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

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.