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A coherent discrete variable representation method for multidimensional systems in physics.

Hua-Gen Yu1

  • 1Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973-5000, USA. hgy@bnl.gov

The Journal of Chemical Physics
|June 11, 2005
PubMed
Summary
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A new zero-dimensional discrete variable representation (ZDVR) method efficiently constructs multidimensional potential-optimized DVR bases. This approach achieves exponential convergence and accurate energy calculations for vibrational models.

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Molecular Modeling

Background:

  • Discrete Variable Representations (DVR) are crucial for solving quantum mechanical problems.
  • Developing efficient multidimensional DVR bases remains a challenge.

Purpose of the Study:

  • To introduce a novel coherent discrete variable representation (ZDVR) for constructing multidimensional potential-optimized DVR bases.
  • To demonstrate the efficacy of the ZDVR method for calculating vibrational energy levels.

Main Methods:

  • Diagonalization of a complex coordinate operator matrix in a finite basis set.
  • Utilizing a c-norm condition during diagonalization.
  • Employing orthonormal eigenvectors to form a collocation matrix linking ZDVR and finite basis sets.

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Main Results:

  • The ZDVR method exhibits exponential convergence for calculating bound states.
  • Accurate energy values were obtained for two vibrational models.
  • A zeroth-order approximation method was successfully derived.

Conclusions:

  • The proposed ZDVR method offers a powerful and efficient approach for multidimensional quantum mechanical calculations.
  • ZDVR provides a significant advancement in computational chemistry and physics for determining molecular properties.