  In this work we present the first beyond closure calculation for the
neutrinoless double beta decay ($0\nu\beta\beta$) of $^{76}$Ge to the first
$2^+$ states of $^{76}$Se. The isospin symmetry restored Quasi-particle random
phase approximation (QRPA) method with the CD-Bonn realistic force is adopted
for the nuclear structure calculations. We analyze the structure of the two
nucleon mechanism nuclear matrix elements, and estimate the uncertainties from
the nuclear many-body calculations. We find $g_{pp}$ plays an important role
for the calculations and if quenching is included, suppression for the
transition matrix element $M_{\lambda}$ is found. Our results for the
transition matrix elements are about one order of magnitude larger than
previous projected Hatree-Fock-Boglyubov results with the closure
approximation.
