MEMORIES OF KONRAD SINGER

On January 14th, 2013, Konrad Singer, emeritus Professor at Royal Holloway College, passed away at the age of 95. Konrad was a modest man and this may explain why it is not widely known that he was the first scientist in the UK to carry Monte Carlo/Molecular Dynamics simulations. Together with his students and postdocs he made important contributions to the field.

Konrad was born to middle-class Jewish parents in 1917 in Bohemia, then part of the Austro-Hungarian Empire. He spent his formative years in Vienna. It was there that he discovered his lifelong passion for music and science. Konrad’s passion for music was developed both passively, through Vienna’s rich opera and concert life of those years, and actively, through his own considerable talent as a pianist.

At the time of the Nazi takeover of Austria in 1938, Konrad was nearing completion of his third year of a chemistry degree at the University of Vienna. His professor there was Herman Mark, a pioneer in polymer science - who would himself become a refugee, to the US - under whose tutelage he had begun a doctoral dissertation on ‘The kinetics of the thermal polymerization of styrene in solution’. Germanic degrees were six-year doctoral programmes, with no formal qualification given after three years. It was Singer’s great fortune to be allowed, not just to escape to the UK, but to continue his studies to Ph.D. level. The former process required a ‘sponsor’ to stand surety financially, and this was undertaken by a remarkable humanitarian, Marian Dunlop, who had not previously met him. The latter was made possible through the International Student Service, an organization established in Geneva to help refugee students, but funded locally by whip-rounds among other students. The local arrangement in this case was the initiative of a young Glasgow lecturer, Alec Cairncross (later to become Sir Alec, economist of distinction, Master of St Peter’s College, Oxford and Chancellor of Glasgow University).

Throughout his life Singer remained conscious of his enormous debt to both these individuals. Amongst his own family, his brother and parents survived the Holocaust, the latter through perilous adventures and a heroic rescue in France; but the vast majority of his extended family, especially on the Czech side, did not.

Konrad took his Ph.D. at Glasgow in 1941 with a thesis on ‘The optical properties of some organic compounds’; and for the remainder of the War worked as an industrial chemist, first as a spectographic analyst with Clyde Alloy Steel in Motherwell, and subsequently, from 1942 to 1947, as a research chemist at a paint factory in the East End of London. In 1947 he obtained a post at Royal Holloway College (University of London), where he would remain until his retirement in 1981. Konrad met his life companion, Jean Longstaff, shortly after moving to Royal Holloway College. Their partnership in life and science lasted until Jean passed away in 1990.

Konrad’s early research covering the period from when he joined the Chemistry Department at Royal Holloway (1947) to the late fifties focussed on kinetic/mechanistic studies on nitration reactions in solution. At this time he was sharing a flat with Trevor Bonner in Twickenham; Konrad commuted to college on a scooter – these were very popular in the UK at the time. Trevor was another new appointment to the chemistry department staff and was a physical organic chemist who pursued much of his career studying acylation and nitration chemistry. It seems likely that Konrad’s interest in nitration was as a result of discussions with Gwyn Williams who was head of the Chemistry Department from 1946 to 1955, dates that include Konrad’s appointment. Gwyn Williams had been involved in war work at King’s College, London on the mechanism of nitration and nitrosation in the context of the efficient manufacture of nitro-containing explosives.

In the late fifties, Konrad’s interests moved to quantum chemistry. In 1950, S.F. Boys had proposed the use of Gaussian wave function in quantum-chemical calculations. Surprisingly, given the near universal use of Gaussian basis sets in quantum chemistry today, Boys initially showed little enthusiasm for pursuing this application. Konrad generalised the application of Gaussians to quantum chemistry problems and, after a friendly meeting with Boys, the two of them decided to publish independently – but back-to-back – in the Proceedings of the Royal Society (1960). Both papers are still cited about equally.

In the early 1960s Konrad turned his attention to the molecular simulation of liquids by classical techniques, then a truly pioneering step in the UK. With Ian McDonald, his post-doctoral assistant, he published three papers in which Monte Carlo was used to calculate the thermodynamic properties of a Lennard-Jones model of argon. This work was motivated in part by the fact that Streett and Staveley had, at about the same, carried out a detailed experimental study of liquid argon. The third and most comprehensive of these papers was published back-to-back with theirs in the same issue of the Journal of Chemical Physics in 1967. One feature of their work was the use of histogram weighting or reweighting. This was a simple method in which the number of times the potential energy of the system was found to lie in a given range was recorded. The entries in the resulting histogram could then be weighted (in the microcanonical ensemble) or reweighted (in the canonical ensemble) to obtain information on neighbouring state points. The method was rediscovered some twenty years later, and subsequently improved, and now plays a major role in finite-size scaling of data obtained by simulation. In 1969 Konrad and Ian published a paper in the Journal of Chemical Physics entitled: “Examination of the adequacy of the 12-6 potential for liquid argon by means of Monte Carlo calculations”, which was essentially an expansion of the work of Wood and Parker but with new and much more detailed experimental results then available, showing that overall the 12-6 potential is a good effective potential for argon. The histogram method they had introduced earlier was in this case used it to optimise the potential parameters (with very little change from the classic values). Konrad then turned his attention to binary liquid mixtures and made, in partnership with Jean (J.V.L. Singer), his wife, a systematic study of the variation of excess thermodynamic properties with changes in the relative values of the size and energy parameters that characterised the two components. At about the same time Les Woodcock started work on a PhD with Konrad, taking as his topic a Monte Carlo study of molten potassium chloride, which turned out to be the first successful use of molecular simulation to study a molten salt (employing the Ewald method). It was Konrad’s mathematical ability that enabled this major development. The work demonstrated very clearly the importance of charge ordering in determining the structure of such systems. Their first paper in Trans. Faraday Soc. 1971 had an immediate wide-ranging impact on the physical chemistry of molten salts, and eventually ionic liquids generally. Also, it has been a major influence on the subsequent explosion of MD applications to real molecules, ionic systems and even water, and solutions; this methodology is widely used in packages — some 45 years on!

It is important to appreciate is that in this period all these calculations were carried out with computing resources that were extremely modest, even pitiful, by the standards of today. Moreover, since at first Royal Holloway College had no computer of its own, all work had to be carried out at the Atlas Laboratory in Didcot, with programs written in Atlas Autocode. The programs themselves were punched on rolls of paper tape that were collected by courier at regular intervals; the results were then delivered a few days later. Any changes in the programs or in the input data required splicing in a new section of tape, which was a tedious business. Eventually the College did acquire a main-frame computer, when they switched to Fortran. At that time the Fortran was far from optimal in its performance and the most time-consuming parts of the calculation had to be programmed in machine code.

By the early 1970s Konrad Singer had set up the first research group in the UK devoted to molecular simulation, extending its scope to include molecular dynamics (MD). Together with Eveline Gosling and Ian McDonald, Konrad published in Molecular Physics in 1973 a non-equilibrium MD simulation of the shear viscosity of a simple liquid. This was just about the first application of non-equilibrium MD (NEMD) to viscosity (published about the same time as the boundary-driven flow paper of Ashurst and Hoover), measured from the velocity profile of a fluid exposed to a sinusoidal-varying force. Good agreement with the Green-Kubo method was obtained, after extrapolation to reach the long-wavelength limit. These data combined with that on diffusion showed that the Stokes relation is satisfied with an effective diameter consistent with that deduced from the peak in the structure factor. This work was followed up some years later in paper by Konrad, Jean and David Fincham, who had also joined the group, on shear viscosity by NEMD in Molecular Physics in 1980 using the difference in trajectories method.

As the 1970s progressed, Konrad’s research interests broadened, and he turned his attention to the simulation of diatomic liquids, in collaboration with post-doctoral assistant C.S. Murthy, and PhD student Keith Carter. Konrad published a paper with S. Romano calculating the entropy of Cl2 and Br2 in Molecular Physics in 1979. He devised a scheme for integrating the equations of motion that was much simpler than those previously used and before the days of constraint methods. It also worked for any linear molecule, which the constraints method in its original form did not. Molten salt simulations were still being actively carried out in his group by John Lewis and David Adams. Simon de Leeuw, a PhD student visitor from the Netherlands collaborated on alkaline earth halides, in which they demonstrated the limitations of the pair potential approach for these partially covalent systems – a field which has been followed up by other research groups since.

With his background in quantum chemistry, Konrad was keen to develop methods incorporating quantum effects in condensed phase simulation and from 1980 onwards he examined several approaches. With N. Corbin, his postgraduate student at Royal Holloway, he began working with Gaussian wavepackets as a semiclassical approach to quantum-corrected molecular dynamics. Extending the work of Heller and others he derived equations of motion for both the molecular centre of mass and the variable Gaussian shape by exploiting McLachlan’s minimisation principle for the time dependent Schrödinger Equation. The early results, obtained in 1982, indicated trouble ahead: the method overestimated the quantum correction to the kinetic energy and the rapid fluctuation of the Gaussian shape made very small time steps essential. Later work in 1986, with collaborator W. Smith, restricted the model to spherically symmetric Gaussians and applied an important correction to the underlying empirical potential. These modifications resulted in a more practical algorithm, which improved results for the thermodynamic properties of neon and demonstrated quantum broadening of the radial distribution function consistent with expected quantum behaviour. Not one to be confined by a single methodology, concurrent with the wavepacket approach, he and his wife Jean, in 1984 performed molecular dynamics simulations of neon based on a Hamiltonian that included first order quantum corrections derived from the Wigner-Kirkwood expansion. The method was direct but required special attention to numerical instabilities arising from the strong short-ranged inter-atomic repulsion.

From 1985 onwards, quantum methods based on Feynman’s path integral theory were beginning to make a significant impact, particularly in the U.S.A. By this novel approach it was possible to transform the time-dependent Schrödinger equation into a partition function identical to that of a classical ring polymer. This made it possible to perform (in principle exact) quantum simulations of many-particle systems for the first time – though at the price of losing the time dependence. Konrad plunged quickly into the new methodology and in 1986, with collaborator W. Smith, published some of the earliest work on fully quantum corrected simulations of condensed phase ideal gases – at the same time demonstrating that the same results were obtained with atomic configurations generated by Monte Carlo, molecular dynamics and Brownian dynamics. He then went further to obtain the quantum corrected free energy of the neon solid state and, with collaborator J. Morales, the free energy of the liquid. Following the success of the path integral approach Konrad returned to the issue of time dependence in many-particle quantum systems. He explored many avenues in his hunt for a practical scheme including: path integral method for calculating time dependent correlation functions (after Thirumalai and Berne); time dependent path integral propagation methods (after Filinov); and discrete methods for propagating the system wave function (after Kosloff), before settling on something different: the propagation of the Wigner-Liouville equation. For this two methods were obtained: propagation by fast Fourier transform and stochastic propagation. Unfortunately, while both of these methods worked, they could not be extended to many particle systems as Konrad required. Nevertheless he continued his quest to find a general method for propagating the many particle time dependent Schrödinger equation well past his retirement from Royal Holloway College.

In the early 1980s Konrad was chairperson and an early driving force behind the newly formed SERC’s Collaborative Project No. 5 (CCP5). David Heyes joined RHC in 1981 as CCP5 coordinator, and this period involved the first interactions of Bill Smith of Daresbury with Konrad that flourished for many years into his retirement. CCP5 still plays, some 30 years later, an important role in fostering molecular simulation developments in the UK and abroad. He had particularly close links with young scientists in India, Italy and Austria. The latter contacts are noteworthy: Konrad was as impatient with any notion of ‘the Jewish race’ as he was with any blanket condemnation of a people because of the misdeeds of their countrymen. The attitude enabled him to retain his affection both for German language and literature and for Vienna, where he returned frequently, especially after retirement, for both pleasure and academic collaboration.

This brief summary illustrates the ground-breaking contributions that Konrad Singer has made to theoretical chemistry in general and to the field of molecular simulations in particular. However, this text cannot possibly do justice to Konrad as a person: gentle, cultured and averse to all bias and prejudice. Konrad was patient with his students and postdoctoral assistants, and a true gentleman in his interactions with others. He was generous with his time and gave considerable latitude to his group members to explore their own areas and publish independently, a rather rare practice at the time, and even today.

His is a lasting legacy, both in the UK and abroad. He will be greatly missed by those who knew him. Konrad Singer is survived by his sons Michael and Peter, and by four grandchildren.

Giovanni Ciccotti

Peter J. Gardner

David M. Heyes

Ian R. McDonald

William Smith

Leslie V. Woodcock