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Gu Q, Zhouyin Z, Pandey SK, Zhang P, Zhang L, E W. Deep learning tight-binding approach for large-scale electronic simulations at finite temperatures with ab initio accuracy. Nat Commun 2024; 15:6772. [PMID: 39117636 PMCID: PMC11310461 DOI: 10.1038/s41467-024-51006-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Accepted: 07/17/2024] [Indexed: 08/10/2024] Open
Abstract
Simulating electronic behavior in materials and devices with realistic large system sizes remains a formidable task within the ab initio framework due to its computational intensity. Here we show DeePTB, an efficient deep learning-based tight-binding approach with ab initio accuracy to address this issue. By training on structural data and corresponding ab initio eigenvalues, the DeePTB model can efficiently predict tight-binding Hamiltonians for unseen structures, enabling efficient simulations of large-size systems under external perturbations such as finite temperatures and strain. This capability is vital for semiconductor band gap engineering and materials design. When combined with molecular dynamics, DeePTB facilitates efficient and accurate finite-temperature simulations of both atomic and electronic behavior simultaneously. This is demonstrated by computing the temperature-dependent electronic properties of a gallium phosphide system with 106 atoms. The availability of DeePTB bridges the gap between accuracy and scalability in electronic simulations, potentially advancing materials science and related fields by enabling large-scale electronic structure calculations.
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Affiliation(s)
- Qiangqiang Gu
- AI for Science Institute, 100080, Beijing, China.
- School of Mathematical Science, Peking University, 100871, Beijing, China.
| | - Zhanghao Zhouyin
- AI for Science Institute, 100080, Beijing, China
- College of Intelligence and Computing, Tianjin University, 300350, Tianjin, China
| | - Shishir Kumar Pandey
- AI for Science Institute, 100080, Beijing, China
- Birla Institute of Technology & Science, Pilani-Dubai Campus, Dubai, 345055, UAE
| | - Peng Zhang
- College of Intelligence and Computing, Tianjin University, 300350, Tianjin, China
| | - Linfeng Zhang
- AI for Science Institute, 100080, Beijing, China
- DP Technology, 100080, Beijing, China
| | - Weinan E
- AI for Science Institute, 100080, Beijing, China
- School of Mathematical Science, Peking University, 100871, Beijing, China
- Center for Machine Learning Research, Peking University, 100871, Beijing, China
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Liu C, Aguirre NF, Cawkwell MJ, Batista ER, Yang P. Efficient Parameterization of Density Functional Tight-Binding for 5 f-Elements: A Th-O Case Study. J Chem Theory Comput 2024; 20:5923-5936. [PMID: 38990696 PMCID: PMC11270830 DOI: 10.1021/acs.jctc.4c00145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Revised: 06/23/2024] [Accepted: 06/26/2024] [Indexed: 07/13/2024]
Abstract
Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th-O system, which was subsequently applied to the study of ThO2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO2. Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.
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Affiliation(s)
- Chang Liu
- Theoretical Division, Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Néstor F. Aguirre
- Theoretical Division, Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Marc J. Cawkwell
- Theoretical Division, Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Enrique R. Batista
- Theoretical Division, Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ping Yang
- Theoretical Division, Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, United States
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Schwade M, Schilcher MJ, Reverón Baecker C, Grumet M, Egger DA. Temperature-transferable tight-binding model using a hybrid-orbital basis. J Chem Phys 2024; 160:134102. [PMID: 38557853 DOI: 10.1063/5.0197986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/13/2024] [Indexed: 04/04/2024] Open
Abstract
Finite-temperature calculations are relevant for rationalizing material properties, yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many explicit first-principles calculations, tight-binding and machine-learning models for the electronic structure emerged as promising alternatives, but transferability of such methods to elevated temperatures in a data-efficient way remains a great challenge. In this work, we suggest a tight-binding model for efficient and accurate calculations of temperature-dependent properties of semiconductors. Our approach utilizes physics-informed modeling of the electronic structure in the form of hybrid-orbital basis functions and numerically integrating atomic orbitals for the distance dependence of matrix elements. We show that these design choices lead to a tight-binding model with a minimal amount of parameters that are straightforwardly optimized using density functional theory or alternative electronic-structure methods. The temperature transferability of our model is tested by applying it to existing molecular-dynamics trajectories without explicitly fitting temperature-dependent data and comparison with density functional theory. We utilize it together with machine-learning molecular dynamics and hybrid density functional theory for the prototypical semiconductor gallium arsenide. We find that including the effects of thermal expansion on the onsite terms of the tight-binding model is important in order to accurately describe electronic properties at elevated temperatures in comparison with experiment.
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Affiliation(s)
- Martin Schwade
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Maximilian J Schilcher
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Christian Reverón Baecker
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Manuel Grumet
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - David A Egger
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
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Hu F, He F, Yaron DJ. Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results. J Chem Theory Comput 2023; 19:6185-6196. [PMID: 37705220 PMCID: PMC10536991 DOI: 10.1021/acs.jctc.3c00491] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Indexed: 09/15/2023]
Abstract
Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.
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Affiliation(s)
- Frank Hu
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Francis He
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - David J. Yaron
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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Bosia F, Zheng P, Vaucher A, Weymuth T, Dral PO, Reiher M. Ultra-fast semi-empirical quantum chemistry for high-throughput computational campaigns with Sparrow. J Chem Phys 2023; 158:054118. [PMID: 36754821 DOI: 10.1063/5.0136404] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE Sparrow.
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Affiliation(s)
- Francesco Bosia
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Peikun Zheng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Alain Vaucher
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Thomas Weymuth
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Pavlo O Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Markus Reiher
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
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McSloy A, Fan G, Sun W, Hölzer C, Friede M, Ehlert S, Schütte NE, Grimme S, Frauenheim T, Aradi B. TBMaLT, a flexible toolkit for combining tight-binding and machine learning. J Chem Phys 2023; 158:034801. [PMID: 36681630 DOI: 10.1063/5.0132892] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Tight-binding approaches, especially the Density Functional Tight-Binding (DFTB) and the extended tight-binding schemes, allow for efficient quantum mechanical simulations of large systems and long-time scales. They are derived from ab initio density functional theory using pragmatic approximations and some empirical terms, ensuring a fine balance between speed and accuracy. Their accuracy can be improved by tuning the empirical parameters using machine learning techniques, especially when information about the local environment of the atoms is incorporated. As the significant quantum mechanical contributions are still provided by the tight-binding models, and only short-ranged corrections are fitted, the learning procedure is typically shorter and more transferable as it were with predicting the quantum mechanical properties directly with machine learning without an underlying physically motivated model. As a further advantage, derived quantum mechanical quantities can be calculated based on the tight-binding model without the need for additional learning. We have developed the open-source framework-Tight-Binding Machine Learning Toolkit-which allows the easy implementation of such combined approaches. The toolkit currently contains layers for the DFTB method and an interface to the GFN1-xTB Hamiltonian, but due to its modular structure and its well-defined interfaces, additional atom-based schemes can be implemented easily. We are discussing the general structure of the framework, some essential implementation details, and several proof-of-concept applications demonstrating the perspectives of the combined methods and the functionality of the toolkit.
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Affiliation(s)
- A McSloy
- Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - G Fan
- Bremen Center of Computational Materials Science, University of Bremen, 28359 Bremen, Germany
| | - W Sun
- Bremen Center of Computational Materials Science, University of Bremen, 28359 Bremen, Germany
| | - C Hölzer
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - M Friede
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - S Ehlert
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - N-E Schütte
- Bremen Center of Computational Materials Science, University of Bremen, 28359 Bremen, Germany
| | - S Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - T Frauenheim
- Bremen Center of Computational Materials Science, University of Bremen, 28359 Bremen, Germany
| | - B Aradi
- Bremen Center of Computational Materials Science, University of Bremen, 28359 Bremen, Germany
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