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Range-separated density-functional theory (DFT) offers faster basis set convergence for electron interactions. This method shows exponential convergence for wave functions and correlation energy, unlike standard DFT.

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Area of Science:

  • Computational Quantum Chemistry
  • Electronic Structure Theory
  • Density-Functional Theory (DFT)

Background:

  • Kohn-Sham density-functional theory (DFT) is a standard method for electronic structure calculations.
  • Range-separated DFT divides electron-electron interactions into long- and short-range components.
  • Long-range interactions are treated with many-body methods, short-range with DFT approximations.

Purpose of the Study:

  • To investigate the basis set convergence properties of range-separated DFT.
  • To analyze the convergence of the long-range wave function and correlation energy.
  • To propose an improved extrapolation scheme for basis set convergence.

Main Methods:

  • Studied basis convergence of range-separated DFT.
  • Analyzed partial-wave expansion convergence of the long-range wave function near electron-electron coalescence.
  • Calculated Møller-Plesset perturbation theory (MP2) correlation energy for He, Ne, N2, and H2O using Dunning basis sets.

Main Results:

  • Demonstrated exponential convergence of the long-range wave function with respect to angular momentum (L).
  • Showed polynomial convergence for the standard Coulomb interaction.
  • Found that correlation energy error in range-separated DFT fits an exponential function of the basis set cardinal number (X).

Conclusions:

  • Range-separated DFT exhibits favorable basis set convergence properties.
  • An exponential fitting of basis set error enables accurate complete-basis-set extrapolation.
  • Proposed a novel three-point complete-basis-set extrapolation scheme based on an exponential formula for range-separated DFT.