Progress of the ABACUS Software for Density Functional Theory and Its Integration and Applications with Deep Learning Algorithms

doi:10.11900/0412.1961.2024.00182

Acta Metall Sin

2024, Vol. 60

Issue (10): 1405-1417 DOI: 10.11900/0412.1961.2024.00182

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Progress of the ABACUS Software for Density Functional Theory and Its Integration and Applications with Deep Learning Algorithms

CHEN Mohan¹^,²(

)

1 HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871, China
2 AI for Science Institute, Beijing 100080, China

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CHEN Mohan. Progress of the ABACUS Software for Density Functional Theory and Its Integration and Applications with Deep Learning Algorithms. Acta Metall Sin, 2024, 60(10): 1405-1417.

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Abstract

Density functional theory (DFT), grounded in the fundamental principles of quantum mechanics, effectively predicts material properties and is now widely used across various research disciplines such as physics, chemistry, materials science, and biology. As research in materials science advances, there is an urgent need to further enhance the accuracy and efficiency of DFT. However, improving accuracy and efficiency is often challenging because these goals can be mutually exclusive. Recently, guided by the concept of AI for science, deep learning-based electronic structure calculation methods have rapidly emerged, offering potential solutions to resolve this accuracy-efficiency dilemma. Nonetheless, developing a stable and reliable DFT software platform remains a substantial challenge in exploring and expanding the use of AI-assisted methods on a broader scale. This paper introduces the open-source DFT package ABACUS (atomic-orbital based ab-initio computation at UStc), focusing on its physical models, deep learning algorithms, and software development aspects. The present discussion emphasizes the progress of the open-source package, highlighting its integration with deep learning algorithms and its evolution from version 2.2 (released in April 2022) to version 3.7 (released in July 2024).

Key words: ABACUS density functional theory open-source software deep learning computational materials science

Received: 29 May 2024

ZTFLH:

O469

Fund: National Natural Science Foundation of China(12122401,12135002)

Corresponding Authors: CHEN Mohan, Tel: (010)62757475, E-mail: mohanchen@pku.edu.cn

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Fig.1 DeePKS algorithm has been implemented within the self-consistent loop in ABACUS^[71] (The Hamiltonian value for the DeePKS and the base methods are depicted as H_DeePKS and H_base, respectively. In addition, the difference of the above two Hamiltonians is labeled as H_δ . The electronic wave function and eigenvalue for the $i$ th state are labeled as ψ_i and ε_i, respectively. E_DeePKS—is the total energy from the DeePKS method) (a); DeePKS algorithm can achieve the accuracy of Hybrid functionals or more precise quantum chemistry methods by incorporating corrections from deep neural networks on top of LDA or GGA functionals (b); and forces on a given single water molecule were calculated using the PBE functional (F_PBE), the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional (F_HSE) and the DeePKS model (F_DeePKS), and the results showed that the DeePKS method's outcomes correspond well with those from the HSE. The label O refers to the oxygen atom while H_A and H_B refer to the two hydrogen atoms of a water molecule, respectively (c)

Fig.2 DPA, a large model based on deep neural networks, is used to train potential functions that can describe various semiconductor materials, where the first-principles training data all come from ABACUS calculations (a); DPA-Semi model generated through training also serves as an interatomic potential function, which can be used in various semiconductor simulations (b); and using the DPA-Semi model, the computed melting points of 19 semiconductors (Si, Ge, SiC, BAs, BN, AlN, AlP, AlAs, InP, InAs, InSb, GaN, GaP, GaAs, CdTe, InTe, CdSe, ZnS, CdS) obtained by the direct heating method (red dots) and the two-phase method (green dots) are relatively close to the experimental melting points (c)^[77]

Fig.3 Based on deep learning methods, an electronic kinetic energy density functional for machine learning is constructed, thus obtaining the electron kinetic energy and electron kinetic energy potential functions. This function introduces descriptors of free electron gas (FEG) and ensures that the electron kinetic energy satisfies physical conditions such as the free electron gas limit (a); new electronic kinetic energy functional machine-learning-based physical-constrained nonlocal (MPN), when applied to metallic systems such as Li, Mg, and Al, attained equilibrium volumes similar to those obtained with the Wang-Teter (WT) and Wang-Godvind-Carter (WGC) electronic kinetic energy functionals and demonstrated superior performance compared to other functionals like the TF $λ$ vW and Luo-Karasiev-Trickey (LKT) functionals. Mean absolute relative error (MARE) of equilibrium volume is shown (V—equilibrium volume) (b); and MPN function has been applied to a variety of alloy systems to predict their formation energy, and compared to the results of the Kohn-Sham density functional theory, MPN exhibits better predictive performance (E—formation energy, OFDFT and KS-BLPS stand for orbital-free density functional theory and Kohn-Sham method with the bulk-derived local pseudopotentials, respectively) (c)^[84]

Date of releasing ABACUS	Version	Content
2022.04.08	v2.2	Version 2.2 went through 3,200 commit modifications on GitHub from version 2.1, and the development team includes developers from various domestic research institutions
2022.07.01	v2.3	Version 2.3 incorporates new plane wave generation and parallel modules, enhancing support for parallel computing with plane wave basis sets; the functionalities of the stochastic wave function density functional theory method have been released
2022.10.01	v3.0	Version 3.0 has been released with the deep learning-based DeePKS functional approach based on periodic boundary conditions. Interfaces with the machine learning potential function method DeePMD-kit and the DP-GEN method have been released, as well as interfaces with the DeepH method for constructing Hamiltonians of electronic systems through machine learning
2023.01.01	v3.1	Version 3.1 has been released with support for GPU and domestic DCU hardware in plane-wave basis set solutions for the Kohn-Sham equations, and introduces new features for the computation of solid-liquid interfaces
2023.04.01	v3.2	Version 3.2 has been released with an interface for Hefei-NAMD software. The coverage of unit tests has increased to 60%, and the total coverage is now 76%
2023.07.13	v3.3	Version 3.3 introduces an interface for calculating hybrid functionals with LibRI, and an interface with ShengBTE software for conducting material thermal conductivity calculations
2023.10.07	v3.4	Version 3.4 primarily supports the DPA method, a machine learning potential function for universal large models, and has reconstructed core algorithms such as more efficient and reliable numerical atomic orbital two-center integrals
2023.12.29	v3.5	Version 3.5 improved the algorithm for charge mixing and supported ultrasoft pseudopotentials for plane-wave basis sets, with targeted code development and optimization for three practical application scenarios: semiconductors, alloys, and batteries
2024.04.01	v3.6	Version 3.6 has released a more stable and reliable DFT + U algorithm function and further optimized the program's computational performance on Sunway DCU hardware
2024.07.01	v3.7	Version 3.7 has further supported the OpenLAM Large Atom Model project on a larger scale

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