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Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies
Guo P Chen1, Matthew M Agee1, Filipp Furche1
1University of California, Irvine , Department of Chemistry , 1102 Natural Sciences II , Irvine , California 92697-2025 , United States.
Journal of Chemical Theory and Computation
|September 22, 2018
Summary
Corrections to random-phase approximation (RPA) calculations improve accuracy for many molecules. However, beyond-RPA methods become unreliable for systems with strong electron correlation, as shown by the effective coupling strength.
Area of Science:
- Quantum chemistry
- Computational physics
Background:
- Random-phase approximation (RPA) is a common method for calculating correlation energies.
- Corrections to RPA are thought to primarily address short-range correlation effects.
- Perturbation theory is a potential approach for refining RPA calculations.
Purpose of the Study:
- To test the hypothesis that beyond-RPA correlation corrections are mainly short-range.
- To evaluate the performance of common perturbative methods beyond RPA.
- To identify the limitations of perturbative corrections for strongly correlated systems.
Main Methods:
- Analysis of formal and numerical results for beyond-RPA methods: bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK).
- Development of efficient algorithms using the resolution-of-the-identity (RI) approximation and numerical frequency integration.
- Benchmark calculations on medium- and large-size molecules with size-independent accuracy.
Main Results:
- The AXK method consistently improves RPA, SOX, and SOSEX for main-group compounds.
- AXK's enhanced accuracy stems from stronger screening of bare SOX.
- For transition-metal compounds, AXK corrections are often insufficient or incorrect, especially for 3d dimers.
- A critical effective coupling strength (α̅ ≈ 0.5) indicates when RPA errors grow and perturbative corrections fail.
Conclusions:
- Perturbation theory can systematically improve RPA, but only for systems where RPA is already qualitatively accurate (small α̅).
- Beyond-RPA methods are limited in strongly correlated systems where perturbative approaches become unreliable.
- The effective coupling strength (α̅) is a key indicator for the applicability of perturbative corrections to RPA.
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