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Related Experiment Video

Updated: Jul 12, 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

Tensor product approximation with optimal rank in quantum chemistry.

Sambasiva Rao Chinnamsetty1, Mike Espig, Boris N Khoromskij

  • 1Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany.

The Journal of Chemical Physics
|September 4, 2007
PubMed
Summary

This study introduces a new compression algorithm for tensor product decompositions, offering an efficient alternative for electronic structure calculations. The method optimizes tensor approximations, improving the evaluation of Coulomb integrals in quantum chemistry.

Related Experiment Videos

Last Updated: Jul 12, 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

Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Numerical Analysis

Background:

  • Traditional Gaussian-type basis functions are computationally intensive in electronic structure calculations.
  • Tensor product decompositions offer a promising alternative for representing complex molecular data.
  • Efficient methods are needed to handle large tensors in quantum chemistry.

Purpose of the Study:

  • To present a novel compression algorithm for tensor product decompositions.
  • To demonstrate the algorithm's effectiveness in approximating electron density and Hartree potentials.
  • To explore applications within density fitting schemes in quantum chemistry.

Main Methods:

  • Utilizing a Newton-based method for optimal tensor product decomposition.
  • Achieving best separable approximations for tensors with fixed Kronecker rank.
  • Employing a stable quadrature scheme for Coulomb interaction evaluation.
  • Representing tensor components in a wavelet basis for efficient storage.

Main Results:

  • The algorithm successfully computes best separable approximations for molecular electron density and Hartree potentials.
  • Tensor product formats enable efficient evaluation of Coulomb integrals.
  • Numerical analysis confirms the viability and potential for improvement of the approach.
  • Individual tensor components are efficiently represented using wavelet bases.

Conclusions:

  • The developed compression algorithm provides an efficient alternative for electronic structure calculations.
  • The method shows significant potential for integration into density fitting schemes.
  • This approach offers a pathway for advancing computational efficiency in quantum chemistry.