One-loop vacuum polarization at $m{\alpha }^7$ order for the two center problem

We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the NRQED formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) as well as antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results of the vacuum polarization contribution at $m{\alpha }^7$ order for the fundamental transitions $(v=0,L=0)\to (v^{\mathrm{\prime }}=1,L^{\mathrm{\prime }}=0)$ in H${}_2^{+}$ and HD${}^{+}$ are presented.