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Variational solution of the three-dimensional Schrödinger equation using plane waves in adaptive coordinates.

José M Pérez-Jordá1

  • 1Departament de Química Física, Universitat d'Alacant, E-03080, Alacant, Spain. jmpj@ua.es

The Journal of Chemical Physics
|December 2, 2011
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Summary

This study enhances Gygi's method for solving the Schrödinger equation using adaptive coordinates and plane waves. The improved approach accurately models atoms and molecules without approximations, achieving high accuracy for electronic structure calculations.

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Area of Science:

  • Computational physics
  • Quantum chemistry
  • Materials science

Background:

  • The Gygi method offers a plane-wave approach to solving the Schrödinger equation in adaptive coordinates.
  • Existing methods often rely on approximations like the supercell approximation and pseudo-potentials.
  • Accurate solutions to the Schrödinger equation are crucial for understanding atomic and molecular behavior.

Purpose of the Study:

  • To present significant improvements to Gygi's method for solving the three-dimensional Schrödinger equation.
  • To enable the application of the method to atoms and molecules without supercell approximations.
  • To eliminate the need for pseudo-potentials by precisely handling electron-nucleus singularities.

Main Methods:

  • Implementation of novel coordinate maps for adaptive representations.
  • Exact removal of electron-nucleus singularities.
  • Minimization of sampling errors in integral evaluations for variational accuracy.

Main Results:

  • The enhanced method successfully models atoms and molecules without the supercell approximation.
  • Electron-nucleus singularities are precisely addressed, removing the necessity for pseudo-potentials.
  • Negligible sampling errors lead to a true variational, second-order energy error procedure.
  • Testing on hydrogen atom and H(2)(+) molecule yields milli-Hartree accuracy.

Conclusions:

  • The presented improvements significantly advance the Gygi method for electronic structure calculations.
  • The method offers a highly accurate and efficient approach for atomic and molecular systems.
  • This work paves the way for more precise quantum mechanical simulations.