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We present calculations of the one-loop vacuum polarization correction(Uehling potential) for the three-body problem in the NRQED formalism. The caseof one-electron molecular systems is considered. Numerical results of thevacuum polarization contribution at m$\alpha$7 and higher orders for thefundamental transitions (v = 0, L = 0) $\rightarrow$ (v ' = 1, L ' = 0) in theH2+ and HD+ molecular ions are presented and compared with calculationsperformed in the adiabatic approximation. The residual uncertainty from thiscontribution on the transition frequencies is shown to be of a few tens of Hz.

One-loop vacuum polarization at m$\alpha$7 and higher orders for three-body molecular systems