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In this work we present and evaluate an implementation of thepurify-shift-and-project method [J. Chem. Phys. 128, 176101 (2008)] for linearscaling computation of multiple eigenvectors around the homo-lumo gap of theFock/Kohn-Sham matrix. Recursive polynomial expansions allow for linear scalingdensity matrix construction if matrices are sufficiently sparse. However, adrawback is that, compared to the traditional diagonalization approach,eigenvectors of the Fock/Kohn-Sham matrix are not readily available. The sharppolynomial filter, constructed in intermediate iterations of the recursivepolynomial expansion, increases the relative separation of eigenvalues near thehomo-lumo gap. The computed density matrix approximation is used to projectaway the uninteresting part of the spectrum, so that the eigenvalues ofinterest become the extreme eigenvalues, enabling fast convergence of a Lanczoseigensolver. We implement the purify-shift-and-project algorithm in the quantumchemistry program Ergo [SoftwareX 7, 107 (2018)]. We illustrate the performanceof the method by computing 30 eigenvectors around the homo-lumo gap for largescale systems.

Multiple eigenvectors around the homo-lumo gap as a cheap by-product in linear scaling electronic structure calculations