Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

2013/07/24 by Andreas Grüneis, James J. Shepherd, Ali Alavi +2 · 72 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Basis (linear algebra) #Basis set #Chemistry #Convergence (economics) #Coulomb #Delocalized electron #Density functional theory #Electron #Electronic correlation #Geminal #Geometry #Mathematical physics #Mathematics #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Plane wave #Quantum electrodynamics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Wave function #Yukawa potential #cond-mat.quant-gas #cond-mat.str-el #physics.chem-ph #physics.comp-ph

paper · pdf · doi:10.1063/1.4818753

published in The Journal of Chemical Physics 139(8), 084112 (American Institute of Physics) · 15 pages, 13 figures

arxiv created 2013/07/24 · openalex publication_date 2013/08/28 · arxiv updated 2014/10/10 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05

Abstract

We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset (MP2) perturbation theory. The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.

Citations

• Integral coalescence conditions in D⩾2, dimension space
• Note on an Approximation Treatment for Many-Electron Systems
• Self-interaction correction to density-functional approximations for many-electron systems
• Efficient iterative schemes forab initiototal-energy calculations using a plane-wave basis set

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