Bootstrap approximation for the exchange-correlation kernel of time-dependent density-functional theory.

Area of Science:

• * Computational physics and materials science.
• * Quantum chemistry and condensed matter theory.

Background:

• * Accurate calculation of electronic properties relies on effective approximations for the exchange-correlation kernel in time-dependent density-functional theory (TD-DFT).
• * Existing methods often require empirical parameters, limiting their predictive power and generalizability.

Purpose of the Study:

• * To develop a new, parameter-free approximation for the exchange-correlation kernel in TD-DFT.
• * To validate the proposed kernel by calculating optical spectra for a wide range of insulating materials.

Main Methods:

• * A self-consistent algorithm was devised to solve the exact Dyson equation for the response alongside an approximate expression for the exchange-correlation kernel.
• * The method yields a simple, parameter-free kernel derived from the dielectric function.

Main Results:

• * Optical spectra were calculated for small band gap (Ge, Si, GaAs, AlN, TiO(2), SiC), large band gap (C, LiF, Ar, Ne), and magnetic (NiO) insulators.
• * The computed spectra demonstrated excellent agreement with experimental data for all tested materials.

Conclusions:

• * The proposed parameter-free exchange-correlation kernel offers a universally applicable and accurate approach for TD-DFT calculations.
• * This advancement simplifies theoretical modeling and enhances the prediction of optical properties in diverse materials.