Local Hamiltonians for quantitative Green's function embedding methods.

Area of Science:

• Computational Physics
• Quantum Chemistry

Background:

• Embedding calculations approximate solutions to the Schrödinger equation for complex systems.
• Current methods involve constructing low-energy model systems, which can be mathematically uncontrolled.

Purpose of the Study:

• To develop a novel, more direct procedure for parametrizing impurity Hamiltonians in embedding calculations.
• To improve the accuracy and efficiency of approximate solutions for large molecules and solids.

Main Methods:

• Developed a new parametrization procedure for impurity Hamiltonians.
• Directly parametrized the impurity Hamiltonian to recover the self-energy of the realistic system at high frequencies.
• Effective interactions are local but implicitly include non-local interactions.

Main Results:

• Achieved excellent total energies and self-energies approximating the realistic system.
• Demonstrated that high-frequency self-energy recovery leads to good total energy and self-energy approximations.
• Proposed two practical methods for evaluating effective integrals for parametrization.

Conclusions:

• The novel parametrization procedure offers a more robust and accurate approach to embedding calculations.
• This method simplifies the process by avoiding the construction of low-energy model systems.
• The findings provide practical strategies for improving computational accuracy in quantum chemistry and condensed matter physics.