QED correction for H$_3^+$

Abstract: A quantum electrodynamics (QED) correction surface for the simplest polyatomic and polyelectronic system H$_3^+$ is computed using an approximate procedure. This surface is used to calculate the shifts to vibration-rotation energy levels due to QED; such shifts have a magnitude of up to 0.25 cm$^{-1}$ for vibrational levels up to 15~000 cm$^{-1}$ and are expected to have an accuracy of about 0.02 cm$^{-1}$. Combining the new H$_3^+$ QED correction surface with existing highly accurate Born-Oppenheimer (BO), relativistic and adiabatic components suggests that deviations of the resulting {\it ab initio} energy levels from observed ones are largely due to non-adiabatic effects.