Computational Materials Science with the WIEN2k code P. Blaha Institute of Materials Chemistry TU Wien pblaha@theochem.tuwien.ac.at http://www.wien2k.at
Computational Materials Science describe materials by quantummechanical simulations(ab initio) simulate: infinite ( perfect ) bulk solids impurities, vacancies in solids surfaces nanostructures atomic and electronic structure stability, phase transitions, mechanical properties, magnetism, chemical bonding,. spectroscopies (IR, Raman, XPS, XAS, XES, EELS,Mössbauer, NMR, STM)
Method: DFT calculations numerical solution of a Schrödinger-like equation (Kohn-Sham) k k k V ( r) i ei i 2 expansion into augmented plane waves basisfunctions f Kn : variational principle 1 2 k = C f K n k n k < E n n 50-100 APWs / atom < H > < E >= < > C k n > =0 generalized eigenvalue problem H C=E S C Setup and diagonalization of (real or complex) matrices of size 10.000 to 50.000 (up to 50 Gb memory, only 10% of e i )
Loops: loop 1: different structures (atomic positions) loop 2: scf-cycle (solve [-½ 2 +V] =E new V iterate) loop 3: k-loop (solve H =E for different k-points) loop 4: setup + diagonalization of H C = E S C largest effort, highest optimization, best parallelization, scaling of time and memory F90, mpi, Scalapack, blas 1 4 2 5 3 6 processors loop over APWs 7 8 9 in parallel (via scripts, slow network, common NFS) 10000-50000 sequential (efficient multi-secant BROYDEN-mixing; L.Marks PRB 78, 075114) coarse grain parallel (different jobs) or sequential (forces new positions)
WIEN2k software package An Augmented Plane Wave Plus Local Orbital Program for Calculating Crystal Properties Peter Blaha Karlheinz Schwarz Georg Madsen Dieter Kvasnicka Joachim Luitz November 2001 Vienna, AUSTRIA Vienna University of Technology http://www.wien2k.at developed over more than 25 years 1400 registered groups 2000 mailinglist users Europe: A, B, CH, CZ, D, DK, ES, F, FIN, GR, H, I, IL, IRE, N, NL, PL, RO, S, SK, SL, SI, UK, ETH Zürich, MPI Stuttgart, FHI Berlin, DESY, TH Aachen, ESRF, Prague, IJS Ljubjlana, Paris, Chalmers, Cambridge, Oxford America: ARG, BZ, CDN, MX, USA (MIT, NIST, Berkeley, Princeton, Harvard, Argonne NL, Los Alamos NL, Oak Ridge NL, Penn State, Purdue, Georgia Tech, Lehigh, John Hopkins, Chicago, Stony Brook, SUNY, UC St.Barbara, UCLA) far east: AUS, China, India, JPN, Korea, Pakistan, Singapore,Taiwan (Beijing, Tokyo, Osaka, Kyoto, Sendai, Tsukuba, Hong Kong) 55 industries (Canon, Eastman, Exxon, Fuji, Hitachi, IBM, Idemitsu Petrochem., Kansai, Komatsu, Konica-Minolta, A.D.Little, Mitsubishi, Mitsui Mining, Motorola, NEC, Nippon Steel, Norsk Hydro, Osram, Panasonic, Samsung, Seiko Epson, Siemens, Sony, Sumitomo,TDK,Toyota).
w2web GUI (graphical user interface) Structure generator spacegroup selection import cif file step by step initialization symmetry detection automatic input generation SCF calculations Magnetism (spin-polarization) Spin-orbit coupling Forces (automatic geometry optimization) Guided Tasks Energy band structure DOS Electron density X-ray spectra Optics command line possible!
current hardware: SFB Aurora IBM Cluster 72 x Dual Xeon 3.6 GHz, 1MB L2 Infiniband Switch (installed 2005) SUN Cluster 72 x Quad-Opterons 2.4 GHz Infiniband Switch (installed 2006) WIEN2k on IBM-BlueGene (2000 processors)
Timing and parallel performance: Task Time (s) r, V eff 151 H, S setup 1176 full diagonalization 2454 iterative diag. 461 3x3 super-cell of a h-bn/ni(111) surface model with 99 atoms/cell (N bas = 16900, 1 scf-cycle on 4 cores) iterative block-davidson diagonalization with improved preconditioner [formally H -1 instead of diag(h-es) -1 ; but only factorization of H required] hand-coded mpi (setup) scalapack (diagonalization) (limitations due to stacked Infiniband switch)
h-bn / Rh(111) nanomesh STM Experiment: M.Corso et al., Science 303, 217(2004) partial double layer model Theory: R.Laskowski et al., PRL 98, 106802 (2007): Corrugated single layer model 12x12 Rh, 13x13 BN, 1108 atoms/cell, HC=ESC (50000x50000, 50 GB memory) 64 cpus, 2h/scf-cycle (was 20h!!) 3 month of computing time N corrugation Theoretical model was confirmed later! H. Dill, et. al.: Science 319, S. 1824(2008)
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