Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches...

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 $N^8$ scaling characterizing DIP-EOMCCSDT(4h-2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $N^7$ 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.