1
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Qian Y, Li X, Chen J. Force and stress calculations with a neural-network wave function for solids. Faraday Discuss 2024. [PMID: 39058255 DOI: 10.1039/d4fd00071d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2024]
Abstract
Accurate ab initio calculations of real solids are of fundamental importance in fields such as chemistry, phases and materials science. Recently, variational Monte Carlo (VMC) based on neural-network wave functions has been developed as a promising option to solve the existing challenges in ab initio calculations. In this study, we discuss the calculation of interatomic forces and stress tensors of real solids with a neural-network-based VMC method. A new scheme for computing forces is proposed based on the space-warp coordination transformation method, which achieves better accuracy, efficiency and robustness than existing methods. In addition, we also designed new periodic features of the neural network to further improve the robustness of force calculations for different lattices. This work paves the way for further extending the application of machine-learning quantum Monte Carlo methods in materials modelling.
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Affiliation(s)
- Yubing Qian
- School of Physics, Peking University, Beijing 100871, People's Republic of China
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Xiang Li
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, People's Republic of China.
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2
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Aldossary A, Campos-Gonzalez-Angulo JA, Pablo-García S, Leong SX, Rajaonson EM, Thiede L, Tom G, Wang A, Avagliano D, Aspuru-Guzik A. In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2402369. [PMID: 38794859 DOI: 10.1002/adma.202402369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 04/28/2024] [Indexed: 05/26/2024]
Abstract
Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.
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Affiliation(s)
- Abdulrahman Aldossary
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | | | - Sergio Pablo-García
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
| | - Shi Xuan Leong
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Ella Miray Rajaonson
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Luca Thiede
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Gary Tom
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Andrew Wang
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Davide Avagliano
- Chimie ParisTech, PSL University, CNRS, Institute of Chemistry for Life and Health Sciences (iCLeHS UMR 8060), Paris, F-75005, France
| | - Alán Aspuru-Guzik
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
- Department of Materials Science & Engineering, University of Toronto, 184 College St., Toronto, ON, M5S 3E4, Canada
- Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5, Canada
- Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 66118 University Ave., Toronto, M5G 1M1, Canada
- Acceleration Consortium, 80 St George St, Toronto, M5S 3H6, Canada
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3
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Li X, Qian Y, Chen J. Electric Polarization from a Many-Body Neural Network Ansatz. PHYSICAL REVIEW LETTERS 2024; 132:176401. [PMID: 38728714 DOI: 10.1103/physrevlett.132.176401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Revised: 12/01/2023] [Accepted: 03/22/2024] [Indexed: 05/12/2024]
Abstract
Ab initio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wave function ansatz combined with quantum Monte Carlo method to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and reestablished its thickness dependence. Overall, this approach provides a powerful tool to accurately describe electron correlation in the modern theory of polarization.
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Affiliation(s)
- Xiang Li
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Yubing Qian
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, People's Republic of China
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4
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Jijila B, Nirmala V, Selvarengan P, Kavitha D, Arun Muthuraj V, Rajagopal A. Employing neural density functionals to generate potential energy surfaces. J Mol Model 2024; 30:65. [PMID: 38340208 DOI: 10.1007/s00894-024-05834-2] [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: 09/18/2023] [Accepted: 01/04/2024] [Indexed: 02/12/2024]
Abstract
CONTEXT With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T). METHODS In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .
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Affiliation(s)
- B Jijila
- Queen Mary's College, Chennai, India
| | - V Nirmala
- Queen Mary's College, Chennai, India.
| | - P Selvarengan
- Kalasalingam Academy of Research & Education, Krishnankoil, India
| | - D Kavitha
- Dr. MGR Educational and Research Institute, Chennai, India
| | | | - A Rajagopal
- Indian Institute of Technology, Madras, India
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5
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Scherbela M, Gerard L, Grohs P. Towards a transferable fermionic neural wavefunction for molecules. Nat Commun 2024; 15:120. [PMID: 38168035 PMCID: PMC10762074 DOI: 10.1038/s41467-023-44216-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Accepted: 12/05/2023] [Indexed: 01/05/2024] Open
Abstract
Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schrödinger equation. However, despite their success and favorable scaling, these methods are still computationally too costly for wide adoption. A significant obstacle is the requirement to optimize the wavefunction from scratch for each new system, thus requiring long optimization. In this work, we propose a neural network ansatz, which effectively maps uncorrelated, computationally cheap Hartree-Fock orbitals, to correlated, high-accuracy neural network orbitals. This ansatz is inherently capable of learning a single wavefunction across multiple compounds and geometries, as we demonstrate by successfully transferring a wavefunction model pre-trained on smaller fragments to larger compounds. Furthermore, we provide ample experimental evidence to support the idea that extensive pre-training of such a generalized wavefunction model across different compounds and geometries could lead to a foundation wavefunction model. Such a model could yield high-accuracy ab-initio energies using only minimal computational effort for fine-tuning and evaluation of observables.
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Affiliation(s)
| | - Leon Gerard
- Research Network Data Science, University of Vienna, Vienna, Austria
| | - Philipp Grohs
- Faculty of Mathematics, University of Vienna, Vienna, Austria.
- Research Network Data Science, University of Vienna, Vienna, Austria.
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria.
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6
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Hermann J, Spencer J, Choo K, Mezzacapo A, Foulkes WMC, Pfau D, Carleo G, Noé F. Ab initio quantum chemistry with neural-network wavefunctions. Nat Rev Chem 2023; 7:692-709. [PMID: 37558761 DOI: 10.1038/s41570-023-00516-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/16/2023] [Indexed: 08/11/2023]
Abstract
Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.
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Affiliation(s)
- Jan Hermann
- Microsoft Research AI4Science, Berlin, Germany
- FU Berlin, Department of Mathematics and Computer Science, Berlin, Germany
| | | | - Kenny Choo
- Department of Physics, University of Zurich, Zurich, Switzerland
- IBM Quantum, IBM Research Zurich, Ruschlikon, Switzerland
| | | | - W M C Foulkes
- Imperial College London, Department of Physics, London, UK
| | - David Pfau
- DeepMind, London, UK.
- Imperial College London, Department of Physics, London, UK.
| | | | - Frank Noé
- Microsoft Research AI4Science, Berlin, Germany.
- FU Berlin, Department of Mathematics and Computer Science, Berlin, Germany.
- FU Berlin, Department of Physics, Berlin, Germany.
- Department of Chemistry,Rice University, Houston, TX, USA.
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7
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Xie H, Li ZH, Wang H, Zhang L, Wang L. Deep Variational Free Energy Approach to Dense Hydrogen. PHYSICAL REVIEW LETTERS 2023; 131:126501. [PMID: 37802941 DOI: 10.1103/physrevlett.131.126501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Revised: 08/01/2023] [Accepted: 08/14/2023] [Indexed: 10/08/2023]
Abstract
We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wave function at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. The predicted equation of state of dense hydrogen under planetary conditions is denser than the findings of ab initio molecular dynamics calculation and empirical chemical model. Moreover, direct access to the entropy and free energy of dense hydrogen opens new opportunities in planetary modeling and high-pressure physics research.
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Affiliation(s)
- Hao Xie
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zi-Hang Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Han Wang
- Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, China
| | - Linfeng Zhang
- DP Technology, Beijing 100080, China
- AI for Science Institute, Beijing 100080, China
| | - Lei Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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8
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Herzog B, Casier B, Lebègue S, Rocca D. Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning. J Chem Theory Comput 2023; 19:2484-2490. [PMID: 37043718 DOI: 10.1021/acs.jctc.2c01216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2023]
Abstract
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.
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Affiliation(s)
- Basile Herzog
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Bastien Casier
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Sébastien Lebègue
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Dario Rocca
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
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9
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Ren W, Fu W, Wu X, Chen J. Towards the ground state of molecules via diffusion Monte Carlo on neural networks. Nat Commun 2023; 14:1860. [PMID: 37012248 PMCID: PMC10070323 DOI: 10.1038/s41467-023-37609-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 03/20/2023] [Indexed: 04/05/2023] Open
Abstract
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. However, the inaccurate nodal structure hinders the application of DMC for more challenging electronic correlation problems. In this work, we apply the neural-network based trial wavefunction in fixed-node DMC, which allows accurate calculations of a broad range of atomic and molecular systems of different electronic characteristics. Our method is superior in both accuracy and efficiency compared to state-of-the-art neural network methods using variational Monte Carlo (VMC). We also introduce an extrapolation scheme based on the empirical linearity between VMC and DMC energies, and significantly improve our binding energy calculation. Overall, this computational framework provides a benchmark for accurate solutions of correlated electronic wavefunction and also sheds light on the chemical understanding of molecules.
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Affiliation(s)
- Weiluo Ren
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China.
| | - Weizhong Fu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, 100871, Beijing, People's Republic of China
| | - Xiaojie Wu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, 100871, Beijing, People's Republic of China.
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, 100871, Beijing, People's Republic of China.
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10
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Li Y, Wang H, Li Y, Ye H, Zhang Y, Yin R, Jia H, Hou B, Wang C, Ding H, Bai X, Lu A. Electron transfer rules of minerals under pressure informed by machine learning. Nat Commun 2023; 14:1815. [PMID: 37002237 PMCID: PMC10066309 DOI: 10.1038/s41467-023-37384-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Accepted: 03/15/2023] [Indexed: 04/03/2023] Open
Abstract
Electron transfer is the most elementary process in nature, but the existing electron transfer rules are seldom applied to high-pressure situations, such as in the deep Earth. Here we show a deep learning model to obtain the electronegativity of 96 elements under arbitrary pressure, and a regressed unified formula to quantify its relationship with pressure and electronic configuration. The relative work function of minerals is further predicted by electronegativity, presenting a decreasing trend with pressure because of pressure-induced electron delocalization. Using the work function as the case study of electronegativity, it reveals that the driving force behind directional electron transfer results from the enlarged work function difference between compounds with pressure. This well explains the deep high-conductivity anomalies, and helps discover the redox reactivity between widespread Fe(II)-bearing minerals and water during ongoing subduction. Our results give an insight into the fundamental physicochemical properties of elements and their compounds under pressure.
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Affiliation(s)
- Yanzhang Li
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Hongyu Wang
- Image Processing Center, Beihang University, 102206, Beijing, China
| | - Yan Li
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China.
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China.
| | - Huan Ye
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Yanan Zhang
- Image Processing Center, Beihang University, 102206, Beijing, China
| | - Rongzhang Yin
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Haoning Jia
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Bingxu Hou
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Changqiu Wang
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Hongrui Ding
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China
| | - Xiangzhi Bai
- Image Processing Center, Beihang University, 102206, Beijing, China.
- State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, 100191, Beijing, China.
- Advanced Innovation Center for Biomedical Engineering, Beihang University, 100083, Beijing, China.
| | - Anhuai Lu
- Beijing Key Laboratory of Mineral Environmental Function, School of Earth and Space Sciences, Peking University, 100871, Beijing, China.
- Key Laboratory of Orogenic Belts and Crustal Evolution, School of Earth and Space Sciences, Peking University, 100871, Beijing, China.
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11
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Entwistle MT, Schätzle Z, Erdman PA, Hermann J, Noé F. Electronic excited states in deep variational Monte Carlo. Nat Commun 2023; 14:274. [PMID: 36650151 PMCID: PMC9845370 DOI: 10.1038/s41467-022-35534-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 12/08/2022] [Indexed: 01/19/2023] Open
Abstract
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.
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Affiliation(s)
- M T Entwistle
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Z Schätzle
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - P A Erdman
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - J Hermann
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
| | - F Noé
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Microsoft Research AI4Science, Berlin, Germany.
- Department of Physics, FU Berlin, Arnimallee 14, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
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12
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Cheng L, Sun J, Deustua JE, Bhethanabotla VC, Miller TF. Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression. J Chem Phys 2022; 157:154105. [PMID: 36272799 DOI: 10.1063/5.0110886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.
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Affiliation(s)
- Lixue Cheng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Jiace Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - J Emiliano Deustua
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Vignesh C Bhethanabotla
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Shmilovich K, Willmott D, Batalov I, Kornbluth M, Mailoa J, Kolter JZ. Orbital Mixer: Using Atomic Orbital Features for Basis-Dependent Prediction of Molecular Wavefunctions. J Chem Theory Comput 2022; 18:6021-6030. [PMID: 36122312 DOI: 10.1021/acs.jctc.2c00555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous studies focuses on generating predictions for only a fixed set of properties. Recent lines of research instead aim to explicitly learn the electronic structure via molecular wavefunctions, from which other quantum chemical properties can be directly derived. While previous methods generate predictions as a function of only the atomic configuration, in this work we present an alternate approach that directly purposes basis-dependent information to predict molecular electronic structure. Our model, Orbital Mixer, is composed entirely of multi-layer perceptrons (MLPs) using MLP-Mixer layers within a simple, intuitive, and scalable architecture that achieves competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies compared to the state-of-the-art.
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Affiliation(s)
- Kirill Shmilovich
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Devin Willmott
- Bosch Center for Artificial Intelligence, Pittsburgh, Pennsylvania 15222, United States
| | - Ivan Batalov
- Bosch Center for Artificial Intelligence, Pittsburgh, Pennsylvania 15222, United States
| | - Mordechai Kornbluth
- Bosch Research and Technology Center, Cambridge, Massachusetts 02139, United States
| | - Jonathan Mailoa
- Tencent Quantum Laboratory, Shenzhen, Guangdong 518057, China
| | - J Zico Kolter
- Bosch Center for Artificial Intelligence, Pittsburgh, Pennsylvania 15222, United States.,Carnegie Mellon University, Pittsburgh, Pennsylvania 15222, United States
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Tran H. Accelerating quantum molecular simulations. NATURE COMPUTATIONAL SCIENCE 2022; 2:292-293. [PMID: 38177814 DOI: 10.1038/s43588-022-00237-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Affiliation(s)
- Huan Tran
- School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA.
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