We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg $n{}^{1,3}P$ states ($n=24–35$). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order $m{\alpha }^4$ (including finite-nuclear-mass recoil), QED contributions of order $m{\alpha }^5$, and partial $m{\alpha }^6$ terms (singlet-triplet mixing, one- and two-loop radiative corrections, and the logarithmic contribution). The remaining higher-order contributions are estimated via $1/n^3$ scaling. The resulting ionization energies achieve kilohertz-level accuracy and are in excellent agreement with independent Hylleraas calculations, thereby providing cross validation between two distinct theoretical approaches. From these data, the quantum-defect parameters are determined and used to extrapolate the ionization energies up to $n=102$. Combining our Rydberg ionization energies with high-precision experimental $2S\to nP$ transition frequencies yields the ionization energies for the metastable $2^{1}S$ and $2^{3}S$ states as $960332040.532{\left(10\right)}_{\mathrm{stat}}{\left(20\right)}_{\mathrm{sys}}$ and $1152842742.7271{\left(52\right)}_{\mathrm{stat}}{\left(25\right)}_{\mathrm{sys}}\mathrm{MHz}$, respectively. The C-BSBF result for the $2{}^{1}S$ state is consistent with the experimental ionization energy obtained from Rydberg-series extrapolation, while for the $2{}^{3}S$ state the difference is 0.019(10) MHz.

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• Atomic & molecular structure
• Atomic spectra
• Electron correlation calculations for atoms & ions
• Electronic excitation & ionization
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions