Perturbation-adapted perturbation theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Rayleigh-Schrödinger perturbation theory is a fundamental tool in quantum chemistry.
• The choice of the zero-order Hamiltonian significantly impacts convergence and accuracy.
• Conventional methods using model Hamiltonians can face divergence or slow convergence, especially in complex systems.

Purpose of the Study:

• To introduce a general and optimal approach for defining the zero-order Hamiltonian.
• To enhance the convergence properties of Rayleigh-Schrödinger perturbation theory.
• To provide a more robust method for electron many-body perturbation theory calculations.

Main Methods:

• A new general approach for constructing the zero-order Hamiltonian is presented.
• The optimal zero-order Hamiltonian is defined as a best fit to the exact Hamiltonian within a chosen functional form.
• The method is applied to many-body perturbation theory for electrons.

Main Results:

• Strongly improved convergence is observed compared to conventional methods.
• The new approach effectively addresses cases where the Fock Hamiltonian diverges or converges slowly.
• Demonstrates enhanced performance in electron many-body perturbation theory.

Conclusions:

• The proposed method offers a superior alternative for defining the zero-order Hamiltonian.
• This advancement leads to more reliable and efficient quantum mechanical calculations.
• The approach holds significant potential for improving the study of electronic structures in molecules and materials.