ABACUS: An Electronic Structure Analysis Package for the AI Era

TL;DR

ABACUS presents a modular, open-source platform for first-principles electronic structure calculations and molecular dynamics that embraces AI-era innovations. It supports both plane-wave and numerical atomic orbital bases and integrates KS-DFT, stochastic DFT, OF-DFT, hybrid functionals, DeePKS, and rt-TDDFT, with scalable implementations on HPC architectures. A key contribution is the deep integration with AI-assisted models (DeePKS, DPA, DeepH, HamGNN, etc.) and data-generation initiatives (OpenLAM, APNS, UniPero), enabling efficient generation of large-scale training data and near-quantum accuracy potentials across thousands of elements. The combination of advanced physics-based methods, ML-enhanced functionals, and broad interoperability (via DeePKS-kit, DeePMD-kit, DP-GEN, LibRI, PEXSI, etc.) positions ABACUS as a versatile engine for AI4ES-driven materials discovery and large-scale simulations.

Abstract

ABACUS (Atomic-orbital Based Ab-initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and molecular dynamics functions and is compatible with both plane-wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, and real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as DPA models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several AI-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, HamGNN, etc.

Figures (34)

• Figure 1: ABACUS is dedicated to building an algorithm platform and data engine for AI4ES (AI for Electronic Structure). Since partnering with the open-source community DeepModeling in 2021, ABACUS has garnered over 7,300 commits under the protection of Continuous Integration (CI) tests. Its adaptable architecture allows developers to incorporate numerous electronic structure algorithms. The AI-assisted functional correction method DeePKS permits ABACUS to achieve precise functional results at a reduced cost. Owing to high-performance implementation at various devices, ABACUS effectively produces extensive first-principles data across multiple sectors. Combining advanced electronic structure algorithms and AI-assisted pre-trained models, one can transfer the precision of quantum mechanics across scales.
• Figure 2: Code architecture of ABACUS. For users, a few input files need to be prepared in advance, including INPUT, STRU, KPT, pseudopotential files, and orbital files (only for numerical atomic orbitals calculations). For developers, the software features a highly modular design that allows for the swift integration of new functionalities. The development team is responsible for formulating and refining key data structures, mathematical routines, and other foundational components in ABACUS. For instance, the HContainer module is utilized for storing sparse matrices under the numerical atomic orbital basis set, such as Hamiltonian and density matrices; the Grid Integral module is implemented for grid integration.
• Figure 3: ABACUS performs self-consistent field (SCF) calculations with two available basis sets: PW and NAOs. The PW basis set employs iterative diagonalization methods like CG and Davidson to solve the Kohn-Sham equations. For NAOs, it uses exact diagonalization or the low-scaling method PEXSI. CMS2009JCPM2013 ABACUS applies different mixing algorithms for various types of calculations, including non-magnetic, collinear, and non-collinear. Additionally, ABACUS supports the density matrix mixing method for DFT+U, hybrid functionals (EXX), and DeePKS calculations with the NAO basis set.
• Figure 4: (a) Differences in SCF performance score ( vide infra) between v3.4 and v3.5 on the selection set of 21 examples. Prior to v3.4, the residual was defined by $\rho_{\uparrow}$ and $\rho_{\downarrow}$, whereas starting from v3.5, the residual is defined by the charge density and the magnetic density, and they are mixed separately. Since some test cases failed to converge in v3.4, we present results with convergence scores rather than directly using convergence steps. The max number of iterations is set to 100 in all calculations, and the SCF convergence threshold scf_thr=1e-6. The SCF score is defined by $|\rm log_{10}(\delta\rho_{\rm last})|\times 10 \times \frac{100}{\rm N_{step}}$, where $\delta \rho_{\rm last}$ is the density difference $R(\rho_{in})$ of the last iteration and $\rm N_{step}$ is the number of convergence iterations. (b) Difference in SCF convergence step ($\rm N_{step}$) for the DFT+U calculation with only mixing charge density and both mixing charge density and density matrix. Here, "JT" represents a structure under Jahn–Teller distortion. 2013-JT-effct For the sake of reproduction, we have made public all the details of the calculations in the link, magnetic-mixing-pr where one can find the complete report and download all input files.
• Figure 5: (a) Diffusion coefficients of D in liquid $\mathrm{Sn_{0.96}D_{0.04}}$, Sn in $\mathrm{Sn_{0.96}D_{0.04}}$, and Sn in pure liquid Sn as a function of temperature. (b) Diffusion coefficients of D and Sn in liquid $\mathrm{Sn_{1-x}D_x}$ at 1073 K with $x$ being 0.009, 0.027, 0.036, 0.044, and 0.085. (Adapted with permission from J. Chem. Phys. 147, 064505 (2017). Copyright 2017 AIP Publishing.)