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Related Experiment Videos

About the variational property of generalized discrete variable representation.

Viktor Szalay1

  • 1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary. szalay.viktor@wigner.mta.hu

The Journal of Physical Chemistry. A
|March 27, 2013
PubMed
Summary

The generalized discrete variable representation is not variational regarding basis set size or grid point selection. This analysis clarifies limitations in quantum chemistry calculations using this method.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • The discrete variable representation (DVR) is a powerful numerical method in quantum mechanics.
  • Variational methods are crucial for obtaining accurate approximations in quantum calculations.
  • Generalized discrete variable representations (GDVR) extend DVR but may introduce complexities.

Purpose of the Study:

  • To investigate the variational nature of the generalized discrete variable representation (GDVR).
  • To determine if GDVR maintains variational properties with respect to basis set truncation and grid point selection.

Main Methods:

  • Theoretical analysis of the GDVR formalism.
  • Examination of the mathematical conditions for variationality in DVR methods.

Main Results:

  • The GDVR is demonstrated to be non-variational concerning basis set truncation.
  • The GDVR is also shown to be non-variational with respect to the choice of grid points.

Conclusions:

  • The GDVR does not inherently satisfy the variational principle for basis set size.
  • The selection of grid points in GDVR also compromises its variational character.
  • These findings highlight important considerations for applying GDVR in quantum mechanical calculations.