1
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García-Risueño P, Armengol E, García-Cerdaña À, García-Lastra JM, Carrasco-Busturia D. Electron-vibrational renormalization in fullerenes through ab initio and machine learning methods. Phys Chem Chem Phys 2024. [PMID: 38984472 DOI: 10.1039/d4cp00632a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/11/2024]
Abstract
The effect of nuclear vibrations on the electronic eigenvalues and the HOMO-LUMO gap is known for several kinds of carbon-based materials, like diamond, diamondoids, carbon nanoclusters, carbon nanotubes and others, like hydrogen-terminated oligoynes and polyyne. However, it has not been widely analysed in another remarkable kind which presents both theoretical and technological interest: fullerenes. In this article we present the study of the HOMO, LUMO and gap renormalizations due to zero-point motion of a relatively large number (163) of fullerenes and fullerene derivatives. We have calculated this renormalization using density-functional theory with the frozen-phonon method, finding that it is non-negligible (above 0.1 eV) for systems with relevant technological applications in photovoltaics and that the strength of the renormalization increases with the size of the gap. In addition, we have applied machine learning methods for classification and regression of the renormalizations, finding that they can be approximately predicted using the output of a computationally cheap ground state calculation. Our conclusions are supported by recent research in other systems.
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Affiliation(s)
| | - Eva Armengol
- Artificial Intelligence Research Institute, (IIIA, CSIC) Carrer de Can Planes, s/n, Campus UAB, 08193 Bellaterra, Catalonia, Spain
| | - Àngel García-Cerdaña
- Artificial Intelligence Research Institute, (IIIA, CSIC) Carrer de Can Planes, s/n, Campus UAB, 08193 Bellaterra, Catalonia, Spain
| | - Juan María García-Lastra
- Department of Energy Conversion and Storage, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - David Carrasco-Busturia
- DTU Chemistry, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
- Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden.
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2
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Griffin C, Karn T, Apple B. Topological learning in multiclass data sets. Phys Rev E 2024; 109:024131. [PMID: 38491638 DOI: 10.1103/physreve.109.024131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 02/01/2024] [Indexed: 03/18/2024]
Abstract
We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multiclass data set. As a by-product, a topological classifier is defined that uses an open subcovering of the data set. This subcovering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open-source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.
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Affiliation(s)
- Christopher Griffin
- Applied Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Trevor Karn
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Benjamin Apple
- Naval Surface Warfare Center Carderock, Bethesda Maryland 20817, USA
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3
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Lewis L, Huang HY, Tran VT, Lehner S, Kueng R, Preskill J. Improved machine learning algorithm for predicting ground state properties. Nat Commun 2024; 15:895. [PMID: 38291046 PMCID: PMC10828424 DOI: 10.1038/s41467-024-45014-7] [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: 03/26/2023] [Accepted: 01/08/2024] [Indexed: 02/01/2024] Open
Abstract
Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only [Formula: see text] data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require [Formula: see text] data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as [Formula: see text] in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.
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Affiliation(s)
- Laura Lewis
- California Institute of Technology, Pasadena, CA, USA
- University of Cambridge, Cambridge, UK
| | - Hsin-Yuan Huang
- California Institute of Technology, Pasadena, CA, USA.
- Massachusetts Institute of Technology, Cambridge, MA, USA.
- Google Quantum AI, Venice, CA, USA.
| | | | | | | | - John Preskill
- California Institute of Technology, Pasadena, CA, USA
- AWS Center for Quantum Computing, Pasadena, CA, USA
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4
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Qi SC, Sun Z, Yang ZH, Zhao YJ, Li JX, Liu XQ, Sun LB. Photo-Responsive Carbon Capture over Metalloporphyrin-C 60 Metal-Organic Frameworks via Charge-Transfer. RESEARCH (WASHINGTON, D.C.) 2023; 6:0261. [PMID: 37881620 PMCID: PMC10595220 DOI: 10.34133/research.0261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 10/10/2023] [Indexed: 10/27/2023]
Abstract
Great efforts have been devoted to the study of photo-responsive adsorption, but its current methodology largely depends on the well-defined photochromic units and their photo-driven molecular deformation. Here, a methodology to fabricate nondeforming photo-responsive sorbents is successfully exploited. With C60-fullerene doping in metalloporphyrin metal-organic frameworks (PCN-M, M = Fe, Co, or Ni) and intensively interacting with the metalloporphyrin sites, effective charge-transfer can be achieved over the metalloporphyrin-C60 architectures once excited by the light at 350 to 780 nm. The electron density distribution and the resultant adsorption activity are thus changed by excited states, which are also stable enough to meet the timescale of microscopic adsorption equilibrium. The charge-transfer over Co(II)-porphyrin-C60 is proved to be more efficient than the Fe(II)- and Ni(II)-porphyrin-C60 sites, as well as than all the metalloporphyrin sites, so the CO2 adsorption capacity (CAC; at 0 °C and 1 bar) over the C60-doped PCN-Co can be largely improved from 2.05 mmol g-1 in the darkness to 2.69 mmol g-1 with light, increased by 31%, in contrast to photo-irresponsive CAC over all C60-undoped PCN-M sorbents and only the photo-loss CAC over C60.
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Affiliation(s)
- Shi-Chao Qi
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Zhen Sun
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Zhi-Hui Yang
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Yun-Jie Zhao
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Jia-Xin Li
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Xiao-Qin Liu
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
| | - Lin-Bing Sun
- State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), College of Chemical Engineering,
Nanjing Tech University, Nanjing 211816, China
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5
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Gibney D, Boyn JN, Mazziotti DA. Comparison of Density-Matrix Corrections to Density Functional Theory. J Chem Theory Comput 2022; 18:6600-6607. [DOI: 10.1021/acs.jctc.2c00625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Gibney
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 United States
| | - Jan-Niklas Boyn
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 United States
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 United States
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6
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Costa E, Scriva G, Fazio R, Pilati S. Deep-learning density functionals for gradient descent optimization. Phys Rev E 2022; 106:045309. [PMID: 36397567 DOI: 10.1103/physreve.106.045309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 09/27/2022] [Indexed: 06/16/2023]
Abstract
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid them by using an ad hoc convolutional architecture featuring an interchannel averaging layer. The main testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the interchannel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.
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Affiliation(s)
- E Costa
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - G Scriva
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
| | - R Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Napoli, Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino, Italy
- INFN-Sezione di Perugia, 06123 Perugia, Italy
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7
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Huang HY, Kueng R, Torlai G, Albert VV, Preskill J. Provably efficient machine learning for quantum many-body problems. Science 2022; 377:eabk3333. [PMID: 36137032 DOI: 10.1126/science.abk3333] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.
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Affiliation(s)
- Hsin-Yuan Huang
- Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA
| | - Richard Kueng
- Institute for Integrated Circuits, Johannes Kepler University, Linz, Austria
| | | | - Victor V Albert
- Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, MD, USA
| | - John Preskill
- Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA.,AWS Center for Quantum Computing, Pasadena, CA, USA
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8
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Di Sante D, Medvidović M, Toschi A, Sangiovanni G, Franchini C, Sengupta AM, Millis AJ. Deep Learning the Functional Renormalization Group. PHYSICAL REVIEW LETTERS 2022; 129:136402. [PMID: 36206431 DOI: 10.1103/physrevlett.129.136402] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Revised: 07/18/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
Abstract
We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional t-t^{'} Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a neural ordinary differential equation solver in a low-dimensional latent space efficiently learns the FRG dynamics that delineates the various magnetic and d-wave superconducting regimes of the Hubbard model. We further present a dynamic mode decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the FRG dynamics. Our Letter demonstrates the possibility of using artificial intelligence to extract compact representations of the four-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.
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Affiliation(s)
- Domenico Di Sante
- Department of Physics and Astronomy, University of Bologna, 40127 Bologna, Italy
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Matija Medvidović
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Department of Physics, Columbia University, New York, New York 10027, USA
| | | | - Giorgio Sangiovanni
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Cesare Franchini
- Department of Physics and Astronomy, University of Bologna, 40127 Bologna, Italy
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, A-1090 Vienna, Austria
| | - Anirvan M Sengupta
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Center for Computational Mathematics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Andrew J Millis
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Department of Physics, Columbia University, New York, New York 10027, USA
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9
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Sajjan M, Li J, Selvarajan R, Sureshbabu SH, Kale SS, Gupta R, Singh V, Kais S. Quantum machine learning for chemistry and physics. Chem Soc Rev 2022; 51:6475-6573. [PMID: 35849066 DOI: 10.1039/d2cs00203e] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Junxu Li
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Raja Selvarajan
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Shree Hari Sureshbabu
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
| | - Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Vinit Singh
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
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10
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Gedeon J, Schmidt J, Hodgson MJP, Wetherell J, Benavides-Riveros CL, Marques MAL. Machine learning the derivative discontinuity of density-functional theory. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac3149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.
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11
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Gibney D, Boyn JN, Mazziotti DA. Density Functional Theory Transformed into a One-Electron Reduced-Density-Matrix Functional Theory for the Capture of Static Correlation. J Phys Chem Lett 2022; 13:1382-1388. [PMID: 35113577 DOI: 10.1021/acs.jpclett.2c00083] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Density Functional Theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically transformed into a one-electron reduced-density-matrix (1-RDM) functional theory, which can address the limitations of DFT while retaining favorable computational scaling compared to wave function based approaches. In addition to relaxing the idempotency restriction on the 1-RDM in the kinetic energy term, we add a quadratic 1-RDM-based term to DFT's density-based exchange-correlation functional. Our approach, which we implement by quadratic semidefinite programming at DFT's computational scaling of O(r3), yields substantial improvements over traditional DFT in the description of static correlation in chemical structures and processes such as singlet biradicals and bond dissociations.
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Affiliation(s)
- Daniel Gibney
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jan-Niklas Boyn
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A Mazziotti
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
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12
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Tsubaki M, Mizoguchi T. Quantum Deep Descriptor: Physically Informed Transfer Learning from Small Molecules to Polymers. J Chem Theory Comput 2021; 17:7814-7821. [PMID: 34846893 DOI: 10.1021/acs.jctc.1c00568] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
In this study, we propose a physically informed transfer learning approach for materials informatics (MI) using a quantum deep descriptor (QDD) obtained from the quantum deep field (QDF). The QDF is a machine learning model based on density functional theory (DFT) and can be trained with a large database of molecular properties. The pre-trained QDF model can provide an effective molecular descriptor that encodes the fundamental quantum-chemical characteristics (i.e., the wave function or orbital, electron density, and energies of a molecule) learned from the large database; we refer to this descriptor as a QDD. We show that a QDD pre-trained with certain properties of small molecules can predict different properties (e.g., the band gap and dielectric constant) of polymers compared with some existing descriptors. We believe that our DFT-based, physically informed transfer learning approach will not only be useful for practical applications in MI but will also provide quantum-chemical insights into materials in the future. All codes used in this study are available at https://github.com/masashitsubaki.
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Affiliation(s)
- Masashi Tsubaki
- National Institute of Advanced Industrial Science and Technology, Tokyo 135-0064, Japan
| | - Teruyasu Mizoguchi
- Institute of Industrial Science, The University of Tokyo, Tokyo 113-0033, Japan
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13
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Han R, Luber S. Fast Estimation of Møller-Plesset Correlation Energies Based on Atomic Contributions. J Phys Chem Lett 2021; 12:5324-5331. [PMID: 34061529 DOI: 10.1021/acs.jpclett.1c00900] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Dynamic correlation plays an important role in the accurate calculation of chemical compounds such as the description of equilibrium structures in chemical systems. A model for the fast estimation of dynamic correlation energy is introduced in this work. This model is based on the idea of decomposition of the contribution of dynamic correlation energy calculated by nth order Møller-Plesset perturbation (MPn) theory with respect to atomic regions. Multiple levels of theory, including MP2, MP2.5, and MP4, are used as the reference, and the corresponding correlation energy densities are calculated. The proposed model is concise, fast, and promising for practical use, such as the prediction of reaction energies. It can also work as a baseline model or pretrained model for follow-up studies of machine learning.
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Affiliation(s)
- R Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - S Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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14
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Li L, Hoyer S, Pederson R, Sun R, Cubuk ED, Riley P, Burke K. Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics. PHYSICAL REVIEW LETTERS 2021; 126:036401. [PMID: 33543980 DOI: 10.1103/physrevlett.126.036401] [Citation(s) in RCA: 56] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2020] [Accepted: 12/03/2020] [Indexed: 05/21/2023]
Abstract
Including prior knowledge is important for effective machine learning models in physics and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H_{2} dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.
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Affiliation(s)
- Li Li
- Google Research, Mountain View, California 94043, USA
| | - Stephan Hoyer
- Google Research, Mountain View, California 94043, USA
| | - Ryan Pederson
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Ruoxi Sun
- Google Research, Mountain View, California 94043, USA
| | - Ekin D Cubuk
- Google Research, Mountain View, California 94043, USA
| | - Patrick Riley
- Google Research, Mountain View, California 94043, USA
| | - Kieron Burke
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
- Department of Chemistry, University of California, Irvine, California 92697, USA
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15
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Tsubaki M, Mizoguchi T. Quantum Deep Field: Data-Driven Wave Function, Electron Density Generation, and Atomization Energy Prediction and Extrapolation with Machine Learning. PHYSICAL REVIEW LETTERS 2020; 125:206401. [PMID: 33258648 DOI: 10.1103/physrevlett.125.206401] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Accepted: 09/23/2020] [Indexed: 06/12/2023]
Abstract
Deep neural networks (DNNs) have been used to successfully predict molecular properties calculated based on the Kohn-Sham density functional theory (KS-DFT). Although this prediction is fast and accurate, we believe that a DNN model for KS-DFT must not only predict the properties but also provide the electron density of a molecule. This Letter presents the quantum deep field (QDF), which provides the electron density with an unsupervised but end-to-end physics-informed modeling by learning the atomization energy on a large-scale dataset. QDF performed well at atomization energy prediction, generated valid electron density, and demonstrated extrapolation.
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Affiliation(s)
- Masashi Tsubaki
- National Institute of Advanced Industrial Science and Technology, 2-3-26 Aomi, Koto-ku, Tokyo 135-0064, Japan
| | - Teruyasu Mizoguchi
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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16
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Saraceni N, Cantori S, Pilati S. Scalable neural networks for the efficient learning of disordered quantum systems. Phys Rev E 2020; 102:033301. [PMID: 33075937 DOI: 10.1103/physreve.102.033301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 08/11/2020] [Indexed: 12/20/2022]
Abstract
Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [Mills et al., Chem. Sci. 10, 4129 (2019)2041-652010.1039/C8SC04578J] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely, a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pretraining performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.
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Affiliation(s)
- N Saraceni
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| | - S Cantori
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| | - S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
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