Bethe-Salpeter equation spectra for very large systems.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate calculation of molecular optical properties is crucial for understanding material behavior.
• Existing methods for large molecules are computationally expensive, limiting their application.
• The Bethe-Salpeter equation provides a rigorous framework for electronic excitation calculations.

Purpose of the Study:

• To develop a highly efficient computational method for extracting optical properties of very large molecules.
• To reduce the computational scaling of Bethe-Salpeter equation calculations.
• To enable the study of complex molecular systems previously inaccessible.

Main Methods:

• Utilizing the Bethe-Salpeter equation for optical property extraction.
• Employing stochastic time-dependent Hartree propagation for the Coulombic interaction.
• Using a reduced set of ten stochastic orbitals instead of the full occupied states.
• Implementing trivial parallelization for enhanced computational efficiency.

Main Results:

• Achieved a computational scaling of at most cubic in system size.
• Successfully applied the method to a carbon-nanohoop bound fullerene system (520 electrons).
• Calculated exciton spectra and electronic density with less than 4000 core hours.
• Demonstrated significant computational savings compared to traditional methods.

Conclusions:

• The presented method offers a highly efficient pathway for calculating optical properties of large molecular systems.
• This approach democratizes the study of complex electronic structures and optical phenomena.
• The method opens new avenues for theoretical investigations in materials science and quantum chemistry.