Achieving spectroscopic accuracy in HeH⁺ with ab-initio theory: nonadiabatic, relativistic, and QED corrections

The helium hydride ion (HeH⁺) is the simplest molecular system composed of nuclei with unequal charges and occupies a unique role as a benchmark for molecular structure theory. By incorporating high-precision nonadiabatic effects together with leading relativistic (mα⁴) and leading and higher-order quantum electrodynamic (QED) corrections (mα⁵, mα⁶), we achieve rovibrational transition energies in agreement with the most accurate spectroscopic measurements at the sub-MHz level. This reconciliation between theory and experiment establishes HeH⁺ as a molecular system alongside H₂, with broad relevance for high-resolution spectroscopy, astrochemical modeling, and precision tests of fundamental physics.