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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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On Pair Functions for Strong Correlations.

Jason K Ellis1, Richard L Martin1, Gustavo E Scuseria2

  • 1Theoretical Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.

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|November 20, 2015
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Summary
This summary is machine-generated.

The study shows how Unrestricted Hartree-Fock (UHF) wave functions capture electron correlation by analyzing orbital overlaps. This method smoothly transitions from simple electron pairing to complex symmetry breaking in hydrogen clusters.

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Area of Science:

  • Quantum chemistry
  • Condensed matter physics

Background:

  • Unrestricted Hartree-Fock (UHF) wave functions can exhibit spin contamination, indicating limitations in describing electron correlation.
  • The overlap between alpha and beta orbitals in UHF solutions serves as a metric for symmetry breaking and correlation strength.

Purpose of the Study:

  • To investigate the relationship between UHF wave function symmetry breaking and electron correlation.
  • To demonstrate the utility of corresponding orbital overlap as a proxy for correlation strength.
  • To explore the behavior of UHF solutions in hydrogen clusters and their connection to the Hubbard model.

Main Methods:

  • Calculations on one- and two-dimensional hydrogen clusters.
  • Analysis of the overlap between alpha and beta corresponding orbitals in UHF solutions.
  • Spin projection of UHF solutions to address strong correlation effects.

Main Results:

  • The overlap of corresponding orbitals quantifies the correlation captured by symmetry breaking in UHF wave functions.
  • UHF orbitals evolve from doubly occupied states at short distances to segregated alpha and beta electrons on sublattices at large distances.
  • Spin-projected UHF solutions effectively capture strong correlations, particularly at intermediate distances where single determinants fail.

Conclusions:

  • Corresponding orbital overlap is a valuable tool for understanding electron correlation in UHF theory.
  • The UHF method, when combined with spin projection, can describe systems with strong electron correlation, bridging the gap between weakly and strongly correlated regimes.