Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Calculating excited states in molecules and nanostructures is crucial for understanding their properties.
• Existing methods often face computational limitations for large systems.

Purpose of the Study:

• To present a novel real-time second-order Green's function (GF) method for computing excited states.
• To achieve efficient computational scaling for complex systems.

Main Methods:

• Utilized a stochastic resolution of the identity to decouple electron repulsion integrals, achieving O(Ne^3) scaling.
• Employed dynamic mode decomposition for improved time propagation and spectral resolution.
• Assessed the method's accuracy and efficiency using hydrogen dimer chains.

Main Results:

• The stochastic GF method accurately reproduced deterministic results for electronic dynamics and excitation energies.
• Demonstrated efficient computation for extended systems with varying boundary conditions.
• Provided a detailed analysis of statistical errors, bias, and extrapolation.

Conclusions:

• The developed real-time second-order GF method offers an efficient computational route for investigating excited states.
• This approach is suitable for studying extended molecular and nanostructure systems.
• The method shows high accuracy comparable to deterministic calculations.