Implementation of energy and gradient for the TDDFT-approximate auxiliary function (aas) method.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Time-dependent density functional theory (TDDFT) is crucial for simulating excited-state properties.
• Accurate calculations of electron integrals in TDDFT can be computationally expensive.
• Existing methods like TDDFT+TB rely on specific parameters, limiting broader applicability.

Purpose of the Study:

• To implement and validate a new approximate TDDFT method, TDDFT-aas, for reduced computational cost.
• To introduce a novel coupling matrix formulation independent of tight-binding parameters.
• To enable the calculation of excited-state gradients for molecular emission energies.

Main Methods:

• Implemented the time-dependent density functional theory approximate auxiliary s function (TDDFT-aas) method.
• Approximated two-center electron integrals in the K coupling matrix to reduce computational expense.
• Utilized a new gamma function in the coupling matrix, independent of tight-binding parameters.

Main Results:

• TDDFT-aas shows good agreement with established TDDFT and TDDFT+TB methods for silver and gold nanoparticle absorption spectra.
• The method successfully reduces computational cost compared to exact integral calculations.
• Analytical excited-state gradients for TDDFT-aas were successfully implemented.

Conclusions:

• TDDFT-aas provides a computationally efficient and accurate alternative for excited-state calculations.
• The method's independence from tight-binding parameters enhances its versatility.
• This work paves the way for calculating molecular emission energies using an approximate TDDFT approach.