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arXiv · 1704.02887

On Born's conjecture about optimal distribution of charges for an infinite ionic crystal

Laurent Bétermin·Hans Knüpfer
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Abstract

We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born's conjecture about the optimality of the rock-salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results holds for a class of completely monotone interaction potentials which includes Coulomb type interactions. In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.

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Laurent Bétermin, Hans Knüpfer. 2018-04-18. On Born's conjecture about optimal distribution of charges for an infinite ionic crystal. https://doi.org/10.1007/s00332-018-9460-3

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