A Third-Order Relativistic Algebraic Diagrammatic Construction Method for Double Ionization Potentials: Theory, Implementation, and Benchmark

We present a relativistic third-order algebraic diagrammatic construction (ADC(3)) approach for calculating double ionization potentials (DIPs). By employing the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with a Cholesky decomposition (CD) representation of two-electron integrals and the frozen natural spinor (FNS) framework for virtual space truncation, we achieve a significant reduction in both memory requirements and computational cost. The DIPs obtained using the X2CAMF Hamiltonian show excellent agreement with results from fully relativistic four-component calculations. We have validated the accuracy of our implementation through comparisons with available experimental and theoretical data for inert gas atoms and diatomic species. The effect of higher-order relativistic corrections is also explored.