Optimality of the triangular lattice for Lennard–Jones type lattice energies: a computer-assisted method

Abstract It is well-known that any Lennard–Jones type potential energy must have a periodic ground state given by triangular lattice in dimension 2. In this paper, we describe computer-assisted method rigorously shows such global minimality result among 2-dimensional lattices once the exponents of been fixed. The applied to widely used classical ( 12 , 6 stretchy="false">) potential, which main work. Furthermore, new bound on inverse density (i.e. co-volume) for minimal derived, improving those found (Bétermin and Zhang 2015 Commun. Contemp. Math. 17 1450049) 2016 SIAM J. Anal. 48 3236–3269). same results are also shown hold other as additional examples conjecture implying optimality parameters stated.