Variational solution of Poisson's equation using plane waves in adaptive coordinates.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Solving Poisson's equation is crucial for electronic structure calculations.
• The supercell approximation is often required for accurate Coulomb potential calculations in isolated systems.
• Existing methods face challenges in efficiently handling long-range interactions.

Purpose of the Study:

• To develop a plane wave method for solving Poisson's equation in adaptive coordinates.
• To enable accurate calculations of Coulomb potentials for isolated atoms and molecules.
• To avoid the computational overhead of the supercell approximation.

Main Methods:

• A trial potential is expressed as a product of a Coulomb weight and a plane wave expansion in adaptive coordinates.
• Variational optimization of the trial potential minimizes the error in Coulomb energy.
• A specific Coulomb weight is chosen to incorporate the long-range behavior of Coulomb potentials.

Main Results:

• The method accurately calculates Coulomb potentials for isolated systems.
• Tests on helium, H2, and H3+ yield Hartree-Fock energies with high accuracy (better than milli-Hartree).
• The approach requires only a moderate number of plane waves, demonstrating efficiency.

Conclusions:

• The described plane wave method offers an efficient and accurate alternative for calculating Coulomb potentials.
• It eliminates the need for the supercell approximation in atomic and molecular electronic structure calculations.
• This method has significant implications for computational chemistry and materials science.