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Page 1 
João Pessoa, 2014 
Roberto DovesiOn the role of quantum mechanical simulation in materials science
Page 2 
João Pessoa, 2014 
Is simulation useful? Does it produce reasonable numbers? Or can only try to reproduce the expe...
Page 3 
João Pessoa, 2014 
In the year 1960-1990, calculations for the structural properties of periodic compounds ( oxide...
Page 4 
João Pessoa, 2014 
How many transistors on a chip? 
Inteli7 Sandy bridge 32nm 
2.27 billions of transistors 434 mm...
Page 5 
João Pessoa, 2014 
Performance of HPC
Page 7 
João Pessoa, 2014 
DFT & Kohn-Sham 
•“Density Functional Theory (DFT) is an incredible success story” * 
•DFT has ...
Page 8 
João Pessoa, 2014 
Is simulation expensive? The last computer we bought…. 
Server Supermicro 64 COREOPTERONeuros 6...
Page 9 
João Pessoa, 2014 
At the other extreme:SUPERCOMPUTERSAvailable, but: 
a)Theyare fragile 
b)Notso muchstandard (co...
Page 10 
João Pessoa, 2014 
The PRACE Tier-0 Resources 
HORNET (HLRS, DE) 
Cray XC30 system -94,656 cores 
CURIE (GENCI, F...
Page 11 
João Pessoa, 2014CRYSTAL parallelversions: MPPcrystalMPPcrystal 
–Distributed data 
–Each processor hold only a p...
Page 12 
João Pessoa, 2014 
The software must be 
a)Easy to use (freindly) 
b)Robust, 
c)Protected 
d)Documented 
e)Genera...
Page 13 
João Pessoa, 2014 
One of the specific features of solids are the 
TENSORIAL PROPERTIES 
that in the liquid or ga...
Page 14 
João Pessoa, 2014 
Tensorial Properties of Crystals 
Second order 
Third order 
Fourth order 
✔Dielectric 
✔Polar...
Page 15 
João Pessoa, 2014Effect of the Crystal Symmetry on TensorsCubic 
Triclinic 
Third Order Tensors: 
Fourth Order Te...
Page 16 
João Pessoa, 2014Tensorial Properties Related to Crystal Strain 
Elastic Tensor 
Piezoelectric TensorPhotoelastic...
Page 17 
João Pessoa, 2014 
Geometry definitionELASTCON[Optional keywords] ENDENDBasis set definitionENDComput. Parameters...
Page 18 
João Pessoa, 2014Geometry optimization and calculation of the cell gradients of the reference structure 
Full sym...
Page 23 
João Pessoa, 2014Six Silicate Garnets 
✔Garnetsconstitute a large class of materials of great geological and tech...
Page 24 
João Pessoa, 2014 
Mg 
AlOSi 
O 
O 
•Cubic Ia-3d 
•160 atoms in the UC (80 in the primitive) 
•O general position...
Page 25 
João Pessoa, 2014 
CRYSTAL14: Elastic Properties 
Pyrope-Mg3Al2(SiO4)3A. Erba, A. Mahmoud, R. Orlando and R. Dove...
Page 26 
João Pessoa, 2014 
A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-0...
Page 27 
João Pessoa, 2014 
CRYSTAL14: Elastic Properties 
From the elastic constants, through Christoffel's equation, sei...
Page 28 
João Pessoa, 2014 
A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) 
DOI 10.1007/s00269-...
Page 29 
João Pessoa, 2014 
A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) 
DOI 10.1007/s00269-...
Page 30 
João Pessoa, 2014 
A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) 
DOI 10.1007/s00269-...
Page 31 
João Pessoa, 2014A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013...
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João Pessoa, 2014 
Are those calculations expensive? 
✔80atoms 
✔1488atomic orbitals 
✔800electrons 
✔48symmetry ...
Page 33 
João Pessoa, 2014 
Geometry optimization and calculation of the cell gradients of the reference structure 
Full s...
Page 34 
João Pessoa, 2014 
Geometry optimization and calculation of the cell gradients of the reference structure 
Full s...
Page 35 
João Pessoa, 2014 
CRYSTAL14: Piezoelectric and Dielectric Properties 
393 K 
278 K 
183 K 
Temperature 
✔BaTiO3p...
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João Pessoa, 2014 
CRYSTAL14: Piezoelectric and Dielectric Properties 
A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. ...
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João Pessoa, 2014 
CRYSTAL14: Piezoelectric and Dielectric Properties 
A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. ...
Page 38 
João Pessoa, 2014 
CRYSTAL14: Photoelastic Properties 
A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orl...
Page 39 
João Pessoa, 2014 
CRYSTAL14: Photoelastic Properties 
A. Erba and R. Dovesi, Phys. Rev. B 88,045121 (2013) 
✔The...
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João Pessoa, 2014 
IR and RAMAN spectraWavenumbers and intensities
Page 41 
João Pessoa, 2014 
Reflectivityis calculated from dielectric constant by means of: (θ is the beam incident angle)...
Page 42 
João Pessoa, 2014 
Garnets: X3Y2(SiO4)3 
Space Group: Ia-3d 
80 atoms in the primitive cell (240 modes) 
Γrid= 3A...
Page 43 
João Pessoa, 2014 
25 modes 
The RAMAN spectrum of Pyrope:
Page 44 
João Pessoa, 2014 
From A1g+Egwavenumbers... 
Ours 
Hofmeister 
Chopelas 
Kolesov 
Sym 
M 
υ(cm-1) 
υ(cm-1) 
Δυ(c...
Page 45 
João Pessoa, 2014 
... to RAMAN spectra!
Page 46 
João Pessoa, 2014 
And now F2gwavenumbers... 
Ours 
Hofmeister 
Chopelas 
Kolesov 
Sym. 
M 
υ(cm-1) 
υ(cm-1) 
Δυ(...
Page 47 
João Pessoa, 2014 
... and the RAMAN spectra! 
A1g peaks also in F2g spectrum caused by the presence of different...
Page 48 
João Pessoa, 2014 
Grossular 
LM, R. Demichelis, R. Orlando, M. De La Pierre, A. Mahmoud, R. Dovesi, J. Raman Spe...
Page 49 
João Pessoa, 2014 
A couple of other examples of RAMAN SPECTRA
Page 50 
João Pessoa, 2014Jadeite 
Experimental spectrum from rruff database 
M. Prencipe, LM, B. Kirtman, S. Salustro, A....
Page 51 
João Pessoa, 2014 
Raman Spectrum of UiO-66 Metal-Organic Framework 
Theory 
Experiment 
Exp. spectra from S. Bor...
Page 55 
João Pessoa, 2014 
Reflectivityis calculated from dielectric constant by means of: 
(θ is the beam incident angle...
Page 56 
João Pessoa, 2014 
IR reflectance spectrum 
Reflectivityis calculated from dielectric constant by means of: 
(θis...
Page 57 
João Pessoa, 2014IR reflectance spectrum of grossularComputedandexperimentalIRreflectancespectraofgrossulargarnet...
Page 58 
João Pessoa, 2014High frequency modesDependenceon lattice parameterIsotopic substitution on X and Y cations: smal...
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João Pessoa, 2014 
•Changing the mass of one atomic species at a time 
–Natural isotopic masses 
–Percentage mass...
Page 60 
João Pessoa, 2014(cm-1) (cm-1) 
100 
350Pyrope : 24Mg →26MgIsotopic shift on the vibrational frequencies of pyrop...
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João Pessoa, 2014 
Isotopic shift on the vibrational frequencies of pyrope when 29Al is substituted for 27Al. (cm...
Page 62 
João Pessoa, 2014 
Isotopic shift on the vibrational frequencies of pyrope when 30Si is substituted for 28Si. (cm...
Page 63 
João Pessoa, 2014 
The PRACE Tier-0 ResourcesHORNET (HLRS, DE) Cray XC30 system -94,656 cores 
CURIE (GENCI, FR) ...
Page 64 
João Pessoa, 2014 
A model for the MCM-41 mesoporous silica material 
O 
Si 
H 
Cell: 41x41x12 Å 
579 atoms in th...
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João Pessoa, 2014 
B3LYP/6-31G(d,p) 
579 atoms in the UC, 7756 AO 
Standard tolerances 
41 Å 
T-CPU(64) SCF+G 900...
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João Pessoa, 2014 
MPPCRYSTAL: Memory Usage 
Memory occupation peak in the SCF calculation of different supercell...
Page 68 
João Pessoa, 2014 
MPPCRYSTAL: Time Scaling 
•Scaling of computational time required for a complete SCF (13 cycle...
Page 71 
João Pessoa, 2014 
CRAMBIN 
Crambin is a small seed storage protein from the Abyssinian cabbage. It belongs to th...
Page 72 
João Pessoa, 2014AB-INITIO PROTEIN OPTIMIZATIONGeometry FULLY optimized at the B3LYP-D*/6-31d level of theory wit...
Page 73 
João Pessoa, 2014 
AB-INITIO PROTEIN INFRARED SPECTRUM 
The FULL vibrational spectrum is computed at the B3LYP-D*...
Page 74 
João Pessoa, 2014 
ELECTROSTATIC POTENTIAL MAPPED ON THE B3LYP DENSITY 
Isovalue: 10-4e 
200x200x200 gridTOTAL TI...
Page 75 
João Pessoa, 2014AB-INITIO PROTEIN OPTIMIZATION –CRYSTAL STRUCTURE 
FULL optimization 
(B3LYP-D*/6-31d) 
**Crysta...
Page 76 
João Pessoa, 2014Ab initio modelling of giantMOFs: when the size mattersMIL-100(M) 
MOF-5 
Comparison between the...
Page 77 
João Pessoa, 2014Running time scaling with the number of computing cores for MIL-100(Al)-N (2720 atoms) on the Su...
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On the role of quantum mechanical simulation in materials science.

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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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On the role of quantum mechanical simulation in materials science.

  1. 1. Page 1 João Pessoa, 2014 Roberto DovesiOn the role of quantum mechanical simulation in materials science
  2. 2. Page 2 João Pessoa, 2014 Is simulation useful? Does it produce reasonable numbers? Or can only try to reproduce the experiments? Connected question: Is simulation expensive?
  3. 3. Page 3 João Pessoa, 2014 In the year 1960-1990, calculations for the structural properties of periodic compounds ( oxides, halides, ..) were performed at the semi-classicalor 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
  4. 4. Page 4 João Pessoa, 2014 How many transistors on a chip? Inteli7 Sandy bridge 32nm 2.27 billions of transistors 434 mm2 GPU NVIDIA GK110 28nm 7.1billions of transistors Gordon Moore The numberoftransistorsper chip doublesevery18 months
  5. 5. Page 5 João Pessoa, 2014 Performance of HPC
  6. 6. Page 7 João Pessoa, 2014 DFT & Kohn-Sham •“Density Functional Theory (DFT) is an incredible success story” * •DFT has enable to tackle complex problems with an accuracy unobtainable by any other approach •DFT methods has now been applied to chemistry, materials science, solid-state physics, but also geology, mineralogy and biology. •Kohn-Sham formalism *fromK.BurkePerspectiveonDensityFunctionalTheoryJCP136(2012)150901
  7. 7. Page 8 João Pessoa, 2014 Is simulation expensive? The last computer we bought…. Server Supermicro 64 COREOPTERONeuros 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……..
  8. 8. Page 9 João Pessoa, 2014 At the other extreme:SUPERCOMPUTERSAvailable, but: a)Theyare fragile b)Notso muchstandard (compiler, libreries) c) The software (thatisalwayslate withrespecttohardware) MUST BE ABLE TO EXPLOIT thishugepower
  9. 9. Page 10 João Pessoa, 2014 The PRACE Tier-0 Resources HORNET (HLRS, DE) Cray XC30 system -94,656 cores CURIE (GENCI, FR) BULL x86 system –80,640 cores (thin nodes) FERMI (CINECA, IT) BlueGeneQ system –163,840 cores SUPERMUC (LRZ, DE) IBM System x iDataPlexsystem–155,656 coresMARENOSTRUM (BSC, SP) IBM System x iDataPlexsystem–48,448 cores JUQUEEN (JÜLICH, DE) BlueGeneQ system –458,752 cores
  10. 10. Page 11 João Pessoa, 2014CRYSTAL parallelversions: MPPcrystalMPPcrystal –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. 11. Page 12 João Pessoa, 2014 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.
  12. 12. Page 13 João Pessoa, 2014 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 •Thttt
  13. 13. Page 14 João Pessoa, 2014 Tensorial Properties of Crystals Second order Third order Fourth order ✔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 13
  14. 14. Page 15 João Pessoa, 2014Effect of the Crystal Symmetry on TensorsCubic Triclinic Third Order Tensors: Fourth Order Tensors: CubicHexagonalTriclinicHexagonalJ. F. Nye, Oxford University Press, (1985)
  15. 15. Page 16 João Pessoa, 2014Tensorial Properties Related to Crystal Strain Elastic Tensor Piezoelectric TensorPhotoelastic TensorOrder of the Tensors 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 Ewith respect to a pair of strains, for a 3D crystal Voigt’snotationisusedaccordingtov,u=1,...6(1=xx,2=yy,3=zz,4=yz,5=xz,6=xy)andi,j=1,2,3(1=x,2=y,3=z). 434
  16. 16. Page 17 João Pessoa, 2014 Geometry definitionELASTCON[Optional keywords] ENDENDBasis set definitionENDComput. ParametersENDTensorial Properties Related to Crystal StrainElastic TensorPiezoelectric Tensor Photoelastic TensorGeometry definitionPIEZOCON[Optional keywords] ENDENDBasis set definitionENDComput. ParametersENDGeometry definitionPHOTOELA[Optional keywords] ENDENDBasis set definitionENDComput. ParametersEND
  17. 17. Page 18 João Pessoa, 2014Geometry 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 CRYSTAL14: Elastic Properties –The Algorithm Numerical fitting of analytical gradients with respect to strain and calculation of elastic constants From a posterioricalculations: seismic wave velocities (through Christoffel's equation), bulk, shearand Young moduli.
  18. 18. Page 23 João Pessoa, 2014Six Silicate Garnets ✔Garnetsconstitute 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 structurewith space groupIa3d ✔80 atomsper unit cellPyraspiteMg3Al2(SiO4)3 Pyrope Fe3Al2(SiO4)3AlmandineMn3Al2(SiO4)3 Spessartine Grossular Ca3Al2(SiO4)3 Ca3Fe2(SiO4)3 Andradite Ca3Cr2(SiO4)3 Uvarovite UgranditeX3Y2(SiO4) 3
  19. 19. Page 24 João Pessoa, 2014 Mg AlOSi 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 distorted dodecahedra tetrahedra octahedra Structure of pyrope: Mg3Al2(SiO4)3
  20. 20. Page 25 João Pessoa, 2014 CRYSTAL14: Elastic Properties Pyrope-Mg3Al2(SiO4)3A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4
  21. 21. Page 26 João Pessoa, 2014 A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4 CRYSTAL14: Elastic Properties Almandine Spessartine Grossular Andradite Uvarovite
  22. 22. Page 27 João Pessoa, 2014 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: Bulk modulus Shear modulus Young modulusPoisson'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. 23. Page 28 João Pessoa, 2014 A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4Voigt-Reuss-Hill averaging scheme CRYSTAL14: Elastic Properties Spessartine Grossular Andradite Uvarovite Almandine Pyrope
  24. 24. Page 29 João Pessoa, 2014 A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4 CRYSTAL14: Elastic Properties Andradite- Ca3Fe2(SiO4)3 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. Vp Vs2 Vs1
  25. 25. Page 30 João Pessoa, 2014 A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4 CRYSTAL14: Elastic Properties Spessartine Grossular Andradite Uvarovite Almandine Pyrope
  26. 26. Page 31 João Pessoa, 2014A. Erba, A. Mahmoud, R. Orlando and R. Dovesi, Phys. Chem. Minerals(2013) DOI 10.1007/s00269-013-0630-4 CRYSTAL14: Elastic Properties Spessartine Grossular Andradite Uvarovite Almandine Pyrope Elastic Anisotropy Seismic wave velocity
  27. 27. Page 32 João Pessoa, 2014 Are those calculations expensive? ✔80atoms ✔1488atomic orbitals ✔800electrons ✔48symmetry operators ✔Geometry optimization + cell gradients ✔2 active deformation (compression, expansion), two geometry optimization + cell gradients each one (cubic crystal symmetry) ✔CPU time: 18146.938 s ≈5 hon 256processors (elastic properties of Pyrope) Per unit cell Pyrope Reference structure
  28. 28. Page 33 João Pessoa, 2014 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 and Berry phaseof strained configurations, for different strain amplitudes Piezoelectric Properties –The Algorithm Berry phasecalculation Piezoelectric constantsare obtained by numerical fitting with respect to the strain
  29. 29. Page 34 João Pessoa, 2014 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 and thedielectric tensor of strained configurations, for different strain amplitudes Photoelastic Properties –The Algorithm Dielectric tensorcalculation through CPHF/KS Photoelastic constantsare obtained by numerical fitting with respect to the strain
  30. 30. Page 35 João Pessoa, 2014 CRYSTAL14: Piezoelectric and Dielectric Properties 393 K 278 K 183 K Temperature ✔BaTiO3prototypical 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 ✔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 polarizationof thematerial is always parallel to this displacement
  31. 31. Page 36 João Pessoa, 2014 CRYSTAL14: Piezoelectric and Dielectric Properties A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013) ✔Two independent dielectric tensorcomponent: є11and є33 ✔Computed as a function of the electric field wavelength λ with four different one-electron Hamiltonians ✔Experimental values atλ = 514.5 nm ✔(є11 = 6.19 and є33= 5.88)
  32. 32. Page 37 João Pessoa, 2014 CRYSTAL14: Piezoelectric and Dielectric Properties A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013)
  33. 33. Page 38 João Pessoa, 2014 CRYSTAL14: Photoelastic Properties A. Mahmoud, A. Erba, Kh. E. El-Kelany, M. Rérat and R. Orlando, Phys. Rev. B (2013) ✔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
  34. 34. Page 39 João Pessoa, 2014 CRYSTAL14: Photoelastic Properties A. Erba and R. Dovesi, Phys. Rev. B 88,045121 (2013) ✔The three independent elasto-optic constants of MgO, computed at PBE level, as a function of the electric field wavelength λ ✔p44is almost wavelength independent ✔p11and p12show a clear dependence from λ ✔Dashed vertical lines in the figure identify the experimental range ofadopted electric field wavelengths
  35. 35. Page 40 João Pessoa, 2014 IR and RAMAN spectraWavenumbers and intensities
  36. 36. Page 41 João Pessoa, 2014 Reflectivityis calculated from dielectric constant by means of: (θ is the beam incident angle) The dielectric function is obtained with the classical dispersion relation(damped harmonic oscillator): IR reflectance spectrum
  37. 37. Page 42 João Pessoa, 2014 Garnets: X3Y2(SiO4)3 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 X Y Name Mg Al Pyrope Ca Al Grossular Fe Al Almandine Mn Al Spessartine Ca Fe Andradite Ca Cr Uvarovite
  38. 38. Page 43 João Pessoa, 2014 25 modes The RAMAN spectrum of Pyrope:
  39. 39. Page 44 João Pessoa, 2014 From A1g+Egwavenumbers... 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 Frequencydifferencesareevaluatedwithrespecttocalculateddata. Hofmeister:Hofmeister& Chopelas,Phys.Chem. Min.,1991 Chopelas:Chaplin&Price&Ross,Am.Mineral., 1998 Kolesov:Kolesov& Geiger,Phys.Chem.Min., 1998
  40. 40. Page 45 João Pessoa, 2014 ... to RAMAN spectra!
  41. 41. Page 46 João Pessoa, 2014 And now F2gwavenumbers... 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 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 Frequencydifferencesareevaluatedwithrespecttocalculateddata. Hofmeister:Hofmeister& Chopelas,Phys.Chem. Min.,1991 Chopelas:Chaplin&Price&Ross,Am.Mineral., 1998 Kolesov:Kolesov& Geiger,Phys.Chem.Min., 1998 B3LYP overstimatesthe lattice parameter!
  42. 42. Page 47 João Pessoa, 2014 ... 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.
  43. 43. Page 48 João Pessoa, 2014 Grossular LM, R. Demichelis, R. Orlando, M. De La Pierre, A. Mahmoud, R. Dovesi, J. Raman Spectrosc., in press
  44. 44. Page 49 João Pessoa, 2014 A couple of other examples of RAMAN SPECTRA
  45. 45. Page 50 João Pessoa, 2014Jadeite Experimental spectrum from rruff database M. Prencipe, LM, B. Kirtman, S. Salustro, A. Erba, R. Dovesi J. Raman Spectrosc., in press
  46. 46. Page 51 João Pessoa, 2014 Raman Spectrum of UiO-66 Metal-Organic Framework Theory Experiment Exp. spectra from S. Bordiga and collaborators
  47. 47. Page 55 João Pessoa, 2014 Reflectivityis calculated from dielectric constant by means of: (θ is the beam incident angle) The dielectric function is obtained with the classical dispersion relation (damped harmonic oscillator): IR reflectance spectrum
  48. 48. Page 56 João Pessoa, 2014 IR reflectance spectrum Reflectivityis calculated from dielectric constant by means of: (θis 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. 49. Page 57 João Pessoa, 2014IR reflectance spectrum of grossularComputedandexperimentalIRreflectancespectraofgrossulargarnet,plusimaginarypartsofεand1/ε.
  50. 50. Page 58 João Pessoa, 2014High frequency modesDependenceon lattice parameterIsotopic substitution on X and Y cations: small dependenceGraphical analysis of eigenvectors: •modes 11-14: bending •modes 15-17: stretching Garnets: compositional trends
  51. 51. Page 59 João Pessoa, 2014 •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 The isotopic substitution
  52. 52. Page 60 João Pessoa, 2014(cm-1) (cm-1) 100 350Pyrope : 24Mg →26MgIsotopic shift on the vibrational frequencies of pyrope when 26Mg is substituted for 24Mg.
  53. 53. Page 61 João Pessoa, 2014 Isotopic shift on the vibrational frequencies of pyrope when 29Al is substituted for 27Al. (cm-1) (cm-1) 300 700 Pyrope : 27Al →29Al
  54. 54. Page 62 João Pessoa, 2014 Isotopic shift on the vibrational frequencies of pyrope when 30Si is substituted for 28Si. (cm-1) (cm-1) 850 1050 Pyrope : 28Si →30Si 250 700 Low ν : rotations and bending of tetrahedra and octahedra (involving by connectivity also Si) High ν: stretching of tetrahedra
  55. 55. Page 63 João Pessoa, 2014 The PRACE Tier-0 ResourcesHORNET (HLRS, DE) Cray XC30 system -94,656 cores CURIE (GENCI, FR) BULL x86 system –80,640 cores (thin nodes) FERMI (CINECA, IT) BlueGeneQ system –163,840 cores SUPERMUC (LRZ, DE) IBM System x iDataPlexsystem–155,656 cores MARENOSTRUM (BSC, SP) IBM System x iDataPlexsystem–48,448 cores JUQUEEN (JÜLICH, DE) BlueGeneQ system –458,752 cores
  56. 56. Page 64 João Pessoa, 2014 A model for the MCM-41 mesoporous silica material 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 FunctionalizableAPPLICATIONSSeparation -Catalysis –Sensors –Drug Delivery
  57. 57. Page 65 João Pessoa, 2014 B3LYP/6-31G(d,p) 579 atoms in the UC, 7756 AO Standard tolerances 41 Å T-CPU(64) SCF+G 9000 s For diagonalizationthe empirical rule is N-AO/60 N-cores Massive parallel performances MCM-41 IBM Power PC 970MP 2.3 GHz BSC MN
  58. 58. Page 66 João Pessoa, 2014 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. X1 X12 X8 X4 X2
  59. 59. Page 68 João Pessoa, 2014 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). •X1 •X8 •X4 •X2 •X12
  60. 60. Page 71 João Pessoa, 2014 CRAMBIN 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: N-term C-term α-HELIX Aα-HELIX Bβ-SHEETRANDOM COIL
  61. 61. Page 72 João Pessoa, 2014AB-INITIO PROTEIN OPTIMIZATIONGeometry FULLY optimized at the B3LYP-D*/6-31d level of theory with CRYSTAL14. B3LYP-D* Experimental RMSD (backbone) 0.668 Å 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. AVERAGE OPTIMIZATION STEP ON 640 CPUs* 323 seconds *SuperMUC (LRZ, Munich)
  62. 62. Page 73 João Pessoa, 2014 AB-INITIO PROTEIN INFRARED SPECTRUM The FULL vibrational spectrum is computed at the B3LYP-D*/6-31d level of theory 3500 3000 2500 2000 1500 1000 500 0 Wavenumber (cm-1) 1900 1850 1800 1750 1700 1650 1600 1550 1500 1450 1400 Wavenumber (cm-1) 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. 63. Page 74 João Pessoa, 2014 ELECTROSTATIC POTENTIAL MAPPED ON THE B3LYP DENSITY Isovalue: 10-4e 200x200x200 gridTOTAL TIME ON 256 CPUs* < 1 minute *SuperMUC (LRZ, Munich)
  64. 64. Page 75 João Pessoa, 2014AB-INITIO PROTEIN OPTIMIZATION –CRYSTAL STRUCTURE FULL optimization (B3LYP-D*/6-31d) **Crystallographic experimental structure has a 30% solvent content (v/v). Here water was removed. AVERAGE OPTIMIZATION STEP ON 640 CPUs* 1064 seconds*SuperMUC (LRZ, Munich) CELL VOLUME: -10% with respect to the experimental structure** P21-1284 total atoms / 642 irreducible atoms
  65. 65. Page 76 João Pessoa, 2014Ab initio modelling of giantMOFs: when the size mattersMIL-100(M) MOF-5 Comparison between the crystallographic unit cells of the giantMIL-100 and MOF-5PRACE Grant: Project 2013081680 M204X68O68[(C6H3)-(CO2)3]204 2788 atoms (primitive u.c.) M= Al, Sc, Cr, Fe 106 atoms (primitive u.c.) (Zn4O)2[(C6H4)-(CO2)2]6
  66. 66. Page 77 João Pessoa, 2014Running time scaling with the number of computing cores for MIL-100(Al)-N (2720 atoms) on the SuperMUC HPC system. 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. MIL-100(Al)-N: MPP-CRYSTAL ScalingB3LYP calculation with 44606 AOs in the unit cell. Speedup=T1024/TnCPUs 94% 86% PRACE Grant: Project 2013081680 Calculations run on SUPERMUCat LRZ: HPC IBM System x iDataPlex powered by 16 Intel cores per node running at 2.7 GHz, with 2 GB/core
  • RaghaviHm

    Nov. 26, 2019
  • AshishManwar

    Nov. 5, 2017
  • Guidigui

    Nov. 10, 2014

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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