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Related Concept Videos

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...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
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.
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
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:

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Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time
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Explicitly correlated multireference configuration interaction: MRCI-F12.

Toru Shiozaki1, Gerald Knizia, Hans-Joachim Werner

  • 1Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany.

The Journal of Chemical Physics
|January 26, 2011
PubMed
Summary

A new computational chemistry method, multireference configuration interaction with explicit electron-electron distance (MRCI-F12), achieves high accuracy with less computational cost. This method offers near complete basis set accuracy for various molecular systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Multireference configuration interaction (MRCI) is a standard method for electronic structure calculations.
  • Traditional MRCI methods suffer from slow basis set convergence, requiring large basis sets for accurate results.
  • Explicitly correlated methods can accelerate basis set convergence.

Purpose of the Study:

  • To develop an efficient explicitly correlated variant of the internally contracted multireference configuration interaction method (MRCI-F12).
  • To assess the performance of the MRCI-F12 method in terms of accuracy and computational cost.
  • To demonstrate the applicability of MRCI-F12 to challenging chemical problems.

Main Methods:

  • Development of an internally contracted multireference configuration interaction method incorporating explicit dependence on the electron-electron distance (MRCI-F12).
  • Utilization of the F12b approximation for computational efficiency.
  • Application of MRCI-F12 to calculate the singlet-triplet separation of methylene, dissociation energy of ozone, properties of diatomic molecules, and the reaction barrier/exothermicity of F + H(2).

Main Results:

  • The MRCI-F12 method exhibits significantly improved basis set convergence compared to traditional MRCI.
  • The method achieves near complete basis set MRCI accuracy even with moderately sized basis sets.
  • Quantitative agreement with experimental data was observed for all tested systems.
  • An explicitly correlated multireference averaged coupled pair functional method (MRACPF-F12) was also implemented.

Conclusions:

  • The MRCI-F12 method provides a computationally efficient and accurate approach for electronic structure calculations.
  • It offers a significant improvement over standard MRCI methods, particularly in basis set convergence.
  • MRCI-F12 is a valuable tool for studying various chemical phenomena with high fidelity.