First-principle polarizabilities of nanosystems from auxiliary density perturbation theory with MINRES

Abstract

The iterative Krylov solver MINRES for linear equation systems has been implemented into auxiliary density perturbation theory. To this end, the MINRES solver was incorporated into the Eirola-Nevanlinna algorithm for large nonsymmetric matrices. As a result, the formal scaling of ADPT is reduced from ${\mathcal {O}}$($N_{\rm {aux}}^4$) to ${\mathcal {O}}$($N_{\rm {aux}}^3$), being $N_{\rm {aux}}$ the number of auxiliary functions. Moreover, with MINRES this scaling can be further reduced by the use of the double asymptotic expansion of the two-center electron repulsion integrals. This state-of-the-art solver allows first-principles quantum-mechanical calculations of response properties for large systems with thousands of atoms at the nanometric scale. Comparison between the analytic and iterative solutions show excellent agreement for static and dynamical polarizabilities. To demonstrate the robustness of this newly implemented methodology, static polarizabilities of microbiologically relevant systems with more than 100,000 auxiliary functions and 28,000 basis functions are presented in this work.