Axel Becke’s ground-breaking contributions to chemical theory underpin computer models in all fields of chemistry.

Axel Becke’s ground-breaking contributions to chemical theory underpin computer models in all fields of chemistry. Photo credit: Natural Science and Engineering Research Council of Canada (NSERC)

Axel Becke has a lot in common with Albert Einstein. Just like the famous physicist, Becke was born in Germany and made his greatest scientific contributions mainly through the medium of pure thought, preferring the cerebral world of mathematical equations to the messiness of the laboratory. Like Einstein, Becke’s discoveries have revolutionized his field of study. But by one measure — albeit a somewhat arbitrary one — Becke is way ahead: his 1993 paper on density functional theory (DFT) has been cited more than 50,000 times, the eighth most cited paper of all time. Einstein doesn’t even crack the top 100.

This past February, the Natural Sciences and Engineering Research Council of Canada (NSERC) presented Becke with the Gerhard Herzberg Canada Gold Medal for Science and Engineering, its highest scientific honour. Named after the German-Canadian scientist who won the 1971 Nobel Prize in Chemistry, the Herzberg recognizes Becke’s lifetime of contributions, specifically, his DFT exchange and correlation functionals. Though these concepts may be obscure even to many chemists, they underpin the vast majority of computer calculations that model chemical reactions today. Such computer modelling is critical to all fields of chemistry, whether one is trying to design new drugs, improve oil sands upgrading or develop innovative plastics. “Without Axel’s fundamental contributions, none of this modelling would be possible,” says Dennis Salahub, a theoretical chemist at the University of Calgary and one of Becke’s colleagues. “In the whole world, there are probably two names that come up most often when researchers think of exchange functionals. Axel’s is one of them.”

Speaking from his office at Dalhousie University, where he holds the Killam Chair in Computational Science, Becke’s manner is professorial: he enunciates well and has a habit of repeating himself, using slightly different language each time to ensure that his meaning is coming through. “Of course it’s very gratifying,” says Becke, referring to the Herzberg gold medal. “In a way it’s like coming full circle. I met Gerhard Herzberg a few times and in fact I used spectroscopic constants from one of his most famous books to test my theories for the first 10 years of my career. So the Herzberg in particular is really nice to receive.”

Born in Esslingen, Germany, Becke came to Canada at the age of three with his parents and younger brother. First in Toronto and then in London, Ont., Becke’s father Helmut worked as a glassblower, creating artistically shaped tubes for neon signs. In the 1960s, he took a job at McMaster University, designing scientific glassware for chemistry and biology labs and eventually went on to create sophisticated furnace tubes and chip-handling glassware for the electronics industry, working in Ottawa at what would later become Nortel Networks.

While his father’s work did interest him, Becke was much more of a tinkerer, spending many quiet childhood hours with Lego and Meccano sets, not to mention the science-themed books his parents bought him. While an engineering physics student at Queen’s University, he even constructed a system for 3D photography, assembling it from cameras, projectors and polarized sunglasses that he modified and twinned. But as his studies in physics advanced, Becke began to move beyond the world of machines and gadgets. “I became more interested in where the formulas came from and the theories behind them, rather than applying them as an engineer,” Becke says. 

The drive to know more about the fundamental workings of the universe led him to graduate studies in the nuclear physics group of Donald Sprung at McMaster University. A noted theorist, Sprung was also the Dean of Science and his busy schedule meant that Becke was given the freedom to pursue whatever branch of physics most interested him. “I got a lot of inspiration from John Slater, who wrote books on everything from nuclear theory to solid-state physics to theoretical chemistry,” says Becke. “That was when I got fascinated by density functional theory, an early forerunner of which Slater espoused in several papers in the 1950s and in his last book.” 

Density functional theory was invented by physicists who wanted to simplify the study of the electrical properties of solid-state materials, such as those used to make transistors, lasers or solar cells. The movement of electrons in an atom or a small molecule could be quite accurately described using quantum-mechanical wavefunctions, which detailed the motions of each individual electron. But when it comes to modelling a bulk material — say a length of copper wire, or a chunk of silicon in a transistor — the number of electrons is essentially infinite and the math becomes unmanageably complex. “Wavefunction calculations cost a lot of computer time,” says Becke. “It was impractical to do them on molecules containing more than a dozen atoms or so.”  

Governor General David Johnston presented Axel Becke with the Herzberg Medal this past February in Ottawa.

Governor General David Johnston presented Axel Becke with the Herzberg Medal this past February in Ottawa. Photo credit: Sgt. Ronald Duchesne, Rideau Hall 

In the mid-1960s, theoretical physicist Walter Kohn — who won the Nobel Prize in Chemistry in 1998 — proposed a way to get around this problem with co-authors Pierre Hohenberg and Lu Jeu Sham. Their equations treated electrons almost like a fluid: you didn’t need to know exactly what each electron was doing, only the total density of the electrons at all points in the material. They proved that every property: energy, conductivity, band gap and anything else an electrical engineer might want to know in order to build a better laser or radio, is uniquely determined by — or a “functional” of — the electron density. Unfortunately the Hohenberg-Kohn theorem was an existence proof only; it showed that properties could be calculated from the electron density but it provided no exact formulas for the actual functionals. Thus, scientists had to rely on approximations and models. One simple approximation suggested by Kohn and Sham was called the “local density approximation” (LDA). 

What fascinated Becke about the LDA was that while it could give reasonably accurate numbers for a chunk of silicon with billions of atoms in it, if applied to simple diatomic molecules, it failed badly. “The DFT approximations that the physicists were using, such as the LDA, gave very poor bond energies even for the simplest molecules,” says Becke. “I wondered why and I wondered if we could make it better.” 

Becke started hanging out with theoretical chemists and experimenting with new functional forms that could translate the electronic density in simple molecules into much better bond energies and other useful properties. Despite technically being a physicist, Becke joined Russell Boyd’s theoretical chemistry group at Dalhousie University to pursue this work as a postdoctoral fellow. “Axel is very passionate about his research interests,” says Boyd, who is now professor emeritus. “He has an exceptional ability to remain focused on a given problem and to not be sidetracked by less significant topics.” 

 strongly correlated systems.

Axel Becke is studying density functional theory’s final frontier: strongly correlated systems. Photo credit: Natural Science and Engineering Research Council of Canada (NSERC)

This impression of Becke’s work ethic is corroborated by Tom Ziegler, who worked in the same building as Becke when he was finishing at McMaster. Ziegler, a long-time professor at the University of Calgary Department of Chemistry, was another theoretical chemist and DFT pioneer who died unexpectedly this past spring. In an email sent only a few weeks earlier, Ziegler recalled that while he and Becke worked in nearby offices, it was some time before they met, as Becke worked almost entirely at night. “Axel is like a top athlete,” he wrote. “During the competition he concentrates exclusively on the task at hand. However, afterward he likes nothing better than a social beer with the boys.” 

The hard work paid off. In 1988 Becke, by then a professor of chemistry at Queen’s University, published a paper in which he described a new exchange functional, the most important piece of the DFT puzzle, known as the Becke 1988 (B88) exchange functional. B88 dramatically improved the accuracy of DFT calculations. For the first time, they began to give accurate predictions not just for bulk materials but for individual molecules in chemistry. The paper would go on to become the 25th most cited of all time. “That’s when chemists started to pay attention,” Becke says. 

Still, not everyone was convinced. “At that time most quantum chemists had an overbearing or hostile attitude towards DFT,” Ziegler wrote. But that was about to change. In 1991, Becke attended the International Congress of Quantum Chemistry, held that year in the town of Menton on the French Riviera. Here he seized an opportunity to lunch with John Pople, a theoretical chemist and lead designer of Gaussian, one of the most widely used software packages for chemical modelling. Over a five-course meal and conversation lasting three hours, Becke convinced Pople that his DFT methods were worth incorporating into the software package. When that happened, everything changed. “In 1992, the world’s quantum chemists came to the Canadian Symposium for Theoretical Chemistry in Montreal,” Ziegler wrote. “They all ‘came clean’ and admitted that they now were convinced supporters of DFT, thanks to the work of Axel.” In 1998 Pople shared the Nobel Prize in Chemistry with Walter Kohn for the development of quantum chemistry technology in general and the rapidly expanding role of DFT in particular.
For his part, Becke was not content to rest on his laurels. He continued searching for even better and more accurate exchange-correlation functionals. In 1993 he published his top-cited paper — the eighth most cited of all time — in The Journal of Chemical Physics, laying out the famous B3LYP (Becke, Lee, Yang and Parr) functional which quickly became the industry standard. The truly remarkable citation record of that paper has made Becke something of a celebrity in certain circles. “I often get stopped at conferences by students who want their photograph taken with me,” he admits with a chuckle. 

In the early 2000s, one of those impressed students was Erin Johnson, at the time an undergraduate at Carleton University. She heard Becke speak during a conference in honour of Walter Kohn at the National Research Council in Ottawa in 2002. “I greatly enjoyed his talks,” she says. “I was already interested in studying density functional theory and with Axel being one of the key researchers in the field, he seemed to be the ideal person to supervise my graduate studies.” 

Johnson joined Becke’s lab in 2004. “Axel was an excellent mentor. As my degree progressed, we would meet every couple of weeks and have long talks about virtually everything. He’s incredibly brilliant, very approachable and passionate about science.” Over the next few years, Johnson and Becke improved exchange-correlation functionals to the point where they could not only describe the bonds within a molecule but also the much more subtle forces between separate molecules. These intermolecular forces — including dipole-dipole interactions, hydrogen bonding, van der Waals forces and London dispersion forces — are critical to understanding the structures and chemistry of proteins, DNA and other biologically important molecules. The new DFT functionals, which are about 50 times more accurate for molecular energies than those known in the 1960s, enable accurate and useful predictions throughout chemistry, including biological chemistry.

The Herzberg Medal comes with a million dollars of award money, to be spent on research. The funds are being used to support a new Herzberg-Becke Chair in Theoretical Chemistry, to which Johnson has been appointed. Since 2010 she’s been working as an associate professor of theoretical chemistry at the University of California, Merced. “I’m very excited to be returning home to Canada,” says Johnson, who took up her new position July 1. “Having Axel as my adviser, friend and mentor is a pleasure and an honour and I am eager to renew our collaboration.” 
The plan is to tackle DFT’s final frontier: strongly correlated systems. These are problems involving the making and breaking of bonds far from their equilibrium geometries, of fundamental importance in describing chemical reaction profiles and in photochemical processes. DFT can’t handle strongly correlated problems yet. If successful, the new models that flow from Johnson and Becke’s work could have just as significant an impact as their previous innovations, impacting everything from industrial catalysis to polymerization and more.  

To colleagues like Dennis Salahub, Becke’s legacy will be his affable doggedness and dedication: after 35 years of working on the same problem, Becke, now 62, shows no signs of tiring. “We’ve been together at numerous conferences and workshops over the past 35 years and it’s always a pleasure to hear what he’s been up to scientifically every time we meet,” says Salahub. “I was truly delighted that Axel’s great worth had been recognized and doubly delighted to learn that he was using the resources to repatriate Erin Johnson. Having both of them in the same place brings all kinds of potential great outcomes to mind. We all hope that Axel Becke’s greatest contributions are still to come.”