Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Correlation of Experimental Data

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...

Correlation

Correlation

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.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:

Probability Distributions

Probability Distributions

The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...

Correlation and Regression

Correlation and Regression

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 negative...

Correlations

Correlations

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...

Calibration Curves: Correlation Coefficient

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional.

The Journal of chemical physics·2024

Same author

Doubling down on density-functional theory.

The Journal of chemical physics·2023

Same author

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database.

The Journal of chemical physics·2023

Same author

Density-functional theory vs density-functional fits: The best of both.

The Journal of chemical physics·2022

Same author

Density-functional theory vs density-functional fits.

The Journal of chemical physics·2022

Same author

Computational modeling of piezochromism in molecular crystals.

The Journal of chemical physics·2020

Same journal

DNA conformation determines the size of DNA-histone H1 nanoscale clusters.

The Journal of chemical physics·2026

Same journal

Confinement-controlled phase behavior of charged colloids under gravity.

The Journal of chemical physics·2026

Same journal

Dissociation line of tetrahydrofuran hydrates from NPH molecular dynamics simulations.

The Journal of chemical physics·2026

Same journal

Development of a magnetic interatomic potential for cubic antiferromagnets: The case of NiO.

The Journal of chemical physics·2026

Same journal

Simulations of solvent effects on excited state dynamics of p-DAPA, a red single benzene-based fluorophore.

The Journal of chemical physics·2026

Same journal

Rotational excitation of thioformaldehyde (H2CS) in collisions with molecular hydrogen.

The Journal of chemical physics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: May 13, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Density functionals for static, dynamical, and strong correlation.

¹Department of Chemistry, Dalhousie University, 6274 Coburg Rd., P.O. Box 15000, Halifax, Nova Scotia B3H 4R2, Canada.

The Journal of Chemical Physics

|March 1, 2013

Summary

This summary is machine-generated.

This study enhances density functional theory for strong correlation in chemistry. It enables accurate calculations for dissociating systems without symmetry issues, showing promising initial results.

More Related Videos

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

Published on: December 1, 2018

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Related Experiment Videos

Last Updated: May 13, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts

Published on: December 1, 2018

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Area of Science:

Quantum Chemistry
Computational Chemistry
Materials Science

Background:

Accurate computational methods are crucial for understanding chemical systems.
Existing density functionals struggle with strong correlation, particularly in dissociating systems.
Symmetry breaking and multi-determinantal methods can be computationally expensive.

Purpose of the Study:

To generalize an exact-exchange-based density functional to accurately describe strong correlation.
To enable symmetry-preserving, single-reference calculations for challenging chemical systems.
To develop and validate a new computational approach for dissociating molecules.

Main Methods:

Generalization of an existing static + dynamical correlation density functional.
Inclusion of "strong" correlation effects.
Development of a strong-correlation benchmark set using symmetrized open-shell atoms.

Main Results:

The generalized functional successfully incorporates strong correlation effects.
Accurate computations on dissociating systems were achieved without breaking space or spin symmetries.
The new functional demonstrates promising performance on the developed benchmark set.

Conclusions:

The generalized density functional provides a robust method for studying strong correlation.
This approach offers a computationally efficient alternative to multi-determinantal methods.
The developed benchmark set is valuable for evaluating strong correlation functionals.