Preconditioning orbital minimization method for planewave discretization

TL;DR

This paper introduces a new preconditioner for the orbital minimization method in planewave discretizations, significantly reducing iteration counts and improving computational efficiency in electronic structure calculations.

Contribution

A novel preconditioner combining approximate Fermi operator projection with a sparsifying preconditioner for planewave discretized Hamiltonians.

Findings

Iteration number reduced to O(1)

Few iterations needed for convergence

Validated performance through numerical experiments

Abstract

We present an efficient preconditioner for the orbital minimization method when the Hamiltonian is discretized using planewaves (i.e., pseudospectral method). This novel preconditioner is based on an approximate Fermi operator projection by pole expansion, combined with the sparsifying preconditioner to efficiently evaluate the pole expansion for a wide range of Hamiltonian operators. Numerical results validate the performance of the new preconditioner for the orbital minimization method, in particular, the iteration number is reduced to $O(1)$ and often only a few iterations are enough for convergence.