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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João Pessoa, 2014
Roberto DovesiOn the role of quantum mechanical simulation in materials science

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Is simulation useful? Does it produce reasonable numbers? Or can only try to reproduce the experiments?
Connected question:
Is simulation expensive?

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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

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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

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Performance of HPC

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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

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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……..

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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

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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

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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

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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.

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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

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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

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João Pessoa, 2014Effect of the Crystal Symmetry on TensorsCubic
Triclinic
Third Order Tensors:
Fourth Order Tensors:
CubicHexagonalTriclinicHexagonalJ. F. Nye, Oxford University Press, (1985)

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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

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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

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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

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IR and RAMAN spectraWavenumbers and intensities

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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

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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

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25 modes
The RAMAN spectrum of Pyrope:

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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

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... to RAMAN spectra!

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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!

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... 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.

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Grossular
LM, R. Demichelis, R. Orlando, M. De La Pierre, A. Mahmoud, R. Dovesi, J. Raman Spectrosc., in press

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A couple of other examples of RAMAN SPECTRA

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

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Raman Spectrum of UiO-66 Metal-Organic Framework
Theory
Experiment
Exp. spectra from S. Bordiga and collaborators

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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

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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 .

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João Pessoa, 2014IR reflectance spectrum of grossularComputedandexperimentalIRreflectancespectraofgrossulargarnet,plusimaginarypartsofεand1/ε.

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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

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•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

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

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Isotopic shift on the vibrational frequencies of pyrope when 29Al is substituted for 27Al. (cm-1) (cm-1)
300
700
Pyrope : 27Al →29Al

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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

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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

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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

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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 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

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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

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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

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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

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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)

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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)

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ELECTROSTATIC POTENTIAL MAPPED ON THE B3LYP DENSITY
Isovalue: 10-4e
200x200x200 gridTOTAL TIME ON 256 CPUs* < 1 minute
*SuperMUC (LRZ, Munich)

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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

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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

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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