Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole-2-Particle Excitations and Three-Body Clusters.

The double ionization potential (DIP) equation-of-motion (EOM) coupled-cluster (CC) method with 4-hole-2-particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIP-EOMCCSD(T)(ã)(4h-2p), that approximates the treatment of 4h-2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the N8 scaling characterizing DIP-EOMCCSDT(4h-2p) and DIP-EOMCCSD(T)(a)(4h-2p) to N7 with the system size N. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIP-EOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl2, Br2, HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10-4.5, the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin-orbit coupling effects.