Quantum Dynamics Simulation of Electrons in Materials on High-Performance Computers André Schleife, Erik W. Draeger, Victor Anisimov, Alfredo A. Correa, and Yosuke Kanai André Schleife: André Schleife is a Blue Waters Assistant Professor in the Department of Materials Science and Engineering at the University of Illinois at Urbana-Champaign. He obtained his Diploma (2006) and Ph.D. (2010) in physics at Friedrich-Schiller-University in Jena, Germany for his theoretical work on transparent conducting oxides. Before he started at UIUC he was a Directorate Postdoctoral Researcher at Lawrence Livermore National Laboratory (2011-2013) working on a description of non-adiabatic electron-ion dynamics. His current research focus is on excited electronic states and their real-time dynamics in various material systems using accurate, first-principles computational methods and making use of modern super computers. He is a member of APS, MRS, DFG, and SPIE. Contact him at [email protected]. Complete contact information: Department of Materials Science and Engineering University of Illinois at Urbana-Champaign 1304 W. Green St. Urbana, IL 61801 Tel : (217)-244-0339 Fax : (217)-333-2736 Erik W. Draeger: Erik Draeger is a staff scientist at the Center for Applied Scientific Computing, in the Computation Directorate at Lawrence Livermore National Laboratory. He received his Bachelor’s degree in physics from the University of California, Berkeley in 1995 and his Ph.D. in theoretical physics from the University of Illinois, Urbana-Champaign in 2001. His primary research interest is the development of massively-parallel scientific applications, with a focus on materials science and biological applications. He currently leads the development of qb@ll, the LLNL branch of the Qbox first-principles molecular dynamics code. Contact him at [email protected] Complete contact information: Center for Applied Scientific Computing 7000 East Ave., L-561 Livermore, CA 94550 Tel : (925)423-3650 Victor Anisimov: Victor Anisimov is a Senior Research Programmer in the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign. He holds Ph.D. degree in Physical Chemistry from Institute of Chemical Physics Russian Academy of Sciences (1997), followed by 5 years of computational chemistry software development with Fujitsu. He performed postdoctoral work in University of Maryland at Baltimore (2003- 2008) and in University of Texas at Houston (2008-2011). Dr. Anisimov specializes in high- performance computing of soft matter and in performance optimization of quantum chemistry codes. He is an author of the linear scaling semiempirical method LocalSCF. Contact him at [email protected]. Complete contact information: National Center for Supercomputing Applications University of Illinois at Urbana-Champaign 1205 W. Clark St. Urbana, IL 61801 Tel : (217)-333-2799 Fax : (217)-244-9757 Alfredo A. Correa: Alfredo A. Correa is Staff Scientist at Lawrence Livermore National Laboratory, Condensed Matter and Materials Division where he was previously a Lawrence Fellow during 2009- 2012. He obtained a B.A. from Instituto Balseiro in 2001 and a Ph.D. in Physics from University of California at Berkeley in 2008, and he was subsequently a post-doctoral scholar at Stanford University, Mechanical Engineering department for 2009. His current research focus is on atomistic simulation of electron-ion dynamics, material at extreme conditions and high energy density physics modeling. Contact him at [email protected]. Complete contact information: Lawrence Livermore National Laboratory 7000 East Avenue Livermore, CA 94550 Tel : (925)-422-0102 Fax: (925)-422-6594 Yosuke Kanai: Yosuke Kanai is Assistant Professor at the University of North Carolina at Chapel Hill in Department of Chemistry and Visiting Scientist in Condensed Matter and Materials Division at Lawrence Livermore National Laboratory, where he was previously a Lawrence Fellow and also served as director of Computational Chemistry and Materials Science Summer Institute for 2009-2011. He obtained a Ph.D. in theoretical chemistry from Princeton University in 2006, and he was subsequently a Berkeley Nanoscience and Nanoengineering Institute post-doctoral scholar at University of California at Berkeley for 2006-2009. His research interests are on development and application of electronic structure methods based on first-principles theory for investigating novel phenomena in materials and condensed matter systems. He is a member of APS, MRS, and ACS. Contact him at [email protected]. Complete contact information: Department of Chemistry Campus Box 3290 The University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3290 Tel : (919)-962-3891 Fax : (919)-962-2388 Abstract: Advancement in high-performance computing allows us to calculate properties of increasingly complex materials with unprecedented accuracy. At the same time, in order to take full advantage of modern leadership-class supercomputers, the calculations need to scale well on hundreds of thousands of processing cores. We demonstrate such high scalability of our recently developed implementation of Ehrenfest non-adiabatic electron-ion dynamics up to 1 million floating-point processing units on two different leadership-class computing architectures. As a representative example of material properties that derive from quantum dynamics of electrons, we demonstrate the accurate calculation of electronic stopping power, which characterizes the rate of energy transfer from a high-energy particle to electrons in materials. We discuss the specific case of crystalline gold with a hydrogen atom as the high- energy particle, and we illustrate detailed scientific insights that can be obtained from the quantum dynamics simulation at electronic structure level. Keywords: Quantum electron dynamics, High-performance computing, Computational Materials Science Introduction Over the past half-century, computation has become an indispensable tool in science and engineering. On the road to exascale, supercomputers with multi-peta-FLOP per second (PFlop/s) performance have become increasingly available. The continued advancement of high-performance computational capabilities allows us to solve mathematical problems of increasing complexity with greater accuracy, providing detailed scientific understanding and insights for technological innovation. At the same time, the increasing scale and complexity of modern supercomputers have exposed the need for a greater emphasis on development of algorithms and methodologies that are tailored for massively-parallel multi-core machines in order to fully take advantage of these capabilities. Computational materials research has traditionally benefited greatly from high-performance computing, and increased effort on addressing this issue is becoming crucial for the continued advancement of the field. In order to systematically design new materials or even to improve existing ones, obtaining structure-function-property relationships with predictive accuracy is essential. Oftentimes this requires a deep understanding of material properties that emerge from many-body interactions of electrons and ions (i.e. atoms with electrons missing) that constitute the material. At the microscopic scale of electrons, quantum mechanical effects play a central role, and the mathematical description of many-body interactions becomes highly non-trivial. Furthermore, many challenging problems in materials research call for predictive calculations without the need for adjustable empirical parameters from experiments (i.e. first-principles approaches). High-performance computing is indispensable for tackling this challenging goal. The behavior of quantum-mechanical particles such as electrons is governed by the many- body Schrödinger equation, a multi-dimensional differential equation. Because a direct solution of this equation has exponential complexity [1], it is computationally intractable for all but the smallest and simplest molecules even on today’s supercomputers. Scientists thus rely on physical and numerical approximations for computing electronic structure to predict material properties. Naturally, the utility of quantum-mechanical calculations depends on the accuracy of these underlying approximations that are involved in first-principles computational approaches. Recent advances of quantum-mechanical calculations are indeed closely tied to the emergence of high-performance computers in the last few decades, and they allow us to employ better approximations which have become highly complicated for numerical calculations. Among various quantum mechanical computational methods for obtaining electronic structure, density functional theory (DFT) has and continues to play a central role in computational materials research [1,2]. Enabled by efficient implementations of DFT methods, “high-throughput” computational searches for optimal materials are becoming popular for various technological applications such as batteries and photo-electrochemical cells, for instance, within the Materials Project [3]. Computational prediction of optical and electronic properties of materials also advanced greatly in recent years with many-body perturbation theory and quantum Monte Carlo methodologies, especially with increasing research effort for solar energy conversion [4]. As for calculating time-dependent properties, dynamical behavior of complex materials and condensed phase systems can be simulated today with first-principles molecular