Introduction
Solidstate
metal
hydrides are considered useful for storing hydrogen although
materials suitable for practical use are still under development.
Magnesium is an important candidate in this respect as it can
reversibly store about 7.6 wt% hydrogen, is light weight and is a
lowcost material. However, its thermodynamic parameters are not
completely favorable and the reaction with hydrogen often shows
sluggish kinetics. Different treatments in Mg based materials have
been proposed to overcome
these drawbacks.
One of these is tailoring Mg nanoparticles in view of an enhancement
on the reaction kinetics and thermodynamics of the MgMgH_{2}
phase transformation [13]. Because
metallic nanoparticles often show size dependent behavior different
from bulk matter, a better understanding of their physicalchemical
properties is necessary. For this purpose, we want to set up a
numerical model to perform first principle calculations based on the
density functional theory (DFT), using CPMD code. To evaluate the
suitable computational demand, we performed benchmarks of the CPMD
code on the HCP ENEA CRESCO computing facilities.
Computational
Details
CarParrinello Molecular
Dynamics (CPMD) code [4,5] is an
abinitio electronic
structure
and molecular dynamics (MD) program which uses a plane
wave/pseudopotential implementation of density functional theory
[6,7]. It is mainly targeted at
CarParrinello MD simulations but also supports geometry
optimizations, BornOppenheimer MD, path integral MD, response
functions, excited states and calculation of some electronic
properties. In abinitio molecular
dynamics simulation, the forces acting on atoms are calculated from
an electronic structure calculation repeated every time step (“on
the fly”). Thanks to electronic structure calculation which uses
density functional methods, simulations of large systems with
hundreds of atoms are now standard. Originally developed by Roberto
Car and Michele Parrinello for applications in solid state physics
and material science, this method has also been used with great
success for the study of molecular systems. Applications of abinitio
CarParrinello Molecular Dynamics
simulations range from the thermodynamics of solids and liquids to
the study of chemical reactions in solution and on metal and oxide
surfaces.
For all the calculations we employed the CPMD
code with GoedeckerTeterHutter pseudopotentials for magnesium,
together with Pade approximant LDA exchangecorrelation potentials
[810]. The electronic wave
functions are expanded in a planewave basis set with a kinetic
energy cutoff equal to 80 Ry. The latter value is optimized by
preliminary calculations both on simple molecules and on the
crystalline structures of metallic hcp Mg (lattice constant: a_{Mg}
= b_{Mg} = 3.15 Å, c_{Mg} = 1.62*a_{Mg}).
Experimental observations have showed that Mg nanoparticles annealed
at 300 °C show evaporation, void formation, and void growth in the
Mg core both in vacuum and under a high pressure gas environment.
This is mainly due to the outward diffusion and evaporation of Mg
with the simultaneously inward diffusion of vacancies leading to void
growth (Kirkendall effect [11]). To approach
numerical studying of Mg nanoparticles, starting from the magnesium
bulk, we have considered the cluster built from the Mg atoms inside a
12 Å radius sphere centered on a Mg atom. To take in consideration
the Kirkendall effect, we then have removed the inner Mg atoms inside
a 5.6 Å radius sphere. The system is composed of a hollow
nanoparticle of 266 magnesium atoms as shown in Figure
1, where magnesium atoms are in blue, outer sphere is in gray,
and inner red sphere is the void space due to the Kirkendall effect.
Figure 1: Mg nanoparticle. Magnesium atoms are in blue, outer sphere is in gray and, inner red sphere is the void space due to the Kirkendall effect.
ENEA
CRESCO computing facilities
CPMD
code runs on many different computer architectures and allows good
scalability up to a large number of processors depending on the
system size. We use the CPMD compiled with Intel Fortran Compiler,
MKL (Math Kernel Library), ACML (AMD Core Math Library) and MPI
(Message
Passing
Interface)
parallelization on the high performance ENEA CRESCO computing
facilities. The benchmark results demonstrate the high performance of
the CPMD parallelization on CRESCO architectures and the good
scalability up to hundreds of cores.
CRESCO
(Computational Research Center for Complex Systems [12])
is
an ENEA (Italian National Agency for New Technologies, Energy and
Sustainable Economic Development [13]) Project,
cofunded by the Italian Ministry of University and Research. The
performance for the CRESCO HPC system ranked 125 in June 2008 top500
list with Rmax= 17,14 Tflops in the HPL benchmark. Please find below
same of the hardware and software specifics.
The
ENEA CRESCO computing facilities are based on the multicore x86_64
architecture and is made
up of various clusters: we tested the CRESCO cluster located in
Portci, Casaccia and, Frascati ENEA centers. The
CRESCO cluster in Portici consists of two main sections: section
POR_1 for
high memory request and moderate parallel scalability; section POR_2
for limited memory and high scalability. We are interested in the
analysis of the POR_2
section performance. This section has 340 compute nodes that are
equipped with three types of Intel Xeon QuadCore processors. The
CRESCO clusters in Casaccia (CAS)
and in Frascati (FRA)
are equipped with AMD Opteron processors. Hardware details of the
clusters are reported in Table 1. The
Operating System (OS) for the three clusters is the Red Hat
Enterprise Linux version 2.6.18194.26.1.el5. We compiled the CPMD
version 3.15.1 using the same version of the mathematical library
MKL. On CRESCO clusters POR_2
and CAS we
used ifort compiler version 11 and OpenMPI version 1.2.8; and on
CRESCO cluster FRA
we used ifort version 12 and OpenMPI version 1.4.2. Finally we
performed a further test on the CRESCO cluster FRA
choosing as mathematical library the ACML version 5.1.0. Table 1
summarizes some of the hardware and software characteristics. Further
details are reported in Ref. [14].
Table 1: Some of the hardware and software characteristics for the CRESCO clusters.

CRESCO Clusters 

POR_2a 
POR_2b 
POR_2c 
CAS 
FRA_mkl 
FRA_acml 

Processor 
Intel Xeon 
Intel Xeon 
Intel Xeon 
AMD 
AMD Opteron 

Clock (GHz) 
2.33 
2.4 
2.4 
2.2 
2.2 

Cores for node 
2 x 4 
2 x 4 
2 x 4 
2 x 6 
2 x 12 

Total cores 
2048 
448 
224 
180 
456 

RAM 
16 GB 
32 GB 
64 GB 

Compiler 
Ifort 11.0.083 
Ifort 12.0.2.137 

MPI Flavor 
OpenMPI 1.2.8 
OpenMPI 1.4.2 

Math. Lib 
MKL 10.0.1.014 
ACML 5.1.0 
Results
and Discussions
The KohnSham
method of DFT simplifies calculations of the electronic density and
energy of a system of N_{e}
electrons in an external field without solving the Schroedinger
equations with 3N_{e}
degrees of freedom, but it takes into consideration the electronic
density as the fundamental quantity (with only 3 degrees of freedom).
The total groundstate energy of the system can be obtained as the
minimum of the KohnSham energy which is an explicit functional
of the electronic density. This leads to a set of equations
(KohnSham equations) that has to be solved selfconsistently in
order to yield density and the total energy of the electronic
groundstate. In the calculations, starting from an initial guess for
the electronic density, the KohnSham equations are solved
iteratively until convergence is reached. To find the better
computational
demand,
we calculated the average time for iteration in the
resolution of the KohnSham equations.
In
Table 2 and Figure 2,
we reported the average time for iteration in
function of the number of cores for the three CRESCO clusters. At the
beginning, for 24 cores case, we observed that the times for the
cluster POR_2
are much longer than the times for cluster CAS
and FRA.
This is due to the peak memory requirement (PMR) for core that is
2697.0 Mbytes, whereas clusters POR_2a,
POR_2b
and, POR_2c
have 2048 Mbytes for cores. For the others cases the cluster POR_2c,
which is equipped with processors Intel Xeon QuadCore Westmere
E5620, has the fastest times, except for the 192 cores case, where as
the cluster FRA
has the best performance. However, the times for the clusters POR_2b,
POR_2c
and, FRA are
very
similar. This is also highlighted
in the Figure 2, where the blue, green and red
lines are overlapped.
Finally, using ACML
library, we observed the performance improvement of the cluster FRA
which has AMD Opteron Magny Cours 6174MS processors. The times in the
last column (FRA_acml)
in Table 2 are reduced in the range of 4.56.0
% compared to those in column FRA_mkl
in which MKL library were used. It is worth pointing out that we have
used the Intel compiler even on AMD processors. In Figure
3 is shown
the speed up. For each cluster, the speed up was calculated with
respect to the 32 cores time. We observed a good scalability of the
code on all the clusters, with the best linear scaling for the CRESCO
cluster FRA
with both MKL and ACML libraries. From the speed up data we also
calculated efficiency that is shown in Figure 4.
This figure confirms
the CRESCO cluster FRA
as the most efficient. In fact, it has an efficiency higher than 75%.
Summary
Magnesium
is seen as one of the most important candidates in the solid media
hydrogen storage. However, to reach this aim same disadvantages have
to be overcome. In this context Mg
nanoparticles could solve some drawbacks of the bulk material. In
view of an extensive characterization of Mg nanoparticles by
numerical simulations, and to evaluate the suitable computational
demand, we performed benchmarks of the CPMD code on the HCP ENEA
CRESCO computing facilities. The benchmark results demonstrate the
high performance of the CPMD parallelization on CRESCO clusters
architectures and the good scalability up to hundreds of cores.
Acknowledgment
The
computing resources and the related technical support used for this
work have been provided by CRESCOENEAGRID High Performance Computing
infrastructure and its staff; see Ref. [12] for
information. CRESCOENEAGRID High Performance Computing
infrastructure is funded by ENEA, the “Italian National Agency for
New Technologies, Energy and Sustainable Economic Development” and
by national and European research programs.
References
[1] PASQUINI L., CALLINI E., PISCOPIELLO E., MONTONE A., VITTORI ANTISARI M. “Metalhydride transformation kinetics in Mg nanoparticles” Appl. Phys. Lett. 94 (2009) 041918.
[2] KRISHNAN G., KOOI B. J., PALASANTZAS G., PIVAK Y,. DAM B. “Thermal stability of gas phase magnesium nanoparticles” J. Appl. Phys. 107 (2010) 053504.
[3] PASQUINI L., CALLINI E., BRIGHI M., BOSCHERINI F., MONTONE A., JENSEN T. R., MAURIZIO C., VITTORI ANTISARI M., BONETTI E. “Magnesium nanoparticle with transition metal decoration for hydrogen storage ” J. Nanopart. Res. 13 (2011) pp. 57275737.
[4] CAR R., PARRINELLO M. “Unified approach for Molecular Dynamics and DensityFunctional Theory” Phys. Rev. Lett. 55 (1985) pp. 24712474.
[5] CPMD V3.15.1 Copyright IBM Corp 19902011, Copyright MPI fuer Festkoerperforschung Stuttgart 19972001.
[6] HOHENBERG P., KOHN W. “Inhomogeneous electron gas” Phys. Rev. 136 (1964) pp. B864B871.
[7] KOHN W., SHAM L. J. “Selfconsistent equations including exchange and correlation effects” Phys. Rev. 140 (1965) pp. A1133A1138.
[8] GOEDECKER S., TETER M., HUTTER J. “Separable dualspace Gaussian pseudopotentials” Phys. Rev. B 54 (1996) pp. 17031710.
[9] HARTWIGSEN C., GOEDECKER S., HUTTER J. “Relativistic separable dualspace Gaussian pseudopotentials from H to Rn” Phys. Rev. B 58 (1998) pp. 36413662.
[10] KRACK M. “Pseudopotentials for H to Kr optimized for gradientcorrected exchangecorrelation functionals” Theor. Chem. Acc. 114 (2005) pp. 145152.
[11] SMIGELSKAS A. D., KIRKENDALL E. O. “Zinc Diffusion in Alpha Brass” Trans. AIME 171 (1947) pp. 130142.
[12] www.cresco.enea.it
[13] www.enea.it
[14] www.afs.enea.it/project/eneagrid/Resources/CRESCO_documents/index.html
last update: 20120508 simone giusepponi