Adaptively Compressed Polarizability Operator for Accelerating Large Scale <i>Ab Initio</i> Phonon Calculations | Multiscale Modeling & Simulation | Vol. 15, No. 1 | Society for Industrial and Applied Mathematics

Phonon calculations based on first principle electronic structure theory, such as the Kohn–Sham density functional theory, have wide applications in physics, chemistry, and material science. The computational cost of first principle phonon calculations typically scales steeply as O(N4 e ), where Ne is the number of electrons in the system. In this work, we develop a new method for reducing the computational complexity of computing the full dynamical matrix, and hence the phonon spectrum, to O(N3 e ). The key concept for achieving this is to compress the polarizability operator adaptively with respect to the perturbation of the potential due to the change of the atomic configuration. Such an adaptively compressed polarizability operator allows accurate computation of the phonon spectrum. The reduction of complexity only weakly depends on the size of the band gap, and our method is applicable to insulators as well as semiconductors with small band gaps. We demonstrate the effectiveness of our method using one-dimensional and two-dimensional model problems.