Hybrid Diagonal Approximation in Time-Dependent Auxiliary Density Functional Theory.

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Quantum Chemistry

Background:

• Time-dependent auxiliary density functional theory (TD-ADFT) is computationally efficient for electronic structure calculations.
• Accurate calculation of vertical excitation energies and oscillator strengths is crucial in quantum chemistry.
• Existing methods may face computational cost limitations for complex systems.

Purpose of the Study:

• To introduce and evaluate a hybrid diagonal approximation (HDA) for TD-ADFT.
• To enable the use of global and range-separated hybrid functionals within TD-ADFT.
• To assess the accuracy and computational efficiency of the HDA for excitation energy calculations.

Main Methods:

• Implementation of a hybrid diagonal approximation (HDA) within the TD-ADFT framework.
• Inclusion of only diagonal elements of exact exchange in TD-ADFT matrices.
• Calculation of vertical excitation energies and oscillator strengths for singlet and triplet excitations.

Main Results:

• The HDA achieves accuracy comparable to four-center electron repulsion integral (ERI) methods for singlet excitations.
• The HDA offers significant computational cost savings compared to traditional ERI implementations.
• Larger deviations were observed for triplet excitations compared to singlet excitations.
• The low-order scaling of TD-ADFT is maintained with the HDA, even with additional integral calculations.

Conclusions:

• The HDA provides an efficient and accurate approach for calculating singlet excitation energies within TD-ADFT.
• The method preserves the computational advantages of TD-ADFT while allowing for hybrid functionals.
• Further investigation may be needed to improve accuracy for triplet excitations.