Finite-Field Approach to Solving the Bethe-Salpeter Equation

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Mechanics

Background:

• Calculating optical spectra and exciton binding energies is crucial for understanding molecular and solid-state properties.
• Existing methods often involve computationally expensive calculations, limiting their application to large systems.

Purpose of the Study:

• To present a novel, efficient computational method for determining optical spectra and exciton binding energies.
• To enable accurate calculations without relying on approximations like the random phase approximation or explicit dielectric matrices.

Main Methods:

• Solving the Bethe-Salpeter equation and calculating the screened Coulomb interaction in a finite field.
• Utilizing localized orbitals derived from Bloch states via bisection techniques.
• Employing hybrid functionals for single-particle wave function calculations.

Main Results:

• Successfully computed optical spectra and exciton binding energies for various molecules.
• Achieved unprecedentedly large-scale absorption spectra calculations for condensed systems, including water and ice.
• Demonstrated a significant reduction in computational complexity compared to traditional methods.

Conclusions:

• The presented method offers an efficient and accurate approach for calculating optical properties of molecules and solids.
• This technique facilitates the study of larger and more complex condensed matter systems.
• The method's efficiency allows for the practical application of advanced computational chemistry techniques.