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Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid

Journal Article · · European Physical Journal. B, Condensed Matter and Complex Systems
 [1];  [2];  [3]
  1. The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Princeton University
  2. Rutgers Univ., Piscataway, NJ (United States); Princeton Univ., NJ (United States)
  3. Princeton Univ., NJ (United States)
+ Show Author Affiliations
The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M3, with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for rs values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Furthermore, two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0017865
OSTI ID:
1860497
Alternate ID(s):
OSTI ID: 1612764
Journal Information:
European Physical Journal. B, Condensed Matter and Complex Systems, Journal Name: European Physical Journal. B, Condensed Matter and Complex Systems Journal Issue: 10 Vol. 91; ISSN 1434-6028
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

References (42)

A natural orbital functional based on an explicit approach of the two-electron cumulant journal February 2012
Perspective on natural orbital functional theory journal March 2014
Ordinary field-theoretic methods for self-consistent wave functions which describe bond formation and dissociation. II. Commutative coupling case journal March 1983
ABCS approach to molecular correlation journal February 1995
Bemerkung zur Elektronentheorie des Ferromagnetismus und der elektrischen Leitf�higkeit journal July 1929
On the trail of the 2-body reduced density matrix journal January 2013
Self-interaction in natural orbital functional theory journal November 2003
Ordinary field-theoretic methods for self-consistent wave functions which describe bond formation and dissociation journal April 1982
Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm journal May 2001
Assessment of simple exchange-correlation energy functionals of the one-particle density matrix journal August 2002
Optimization of density matrix functionals by the Hartree–Fock–Bogoliubov method journal December 2002
The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions journal February 2004
Phase dilemma in density matrix functional theory journal April 2004
Transposition of the Theories Describing Superconducting Systems to Molecular Systems. Method of Biorbitals journal October 1965
Reduction of the N ‐Particle Variational Problem journal December 1964
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers journal September 1965
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian journal October 2008
The Bardeen–Cooper–Schrieffer approach to electron correlation in the density matrix formalism journal July 1997
The improved Bardeen–Cooper–Schrieffer method in polymers journal May 2000
The intrapair electron correlation in natural orbital functional theory journal December 2013
A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions journal March 2018
A well-scaling natural orbital theory journal November 2016
Calculations on molecular systems with the Hartree-Fock-Bogoliubov self-consistent-field method journal June 1970
Microscopic Theory of Superconductivity journal April 1957
Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions journal August 1960
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction journal March 1955
Necessary and sufficient conditions for the N -representability of density functionals journal February 2007
Hohenberg-Kohn theorem for nonlocal external potentials journal September 1975
Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions journal October 1978
Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas journal July 1994
Erratum: Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas [Phys. Rev. B 50 , 1391 (1994)] journal October 1997
Tensor product expansions for correlation in quantum many-body systems journal March 2000
Performance of one-body reduced density-matrix functionals for the homogeneous electron gas journal May 2007
Spin polarization of the low-density three-dimensional electron gas journal September 2002
Parametrization of the Two-Electron Reduced Density Matrix for its Direct Calculation without the Many-Electron Wave Function journal December 2008
Global Method for Electron Correlation journal August 2017
Interpretation of Recent Results on He 3 below 3 mK: A New Liquid Phase? journal October 1972
Ground State of the Electron Gas by a Stochastic Method journal August 1980
Structure of Fermion Density Matrices journal July 1963
Electron Pairs in the Theory of Superconductivity journal March 1960

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