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Inertia Tensor01:24

Inertia Tensor

The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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Extraction: Partition and Distribution Coefficients

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Cartesian Form for Vector Formulation01:26

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Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Related Experiment Video

Updated: Jun 10, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

An efficient matrix-matrix multiplication based antisymmetric tensor contraction engine for general order coupled

Michael Hanrath1, Anna Engels-Putzka

  • 1Institute for Theoretical Chemistry, University of Cologne, Greinstrasse 4, 50939 Cologne, Germany. michael.hanrath@uni-koeln.de

The Journal of Chemical Physics
|August 17, 2010
PubMed
Summary

We developed an efficient tensor contraction method for coupled-cluster calculations. This new approach significantly improves computational performance for complex quantum chemistry simulations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • Coupled-cluster (CC) methods are crucial for accurate electronic structure calculations.
  • Efficient evaluation of tensor contractions is vital for CC program performance.

Purpose of the Study:

  • To present an efficient, flexible implementation of general tensor contractions for CC programs.
  • To handle CC-type expressions of arbitrary excitation levels.

Main Methods:

  • A three-step procedure: tensor data rearrangement into matrices, matrix-matrix multiplication, and result back-transformation.
  • A generic procedure for contractions of two tensors, independent of their structure.

Main Results:

  • The implementation demonstrates significantly improved efficiency compared to previous methods.
  • The approach maintains flexibility for arbitrary excitation levels in CC calculations.

Conclusions:

  • The developed tensor contraction method offers a substantial performance enhancement for CC calculations.
  • This advancement facilitates more complex and higher-level CC simulations.