Efficient basis sets for core-excited states motivated by Slater's rules.

Area of Science:

• Computational Chemistry
• Materials Science
• Spectroscopy

Background:

• X-ray photoemission spectroscopy (XPS) analyzes atomic chemistry by measuring core-electron binding energies (CEBEs).
• Accurate CEBE calculations require specialized methods beyond standard ground-state electronic structure calculations.
• Existing methods face challenges in accurately describing core-excited electronic structures.

Purpose of the Study:

• To develop computationally efficient and physically motivated methods for calculating CEBEs.
• To improve the numerical accuracy of CEBEs derived from theoretical models.
• To enhance the interpretation of XPS data for molecular and material characterization.

Main Methods:

• Development of physically motivated contractions for core-excited atomic orbitals, inspired by Slater's rules.
• Application of these core-excited basis sets within the $\Delta$SCF method using a hybrid exact-exchange density functional (B3LYP).
• Validation against experimental data for carbon 1s excitations and assessment of performance for heavier elements (N, O).

Main Results:

• Calculated CEBEs for carbon 1s excitations achieved experimental accuracy (∼0.1 eV).
• Satisfactory mean average error (∼0.2 eV) for relative CEBEs of heavier elements (N, O), despite missing relativistic effects.
• Demonstrated the connection between core-level binding energy variability and local atomic charge, impacting model transferability.

Conclusions:

• The developed core-excited basis sets significantly improve the accuracy of calculated CEBEs.
• The approach provides a reliable tool for interpreting XPS measurements across various molecules and materials.
• Future work includes extending the methodology to a broader range of elements and addressing relativistic effects.