2015 年 14 巻 3 号 p. 52-53
Electronic structure calculation is necessary for metal nanoparticles composed of more than 1000 atoms to understand the intrinsic physical and chemical properties of nanoparticles. In this study, we analyzed the parallel performance of electronic structure calculation for metal nanoparticles by using the Vienna Ab-initio Simulation Package (VASP) program with large-scale computational resources. We found that VASP is suitable for the large-scale electronic structure calculation because the parallelization efficiency improved with increasing metal nanoparticle size (Pd405, Pd807, and Pd1289).
Metal nanoparticles are widely used as catalysts for environmental and energy related devices, such as fuel cells and exhaust gas cleanup, hydrogen storage materials. Recently, the unique properties of metal nanoparticles were experimentally found, which are not observed in bulk metal systems [1,2]. Especially, Kusada et al. succeeded in the synthesis of Ru nanoparticle having face-centered-cubic (fcc) and hexagonal- close-packed (hcp) structures, although only the hcp structure is known as bulk Ru [2]. In addition, they found that the nanoparticle size dependency for CO oxidation activity; i.e., fcc-Ru nanoparticle shows higher CO oxidation activity with increasing particle size while hcp-Ru shows better catalytic effect with smaller nanoparticle size around 2 nm. It is expected that these physical and chemical properties of metal nanoparticles are based on not only geometrical effects but also their electronic structures.
Recently, electronic structure calculations of metal nanoparticles composed of 300∼400 atoms (around 2 nm) were reported [3,4]. However, the electronic structure calculation for larger metal nanoparticles around 4 nm is necessary to understand the physical and chemical properties of metal nanoparticles, such as size dependency.
In this study, we analyzed the parallelization efficiency of electronic structure calculation for metal nanoparticles based on density functional theory (DFT) coupled with large-scale computational resources.
We prepared three different sizes of Pd nanoparticles, which is one of the most popular nanoparticles, as model structures. The diameters of Pd405, Pd807, and Pd1289 systems are about 2.3, 3.0, and 3.5 nm, respectively. All calculations were performed on the Vienna Ab-initio Simulation Package (VASP) program [5,6] under the GGA-PBE [7] with projector augmented wave (PAW) method by using the HA8000-tc/HT210 system (Intel Xeon E5-2697 v2 (2.7 GHz, 12core) × 2/node, 128 nodes) of Research Institute for Information Technology in Kyushu University.
We show in Figure 1 the dependency of the computational time necessary for single self-consistent field (SCF) cycle of Pd405, Pd807, Pd1289 models on the number of cores. The computational time became shorter when the number of cores increased in all cases. The computational time for Pd807 and Pd1289 was about 2.7 and 6.7 times longer than that for Pd405 although the number of atoms was about 2 and 3 times. The parallelization efficiency for Pd405, Pd807, and Pd1289 was estimated to be 99.79, 99.87, and 99.89%, respectively. This result indicates that VASP is highly suitable for large-scale electronic structure calculation because the parallelization efficiency was improved with increasing the size of metal nanoparticle. We also analyzed the effect of "NPAR," which is one of keywords in input about parallelization and data distribution over bands. The computational times for Pd405 at 384 cores by changing the number of NPAR are plotted in Figure 2. The computational time was about 10% reduced by changing the value of NPAR. Optimization of NPAR value is effective to reduce the computational time of metal nanoparticles.
Computational time of single SCF cycle with various numbers of cores (nodes). Diamond, square, and triangle means Pd405, Pd807, and Pd1289, respectively.
Computational time of single SCF cycle with various numbers of NPAR at 384 cores in case of Pd405.
From parallel performance analysis of VASP by using large-scale computational resources, we showed the possibility of electronic structure calculation of metal nanoparticles. In addition, the optimization of the number of NPAR was effective to reduce the computational time.
The activities of INAMORI Frontier Research Center are supported by Kyocera Corporation. This work is supported by the "Advanced Computational Scientific Program" of Research Institute for Information Technology, Kyushu University.
