Linked-Cluster Formulation of Electron-Hole Interaction Kernel in Real-Space Representation without Using Unoccupied...

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• The electron-hole interaction kernel is crucial for understanding electronic excitations and calculating optical properties in many-electron systems.
• Accurate determination of this kernel is challenging, particularly within the GW+Bethe-Salpeter Equation (BSE) formalism.
• Traditional methods rely on unoccupied states, posing significant computational limitations for larger systems.

Purpose of the Study:

• To develop an alternative derivation of the electron-hole interaction kernel that avoids the use of computationally expensive unoccupied states.
• To enable more efficient and accurate calculations of electronic excitation properties for larger and more complex systems.

Main Methods:

• Introduced an alternative derivation of the electron-hole interaction kernel using explicitly correlated geminal functions.
• Employed diagrammatic and algebraic techniques to express the kernel solely in terms of linked closed-loop diagrams.
• Validated the approach by calculating excitation energies in many-electron systems.

Main Results:

• Successfully derived the electron-hole interaction kernel without relying on unoccupied states, overcoming a major computational bottleneck.
• The derived kernel, expressed using linked closed-loop diagrams, showed good agreement with established methods like Equation-of-Motion Coupled-Cluster with Singles and Doubles (EOM-CCSD) and GW+BSE.
• Demonstrated the method's effectiveness for calculating excitation energies in large finite systems, such as quantum dots and nanorods.

Conclusions:

• The developed method provides a computationally efficient pathway to accurately determine the electron-hole interaction kernel.
• This breakthrough facilitates precise calculations of optical properties and electronic excitations in extended systems.
• The approach holds significant promise for advancing the study of nanomaterials and other large molecular systems.