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Related Concept Videos

Calibration Curves: Correlation Coefficient01:10

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...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

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. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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...
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...

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Related Experiment Video

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Linear scaling coupled cluster method with correlation energy based error control.

Marcin Ziółkowski1, Branislav Jansík, Thomas Kjaergaard

  • 1Department of Chemistry, The Lundbeck Foundation Center for Theoretical Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Arhus C, Denmark. marcin@chem.au.dk

The Journal of Chemical Physics
|July 10, 2010
PubMed
Summary

This study introduces a novel computational method for large molecular systems using coupled cluster calculations on small orbital fragments. The approach ensures controlled accuracy in correlation energy calculations, offering a scalable and parallelizable solution.

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Area of Science:

  • Quantum Chemistry
  • Computational Molecular Science

Background:

  • Coupled cluster (CC) calculations are accurate but computationally expensive for large molecular systems.
  • Accurate correlation energy calculations are crucial for understanding molecular properties and reactions.

Purpose of the Study:

  • To develop a computationally efficient method for performing coupled cluster calculations on large molecular systems.
  • To control the error in correlation energy by optimizing fragment calculations.
  • To enable CC calculations on systems previously inaccessible due to computational cost.

Main Methods:

  • Utilizes small orbital fragments of the full molecular orbital space for calculations.
  • Employs a "black box" approach for determining orbital spaces, independent of user-defined fragmentation.
  • Orbital spaces are dynamically selected and extended to achieve specified precision in fragment energies.

Main Results:

  • The method scales linearly with the size of the molecular system.
  • The computational approach is massively parallel, allowing for efficient execution on modern hardware.
  • Error in the full system's correlation energy is directly controlled by fragment calculation precision.

Conclusions:

  • This fragment-based coupled cluster approach offers a scalable and accurate solution for large molecular systems.
  • The automated orbital space selection simplifies the application of high-level CC theory.
  • The method significantly expands the scope of accurate quantum chemical calculations in molecular science.