Description of core excitations by time-dependent density functional theory with local density approximation,...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Spectroscopy

Background:

• Accurate calculation of core-excitation energies is crucial for understanding electronic structure and chemical bonding.
• Time-dependent density functional theory (TDDFT) is a widely used method for electronic excitation calculations.
• The choice of exchange-correlation functional significantly impacts the accuracy of TDDFT results.

Purpose of the Study:

• To investigate the dependence of vertical core-excitation energies on various exchange-correlation functionals within TDDFT.
• To evaluate the performance of different functional approximations, including LDA, GGA, meta-GGA, and hybrid functionals.
• To analyze the atom-dependence of excitation energy errors for different functional types.

Main Methods:

• Time-dependent density functional theory (TDDFT) calculations were performed.
• Vertical core-excitation energies (X1s→π*) were computed for H, C, N, O, and F atoms.
• A range of functionals were tested: Local Density Approximation (LDA), Generalized Gradient Approximation (GGA), meta-GGA, and hybrid functionals (including Becke-Half-and-Half-Lee-Yang-Parr - BHHLYP).

Main Results:

• Pure TDDFT functionals (LDA, GGA, meta-GGA) severely underestimate core excitation energies by over 13 eV.
• Time-dependent Hartree-Fock (TDHF) overestimates excitation energies by over 6 eV.
• Hybrid functionals show improved accuracy due to the inclusion of Hartree-Fock (HF) exchange.
• The BHHLYP functional, with 50% HF exchange, yields the smallest error for core excitations.
• Deviations for TDHF and pure TDDFT functionals increase with atomic number, indicating strong atom-dependence.
• Hybrid functionals exhibit significantly less atom-dependence.

Conclusions:

• Hybrid functionals are superior to pure TDDFT functionals for calculating core-excitation energies.
• The BHHLYP functional demonstrates excellent performance for core excitation calculations.
• Understanding functional dependence and atom-dependence is critical for accurate theoretical predictions in core-level spectroscopy.