A perspective on the density matrix purification for linear scaling electronic structure calculations

Abstract

Density matrix purification is a linear scaling algorithm to solve the self-consistent field (SCF) electronic structure problem. A brief review is made of the two usages of the purification method in SCF calculations, namely in direct energy minimization and for iterative calculation of density matrix from Hamiltonian. Density matrix purification can be viewed as a minimization algorithm of the particularly defined objective function such as , and hence, this objective function plays a key role in the developments of purification polynomials. Indeed, in this perspective, we show that a carefully chosen objective function can lead to significantly improved algorithms and numerical results.