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Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations.

Merzuk Kaltak1, Jiří Klimeš1, Georg Kresse1

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This study introduces efficient imaginary grids for calculating electronic correlation energies. The Minimax quadrature and a novel transformation improve computational efficiency for large systems in perturbation theory and random phase approximation.

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Area of Science:

  • Computational chemistry
  • Quantum mechanics
  • Materials science

Background:

  • Accurate calculation of electronic correlation energy is crucial for predicting material properties.
  • Second-order Møller-Plesset (MP) perturbation theory and random phase approximation (RPA) are widely used methods.
  • Computational cost often limits the application of these methods to large systems.

Purpose of the Study:

  • To determine efficient imaginary frequency and time grids for MP2 calculations.
  • To compare least-squares and Minimax quadratures for periodic systems.
  • To enable efficient calculation of RPA correlation energies for large systems.

Main Methods:

  • Comparison of least-squares and Minimax quadratures for periodic systems.
  • Development and testing of imaginary frequency grids for MP2.
  • Utilizing the duality between imaginary time and frequency grids for Fourier transformation.

Main Results:

  • Minimax quadrature shows slightly better performance for the studied materials.
  • Developed imaginary frequency grids are effective for MP2 and RPA correlation energy calculations.
  • Fourier transformation from imaginary time to frequency reduces computational complexity to cubic.

Conclusions:

  • Efficient imaginary grids significantly enhance the applicability of MP2 and RPA methods.
  • The Minimax quadrature is a robust choice for periodic systems.
  • The developed methodology paves the way for large-scale electronic structure calculations.