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Information about On the role of quantum mechanical simulation in materials science.

Plenary lecture of the XIII SBPMat (Brazilian MRS) meeting, given on October 1st 2014 in João Pessoa (Brazil) by Roberto Dovesi, professor at Universita' degli Studi di Torino (Italy).

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2. Page 2 Is simulation useful? Does it produce reasonable numbers? Or can only try to reproduce the experiments? Connected question: Is simulation expensive? João Pessoa, 2014

3. Page 3 In the year 1960-1990, calculations for the structural properties of periodic compounds ( oxides, halides, ..) were performed at the semi-classical or force-field level (Catlow, Gale, Macrodt and others) The first quantum mechanical ab initio calculations of periodic systems date back to 1979-1981 (diamond, silicon, cubic BN: band structure, total energy, charge density maps) The first periodic code publicly available to the scientific community is released in 1988 (CRYSTAL through QCPE, Quantum Chemistry Program Exchange)… Afterwards………..very quick evolution João Pessoa, 2014

4. Page 4 How many transistors on a chip? João Pessoa, 2014 Gordon Moore Intel i7 Sandy bridge 32 nm 2.27 billions of transistors 434 mm2 GPU NVIDIA GK110 28 nm 7.1 billions of transistors The number of transistors per chip doubles every 18 months

5. Page 5 Performance of HPC João Pessoa, 2014

6. Page 7 DDFFTT && KKoohhnn--SShhaamm • “Density Functional Theory (DFT) is an incredible success story” * • DFT has enable to tackle complex problems with an accuracy unobtainable by any other João Pessoa, 2014 approach • DFT methods has now been applied to chemistry, materials science, solid-state physics, but also geology, mineralogy and biology. • Kohn-Sham formalism * from K. Burke Perspective on Density Functional Theory JCP 136 (2012) 150901

7. Page 8 Is simulation expensive? The last computer we bought…. Server Supermicro 64 CORE OPTERON euros 6.490 ,00 1 x Chassis 2U - 6 x SATA/SAS - 1400W 4 x CPU AMD Opteron 16-Core 6272 2,1Ghz 115W 8 x RAM 8 GB DDR3-1333 ECC Reg. (1GB/core) 1 x Backplane SAS/SATA 6 disks 1 x HDD SATAII 500 GB 7.200 RPM hot-swap 1 x SVGA Matrox G200eW 16MB 2 x LAN interface 1 Gbit 1 x Management IPMI 2.0 Cheap… but 64 cores- Parallel computing Much less than most of the experimental equipments 64 cores enough for large calculation…….. João Pessoa, 2014

8. Page 9 At the other extreme: SUPERCOMPUTERS Available, but: a)They are fragile b)Not so much standard (compiler, libreries) c) The software (that is always late with respect to hardware) MUST BE ABLE TO EXPLOIT this huge power João Pessoa, 2014

9. Page 10 The PPRRAACCEE TTiieerr--00 RReessoouurrcceess HHOORRNNEETT ((HHLLRRSS,, DDEE)) Cray XC30 system - 94,656 cores CCUURRIIEE ((GGEENNCCII,, FFRR)) João Pessoa, 2014 BULL x86 system – 80,640 cores (thin nodes) FFEERRMMII ((CCIINNEECCAA,, IITT)) BlueGene Q system – 163,840 cores SSUUPPEERRMMUUCC ((LLRRZZ,, DDEE)) IBM System x iDataPlex system– 155,656 cores MMAARREENNOOSSTTRRUUMM ((BBSSCC,, SSPP)) IBM System x iDataPlex system– 48,448 cores JJUUQQUUEEEENN ((JJÜÜLLIICCHH,, DDEE)) BlueGene Q system – 458,752 cores

10. Page 11 CRYSTAL parallel versions: MPPcrystal MMPPPPccrryyssttaall João Pessoa, 2014 – Distributed data – Each processor hold only a part of each of the matrices used in the linear algebra – Most but not all of CRYSTAL implemented – Will fail quickly and cleanly if requested feature not implemented – Good for large problems on large processor counts – For large systems can scale well, but not so good for small to medium size ones – Size of linear algebra matrices is, at present, not an issue given enough processors

11. Page 12 The software must be a) Easy to use (freindly) b) Robust, c) Protected d) Documented e) General as much as possible f) Transferable g) Parallel h) ……….. I few axamples referring to the CRYSTA14 code, that uses a guassian basis set. João Pessoa, 2014

12. Page 13 One of the specific features of solids are the TENSORIAL PROPERTIES that in the liquid or gas phase can be known (measured or calculated ) only as mean values (invariants of the tensor) Many of them can be computed João Pessoa, 2014 • Thttt

13. Page 14 Tensorial Properties of Crystals SSeeccoonndd oorrddeerr TThhiirrdd oorrddeerr FFoouurrtthh oorrddeerr João Pessoa, 2014 ✔ Dielectric ✔ Polarizability ✔ Piezoelectric ✔ First hyperpolarizability ✔ Elastic ✔ Photoelastic ✔ Second hyperpolarizability Maximum number of independent elements according to crystal symmetry: 6 18 21 Minimum number of independent elements according to crystal symmetry: 1 1 3

14. Page 15 Effect of the Crystal Symmetry on Tensors Triclinic Cubic João Pessoa, 2014 Third Order Tensors: Fourth Order Tensors: Cubic Hexagonal Triclinic Hexagonal J. F. Nye, Oxford University Press, (1985)

15. Page 16 Tensorial Properties Related to Crystal Strain Elastic Tensor Piezoelectric Tensor Photoelastic Tensor 4 3 4 Order of the Tensors João Pessoa, 2014 First derivative of the inverse dielectric tensor (difference with respect to the unstrained configuration) with respect to strain First derivative of the polarization P (computed through the Berry phase approach) with respect to the strain Second derivatives of the total energy E with respect to a pair of strains, for a 3D crystal Voigt’s notation is used according to v, u = 1, . . . 6 (1 = xx, 2 = yy, 3 = zz, 4 = yz, 5 =xz, 6 = xy) and i,j =1, 2, 3 (1 = x , 2 = y, 3 = z).

16. Page 17 Tensorial Properties Related to Crystal Strain Elastic Tensor Piezoelectric Tensor Photoelastic Tensor João Pessoa, 2014 Geometry definition ELASTCON [Optional keywords] END END Basis set definition END Comput. Parameters END Geometry definition PIEZOCON [Optional keywords] END END Basis set definition END Comput. Parameters END Geometry definition PHOTOELA [Optional keywords] END END Basis set definition END Comput. Parameters END

17. Page 18 CRYSTAL14: Elastic Properties – The Algorithm Geometry optimization and calculation of the cell gradients of the reference structure Full symmetry analysis and definition of minimal set of strains Application of each strain and calculation of cell gradients of strained configurations, for different strain amplitudes Numerical fitting of analytical gradients with respect to strain and calculation of elastic constants From a posteriori calculations: seismic wave velocities (through Christoffel's equation), bulk, shear and Young moduli. João Pessoa, 2014

18. Page 23 Six Silicate Garnets ✔Garnets constitute a large class of materials of great geological and technological interest ✔ Silicate garnets are among the most important rock-forming minerals ✔ Earth’s lower crust, upper mantle and transition zone ✔ Interest in discussion of different models for Earth's interior ✔ Characterized by a cubic structure with space group Ia3d ✔ 80 atoms per unit cell X3Y2(SiO4)3 Ca3Al2(SiO4)3 Ca3Fe2(SiO4)3 João Pessoa, 2014 Pyraspite Mg3Al2(SiO4)3 Pyrope Fe3Al2(SiO4)3 Almandine Mn3Al2(SiO4)3 Spessartine Grossular Andradite Ca3Cr2(SiO4)3 Uvarovite Ugrandite

19. Page 24 Mg distorted dodecahedra João Pessoa, 2014 Al O Si O O •Cubic Ia-3d •160 atoms in the UC (80 in the primitive) •O general position (48 equivalent) •Mn (24e) Al (16a) Si (24d) site positions tteettrraahheeddrraa ooccttaahheeddrraa Structure of pyrope: Mg3Al2(SiO4)3

20. Page 25 CRYSTAL14: Elastic Properties João Pessoa, 2014 Pyrope--Mg3Al2(SiO4)33 A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4

21. Page 26 CRYSTAL14: Elastic Properties A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4 João Pessoa, 2014 Almandine Spessartine Grossular Andradite Uvarovite

22. Page 27 CRYSTAL14: Elastic Properties From the elastic constants, through Christoffel's equation, seismic wave velocities can be computed: Some elastic properties of an isotropic polycrystalline aggregate can be computed from the elastic and compliance constants defined above via the Voigt-Reuss-Hill averaging scheme: João Pessoa, 2014 Bulk modulus Shear modulus Young modulus Poisson's ratio Anisotropy index The average values of transverse (shear), vs, and longitudinal, vp, seismic wave velocities, for an isotropic polycrystalline aggregate, can be computed

23. Page 28 CRYSTAL14: Elastic Properties Voigt-Reuss-Hill averaging scheme Pyrope Almandine A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4 João Pessoa, 2014 Spessartine Grossular Andradite Uvarovite

24. Page 29 CRYSTAL14: Elastic Properties Directional seismic wave velocities of an andradite single-crystal, as computed ab initio in the present study (continuous lines) and as measured by Brillouin scattering at ambient pressure by Jiang et al (2004) (black symbols). Seismic wave velocities are reported along an azimuthal angle θ defined in the inset. Computed values are down shifted by 0.1 km/s. A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4 João Pessoa, 2014 Andradite-Ca3Fe2(SiO4)3 Vp Vs2 Vs1

25. Page 30 CRYSTAL14: Elastic Properties Pyrope Almandine A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4 João Pessoa, 2014 Spessartine Grossular Andradite Uvarovite

26. Page 31 CRYSTAL14: Elastic Properties Pyrope Almandine Elastic Anisotropy Seismic wave velocity A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals (2013) DOI 10.1007/s00269-013-0630-4 João Pessoa, 2014 Spessartine Grossular Andradite Uvarovite

27. Page 32 Are those calculations expensive? Pyrope Per unit cell João Pessoa, 2014 ✔ 80 atoms ✔ 1488 atomic orbitals ✔ 800 electrons ✔ 48 symmetry operators ✔ Geometry optimization + cell gradients ✔ 2 active deformation (compression, expansion), two geometry optimization + cell gradients each one (cubic crystal symmetry) Reference structure ✔ CPU time: 18146.938 s ≈ 5 h on 256 processors (elastic properties of Pyrope)

28. Page 33 Piezoelectric Properties – The Algorithm Geometry optimization and calculation of the cell gradients of the reference structure Berry phase calculation Full symmetry analysis and definition of minimal set of strains Application of each strain and calculation of cell gradients and Berry phase of strained configurations, for different strain amplitudes Piezoelectric constants are obtained by numerical fitting with respect to the strain João Pessoa, 2014

29. Page 34 Photoelastic Properties – The Algorithm Geometry optimization and calculation of the cell gradients of the reference structure Dielectric tensor calculation through CPHF/KS Full symmetry analysis and definition of minimal set of strains Application of each strain and calculation of cell gradients and the dielectric tensor of strained configurations, for different strain amplitudes Photoelastic constants are obtained by numerical fitting with respect to the strain João Pessoa, 2014

30. Page 35 CRYSTAL14: Piezoelectric and Dielectric Properties ✔ Upon cooling, three consecutive ferroelectric transitions occur starting from the cubic structure, due to the displacement of Ti ions along different crystallographic directions ✔ The resulting macroscopic polarization of the material is always parallel to this displacement 393 K 278 K 183 K João Pessoa, 2014 Temperature ✔ BaTiO3 prototypical ferroelectric oxide ✔ ABO3-type perovskite crystal structure ✔ Advanced technological applications: ✔ capacitor ✔ component of non-linear optical, piezoelectric and energy/data-storage devices. Cubic Tetragonal Orthorhombic Rhomohedral

31. Page 36 CRYSTAL14: Piezoelectric and Dielectric Properties ✔ Two independent dielectric tensor component: є11 and є33 ✔ Computed as a function of the electric field wavelength λ with four different one-electron Hamiltonians ✔ Experimental values at λ = 514.5 nm A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013) João Pessoa, 2014 ✔ (є11 = 6.19 and є33 = 5.88)

32. Page 37 CRYSTAL14: Piezoelectric and Dielectric Properties A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013) João Pessoa, 2014

33. Page 38 CRYSTAL14: Photoelastic Properties ✔ Elasto-optic constants here refer to the λ → ∞ limit ✔ No experimental data are currently available to compare with ✔ From previous studies, we expect the hybrid PBE0 scheme to give the best description of elastic properties and the PBE functional the best description of photoelastic properties ✔ Electronic “clamped-ion” and total “nuclear-relaxed” values are reported A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013) João Pessoa, 2014

34. Page 39 CRYSTAL14: Photoelastic Properties ✔ The three independent elasto-optic constants of MgO, computed at PBE level, as a function of the electric field wavelength λ ✔ p44 is almost wavelength independent ✔ p11 and p12 show a clear dependence from λ ✔ Dashed vertical lines in the figure identify the experimental range of adopted electric field wavelengths A. Erba and R. Dovesi, Phys. Rev. B 88, 045121 (2013) João Pessoa, 2014

35. Page 40 IR and RAMAN spectra Wavenumbers and intensities João Pessoa, 2014

36. Page 41 IR reflectance spectrum Reflectivity is calculated from dielectric constant by means of: João Pessoa, 2014 (θ is the beam incident angle) The dielectric function is obtained with the classical dispersion relation (damped harmonic oscillator):

37. Page 42 Garnets: X3Y2(SiO4)3 X Y Name Mg Al Pyrope Ca Al Grossular Fe Al Almandine Mn Al Spessartine Ca Fe Andradite Ca Cr Uvarovite Space Group: Ia-3d 80 atoms in the primitive cell (240 modes) Γrid = 3A1g + 5A2g + 8Eg + 14 F1g + 14 F2g + 5A1u + 5 A2u+ 10Eu + 18F1u + 16F2u 17 IR (F1u) and 25 RAMAN (A1g, Eg, F2g) active modes João Pessoa, 2014

38. Page 43 The RAMAN spectrum of Pyrope: 25 modes João Pessoa, 2014

39. Page 44 From A1g+Eg wavenumbers... Ours Hofmeister Chopelas Kolesov Sym M υ (cm-1) υ (cm-1) Δυ (cm-1) υ (cm-1) Δυ (cm-1) υ (cm-1) Δυ (cm-1) 1 352.5 362 -10 362 -10 364 -12 A1g 2 564.8 562 3 562 3 563 2 3 926.0 925 1 925 1 928 -2 4 209.2 203 6 203 6 211 -2 5 308.5 309 -1 284 25 6 336.5 342 -6 344 -8 7 376.9 365 12 379 -2 375 2 Eg A 439 439 8 526.6 524 3 524 3 525 2 9 636.0 626 10 626 10 626 10 10 864.4 867 -3 B 911 11 937.4 938 -1 938 -1 945 -8 João Pessoa, 2014 Frequency differences are evaluated with respect to calculated data. Hofmeister: Hofmeister & Chopelas, Phys. Chem. Min., 1991 Chopelas: Chaplin & Price & Ross, Am. Mineral., 1998 Kolesov: Kolesov & Geiger, Phys. Chem. Min., 1998

40. Page 45 ... to RAMAN spectra! João Pessoa, 2014

41. Page 46 And now F2g wavenumbers... Ours Hofmeister Chopelas Kolesov Sym. M υ (cm-1) υ (cm-1) Δυ (cm-1) υ (cm-1) Δυ (cm-1) υ (cm-1) Δυ (cm-1) 12 97.9 - - - - 135 -37 13 170.1 - - - - - - 14 203.7 208 -4 208 -4 212 -8 C 230 230 15 266.9 272 -5 272 -5 - - D 285 16 319 318 1 318 1 322 -3 João Pessoa, 2014 F2g E 342 17 350.6 350 1 350 1 353 -2 18 381.9 379 3 379 3 383 -1 19 492.6 490 3 490 3 492 1 20 513.5 510 4 510 4 512 2 21 605.9 598 8 598 8 598 8 22 655.3 648 7 648 7 650 5 23 861 866 -5 866 -5 871 -10 24 896.7 899 -2 899 -2 902 -5 25 1068.4 1062 6 1062 6 1066 2 B3LYP overstimates the lattice parameter! Frequency differences are evaluated with respect to calculated data. Hofmeister: Hofmeister & Chopelas, Phys. Chem. Min., 1991 Chopelas: Chaplin & Price & Ross, Am. Mineral., 1998 Kolesov: Kolesov & Geiger, Phys. Chem. Min., 1998

42. Page 47 ... and the RAMAN spectra! A1g peaks also in F2g spectrum caused by the presence of different crystal orientations and/or rotation of the polarized light. João Pessoa, 2014

43. Page 48 Grossular LM, R. Demichelis, R. Orlando, M. De La Pierre, A. Mahmoud, R. Dovesi, J. Raman Spectrosc., in press João Pessoa, 2014

44. Page 49 A couple of other examples of RAMAN SPECTRA João Pessoa, 2014

45. Page 50 Jadeite Experimental spectrum from rruff database M. Prencipe, LM, B. Kirtman, S. Salustro, A. Erba, R. Dovesi J. Raman Spectrosc., in press João Pessoa, 2014

46. Page 51 Raman Spectrum of UiO-66 Metal-Organic Framework João Pessoa, 2014 Theory Experiment Exp. spectra from S. Bordiga and collaborators

47. Page 55 IR reflectance spectrum Reflectivity is calculated from dielectric constant by means of: João Pessoa, 2014 (θ is the beam incident angle) The dielectric function is obtained with the classical dispersion relation (damped harmonic oscillator):

48. Page 56 IR reflectance spectrum João Pessoa, 2014 Reflectivity is calculated from dielectric constant by means of: (θ is the beam incident angle) The dielectric function is obtained with the classical dispersion relation: Comparison of computed and experimental IR reflectance spectra for garnets: a) pyrope b) grossular c) almandine .

49. Page 57 IR reflectance spectrum of grossular Computed and experimental IR reflectance spectra of grossular garnet, plus imaginary parts of ε and 1/ε. João Pessoa, 2014

50. Page 58 Garnets: compositional trends João Pessoa, 2014 High frequency modes Dependence on lattice parameter Isotopic substitution on X and Y cations: small dependence Graphical analysis of eigenvectors: • modes 11-14: bending • modes 15-17: stretching

51. Page 59 The isotopic substitution • Changing the mass of one atomic species at a time – Natural isotopic masses – Percentage mass variations – Infinite mass • Hessian re-diagonalization not required (zero computational cost) • Tool for the assignment of the modes and the interpretation of the spectrum João Pessoa, 2014

52. Page 60 Pyrope : 24Mg → 26Mg João Pessoa, 2014 Dn (cm-1) 100 350 n (cm-1) Isotopic shift on the vibrational frequencies of pyrope when 26Mg is substituted for 24Mg.

53. Page 61 Pyrope : 27Al → 29Al Isotopic shift on the vibrational frequencies of pyrope when 29Al is substituted for 27Al. João Pessoa, 2014 Dn (cm-1) 300 700 n (cm-1)

54. Page 62 Pyrope : 28Si → 30Si Isotopic shift on the vibrational frequencies of pyrope when 30Si is substituted for 28Si. João Pessoa, 2014 Dn (cm-1) n (cm-1) 850 1050 250 700 Low ν : rotations and bending of tetrahedra and octahedra (involving by connectivity also Si) High ν: stretching of tetrahedra

55. Page 63 The PPRRAACCEE TTiieerr--00 RReessoouurrcceess HHOORRNNEETT ((HHLLRRSS,, DDEE)) Cray XC30 system - 94,656 cores CCUURRIIEE ((GGEENNCCII,, FFRR)) João Pessoa, 2014 BULL x86 system – 80,640 cores (thin nodes) FFEERRMMII ((CCIINNEECCAA,, IITT)) BlueGene Q system – 163,840 cores SSUUPPEERRMMUUCC ((LLRRZZ,, DDEE)) IBM System x iDataPlex system– 155,656 cores MMAARREENNOOSSTTRRUUMM ((BBSSCC,, SSPP)) IBM System x iDataPlex system– 48,448 cores JJUUQQUUEEEENN ((JJÜÜLLIICCHH,, DDEE)) BlueGene Q system – 458,752 cores

56. Page 64 A model for the MCM-4411 mmeessooppoorroouuss ssiilliiccaa mmaatteerriiaall João Pessoa, 2014 30 Å O Si H Cell: 41x41x12 Å 579 atoms in the unit cell (Si142O335H102) Ordered arrangement of cylindrical pores Pores: mesoporous size (2-10 nm) High surface area: up to 1000 m2g-1 Functionalizable APPLICATIONS Separation - Catalysis – Sensors – Drug Delivery

57. Page 65 Massive parallel performances João Pessoa, 2014 MCM-41 41 Å B3LYP/6-31G(d,p) 579 atoms in the UC, 7756 AO Standard tolerances T-CPU(64) SCF+G 9000 s For diagonalization the empirical rule is N-AO/60 » N-cores IBM Power PC 970MP 2.3 GHz BSC MN

58. Page 66 MPPCRYSTAL: Memory Usage Memory occupation peak in the SCF calculation of different supercells of the mesoporous silica MCM-41, with a 6-31G** basis set and B3LYP functional. The single unit cell (X1) contains 579 atoms and 7756 atomic orbitals. The largest cell (X12) contains 6948 atoms and 93072 atomic orbitals. João Pessoa, 2014 X1 X12 X8 X4 X2

59. Page 68 MPPCRYSTAL: Time Scaling •Scaling of computational time required for a complete SCF (13 cycles) with the size of the MCM-41 supercell, •on 1024 processors at SUPERMUC (Munich). João Pessoa, 2014 •X1 •X8 • •X4 X2 •X12

60. Page 71 CCRRAAMMBBIINN João Pessoa, 2014 Crambin is a small seed storage protein from the Abyssinian cabbage. It belongs to thionins. It has 46 aminoacids (642 atoms). Primary structure: Secondary structure: RANDOM COIL N-term C-term α-HELIX A β-SHEET α-HELIX B

61. Page 72 AB-INITIO PPRROOTTEEIINN OOPPTTIIMMIIZZAATTIIOONN Geometry FULLY optimized at the B3LYP-D*/6-31d level of theory with CRYSTAL14. João Pessoa, 2014 B3LYP-D* Experimental RMSD (backbone) 0.668 Å AVERAGE OPTIMIZATION STEP ON 640 CPUs* 323 seconds *SuperMUC (LRZ, Munich) Notes: -Crystallographic structure has a 30% solvent content (v/v). -Nakata et al., who optimized crambin using the Fragment Molecular Orbital method (HF/6-31d) with the polarizable continuum model, report a RMSD of 0.525 Å with respect to PDB structure 1CRN.

62. Page 73 AB-INITIO PROTEIN IINNFFRRAARREEDD SSPPEECCTTRRUUMM The FULL vibrational spectrum is computed at the B3LYP-D*/6-31d level of theory João Pessoa, 2014 AMIDE I AMIDE II AMIDE I: C=O stretching (backbone) AMIDE II: N-H bending and C-N stretching (backbone) TOTAL TIME ON 1024 CPUs* 222 hours *SuperMUC (LRZ, Munich)

63. Page 74 ELECTROSTATIC POTENTIAL MAPPED OONN TTHHEE BB33LLYYPP DDEENNSSIITTYY João Pessoa, 2014 Isovalue: 10-4 e 200x200x200 grid TOTAL TIME ON 256 CPUs* < 1 minute *SuperMUC (LRZ, Munich)

64. Page 75 AB-INITIO PROTEIN OPTIMIZATION –– CCRRYYSSTTAALL SSTTRRUUCCTTUURREE João Pessoa, 2014 FULL optimization (B3LYP-D*/6-31d) AVERAGE OPTIMIZATION STEP ON 640 CPUs* 1064 seconds *SuperMUC (LRZ, Munich) CELL VOLUME: -10% with respect to the experimental structure** **Crystallographic experimental structure has a 30% solvent content (v/v). Here water was removed. P21 - 1284 total atoms / 642 irreducible atoms

65. Page 76 Ab initio mmooddeelllliinngg ooff ggiiaanntt MMOOFFss:: wwhheenn tthhee ssiizzee mmaatttteerrss Comparison between the crystallographic unit cells of the giant MIL-100 and MOF-5 João Pessoa, 2014 MMIILL--110000(MM) MMOOFF--55 PRACE Grant: Project 2013081680 M204X68O68[(C6H3)-(CO2)3]204 2788 atoms (primitive u.c.) M= Al, Sc, Cr, Fe (Zn4O)2[(C6H4)-(CO2)2]6 106 atoms (primitive u.c.)

66. Page 77 Al MIL-100(Al)--NN:: MMPPPP--CCRRYYSSTTAALL SSccaalliinngg Running time scaling with the number of computing cores for MIL-100(Al)-N (2720 atoms) on the SuperMUC HPC system. João Pessoa, 2014 Timings on 1024 cores: • one SCF cycle = 767 sec • Gradient (atoms) = 1801 sec MIL-100(Al)-N is a model system in which a N atom substitutes the O at the center of the inorganic unit. It consists of a primitive unit cell containing 2720 atoms without symmetry. B3LYP calculation with 44606 AOs in the unit cell. Speedup=T1024 /TnCPUs 94% 86% PRACE Grant: Project 2013081680 Calculations run on SUPERMUC at LRZ: HPC IBM System x iDataPlex powered by 16 Intel cores per node running at 2.7 GHz, with 2 GB/core

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