ADAPTIVELY COMPRESSED POLARIZABILITY OPERATOR FOR ACCELERATING LARGE SCALE AB INITIO PHONON CALCULATIONS

作者：Lin Lin^*; Xu Ze; Ying Lexing

来源：Multiscale Modeling and Simulation, 2017, 15(1): 29-55.

DOI：10.1137/16M1077325

• density functional perturbation theory
• phonon calculations
• adaptive compression
• polarizability operator
• Sternheimer equation
• Dyson equation

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(N-e(4)), where N-e, 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(N-e(3)). 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.

• 出版日期2017