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Kohn-Sham exchange-correlation potentials from second-order reduced density matrices.

Rogelio Cuevas-Saavedra1, Paul W Ayers2, Viktor N Staroverov1

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|January 3, 2016
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This study presents a new algorithm to construct Kohn-Sham potentials from reduced density matrices, offering unambiguous results in finite basis sets. The method also aids in separating exchange and correlation potentials for complex systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Kohn-Sham (KS) theory is central to density functional theory (DFT) for electronic structure calculations.
  • Traditional KS inversion methods rely on ground-state electron densities, which can lead to ambiguities in finite basis sets.
  • Extracting accurate KS potentials is crucial for reliable electronic structure predictions.

Purpose of the Study:

  • To develop a practical algorithm for constructing KS exchange-correlation potentials directly from second-order reduced density matrices (2-RDM).
  • To overcome limitations of conventional KS inversion methods, particularly in finite basis set calculations.
  • To enable the approximate separation of exchange and correlation potentials for many-electron systems.

Main Methods:

  • Developed a novel inversion algorithm to derive KS potentials from a given 2-RDM.
  • Implemented the algorithm for configuration-interaction (CI) wave functions.
  • Validated the approach using numerical examples to demonstrate its performance and accuracy.

Main Results:

  • The proposed algorithm provides unambiguous KS potentials when using finite basis sets.
  • Demonstrated the capability to approximately separate exchange and correlation potentials.
  • Numerical examples confirm the practical utility and effectiveness of the method.

Conclusions:

  • The new algorithm offers a robust alternative for KS potential construction, especially when 2-RDMs are known.
  • This method enhances the reliability of electronic structure calculations by avoiding density-based ambiguities.
  • The ability to separate exchange and correlation potentials opens new avenues for theoretical investigations.