Berni Julian Alder, Theoretical Physicist and Inventor of Molecular Dynamics, 1925–2020 Downloaded by Guest on September 24, 2021 9 E

RETROSPECTIVE

BerniJulianAlder,theoreticalphysicistandinventor

of molecular dynamics, 1925–2020 RETROSPECTIVE

David M. Ceperleya and Stephen B. Libbyb,1

Berni Julian Alder, one of the leading figures in the invention of molecular dynamics simulations used for a wide array of problems in physics and chemistry, died on September 7, 2020. His career, spanning more than 65 years, transformed statistical mechanics, many body physics, the study of chemistry, and the microscopic dynamics of fluids, by making atomistic computational simulation (in parallel with traditional theory and experiment) a new pathway to unexpected discoveries. Among his many honors, the CECAM prize, recognizing exceptional contributions to the simulation of the microscopic properties of matter, is named for him. He was awarded the National Medal of Science by President Berni Julian Alder in 2015. Image credit: Lawrence Obama in 2008. Livermore National Laboratory. Alder was born to Ludwig Adler and Otillie n ´ee Gottschalk in Duisburg, Germany on September 9, sampling algorithm that was to revolutionize statistical 1925. Alder’s father Ludwig was a chemist who worked physics (1). Teller recruited Alder to the just-founded in the German aluminum industry. When the Nazis Lawrence Radiation Laboratory (later, the Lawrence Liv- came to power in 1933, Alder, his parents, elder ermore National Laboratory), where he, along with brother Henry, and twin brother Charles fled to Zurich, other young talented scientists, built a unique “can Switzerland. In 1941, they further emigrated to the do” scientific culture that thrives to this day. United States (becoming “Alders” in the process), Beginning in the mid-1950s, Alder, who possessed where they settled in Berkeley, California. From then a striking, intuitive understanding of many body sta- on, he and his family lived and worked in the Bay Area, tistical systems, began—with his collaborators—a se- which they considered their “slice of heaven.” Alder ries of remarkable numerical simulations of a simple completed his senior year of high school there and model system, a collection of hard spheres. These then did his undergraduate studies at the University carefully chosen simulations, though at first seemingly of California, Berkeley. Alder’s education was interrup- oversimplified, repeatedly got to the heart of key ted by his service in the US Navy as a radar technician physical questions. This novel reliance on numerical in the Pacific Theater. Later, he and his wife Esther simulation in research was natural at Livermore, which raised their two sons and a daughter in the Bay Area had embraced the use of advanced computing from community of El Cerrito. its founding days. Because his calculations involved As a Berkeley undergraduate, Alder’s mentor was simple classic dynamics that could be paused and the great chemist Joel Hildebrand, who influenced his restarted at any stage with modest memory overhead, early thinking about chemical systems. Later, circa Alder was able to develop a very effective system of 1951, as a student of J. G. Kirkwood at the California running jobs in the background (termed “free standby” Institute of Technology, Alder began to explore the decades ago) that accumulated results at statistical pre- idea of Monte Carlo sampling applied to atomistic sys- cisions that were famously decades ahead of their time. tems. This early work brought him to the attention of For nearly 70 years, Alder applied an inquisitive, Edward Teller who, with Nicolas Metropolis, Marshall open minded, and dauntless research method, based Rosenbluth, Arianna Rosenbluth, and Augusta Teller, on a kind of Socratic dialogue with his research group, had invented the famous “Metropolis” Monte Carlo that led them to several important discoveries in

aPhysics Department, University of Illinois at Urbana–Champaign, Urbana, IL 61801; and bPhysics Department, Lawrence Livermore National Laboratory, Livermore, CA 94550 Author contributions: D.M.C. and S.B.L. wrote the paper. The authors declare no competing interest. Published under the PNAS license. 1To whom correspondence may be addressed. Email: [email protected]. Published February 23, 2021.

PNAS 2021 Vol. 118 No. 11 e2024252118 https://doi.org/10.1073/pnas.2024252118 | 1of3 Downloaded by guest on September 24, 2021 phase transition mechanism and its elaboration to in- clude further intermediate “hexatic phases” (7, 8) are all continuous phase transitions. However, in their 1962 simulations, Alder and Wainwright found clear numerical evidence for a first-order transition to a fluid. Their simulation data, obtained from following 870 disks for ∼107 collisions on the Livermore LARC computer, still stands up well after 50 years when compared with the current state-of-the-art simulations featuring ∼106 disks, definitively confirming the first-order transition (9). Having successfully resolved important questions with hard spheres, in the 1970s Alder began investi- gating the possibilities for simulating many-body systems at the more fundamental quantum level. The Berni Alder (standing) with his collaborators, Mary Ann work came to fruition in 1980 with the definitive cal- Mansigh and Tom Wainwright, in 1962 with their culation of the simplest model of interacting electrons, computational results showing the 2D melting phase namely the electron gas (10), which crucially enabled transition. Image credit: Lawrence Livermore National the success of the density functional method in mod- Laboratory. ern computational physics, chemistry, and materials science. Alder’s collaborators went on to develop statistical mechanics. It is now a commonplace truism methods to treat quantum systems at nonzero temper- that computational simulations have become a third ature, including the phenomena of Bose condensation pillar of the scientific method (along with theory and and superfluidity (11). experiment). However, it can also be said that true At Livermore, from the 1950s onward, Alder played discoveries that changed our fundamental understand- a major role in building up the laboratory’s program in ing of nature, originating in such simulations, have materials equations of state, a major need of the labo- remained quite infrequent. As the theorist Leo Kadanoff ratory’s defense mission. In 1963, with Teller and others, once remarked, there have been only a few big discov- Alder cofounded the University of California, Davis De- eries in physics driven by simulation since the late 1940s. partment of Applied Physics, which focused on training Alder and his colleague Tom Wainwright were arguably graduate students in areas relevant to the laboratory’s responsible for several of these: Discovering in 1957 that programs, such as plasma and high-pressure physics, ra- – aliquidsolid (freezing) phase transition could occur in diation transfer, and laser fusion. Alder was also one of the system with only repulsive interactions (2), the even more founders and the editor of the Journal of Computational remarkable result in 1962 that that a two-dimensional Physics. (2D) system with short-range forces could have a subtle Alder mentored many successful students and post – ordering phase transition (3 5), and the 1967 to 1970 doctorates over the decades, and it was always a discovery (6) that nonequilibrium fluids relax to equilib- special treat to join with him and his group at their rium far more slowly than previously thought. lunchtime meeting in the Livermore cafeteria. He Alder and Wainwright’s extraordinary 1962 result always conducted these discussions in a friendly man- that a 2D system of hard disks with short-range inter- ner, while still thoughtfully questioning assumptions actions could indeed have a freezing/melting phase and conclusions. Whether one was a beginning grad- transition, was remarkable in two ways. First, the result uate student, a senior scientist, or anything in between, flatly contradicted powerful arguments going back to it didn’t matter. One always came away from these di- Landau and Peierls that there couldn’t be a true, long- alogs with a deepened understanding of physics. range ordered state in a 2D system with continuous symmetry. This contradiction was an essential motivator Acknowledgments of Kosterlitz and Thouless’s 1973 theory (K-T) of phase This work was partly performed under the auspices of the US transitions in 2D systems mediated by topological, vortex- Department of Energy by Lawrence Livermore National Labora- like defects (4, 5). Second, the basic vortex-mediated K-T tory, under Contract DE-AC52-07NA27344.

1 N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953). 2 B. J. Alder, T. E. Wainwright, Phase transition for a hard sphere system. J. Chem. Phys. 27, 1208–1209 (1957). 3 B. J. Alder, T. E. Wainwright, Phase transition in elastic disks. Phys. Rev. 127, 359–361 (1962). 4 J. M. Kosterlitz, D. J. Thouless, Long range order and metastability in two dimensional solids and superfluids. (Application of Dislocation Theory). J. Phys. C Solid State Phys. 5, L124 (1972). 5 J. M. Kosterlitz, D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C Solid State Phys. 6, 1181 (1973). 6 B. J. Alder, T. E. Wainwright, Decay of the velocity autocorrelation function. Physical Review A 1,18–21 (1970). 7 B. I. Halperin, D. R. Nelson, Theory of two-dimensional melting. Phys. Rev. Lett. 42, 121 (1978). 8 A. P. Young, On the theory of the phase transition in the two-dimensional planar spin model. J. Phys. C Solid State Phys. 11, L453 (1978).

2of3 | PNAS Ceperley and Libby https://doi.org/10.1073/pnas.2024252118 Berni Julian Alder, theoretical physicist and inventor of molecular dynamics, 1925–2020 Downloaded by guest on September 24, 2021 9 E. P. Bernard, W. Krauth, Two-step melting in two dimensions: First-order liquid-hexatic transition. Phys. Rev. Lett. 107, 155704 (2011). 10 D. M. Ceperley, B. J. Alder, Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980). 11 E.L. Pollock, D.M. Ceperley, Simulation of quantum many-body systems by path integral methods. Phys. Rev. B Condens. Matter 30, 2555–2568 (1984).

Ceperley and Libby PNAS | 3of3 Berni Julian Alder, theoretical physicist and inventor of molecular dynamics, https://doi.org/10.1073/pnas.2024252118 1925–2020 Downloaded by guest on September 24, 2021