Frozen Natural Orbital-Based Extended Second-Order Algebraic Diagrammatic Construction for Core Ionization: Theory, Implementation, and Benchmark

We have developed a low-cost method using the extended version of the second-order algebraic diagrammatic construction method for core-ionization potential calculations (IP-ADC(2)-x). The efficiency of the method is enhanced by the incorporation of frozen natural orbitals (FNOs) and natural auxiliary functions (NAFs) in combination with the core-valence separation (CVS) and density fitting (DF) approximations. This approach balances computational efficiency and precision remarkably well. Employing natural orbitals significantly reduces the size of the virtual space while maintaining a systematically controlled accuracy, delivering a substantial speed-up compared to the standard method. Furthermore, the error due to the truncation of the virtual orbital space can be reduced by adding a simple correction to the FNO-IP-ADC(2)-x results. The overall accuracy of the method is governed by setting up FNO and NAF thresholds. The use of the spin-free exact two-component Hamiltonian (SFX2C1e) improves the agreement with experimental values. We have also investigated the use of projector-based embedding theory to calculate core-ionization potentials for large molecules. Using the embedded FNO-IP-ADC(2)-x method, we have successfully computed the core-ionization energies of N-doped fullerene (azafullerene) and chlorophyll-a molecules, with approximately 2600 and 4000 basis functions, respectively, with an impressive speed-up.