Gaussian-Approximated Poisson Preconditioner for Iterative Diagonalization in Real-Space Density Functional Theory.

Area of Science:

• Computational Materials Science
• Quantum Chemistry
• Biophysics

Background:

• Real-space methods are crucial for large-scale density functional theory (DFT) calculations of materials and biomolecules on parallel computers.
• Iterative diagonalization of the Hamiltonian matrix presents a significant computational bottleneck in these real-space DFT calculations.
• Existing iterative eigensolvers are limited by the lack of efficient real-space preconditioners, hindering overall computational efficiency.

Purpose of the Study:

• To develop an efficient real-space preconditioner that accelerates convergence and minimizes computational cost for DFT calculations.
• To introduce the Gaussian-approximated Poisson preconditioner (GAPP) as a solution to the bottleneck in iterative eigensolvers.

Main Methods:

• Proposed a novel Gaussian-approximated Poisson preconditioner (GAPP).
• Achieved low computational cost by approximating the Poisson Green's function with Gaussian functions.
• Ensured fast convergence by optimizing Gaussian coefficients to accurately represent Coulomb energies.

Main Results:

• The GAPP preconditioner satisfies the dual requirements of accelerated convergence and inexpensive computation.
• Evaluated GAPP's performance on various molecular and extended systems.
• GAPP demonstrated superior efficiency compared to existing preconditioners used in real-space DFT codes.

Conclusions:

• The GAPP preconditioner is a highly efficient and suitable tool for real-space DFT calculations.
• This method effectively addresses the computational bottleneck in large-scale electronic structure calculations.
• GAPP significantly enhances the performance of real-space electronic structure codes.