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Title: Coupled cluster channels in the homogeneous electron gas

Abstract

We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yieldmore » divergent energies; incorporation of mosaic terms prevents this from happening.« less

Authors:
;  [1]
  1. Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892 (United States)
Publication Date:
OSTI Identifier:
22253395
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; EIGENVALUES; ELECTRON GAS; HAMILTONIANS; NUMERICAL ANALYSIS; RANDOM PHASE APPROXIMATION

Citation Formats

Shepherd, James J., E-mail: jjs6@rice.edu, E-mail: jamesjshepherd@gmail.com, Henderson, Thomas M., and Scuseria, Gustavo E. Coupled cluster channels in the homogeneous electron gas. United States: N. p., 2014. Web. doi:10.1063/1.4867783.
Shepherd, James J., E-mail: jjs6@rice.edu, E-mail: jamesjshepherd@gmail.com, Henderson, Thomas M., & Scuseria, Gustavo E. Coupled cluster channels in the homogeneous electron gas. United States. https://doi.org/10.1063/1.4867783
Shepherd, James J., E-mail: jjs6@rice.edu, E-mail: jamesjshepherd@gmail.com, Henderson, Thomas M., and Scuseria, Gustavo E. 2014. "Coupled cluster channels in the homogeneous electron gas". United States. https://doi.org/10.1063/1.4867783.
@article{osti_22253395,
title = {Coupled cluster channels in the homogeneous electron gas},
author = {Shepherd, James J., E-mail: jjs6@rice.edu, E-mail: jamesjshepherd@gmail.com and Henderson, Thomas M. and Scuseria, Gustavo E.},
abstractNote = {We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.},
doi = {10.1063/1.4867783},
url = {https://www.osti.gov/biblio/22253395}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 12,
volume = 140,
place = {United States},
year = {Fri Mar 28 00:00:00 EDT 2014},
month = {Fri Mar 28 00:00:00 EDT 2014}
}