Inclusion of Three-body Correction to Relativistic Equation-of-Motion Coupled Cluster Method: The Application to Electron Detachment Problem

Abstract: We present the formulation and implementation of triples correction scheme to the relativistic equation-of-motion coupled-cluster method for ionization potential. 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 that triple excitations are essential for achieving quantitative ionization potentials, reducing mean absolute errors to approximately 0.01--0.08~eV relative to reference and experimental values. The X2CAMF approximation reproduces four-component Dirac-Coulomb results with negligible deviations, while the CD-FNS strategy yields substantial reductions in wall time. The resulting partial triples correction scheme scales as non-iterative $\mathcal{O}(n^7)$ with storage comparable to CCSD, offering an accurate and practical route for relativistic ionization energy calculations in heavy-element systems.