LAUSR

In this paper, we present the first beyond closure calculation for the neutrinoless double-$\ensuremath{\beta}$ decay of $^{76}\mathrm{Ge}$ to the first ${2}^{+}$ states of $^{76}\mathrm{Se}$ within the two nucleon mechanism. The isospin symmetry restored quasiparticle random-phase approximation method with the charge-dependent-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the nuclear matrix elements and estimate the uncertainties from our nuclear many-body calculations. We find ${g}_{\mathrm{pp}}$ plays an important role for the calculations, and if quenching is included, suppression for the transition matrix element ${M}_{\ensuremath{\lambda}}$ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hartree-Fock-Bogolyubov results with the closure approximation.