Coupled cluster channels in the homogeneous electron gas

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Coupled cluster doubles (CCD) is a powerful quantum chemistry method.
• Approximations to CCD are needed for computational efficiency.
• Diagrammatic expansions offer pathways to these approximations.

Purpose of the Study:

• To investigate diagrammatic modifications of CCD equations.
• To evaluate approximations like ring-only, ladder-only, crossed-ring-only, and mosaic-only CCD.
• To benchmark these methods for the uniform electron gas (UEG).

Main Methods:

• Diagrammatic expansions of CCD equations.
• Analysis of ring, ladder, crossed-ring, and mosaic terms.
• Benchmarking on finite uniform electron gas (UEG) systems.
• Numerical analysis in the thermodynamic limit.

Main Results:

• Rings tend to overcorrelate, while ladders tend to undercorrelate electron systems.
• Mosaic-only CCD provides results surprisingly close to full CCD.
• Mosaic terms, via Brueckner Hamiltonian renormalization, open a gap at the Fermi energy.

Conclusions:

• Methods incorporating mosaic terms exhibit convergent energies in the thermodynamic limit.
• Mosaic-only CCD, a renormalized MP2, converges.
• Single-channel methods (ladder-only, ring-only, crossed-ring-only CCD) appear to diverge without mosaic terms.