Inclusion of three-body corrections in the relativistic equation-of-motion coupled cluster method: Application to electron detachment.

We present the formulation and implementation of a triples-correction scheme for relativistic equation-of-motion coupled-cluster calculations of ionization potentials. Both full and partial triples-correction schemes are implemented using the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with Cholesky decomposition (CD) of two-electron integrals and a frozen natural spinor (FNS) truncation scheme to reduce computational cost. Benchmark calculations on halide anions, noble-gas atoms, hydrogen halides, and dihalogen molecules demonstrate the importance of triple excitations for the quantitative prediction of ionization potentials. The CCSD(T)(a)* scheme achieves a mean absolute error of ∼0.01 eV relative to full CCSDT for halide anions and noble-gas atoms and ∼0.08 eV relative to the experiment for dihalogen molecules. The X2CAMF approximation reproduces four-component Dirac-Coulomb results with negligible deviations, while the CD-FNS strategy substantially reduces the computational cost. The resulting partial triples-correction scheme scales as O(n7) with storage comparable to CCSD, providing an accurate and practical approach for relativistic ionization-energy calculations in heavy-element systems.