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Le Roy Radius

Some notes on R.J. Le Roy and the "Le Roy radius"

The quantity which has come to be identified in the literature as the "Le Roy radius" is mentioned in the current Ontario high school chemistry textbooks, and the this link attempts to address some questions students have asked regarding this topic.

Q: Where and when were you born and where did you grow up?

I was born Sept. 30, 1943 in Ottawa, where my father was at that time a research scientist in the National Research Council (NRC) laboratories, working with the superb scientist and scientific administrator E.W.R. Steacie who was at the time also the President of NRC. In 1944 my dad moved to become a professor of chemistry at the University of Toronto, where he later became Head of Department, a position he held when I was an undergrad in the 1960's. He later re-connected to Ottawa, and in the early 70's was the Vice President of the National Research Council in charge of the University Grants program (later spun off as the now-independent National Scientific and Engineering Research Council, NSERC), while at the same time continuing to maintain an active research lab doing fundamental studies of chemical kinetics at U. of T. My older brother Rodney also obtained a PhD in physical chemistry and had a very successful career in chemical in industry in Canada, first at Noranda Research and later as the founding president of the spin-off company Noranda Advanced Materials. However, there is at best only a weak genetic component associated with this prediliction for research in physical chemistry, as my father was the first person in his extended family to even attend university, and there is no sign (yet, anyway) of any research scientists appearing from among the 13 grandchildren comprising the next generation. On the other hand, my two younger brothers, Alex and John (we were four boys - two years apart - pity my courageous mother!) also went through University and into the education business. Alex was a science teacher, then a Department Head, and then a very successful and much admired Principal an a series on junior and senior high schools in North York, and my youngest brother John was (until his recent retirement) an extremely energetic, effective and much admired grade school teacher in Ottawa.

A noteworthy Le Roy of the next generation is my great-nephew Adrian Corey Le Roy, who is (among other things) an extremely graceful and skilled soccer player and a superb all-round athlete. His handsome image is featured here because some of his classmates seemed reluctant to believe that he is my nephew, and this documentation was posted to help him win a bet.

Q: Where and when did you study?

Grade school - Allenby Public school on Avenue Road in North Toronto, to grade 8.
High school, North Toronto Collegiate, graduating 1961

B.Sc. from the University of Toronto in `Mathematics and Chemistry', an intensive stream of an already intensive program, graduating in 1965.

M.Sc. in Chemistry, again at the University of Toronto, completed in January 1967. My research was initially on experimental kinetics, but switched to the theoretical/computational area which has been my focus ever since. I really liked the hands-on part of experimental chemistry - building apparatus, putting together electronics, and glass-blowing vacuum lines, but I also grew to love even more the hands-on work of designing and writing and using computer codes to ask interesting questions about molecules, and the latter won out. In those days, though, a modest-size program was a couple of thousand computer cards packed solid in boxes a couple of feet (2/3 meter) long, which had to be lugged about, to the keypunch machine, card reader, and then back to the office, so even theoreticians got their exercise.

PhD in Chemistry at University of Wisconsin in Madison, completed in January 1971, working with R.B. Bernstein, one of the great founding fathers of the field of molecular beam and collisional studies.

Postdoctoral work in the Department of Physics at the University of Toronto with J. van Kranendonk, arguably Canada's leading theoretical physicist of the day, from February 1971 to June 1972.

July 1972 - present: Professor of Chemistry at the University of Waterloo.

Fall 1976 and 1979-81: visiting Fellow in the Department of Theoretical Chemistry at Oxford University

Q: What is your primary area of study?

Theoretical and computational chemical physics - the study of the "sex life" of simple molecules. I am interested in learning about the interatomic and intermolecular forces which determine the properties of solid, liquid and gaseous systems, and the binding energies and structures of molecules themselves. My research involves using quantum mechanical theory to understand and explain how observable properties of molecular systems are due to such forces, and in particular, to quantitatively determine those forces (or intermolecular potential energy functions) from measurments of various properties. For example, the characteristic pattern of particular colours (or frequencies) of light absorbed and emitted by a molecule contains information telling us about the shape and structure of the molecule, the forces in the bonds, the dissociation energy, and the nature of the fragments formed on dissociation. One part of my work involves developing and applying methods for extracting such in

Q: Could you explain why you chose this field?

Many (most?) life choices like this are partly or largely accidental, and individuals could have gone in different directions with the expectation of equally satisfying outcomes, so my answer is anecdotal, and not indicative of any long term plan. When I was an M.Sc. student, I built and used a complex experimental apparatus for measuring rate constants for elementary atomic recombination reactions such as I + I + M -> I2 + M ; when we got results we explained them empirically in terms of "who did what to whom", but I always wondered 'why' the results were what they were. This interest in getting to the root of 'why' things were what they were led my supervisor George Burns to direct me at a computational project associated with our measurements, which I found really stimulating and challenging, so while I did published one paper with him on the experimental kinetics, my MSc thesis was a theoretical/computational project (which turned out to have been quite innovative for the time

Q: In your research, what is one question you have tried to answer?

All molecular processes and properties are guided/governed by the intermolecular and intramolecular forces between the atoms in a molecule, or between molecules. However, except for the simplest systems, our knowledge of such interactions is fairly primitive. I am interested in developing and applying methods for determining the precise details of these interactions from experimental data, and in applying the resulting knowledge to explain and predict physical phenomena. In the grand schemei of things, such forces govern all biological life processes, and all reactive and collisional events, so this work has grand long-term implications. However, my real personal motivation is based on wanting to understand how to determine and apply them now to explain experimental observables for simple systems.

Q: What inspired you to ask this question?

The history outlined above and the fact that the molecular collision processes experimentally studied by Bernstein's group (and others) are all governed by intermolecular forces, and can be explained if we accurately knew those forces, directed me at this area early in my scientific life, and with a variety of diversions, I have been following this theme ever since.

Q: What part of your profession do you find most gratifying (i.e. teaching, research, some other aspect)?

I love both research and the part of teaching which involves student contact (lecturing and discussions and advising); I am less enthused about the extensive effort required to prepare and mark good problem sets, tests and exams. Lecture material preparation is also a chore, but it is usually rewarding in that I learn things myself in the process too. Some parts of even the service or administration side of the job can also be gratifying, as one sometimes has the chance to make good things happen: e.g., helping to organize the excellent student PC computing lab environment we have here at Waterloo; organizing the annual national conference on Chemical Physics held every fall at UW. However, the underlying spark is provided by the curiosity and exhilaration associated with research.

Q: Are there any words of wisdom you could pass on to a novice in the world of science?

Finding something which interests you enough that you are willing to work really hard on it, and which challenges you to use your abilities to the fullest, is the key to a fulfilling and enjoyable life. Whether this involves basic or applied science (as in my case) or any other area of human endeavour is immaterial. and whether or not it pays particularly well, is also of no matter. Don't choose something because it is easy - choose it because it is challenging and worthwhile.

Q: What's this "Le Roy radius" all about, and how did you come up with it?

My PhD work with Richard Bernstein included our development of what I call 'near-dissociation theory' (and some others call LeRoy-Bernstein theory). It started from our observation that if molecules were in high vibrational levels lying very close to dissociation [i.e., molecules vibrating so energetically that they are on the threshold of breaking apart], their properties depended mainly on the long-range part of the intermolecular potential energy function. In this long-range region, quantum mechanical theory tells us that the interaction energy could be represented by a sum of terms depending on inverse-powers of the internuclear distance, which at very large distances became dominated by the single lowest-power term in that sum. For example, for neutral atoms with spherical electronic orbitals (S-state atoms), this limiting long-range interaction energy is V(r) = D - C6/r6. These are the types of interactions called "Van der Waals" forces. Putting these two ideas together, a little algebra and (year-1 level) calculus gave us simple analytic expressions for describing the dependence on energy, and hence on vibrational quantum number, of vibrational level spacings [ Journal of Chemical Physics Vol. 52, 3869 (1970)], rotational constants [Canadian Journal of Physics Vol. 50, 953 (1972); Canadian Journal of Physics Vol. 53, 1983 (1975)], expectation values of (powers of) the bond length, and other properties of molecules in levels lying very near dissociation. These expressions have proved to be remarkably powerful tools for a number of applications, including determining more accurate bond dissociation energies, and predicting the number and energies (and other properties) of levels lying above the highest ones observed. The latter point is very important if one wants to use statistical mechanics to predict thermodynamic properties and dissociation equilibrium constants at high temperatures! This 'near-dissociation theory' has also figured prominently in the interpretation of the spectroscopy of molecules

Anyway, back at the beginning, I was quite worried about how to estimate a bound on the region in which this theory would work, and came up with [Molecular Spectroscopy Vol. 1, a Specialist Periodical Report of the Chemical Society of London, p. 120 (1973)] what people later came to call the 'Le Roy radius' [see Chemical Physics Letters Vol. 236, 242 (1995) for a paper published 20 years later, devoted to refining my expression for this quantity]. In effect, this 'radius' tries to define the boundary between the long-range region where all atoms and/or molecules interact simply through the classical physics of independent charge distributions, and the shorter-range `chemical' region where electron exchange energies take over. More particularly, I was trying to set a bound on the region where the pure inverse-power sum of Eq.(2.31) in my course notes (see below) could be trusted. The fact that the name 'Le Roy radius' has been attached to this property and stuck around for a number pof years indicates that it provides a useful way of delineating a property of molecular systems.

The slides from a talk I gave to a high school class a couple of years ago which attempted to explain this material at an accessible level are posted here .

Q: Can you describe how you derived the Le Roy radius?

There was no process one might think of as a formal mathematical development. Rather, I mused for some time about the problem mentioned above - of charactereizing a limit to the region where our new limiting long-range theory could be trusted. Some very important work of the outstanding Canadian theoreticial chemist William J. (Bill) Meath, a long-time Chem Prof at UWO (now retired), had quantitatively showed where and how the limiting inverse-power description of intermolecular forces broke down for a few particular cases. I looked up a variety of atomic properties which would be expected to correlate with atomic size, and tried to see if I could use one of them to devise a simple algebraic expression which would predict the breakdown points which Meath had numerically determined. I published what I found at the time to be the most successful of these formulae, and over time other researchers began using it and calling it the 'Le Roy radius'.

In the context of a grad course I have given (and a book I am hoping to write from it), I have summarized some of the background theory for all of this in the first couple of chapters of the course notes. The 'Le Roy radius' appears in Eqs.(2.36) & (2.37) (p.22). The discussion of 'near-dissociation theory' will appear in Chapter 5, which is still only partly written.

Q: How has the work you have done helped today's society?

I do "basic research" in which my particular motivation is about helping my experimental colleagues understand and extract basic physical information, most notably, information about intermolecular forces, from their data. Thus, I develop computer codee and models for interactions which others use to help us understand simple molecules. Of course that understanding, several steps removed from my particular work, helps us understand (for example) data that satellites collect to tell us about the composition of and reactions in the earth's atmosphere, and a wide range of analytical applications. My basic satisfaction there is not in seeing some explicit practical application, but rather in seeing that others use my methods and results, in the certain knowledge that farther down the knowledge 'food chain' it will have practical import.