Nanocluster shape averaging with icosahedral symmetry

At lower temperature, the surface atoms of nanocluster only fluctuate around their bounding positions, thus the surface shape of nanocluster remains static. At higher temperature, not only the surface atoms travel across the surface and between layers, but also the whole surface shape fluctuates a lot. However, the fluctuation is around a equilibrium shape at the given temperature. The concept has been described on this page.

On the above page, the spherical shell is divided into cells unevenly by solid angle. A better method is to divide the spherical shell evenly by the points with icosahedral symmetry, whose coordinates are given by the tables developed by R. H. Hardin, N. J. A. Sloane and W. D. Smith. Best covering coordinates have been used here.

C++ implementation: ihsurf.C with the support of vector.h. Also given is an example xyz file with 1212 points on the spherical surface. One results for the gold icosahedral nanocluster with 5082 atoms (central atom missing) has been given by this page.

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