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Related Concept Videos

Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
Relating Angular And Linear Quantities - II01:05

Relating Angular And Linear Quantities - II

In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the relation:
Relating Angular And Linear Quantities - I01:09

Relating Angular And Linear Quantities - I

If the rotational definitions are compared with the definitions of linear kinematic variables from motion along a straight line and motion in two and three dimensions, we can observe a mapping of the linear variables to the rotational ones.
When comparing the linear and rotational variables individually, the linear variable of position has physical units of meters, whereas the angular position variable has dimensionless units of radians, as it is the ratio of two lengths. The linear velocity...
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.
Introduction to Scalers01:21

Introduction to Scalers

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume, temperature, and energy are some examples of scalar quantities.
Scalar...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.

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Related Experiment Video

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Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

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Published on: October 1, 2011

Linear scaling multireference singles and doubles configuration interaction.

Tsz S Chwee1, Andrew B Szilva, Roland Lindh

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|June 17, 2008
PubMed
Summary
This summary is machine-generated.

A new linear scaling multireference singles and doubles configuration interaction (MRSDCI) method accelerates quantum chemistry calculations. This approach enables efficient computation of potential energy surfaces for larger chemical systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Multireference singles and doubles configuration interaction (MRSDCI) is computationally demanding.
  • Existing methods face bottlenecks in calculating electron repulsion integrals and diagonalizing the CI Hamiltonian matrix.

Purpose of the Study:

  • To develop a linear scaling MRSDCI method.
  • To reduce the computational cost of MRSDCI calculations.

Main Methods:

  • Utilized localized bases for occupied and virtual subspaces.
  • Implemented local truncation schemes and integral screening.
  • Achieved linear scaling in integral evaluation, transformation, and Hamiltonian diagonalization.

Main Results:

  • Demonstrated linear scaling of the MRSDCI method with system size using alkane chains.
  • Successfully generated smooth potential energy surfaces.
  • Calculated the dissociation of trans-6-dodecene along its central C=C bond.

Conclusions:

  • The developed linear scaling MRSDCI method significantly enhances computational efficiency.
  • This method is capable of accurately modeling chemical processes and molecular properties for larger systems.