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Extending the domain of quantum mechanical simulations with HPCx

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Dario Alfè

Dept. of Earth Sciences and Dept. of Physics and Astronomy, University College London

Eighteen years ago the computational physics community was shaken by the seminal work of Car and Parrinello, who introduced the idea of first principles molecular dynamics, i.e. moving the atoms of a real system using quantum mechanical based forces. Their idea was so powerful and forward looking that it spread widely, even crossing the boundary of computational physics, and nowadays similar techniques are used in a wide range of disciplines, including chemistry, geophysics and biology. In 1985 Car and Parrinello were able to calculate the frequency of a chosen mode of vibration of a silicon crystal, and for doing that they simulated the motion of a system containing 8 atoms of silicon for a fraction of a picosecond. Since then, computers have multiplied their capabilities, codes have improved, and the frontiers have been regularly pushed, so that now simulations on ~100 atoms for ~1-10 ps are routinely carried out.

Fig.1 (Movie) First principles simulation of solid and liquid aluminium in co-existence. The simulation lasts for 15 ps and the cell contains 1000 atoms.

This work represents one of these moments in which previous boundaries are being extended: Using molecular dynamics based on density functional theory I have simulated a 1000-atom system of solid and liquid aluminium in co-existence for 15 ps (a snapshot of this simulation is displayed in Fig. 1). From these simulations I have extracted points on the melting curve of aluminium which are shown in Fig. 2. At the same time, I have also simulated a few 512-atom systems for 40 ps; the points on the melting curve extracted using these simulations are also reported in Fig. 2. The difference between the results obtained with 512 and 1000 atoms suggests that 512 atoms are still too few. In Fig. 2 I also report the melting curve of aluminium calculated previously using different techniques, based on the calculation of the free energies of solid and liquids [1].

The very good agreement between the two sets of calculations is gratifying, and therefore the two techniques support each other. This work has only been possible thanks to HPCx, and each simulation has been completed in little over two weeks of continuous running on 128 processors. Over that period, roughly half of the machine was dedicated to the running of all these simulations. This result is extremely important for at least two reasons. The first is that a number of melting properties have been calculated using free energy techniques, and the present findings strongly support the adequacy of those techniques used in the past. The second is related to a shift of paradigm: co-existence simulations are more easily carried out than free energy calculations, and the main effort is relieved from the human to be relocated on the computer. I believe that in the future we will witness broad applications of these types of simulations, while we wait for the next edge to be set.

Fig. 2 Melting points of aluminium calculated using the method of the co-existence of phases: 1000-atom simulations (circles) and 512-atom simulations (triangles). The continuous line represents previous results obtained using the free energy approach [1]; dashed lines represents errors.

References

[1] L. Vocadlo and D. Alfe, Phys Rev B, 65, 214105, (2002)
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