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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
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Mutual Correlation.

Francesco A Evangelista1

  • 1Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States.

Journal of Chemical Theory and Computation
|July 29, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces mutual correlation, a new method to quantify complex interactions in quantum systems. It helps in understanding electronic states and selecting relevant orbitals for computational chemistry and physics.

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Area of Science:

  • Quantum many-body physics
  • Theoretical and computational chemistry
  • Quantum information science

Background:

  • Quantifying correlation and complexity is crucial for advancing quantum sciences.
  • Existing methods may not fully capture nonadditive correlations among subsystems.

Purpose of the Study:

  • Introduce a novel framework, mutual correlation, to quantify nonadditive correlations in quantum many-body states.
  • Assess the framework's ability to identify orbital interactions and compare it with existing metrics.

Main Methods:

  • Developed a novel framework based on the Frobenius norm squared of the two-body reduced density matrix cumulant.
  • Systematically partitioned the cumulant norm to quantify nonadditive correlations.
  • Performed benchmark studies on model systems (H10, N2, p-benzyne) and compared with orbital mutual information.
  • Considered maximally correlated orbitals to identify basis-independent correlation partitioning.

Main Results:

  • Mutual correlation quantifies nonadditive correlations among interacting subsystems.
  • Demonstrated the framework's effectiveness in identifying orbital interactions through benchmark studies.
  • Showcased maximally correlated orbitals for basis-independent correlation partitioning.

Conclusions:

  • Mutual correlation is a broadly applicable metric for quantum many-body systems.
  • The framework is useful for active space selection and interpreting electronic states in chemistry and physics.