A new time dependent density functional algorithm for large systems and plasmons in metal clusters.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Time Dependent Density Functional Theory (TDDFT) is crucial for predicting electronic excitations.
• Traditional TDDFT methods often face computational bottlenecks, particularly Davidson diagonalization.
• Efficient algorithms are needed to extend TDDFT applications to larger and more complex systems.

Purpose of the Study:

• To develop and implement a new, efficient algorithm for solving TDDFT equations.
• To enable accurate calculation of excitation spectra across a wide range of photon energies.
• To facilitate in-depth analysis of TDDFT results for various chemical systems.

Main Methods:

• Developed a new algorithm for TDDFT within a density fitting auxiliary basis set framework.
• Implemented a method to extract spectra from the imaginary part of polarizability.
• Simplified the calculation of dielectric susceptibility by expressing it as a linear combination of matrices with energy-dependent coefficients.

Main Results:

• The new algorithm efficiently calculates excitation spectra, avoiding Davidson diagonalization.
• Applied to systems ranging from H2 to [Au147](-), demonstrating broad applicability.
• Achieved maximum deviations in excitation energies below 0.2 eV compared to established codes.

Conclusions:

• The developed TDDFT algorithm is highly efficient and accurate for diverse systems.
• The method allows for flexible spectrum calculation at any desired photon energy.
• Integrated tools for detailed analysis, including transition contribution maps and induced density analysis, enhance result interpretability.