Dynamical kernels for optical excitations

Area of Science:

• * Computational physics and chemistry.
• * Quantum mechanics and electronic structure theory.

Background:

• * Linear response theory is crucial for calculating optical excitations.
• * Dynamical kernels, frequency-dependent, offer a more accurate approach than static kernels.
• * Previous studies have highlighted issues with spurious excitations in approximate kernels.

Purpose of the Study:

• * To evaluate the physical properties and accuracy of three distinct dynamical kernels.
• * To investigate the capability of dynamical kernels in capturing higher-order excitations.
• * To analyze the emergence of spurious excitations from approximate dynamical kernels.

Main Methods:

• * Implementation and analysis of three dynamical kernels: a dressed time-dependent density-functional theory (TDDFT) inspired kernel, a Bethe-Salpeter equation (BSE) kernel, and a second-order BSE kernel.
• * Utilizing a simple two-level model for calculations.
• * Examining prototypical examples of valence, charge-transfer, and Rydberg excited states.

Main Results:

• * Dynamical kernels provide additional excitations, including those corresponding to double excitations, which are often missed by static approaches.
• * The frequency-dependent nature of these kernels is key to capturing these higher-order phenomena.
• * Spurious excitations were identified in each kernel, stemming from their approximate formulations.

Conclusions:

• * Dynamical kernels are valuable for a more complete description of optical excitations, particularly for higher-order states.
• * Careful consideration of kernel approximations is necessary to avoid unphysical results.
• * The study provides insights into the strengths and weaknesses of different dynamical kernel approaches in electronic structure calculations.