Grid computing applications in modeling and simulations of molecular nanomagnets and classical charged particles

Michał Antkowiak

Faculty of Physics, A. Mickiewicz University, Poznań, PolandEuropean Institute of Molecular Magnetism, Florence, Italy

P. Sobczak, G. Musiał, G. Kamieniarz, B. Błaszkiewicz

Outline

Molecular nanomagnets Classical charged particles PEARL-AMU site

Molecular nanomagnets

• Quantum molecular rings

• Spin models and thermodynamic quantities

• Exact Diagonalization Technique

• Results for Cr – based rings

Cr8

(Cr8F8Piv16)

Cr9

[Pr2NH2][Cr9F9Cl2(Piv)17]

Cr7Cd

[(CH3)2NH2][Cr7CdF8{OOCC(CH3)3}16]

)sincos()(

)( =

B2

1||111=

xj

zj

zj

zj

zj

yj

yj

xj

xj

n

j

ssBgsD

ssJssssJ

H

Sj - spin operators (s=3/2)n – number of sitesB – magnetic field

The quantum molecular rings model

θ

HB TreZZTkF ,ln

BTBTB

F

T

FTC

F

-S ,,2

2

2

2

222 )()( zzBz SSg

•Free energy

•Specific heat C, susceptibility χ and entropy S as derivatives of the free energy

•Specific heat C and susceptibility χz as functions of the spin moments

Thermodynamic quantities

Exact diagonalization technique

•Size of the Hamiltonian matrix• Cr8: 48 x 48 (65536 x 65536 = 32GB)• Cr9: 49 x 49 (262144 x 262144 = 512GB)

•For θ=0• quasi diagonal form of the Hamiltonian• matrix blocks labeled by

• eigenvalues M of Sz

• Symmetry (a) of the eigenstate• Cr8: 48 blocks (max. size: 4068 x 4068 = 0.12GB)• Cr9: 52 blocks (max. size: 15180 x 15180 = 1.7GB)

•For θ≠0 -> only 2 blocks labeled by symmetry

Sizes of the Hamiltonian matrix blocks (Cr8)

Parallel programming tasks and models

MPI library Master-slave model Star-like

LPT algorithm

Processing times for different blocks (Cr8)

Speedup (Cr8) u = tseq/tpar

Efficiency (Cr8) E = u/p

Limited scalability

Results

Magnetisation Cr7Cd

Susceptibility

Susceptibility Cr7Cd

Susceptibility

Classical charged particles

• Subject of the research

• Models

• Genetic algorithm

• Results

Subject of the research

2D system Coulomb potential (1), 9≤N≤30 Logarithmic potential (2), 9≤N≤30

3D system Coulomb potential (1), 17≤N≤70 Logarithmic potential (2), 10≤N≤50

N

=i

N

=i

N

+ij= ji

jii

rr

qq+r=U

1

1

1 1

2

N

=i

N

=i

N

+ij= ji

jii

rr

qq+r=U

1

1

1 1

2 ln2(1) (2)

Uniform particles: qi = qj = 1

The classical charged particles models

2D system One chromosome = one solution One gene = one coordinate (x or y).

x1

x2

… xN Chromosome

y1

y2

… yN gene

Genetic algorithm method

Ns (generations): 106 - 107

S (chromosomes): 200 – 500Pc (crossing probability): 0.1 - 0.9Pm (mutation probability): 0.02 – 0.2

N=302D system results

N=302D system results

Ground-state configuration Metastable state configuration

Higher symmetry = lower energy

Conclusions

Despite more and more advanced algorithmslarge computing resources are still needed

More complicated systems = more computing resources(both quantum and classical)(ED – higher scalability)

Grid resources improve computational infrastructure and enable simulations of more complicated systems

G. Kamieniarz W. FlorekG. MusiałL. DębskiP. KozłowskiK. PacerD. TomeckaP. SobczakP. GąbkaL. KaliszanM. HaglauerT. ŚlusarskiB. BłaszkiewiczŁ. KucharskiM. Antkowiak

Team

19 CPUs (32 cores) AMD x86_64 Opteron Dual Core: 2.0 and 2.4 GHz Xeon Dual Core: 2.66GHz ~ 4 cores per node

Rpeak = 153 GFlops 41 GB RAM

4 GB – 12 GB per node 1.22 TB disc space Wien2k, FPLO, NWChem, Molpro, Turbomole,

numerical NAG library

PEARL-AMU site

PEARL-AMU node

Galera1344 x quad-core Xeon 2,33 GHz

Reef46 x dual-core Xeon EM64T 3GHz

Computing grants in HPC centers

JUMP448 x Power6 4.7 GHz

Acknowledgements

European Network of Excellence MAGMANet

Polish Ministry of Science and Higher Education

Thank you for your attention!