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It is well-known that any Lennard-Jones type potential energy must have aperiodic ground state given by a triangular lattice in dimension 2. In thispaper, we describe a computer-assisted method that rigorously shows such globalminimality result among $2$-dimensional lattices once the exponents of thepotential have been fixed. The method is applied to the widely used classical$(12,6)$ Lennard-Jones potential, which is the main result of this work.Furthermore, a new bound on the inverse density (i.e. the co-volume) for whichthe triangular lattice is minimal is derived, improving those found in [L.B\'etermin and P. Zhang, \textit{Commun. Contemp. Math.}, 17 (2015), 1450049]and [L. B\'etermin, \textit{SIAM J. Math. Anal.}, 48 (2016), 3236--3269]. Thesame results are also shown to hold for other exponents as additional examplesand a new conjecture implying the global optimality of a triangular lattice forany parameters is stated.

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