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 $malpha^7$ order for the fundamental transitions $(v=0,L=0)to(v=1,L=0)$ in H$_2^+$ and HD$^+$ are presented.
The malpha^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm. Results are in go
od agreement with the high precision experiment carried out by Jefferts in 1969.
