Excited-State Forces with GW-BSE Through the Hellmann-Feynman Theorem.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Calculating atomic forces in excited states is crucial for understanding photochemical reactions and material properties.
• Existing methods often face computational challenges, particularly for extended systems and excited electronic states.
• The GW-BSE (Bethe-Salpeter Equation) approach is a powerful tool for describing excited states.

Purpose of the Study:

• To develop and implement a novel method for computing excited-state atomic forces.
• To apply this method within the GW-BSE framework using the Tamm-Dancoff approximation.
• To validate the accuracy of the new method against established computational chemistry techniques.

Main Methods:

• Calculation of atomic forces via finite differences of the excitonic Hamiltonian derivative.
• Utilization of projectors for applying the method to excited states.
• Implementation using batch representation of electron-hole amplitudes to avoid summing over unoccupied orbitals.

Main Results:

• The developed method successfully calculates atomic forces for excited molecular systems.
• Excellent agreement was achieved between the calculated geometries of excited CO and CH2O molecules and results from quantum chemistry methods.
• The implementation efficiently handles electron-hole amplitudes, optimizing computational cost.

Conclusions:

• The new finite-difference approach provides an accurate and efficient way to compute excited-state atomic forces.
• This method enhances the capabilities of the GW-BSE approach for studying excited-state properties.
• The findings pave the way for more reliable theoretical investigations of excited-state dynamics and photochemistry.