Department of Physics, NCU
NOPAIN: A Method for Efficient Evaluation of Quantum Nonlocal Operators with Applications to Solids
Speaker
Dr. Ying-Chih Chen
Physics Department, McGill University
Date 2019.02.21 (Thur)
Time 14:00-16:00
Place S4-208I (Center for Mathematics and Theoretical Physics)
Abstract:
The computation efficiency of numerical atomic orbitals (NAOs) is high due to its localized property, i.e., the orbital spatial value is strictly zero beyond a given radius cutoff. If two NAOs do not spatially overlap, the matrix element of any local operator is zero. This makes NAOs attractive for the research of order-N methods, for which the computational scaling is linear with the basis size N. However, the matrix element of a nonlocal operator is not always zero if two NAOs do not spatially overlap. Thus all matrix elements should be calculated to ensure accuracy. While this is not a problem for isolated systems like molecules, an artificial distance truncation is usually applied for periodic systems. The artificial distance truncation assumes that if the distance between two atoms is larger than a manually defined distance, the corresponding matrix element is zero. This assumption is in general not true since the Coulomb operator, as well as many other nonlocal operators, are long-range. Its spatial interaction strength decays slowly and such approximation degrades accuracy.
We solved this problem by developing a novel method which combines plane waves (PWs) and NAOs to efficiently evaluate nonlocal operators under periodic boundary conditions. Our method is denoted as NOPAIN (Nonlocal Operators with Plane wAves Integrated into Numerical atomic orbitals). Nonlocal operators are first expanded using PWs and then transformed to an NAO representation so that the problem of distance-truncation is avoided. In the meantime, the computation complexity is reduced due to NAO basis sets, thus makes this method applicable to large systems. The general formalism has been implemented in the RESCU package, a MATLAB-based density-functional theory (DFT) software, within the hybrid functional approach where the nonlocal operator is the (short-range) Fock exchange. Comparison of electronic structures of a wide range of semiconductors to a pure PW scheme validates the accuracy of NOPAIN. Furthermore, we applied our method to two realistic systems which require the hybrid-functional to accurately calculate the band gap and the band alignment. Both systems contain hundreds to a thousand atoms in the supercell which could hardly be investigated at the hybrid-functional level before even using supercomputers.