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Second-order Kohn-Sham perturbation theory: correlation potential for atoms in a cavity
1Center for Scientific Computing, Johann Wolfgang Goethe-Universität Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany.
The Journal of Chemical Physics
|December 27, 2005
Summary
This study investigates the MP2 correlation potential (v(c) (MP2)) for atoms in a cavity. While it captures shell structure, it overestimates oscillations and shows variational instability for some atoms.
Area of Science:
- Quantum Chemistry
- Computational Physics
- Density Functional Theory
Background:
- Second-order perturbation theory yields an implicit density functional for correlation energy (E(c) (MP2)).
- The MP2 correlation potential (v(c) (MP2)) exhibits problematic asymptotic behavior, either diverging or matching the exact potential depending on spectral properties.
- Previous studies highlighted issues with v(c) (MP2) divergence and asymptotic behavior.
Purpose of the Study:
- To investigate the behavior of the MP2 correlation potential (v(c) (MP2)) for atoms confined within a spherical cavity.
- To develop a method for normalizing v(c) (MP2) to match the exact potential's asymptotic behavior for free atoms.
- To assess the accuracy and limitations of v(c) (MP2) for various atomic systems.
Main Methods:
- Employed a basis-set-free finite differences approach with hard-wall boundary conditions to create a discrete atomic spectrum.
- Utilized a numerical continuation procedure to normalize v(c) (MP2) in the asymptotic region.
- Calculated v(c) (MP2) for closed-shell and spherical open-shell atoms up to argon, including high-energy virtual states.
Main Results:
- v(c) (MP2) successfully reproduces the shell structure of the exact correlation potential but overestimates shell oscillations.
- For spin-polarized atoms, a strong interrelation between spin channels was observed, unlike in standard density functionals.
- Variational instability of E(c) (MP2) was identified for beryllium, leading to a breakdown in self-consistent Kohn-Sham iterations.
Conclusions:
- The MP2 correlation functional is a foundational step but insufficient for a complete implicit correlation functional.
- Normalization and inclusion of high-energy virtual states are crucial for studying v(c) (MP2) in confined systems.
- Despite reproducing shell structure, v(c) (MP2) does not improve Kohn-Sham calculations and exhibits fundamental instabilities.
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