Duality relations for the Gaussian core model

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Abstract
On account of self-similarity of the Gaussian function under Fourier transformation, the lattice energy of the Gaussian core model at absolute-zero temperature exhibits duality relations. In the cases of one and two dimensions the duality involves high- and low-density pairs for the single stable lattice structure. In three dimensions lattice energies for the two stable crystal forms (fcc at low density, bcc at high density) are paired. The results demonstrate that lattice energy loses its dependence on structure in the high-density limit, and they suggest (but do not prove) an asymptotic scaling for melting and freezing temperatures in the same limit. DOI: http://dx.doi.org/10.1103/PhysRevB.20.299 © 1979 The American Physical Society