate Chemistry (London: Macmillan).
 Boys, S. F., and Corner, J., 1949, Proc. R. Soc. [London], A 197, 90.
 Boys, S. F., 1953, Proc. R. Soc. [London], A 217, 235.
 Boys, S. F., 1950, Proc. R. Soc. [London], A 200, 542.
Read it here!
 Boys, S. F., Cook, G. B., Reeves, C. M., and Shavitt, I., 1956,
Nature, 178, 1207.
 Boys, S. F., and Shavitt, I., 1960, Proc. R. Soc. [London],
A 254, 487, 499.
 Boys, S. F. et al., 1960, Rev. Mod. Phys., 32, 285, 296, 300, 303, 305.
 Boys, S. F., 1968, Symp. Faraday Soc., 2, 95.
 Shavitt, I., 1957, Ph.D. Dissertation, Cambridge University.
 Coulson, C. A., 1973, Bio. Memoires R. Soc. [London], 19, 90.
Last updated : July 6, 2003 - 18:21 CET