Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Correlation01:09

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:
Correlations02:20

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...
Coefficient of Correlation01:12

Coefficient of Correlation

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.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...
Correlation of Experimental Data01:23

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...
Static Equilibrium - II01:07

Static Equilibrium - II

Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...
Correlation and Regression00:53

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...

You might also read

Related Articles

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

Sort by
Same author

The Iso-Inverse: A Contravariant Sparse Approximate Inverse Matrix.

The journal of physical chemistry. A·2024
Same author

How delocalized are the polyacenes?

Journal of computational chemistry·2023
Same author

Economical Models for Electron Densities.

The journal of physical chemistry. A·2023
Same author

Ferrocenium Boronic Acid Catalyzed Deoxygenative Coupling of Alcohols with Carbon- and Nitrogen-Based Borate and Silane Nucleophiles.

The Journal of organic chemistry·2023
Same author

Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations.

The journal of physical chemistry. A·2023
Same author

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

Physical chemistry chemical physics : PCCP·2022
Same journal

Anharmonic phonons via quantum thermal bath simulations.

The Journal of chemical physics·2026
Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026
Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026
Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026
Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026
Same journal

Time reversal breaking of colloidal particles in cells.

The Journal of chemical physics·2026
See all related articles

Related Experiment Video

Updated: Jun 3, 2026

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
06:51

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

Published on: August 2, 2018

The two faces of static correlation.

Joshua W Hollett1, Peter M W Gill

  • 1Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia. jhollett@rsc.anu.edu.au

The Journal of Chemical Physics
|March 25, 2011
PubMed
Summary
This summary is machine-generated.

Investigating beryllium-like ions reveals that Restricted Hartree-Fock (RHF) to Unrestricted Hartree-Fock (UHF) instability vanishes for nuclear charge Z > 4.5. This study differentiates static correlation into two types, one captured by UHF and one not.

More Related Videos

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
14:12

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

Published on: December 11, 2021

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts
08:43

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

Published on: December 1, 2018

Related Experiment Videos

Last Updated: Jun 3, 2026

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
06:51

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

Published on: August 2, 2018

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
14:12

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

Published on: December 11, 2021

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts
08:43

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

Published on: December 1, 2018

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Atomic Physics

Background:

  • Restricted Hartree-Fock (RHF) and Unrestricted Hartree-Fock (UHF) are fundamental methods for approximating electronic wavefunctions.
  • Understanding electron correlation is crucial for accurate molecular and atomic property predictions.
  • Beryllium-like ions provide a tractable system for studying electron correlation effects.

Purpose of the Study:

  • To investigate the triplet instability of RHF wavefunctions transitioning to UHF wavefunctions for beryllium-like ions.
  • To analyze the behavior of correlation energy as a function of nuclear charge (Z).
  • To elucidate the nature of static correlation and its dependence on electronic near-degeneracy.

Main Methods:

  • Calculation of RHF and UHF wavefunctions using a near-complete Slater basis set.
  • Systematic study of the RHF → UHF instability for nuclear charges 3 ≤ Z ≤ 5.
  • Analysis using a minimal-basis model and comparison with the stretched H(2) molecule.

Main Results:

  • The RHF → UHF instability was found to vanish for nuclear charges Z > 4.5.
  • A minimal-basis model successfully reproduced this vanishing instability.
  • Static correlation was identified as having two distinct types (Type A and Type B).

Conclusions:

  • The study clarifies the dichotomy of static correlation, distinguishing between absolute and relative near-degeneracy.
  • Type A static correlation can be captured by UHF, while Type B cannot.
  • The findings provide a deeper understanding of electron correlation in atomic and molecular systems.