[Paper Review] Large-scale ab initio simulations based on systematically improvable atomic basis

Pengfei Li, Xiaohui Liu+6 more|arXiv (Cornell University)|Feb 28, 2015

Electron and X-Ray Spectroscopy Techniques4 citations

TL;DR

This paper presents ABACUS, a first-principles DFT code based on systematically improvable numerical atomic basis sets derived from the Chen-Guo-He scheme. It enables large-scale, accurate simulations of molecules, solids, surfaces, and defects with efficient force calculations using optimized basis sets and linear-scaling algorithms.

ABSTRACT

We present a first-principles computer code package (ABACUS) that is based on density functional theory and numerical atomic basis sets. Theoretical foundations and numerical techniques used in the code are described, with focus on the accuracy and transferability of the hierarchical atomic basis sets as generated using a scheme proposed by Chen, Guo and He [J. Phys.:Condens. Matter extbf{22}, 445501 (2010)]. Benchmark results are presented for a variety of systems include molecules, solids, surfaces, and defects. All results show that the ABACUS package with its associated atomic basis sets is an efficient and reliable tool for simulating both small and large-scale materials.

Motivation & Objective

• To develop a scalable, accurate, and reliable first-principles DFT code for large-scale materials simulations.
• To implement a systematically improvable atomic basis set generation scheme that ensures transferability and accuracy across diverse materials.
• To enable efficient force calculations using numerical atomic orbitals, including Feynman-Hellmann, Pulay, and non-orthogonality forces.
• To support both atomic orbital and plane-wave basis sets for cross-verification and consistency checks.
• To integrate advanced functionals such as LDA, GGA (PBE), and DFT-D2 for van der Waals corrections.

Proposed method

• Employs density functional theory (DFT) with Kohn-Sham formalism and numerical atomic orbitals as basis functions.
• Uses the Chen-Guo-He scheme to generate hierarchical, systematically improvable atomic basis sets with high transferability.
• Implements the Pole-Expanion and Selected Inversion (PEXSI) method to achieve sub-cubic scaling (≤O(N²)) for large systems.
• Calculates forces via the Feynman-Hellmann, Pulay, and non-orthogonality contributions using two-center integral techniques.
• Evaluates derivatives of atomic orbitals with respect to atomic coordinates using radial grid interpolation and real spherical harmonics.
• Supports pseudopotentials in the Unified Pseudopotential Format (UPF) and includes LDA, GGA, and DFT-D2 functionals.

Experimental results

Research questions

• RQ1 Can a first-principles code based on systematically improvable atomic basis sets achieve high accuracy and transferability across diverse materials?
• RQ2 How efficiently can such a code perform large-scale DFT simulations with linear-scaling algorithms?
• RQ3 What is the accuracy of force calculations, including Pulay and non-orthogonality contributions, in systems with non-orthogonal atomic orbitals?
• RQ4 Can the dual basis capability (atomic orbitals and plane waves) ensure consistency and reliability in benchmark simulations?
• RQ5 How well do the optimized basis sets perform for complex systems such as surfaces, defects, and extended solids?

Key findings

• The ABACUS package successfully performs large-scale ab initio simulations with both small and large systems, demonstrating high efficiency and reliability.
• Benchmark results for molecules, solids, surfaces, and defects confirm the accuracy and transferability of the Chen-Guo-He generated basis sets.
• The use of PEXSI enables Kohn-Sham DFT calculations with scaling as low as O(N^α), where α ≤ 2, for both insulating and metallic systems.
• Force calculations are accurate and efficient, with the Feynman-Hellmann, Pulay, and non-orthogonality forces computed via optimized numerical and analytical techniques.
• The dual-basis capability (atomic orbitals and plane waves) allows for cross-verification and consistency checks, enhancing confidence in simulation results.
• The implementation of LDA, GGA (PBE), and DFT-D2 functionals enables accurate treatment of exchange-correlation effects, including van der Waals interactions.