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Related Concept Videos

Correlations02:20

Correlations

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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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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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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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Correlative Microscopy for 3D Structural Analysis of Dynamic Interactions
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Singling Out Dynamic and Nondynamic Correlation.

Mireia Via-Nadal1,2, Mauricio Rodríguez-Mayorga1,2,3, Eloy Ramos-Cordoba1,2

  • 1Donostia International Physics Center (DIPC) , 20018 Donostia , Euskadi , Spain.

The Journal of Physical Chemistry Letters
|July 6, 2019
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Summary
This summary is machine-generated.

This study analyzes electron pair density to classify molecular systems by dynamic or nondynamic correlation. It identifies components responsible for London dispersion forces and universal decay, aiding new electronic structure method development.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Understanding electron correlation is crucial for accurate molecular modeling.
  • Pair density analysis offers insights into electronic interactions at different ranges.
  • Existing methods struggle to universally capture dynamic and nondynamic correlation effects.

Purpose of the Study:

  • To separate pair density into short- and long-range correlation components.
  • To classify molecular systems based on prevailing correlation types (dynamic vs. nondynamic).
  • To identify the pair density component responsible for London dispersion forces.

Main Methods:

  • Analysis of the intracular part of pair density components.
  • Study of long-range asymptotics of pair density.
  • Range-separation of electron correlation.

Main Results:

  • Successful separation of pair density into short- and long-range components.
  • Classification of molecular systems into dynamic or nondynamic correlation regimes.
  • Identification of a universal decay in pair density related to interelectronic distance and London dispersion forces.

Conclusions:

  • The developed range-separation provides a natural way to analyze electron correlation.
  • The identified dispersion component is key for describing London forces.
  • This framework is expected to advance wave function, density, and reduced density-matrix functional theories for electronic structure calculations.