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). Inclusion of third-order terms significantly improves the performance of the algebraic diagrammatic construction method for DIPs. By employing the exact two-component atomic mean-field (X2CAMF) Hamiltonian in combination with a Cholesky decomposition representation of two-electron integrals and the frozen natural spinor 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. The efficiency of our implementation is demonstrated by computing the lowest DIP of the tungsten hexacarbonyl, W(CO)6, complex using a large basis set.