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Exact exchange-correlation potentials of singlet two-electron systems.

Ilya G Ryabinkin1, Egor Ospadov2, Viktor N Staroverov2

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We present a new analytic method to calculate the exchange-correlation potential for two-electron systems. This approach offers accurate results without the issues found in the Kohn-Sham inversion technique.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Electronic Structure Theory

Background:

  • The exchange-correlation potential (vXC(r)) is crucial for accurate electronic structure calculations.
  • Existing methods like Kohn-Sham inversion can yield unphysical potentials, especially in finite basis sets.
  • Accurate vXC(r) is essential for understanding chemical bonding and material properties.

Purpose of the Study:

  • To develop a non-iterative, analytic method for constructing the exchange-correlation potential (vXC(r)) for singlet ground-state two-electron systems.
  • To provide a computationally efficient and physically meaningful alternative to the Kohn-Sham inversion technique.
  • To demonstrate the method's effectiveness using various two-electron systems and common computational chemistry approaches.

Main Methods:

  • A novel analytic formula for vXC(r) derived from the electronic wave function.
  • Application of the formula to wave functions obtained from common ab initio methods and Gaussian basis sets.
  • Comparison with the Kohn-Sham inversion technique, highlighting differences in potential behavior.

Main Results:

  • The proposed method successfully constructs accurate exchange-correlation potentials for two-electron systems.
  • Unlike Kohn-Sham inversion, this method avoids unphysical oscillations and divergences in the potential when using finite basis sets.
  • Accurate vXC(r) was computed for the helium isoelectronic series, H2, and H3+.

Conclusions:

  • The non-iterative analytic method provides a robust and accurate way to determine the exchange-correlation potential for two-electron systems.
  • This approach overcomes limitations of the Kohn-Sham inversion, particularly concerning basis set effects.
  • The method offers a valuable tool for electronic structure calculations in quantum chemistry and condensed matter physics.