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A novel method optimizes the zero-order Hamiltonian in perturbation theory. This approach improves convergence for electron many-body calculations, overcoming issues with traditional methods.

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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.