1
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Hou L, Irons TJP, Wang Y, Furness JW, Wibowo-Teale AM, Sun J. Ab Initio Calculation of Coupling-Constant Averaged Exchange-Correlation Holes for Spherically Symmetric Atoms. J Phys Chem A 2024; 128:8521-8532. [PMID: 39312646 DOI: 10.1021/acs.jpca.4c02717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/25/2024]
Abstract
Accurate approximation of the exchange-correlation (XC) energy in density functional theory (DFT) calculations is essential for reliably modeling electronic systems. Many such approximations are developed from models of the XC hole; accurate reference XC holes for real electronic systems are crucial for evaluating the accuracy of these models however the availability of reliable reference data is limited to a few systems. In this study, we employ the Lieb optimization with a coupled cluster singles and doubles (CCSD) reference to construct accurate coupling-constant averaged XC holes, resolved into individual exchange and correlation components, for five spherically symmetric atoms: He, Li, Be, N, and Ne. Alongside providing a new set of reference data for the construction and evaluation of model XC holes, we compare our data against the exchange and correlation hole models of the established local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) density functional approximations. Our analysis confirms the established rationalization for the limitations of LDA and the improvement observed with PBE in terms of the hole depth and its long-range decay, which is demonstrated in real-space for this series of spherically symmetric atoms.
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Affiliation(s)
- Lin Hou
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Tom J P Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Yanyong Wang
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Andrew M Wibowo-Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
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2
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Yang Z, Shi A, Zhang R, Ji Z, Li J, Lyu J, Qian J, Chen T, Wang X, You F, Xie J. When Metal Nanoclusters Meet Smart Synthesis. ACS NANO 2024. [PMID: 39316700 DOI: 10.1021/acsnano.4c09597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2024]
Abstract
Atomically precise metal nanoclusters (MNCs) represent a fascinating class of ultrasmall nanoparticles with molecule-like properties, bridging conventional metal-ligand complexes and nanocrystals. Despite their potential for various applications, synthesis challenges such as a precise understanding of varied synthetic parameters and property-driven synthesis persist, hindering their full exploitation and wider application. Incorporating smart synthesis methodologies, including a closed-loop framework of automation, data interpretation, and feedback from AI, offers promising solutions to address these challenges. In this perspective, we summarize the closed-loop smart synthesis that has been demonstrated in various nanomaterials and explore the research frontiers of smart synthesis for MNCs. Moreover, the perspectives on the inherent challenges and opportunities of smart synthesis for MNCs are discussed, aiming to provide insights and directions for future advancements in this emerging field of AI for Science, while the integration of deep learning algorithms stands to substantially enrich research in smart synthesis by offering enhanced predictive capabilities, optimization strategies, and control mechanisms, thereby extending the potential of MNC synthesis.
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Affiliation(s)
- Zhucheng Yang
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207, P. R. China
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore
| | - Anye Shi
- Systems Engineering, College of Engineering, Cornell University, Ithaca, New York 14583, United States
| | - Ruixuan Zhang
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207, P. R. China
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore
| | - Zuowei Ji
- School of Humanities and Social Sciences, The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, P. R. China
| | - Jiali Li
- Department of Chemistry, National University of Singapore, Singapore 117543, Singapore
| | - Jingkuan Lyu
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207, P. R. China
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore
| | - Jing Qian
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207, P. R. China
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore
| | - Tiankai Chen
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, P. R. China
| | - Xiaonan Wang
- Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China
| | - Fengqi You
- Systems Engineering, College of Engineering, Cornell University, Ithaca, New York 14583, United States
- Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States
- Cornell University AI for Science Institute (CUAISci), Cornell University, Ithaca, New York 14853, United States
| | - Jianping Xie
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207, P. R. China
- Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singapore
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3
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Bystrom K, Falletta S, Kozinsky B. Training Machine-Learned Density Functionals on Band Gaps. J Chem Theory Comput 2024; 20:7516-7532. [PMID: 39178337 DOI: 10.1021/acs.jctc.4c00999] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/25/2024]
Abstract
The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is intimately related to self-interaction and delocalization errors, which make the study of charge transfer mechanisms with DFT difficult. To expand the range of available tools for addressing the band gap problem, we design an approach for machine learning density functionals based on Gaussian processes to explicitly fit single-particle energy levels. We also introduce nonlocal features of the density matrix that are expressive enough to fit these single-particle levels. Combining these developments, we train a machine-learned functional for the exact exchange energy that predicts molecular energy gaps and reaction energies of a wide range of molecules in excellent agreement with reference hybrid DFT calculations. In addition, while being trained solely on molecular data, our model predicts reasonable formation energies of polarons in solids, showcasing its transferability and robustness. We discuss how this approach can be generalized to full exchange-correlation functionals, thus paving the way to the design of state-of-the-art functionals for the prediction of electronic properties of molecules and materials.
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Affiliation(s)
- Kyle Bystrom
- Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States
| | - Stefano Falletta
- Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States
| | - Boris Kozinsky
- Harvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, United States
- Robert Bosch LLC Research and Technology Center, Cambridge, Massachusetts 02139, United States
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4
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Lu T. A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn. J Chem Phys 2024; 161:082503. [PMID: 39189657 DOI: 10.1063/5.0216272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2024] [Accepted: 08/07/2024] [Indexed: 08/28/2024] Open
Abstract
Analysis of electron wavefunction is a key component of quantum chemistry investigations and is indispensable for the practical research of many chemical problems. After more than ten years of active development, the wavefunction analysis program Multiwfn has accumulated very rich functions, and its application scope has covered numerous aspects of theoretical chemical research, including charge distribution, chemical bond, electron localization and delocalization, aromaticity, intramolecular and intermolecular interactions, electronic excitation, and response property. This article systematically introduces the features and functions of the latest version of Multiwfn and provides many representative examples. Through this article, readers will be able to fully understand the characteristics and recognize the unique value of Multiwfn. The source code and precompiled executable files of Multiwfn, as well as the manual containing a detailed introduction to theoretical backgrounds and very rich tutorials, can all be downloaded for free from the Multiwfn website (http://sobereva.com/multiwfn).
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Affiliation(s)
- Tian Lu
- Beijing Kein Research Center for Natural Sciences, Beijing 100024, People's Republic of China
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5
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Wang Y, Lin Z, Ouyang R, Jiang B, Zhang IY, Xu X. Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory. JACS AU 2024; 4:3205-3216. [PMID: 39211596 PMCID: PMC11350721 DOI: 10.1021/jacsau.4c00488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Revised: 07/26/2024] [Accepted: 08/06/2024] [Indexed: 09/04/2024]
Abstract
Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.
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Affiliation(s)
- Yizhen Wang
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
| | - Zihan Lin
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
| | - Runhai Ouyang
- Materials
Genome Institute, Shanghai University, Shanghai 200444, China
| | - Bin Jiang
- Key
Laboratory of Precision and Intelligent Chemistry, Department of Chemical
Physics, University of Science and Technology
of China, Hefei, Anhui 230026, China
- Hefei
National Laboratory, Hefei 230088, China
| | - Igor Ying Zhang
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
- Hefei
National Laboratory, Hefei 230088, China
- Shanghai
Key Laboratory of Bioactive Small Molecules, Shanghai200032, China
| | - Xin Xu
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
- Hefei
National Laboratory, Hefei 230088, China
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6
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Masuda K, Abdullah AA, Pflughaupt P, Sahakyan AB. Quantum mechanical electronic and geometric parameters for DNA k-mers as features for machine learning. Sci Data 2024; 11:911. [PMID: 39174574 PMCID: PMC11341866 DOI: 10.1038/s41597-024-03772-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 08/13/2024] [Indexed: 08/24/2024] Open
Abstract
We are witnessing a steep increase in model development initiatives in genomics that employ high-end machine learning methodologies. Of particular interest are models that predict certain genomic characteristics based solely on DNA sequence. These models, however, treat the DNA as a mere collection of four, A, T, G and C, letters, dismissing the past advancements in science that can enable the use of more intricate information from nucleic acid sequences. Here, we provide a comprehensive database of quantum mechanical (QM) and geometric features for all the permutations of 7-meric DNA in their representative B, A and Z conformations. The database is generated by employing the applicable high-cost and time-consuming QM methodologies. This can thus make it seamless to associate a wealth of novel molecular features to any DNA sequence, by scanning it with a matching k-meric window and pulling the pre-computed values from our database for further use in modelling. We demonstrate the usefulness of our deposited features through their exclusive use in developing a model for A->C mutation rates.
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Affiliation(s)
- Kairi Masuda
- MRC WIMM Centre for Computational Biology, MRC Weatherall Institute of Molecular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 9DS, UK
| | - Adib A Abdullah
- MRC WIMM Centre for Computational Biology, MRC Weatherall Institute of Molecular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 9DS, UK
| | - Patrick Pflughaupt
- MRC WIMM Centre for Computational Biology, MRC Weatherall Institute of Molecular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 9DS, UK
| | - Aleksandr B Sahakyan
- MRC WIMM Centre for Computational Biology, MRC Weatherall Institute of Molecular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, OX3 9DS, UK.
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7
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Cao Y, Balduf T, Beachy MD, Bennett MC, Bochevarov AD, Chien A, Dub PA, Dyall KG, Furness JW, Halls MD, Hughes TF, Jacobson LD, Kwak HS, Levine DS, Mainz DT, Moore KB, Svensson M, Videla PE, Watson MA, Friesner RA. Quantum chemical package Jaguar: A survey of recent developments and unique features. J Chem Phys 2024; 161:052502. [PMID: 39092934 DOI: 10.1063/5.0213317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Accepted: 07/12/2024] [Indexed: 08/04/2024] Open
Abstract
This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.
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Affiliation(s)
- Yixiang Cao
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Ty Balduf
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Michael D Beachy
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - M Chandler Bennett
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Art D Bochevarov
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Alan Chien
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Pavel A Dub
- Schrödinger, Inc., 9868 Scranton Road, Suite 3200, San Diego, California 92121, USA
| | - Kenneth G Dyall
- Schrödinger, Inc., 101 SW Main St., Suite 1300, Portland, Oregon 97204, USA
| | - James W Furness
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Mathew D Halls
- Schrödinger, Inc., 9868 Scranton Road, Suite 3200, San Diego, California 92121, USA
| | - Thomas F Hughes
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Leif D Jacobson
- Schrödinger, Inc., 101 SW Main St., Suite 1300, Portland, Oregon 97204, USA
| | - H Shaun Kwak
- Schrödinger, Inc., 101 SW Main St., Suite 1300, Portland, Oregon 97204, USA
| | - Daniel S Levine
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Daniel T Mainz
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Kevin B Moore
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Mats Svensson
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Pablo E Videla
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Mark A Watson
- Schrödinger, Inc., 1540 Broadway, Floor 24, New York, New York 10036, USA
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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8
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Li S, Xie BB, Yin BW, Liu L, Shen L, Fang WH. Construction of Highly Accurate Machine Learning Potential Energy Surfaces for Excited-State Dynamics Simulations Based on Low-Level Data Sets. J Phys Chem A 2024; 128:5516-5524. [PMID: 38954640 DOI: 10.1021/acs.jpca.4c02028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2024]
Abstract
Machine learning is capable of effectively predicting the potential energies of molecules in the presence of high-quality data sets. Its application in the construction of ground- and excited-state potential energy surfaces is attractive to accelerate nonadiabatic molecular dynamics simulations of photochemical reactions. Because of the huge computational cost of excited-state electronic structure calculations, the construction of a high-quality data set becomes a bottleneck. In the present work, we first built two data sets. One was obtained from surface hopping dynamics simulations at the semiempirical OM2/MRCI level. Another was extracted from the dynamics trajectories at the CASSCF level, which was reported previously. The ground- and excited-state potential energy surfaces of ethylene-bridged azobenzene at the CASSCF computational level were constructed based on the former low-level data set. Although non-neural network machine learning methods can achieve good or modest performance during the training process, only neural network models provide reliable predictions on the latter external test data set. The BPNN and SchNet combined with the Δ-ML scheme and the force term in the loss functions are recommended for dynamics simulations. Then, we performed excited-state dynamics simulations of the photoisomerization of ethylene-bridged azobenzene on machine learning potential energy surfaces. Compared with the lifetimes of the first excited state (S1) estimated at different computational levels, our results on the E isomer are in good agreement with the high-level estimation. However, the overestimation of the Z isomer is unimproved. It suggests that smaller errors during the training process do not necessarily translate to more accurate predictions on high-level potential energies or better performance on nonadiabatic dynamics simulations, at least in the present case.
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Affiliation(s)
- Shuai Li
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
| | - Bin-Bin Xie
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, Hangzhou 311231, Zhejiang, P. R. China
| | - Bo-Wen Yin
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, Hangzhou 311231, Zhejiang, P. R. China
| | - Lihong Liu
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
| | - Lin Shen
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
- Yantai-Jingshi Institute of Material Genome Engineering, Yantai 265505, Shandong, P. R. China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China
- Shandong Laboratory of Yantai Advanced Materials and Green Manufacturing, Yantai 264006, Shandong, P. R. China
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9
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Gould T, Chan B, Dale SG, Vuckovic S. Identifying and embedding transferability in data-driven representations of chemical space. Chem Sci 2024; 15:11122-11133. [PMID: 39027290 PMCID: PMC11253166 DOI: 10.1039/d4sc02358g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2024] [Accepted: 06/02/2024] [Indexed: 07/20/2024] Open
Abstract
Transferability, especially in the context of model generalization, is a paradigm of all scientific disciplines. However, the rapid advancement of machine learned model development threatens this paradigm, as it can be difficult to understand how transferability is embedded (or missed) in complex models developed using large training data sets. Two related open problems are how to identify, without relying on human intuition, what makes training data transferable; and how to embed transferability into training data. To solve both problems for ab initio chemical modelling, an indispensable tool in everyday chemistry research, we introduce a transferability assessment tool (TAT) and demonstrate it on a controllable data-driven model for developing density functional approximations (DFAs). We reveal that human intuition in the curation of training data introduces chemical biases that can hamper the transferability of data-driven DFAs. We use our TAT to motivate three transferability principles; one of which introduces the key concept of transferable diversity. Finally, we propose data curation strategies for general-purpose machine learning models in chemistry that identify and embed the transferability principles.
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Affiliation(s)
- Tim Gould
- Queensland Micro- and Nanotechnology Centre, Griffith University Nathan Qld 4111 Australia
| | - Bun Chan
- Graduate School of Engineering, Nagasaki University Bunkyo 1-14 Nagasaki 852-8521 Japan
| | - Stephen G Dale
- Queensland Micro- and Nanotechnology Centre, Griffith University Nathan Qld 4111 Australia
- Institute of Functional Intelligent Materials, National University of Singapore 4 Science Drive 2 Singapore 117544
| | - Stefan Vuckovic
- Department of Chemistry, University of Fribourg Fribourg Switzerland
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10
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Burgess AC, Linscott E, O'Regan DD. Tilted-Plane Structure of the Energy of Finite Quantum Systems. PHYSICAL REVIEW LETTERS 2024; 133:026404. [PMID: 39073931 DOI: 10.1103/physrevlett.133.026404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2023] [Revised: 04/18/2024] [Accepted: 05/17/2024] [Indexed: 07/31/2024]
Abstract
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.
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11
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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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12
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Brütting M, Bahmann H, Kümmel S. Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional. J Phys Chem A 2024; 128:5212-5223. [PMID: 38905018 DOI: 10.1021/acs.jpca.4c02787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/23/2024]
Abstract
Some of the most successful exchange-correlation approximations in density functional theory are "hybrids", i.e., they rely on combining semilocal density functionals with exact nonlocal Fock exchange. In recent years, two classes of hybrid functionals have emerged as particularly promising: range-separated hybrids on the one hand, and local hybrids on the other hand. These functionals offer the hope to overcome a long-standing "observable dilemma", i.e., the fact that density functionals typically yield either a good description of binding energies, as obtained, e.g., in global and local hybrids, or physically interpretable eigenvalues, as obtained, e.g., in optimally tuned range-separated hybrids. Obtaining both of these characteristics from one and the same functional with the same set of parameters has been a long-standing challenge. We here discuss combining the concepts of local range separation and local hybrids as part of a constraint-guided quest for functionals that overcome the observable dilemma.
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Affiliation(s)
- Moritz Brütting
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Hilke Bahmann
- Physical and Theoretical Chemistry, University of Wuppertal, 42097 Wuppertal, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
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13
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Kaupp M, Wodyński A, Arbuznikov AV, Fürst S, Schattenberg CJ. Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density. Acc Chem Res 2024; 57:1815-1826. [PMID: 38905497 PMCID: PMC11223257 DOI: 10.1021/acs.accounts.4c00209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/23/2024]
Abstract
ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.
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Affiliation(s)
- Martin Kaupp
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Alexei V. Arbuznikov
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Susanne Fürst
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
| | - Caspar J. Schattenberg
- Institut für Chemie,
Theoretische Chemie/Quantenchemie, Technische
Universität Berlin, Sekr. C7, Strasse des 17. Juni 115, 10623 Berlin, Germany
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14
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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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15
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Fan L, Shen Y, Lou D, Gu N. Progress in the Computer-Aided Analysis in Multiple Aspects of Nanocatalysis Research. Adv Healthc Mater 2024:e2401576. [PMID: 38936401 DOI: 10.1002/adhm.202401576] [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: 04/29/2024] [Revised: 06/08/2024] [Indexed: 06/29/2024]
Abstract
Making the utmost of the differences and advantages of multiple disciplines, interdisciplinary integration breaks the science boundaries and accelerates the progress in mutual quests. As an organic connection of material science, enzymology, and biomedicine, nanozyme-related research is further supported by computer technology, which injects in new vitality, and contributes to in-depth understanding, unprecedented insights, and broadened application possibilities. Utilizing computer-aided first-principles method, high-speed and high-throughput mathematic, physic, and chemic models are introduced to perform atomic-level kinetic analysis for nanocatalytic reaction process, and theoretically illustrate the underlying nanozymetic mechanism and structure-function relationship. On this basis, nanozymes with desirable properties can be designed and demand-oriented synthesized without repeated trial-and-error experiments. Besides that, computational analysis and device also play an indispensable role in nanozyme-based detecting methods to realize automatic readouts with improved accuracy and reproducibility. Here, this work focuses on the crossing of nanocatalysis research and computational technology, to inspire the research in computer-aided analysis in nanozyme field to a greater extent.
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Affiliation(s)
- Lin Fan
- Medical School of Nanjing University, Nanjing, 210093, P. R. China
- School of Integrated Circuit Science and Engineering (Industry-Education Integration School), Nanjing University of Posts and Telecommunications, Nanjing, 210023, P. R. China
| | - Yilei Shen
- School of Integrated Circuit Science and Engineering (Industry-Education Integration School), Nanjing University of Posts and Telecommunications, Nanjing, 210023, P. R. China
| | - Doudou Lou
- Nanjing Institute for Food and Drug Control, Nanjing, 211198, P. R. China
| | - Ning Gu
- Medical School of Nanjing University, Nanjing, 210093, P. R. China
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16
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Hehn L, Deglmann P, Kühn M. Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods? J Chem Theory Comput 2024; 20:4545-4568. [PMID: 38805381 DOI: 10.1021/acs.jctc.3c01375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.
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Affiliation(s)
- Lukas Hehn
- Next Generation Computing, BASF SE, Pfalzgrafenstr. 1, 67061 Ludwigshafen, Germany
| | - Peter Deglmann
- Quantum Chemistry, BASF SE, Carl-Bosch-Str. 38, 67063 Ludwigshafen, Germany
| | - Michael Kühn
- Next Generation Computing, BASF SE, Pfalzgrafenstr. 1, 67061 Ludwigshafen, Germany
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17
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Zhang R, Yuan R, Tian B. PointGAT: A Quantum Chemical Property Prediction Model Integrating Graph Attention and 3D Geometry. J Chem Theory Comput 2024; 20:4115-4128. [PMID: 38727259 DOI: 10.1021/acs.jctc.3c01420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
Predicting quantum chemical properties is a fundamental challenge for computational chemistry. While the development of graph neural networks has advanced molecular representation learning and property prediction, their performance could be further enhanced by incorporating three-dimensional (3D) structural geometry into two-dimensional (2D) molecular graph representation. In this study, we introduce the PointGAT model for quantum molecular property prediction, which integrates 3D molecular coordinates with graph-attention modeling. Comparison with other current models in molecular prediction tasks showed that PointGAT could provide higher predictive accuracy in various benchmark data sets from MoleculeNet, including ESOL, FreeSolv, Lipop, HIV, and 6 out of 12 tasks of the QM9 data set. To further examine PointGAT prediction of quantum mechanical (QM) energies, we constructed a C10 data set comprising 11,841 charged and chiral carbocation intermediates with QM energies calculated at the DM21/6-31G*//B3LYP/6-31G* levels. Notably, PointGAT achieved an R2 value of 0.950 and an MAE of 1.616 kcal/mol, outperforming even the best-performing graph neural network model with a reduction of 0.216 kcal/mol in MAE and an improvement of 0.050 in R2. Additional ablation studies indicated that incorporating molecular geometry into the model resulted in markedly higher predictive accuracy, reducing the MAE value from 1.802 to 1.616 kcal/mol. Moreover, visualization of PointGAT atomic attention weights suggested its predictions were interpretable. Findings in this study support the application of PointGAT as a powerful and versatile tool for quantum chemical property prediction that can facilitate high-accuracy modeling for fundamental exploration of chemical space as well as drug design and molecular engineering.
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Affiliation(s)
- Rong Zhang
- MOE Key Laboratory of Bioinformatics, State Key Laboratory of Molecular Oncology, School of Pharmaceutical Sciences, Tsinghua University, Beijing 100084, China
| | - Rongqing Yuan
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Boxue Tian
- MOE Key Laboratory of Bioinformatics, State Key Laboratory of Molecular Oncology, School of Pharmaceutical Sciences, Tsinghua University, Beijing 100084, China
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18
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Duan S, Tian G, Luo Y. Theoretical and computational methods for tip- and surface-enhanced Raman scattering. Chem Soc Rev 2024; 53:5083-5117. [PMID: 38596836 DOI: 10.1039/d3cs01070h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
Raman spectroscopy is a versatile tool for acquiring molecular structure information. The incorporation of plasmonic fields has significantly enhanced the sensitivity and resolution of surface-enhanced Raman scattering (SERS) and tip-enhanced Raman spectroscopy (TERS). The strong spatial confinement effect of plasmonic fields has challenged the conventional Raman theory, in which a plane wave approximation for the light has been adopted. In this review, we comprehensively survey the progress of a generalized theory for SERS and TERS in the framework of effective field Hamiltonian (EFH). With this approach, all characteristics of localized plasmonic fields can be well taken into account. By employing EFH, quantitative simulations at the first-principles level for state-of-the-art experimental observations have been achieved, revealing the underlying intrinsic physics in the measurements. The predictive power of EFH is demonstrated by several new phenomena generated from the intrinsic spatial, momentum, time, and energy structures of the localized plasmonic field. The corresponding experimental verifications are also carried out briefly. A comprehensive computational package for modeling of SERS and TERS at the first-principles level is introduced. Finally, we provide an outlook on the future developments of theory and experiments for SERS and TERS.
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Affiliation(s)
- Sai Duan
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China.
| | - Guangjun Tian
- State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China
| | - Yi Luo
- Hefei National Research Center for Physical Science at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
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19
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Sahoo SJ, Xu Q, Lei X, Staros D, Iyer GR, Rubenstein B, Suryanarayana P, Medford AJ. Self-Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces. Chemphyschem 2024; 25:e202300688. [PMID: 38421371 DOI: 10.1002/cphc.202300688] [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: 09/22/2023] [Revised: 02/23/2024] [Accepted: 02/25/2024] [Indexed: 03/02/2024]
Abstract
The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as "Jacob's ladder." This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBE α ${\alpha }$ framework with α ${\alpha }$ being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.
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Affiliation(s)
| | - Qimen Xu
- Georgia Institute of Technology, Atlanta, GA
- National Supercomputing Center, Shenzhen, People's Republic of China
| | | | - Daniel Staros
- Department of Chemistry, Brown University, Providence, RI
| | - Gopal R Iyer
- Department of Chemistry, Brown University, Providence, RI
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20
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Kjær ETS, Anker AS, Kirsch A, Lajer J, Aalling-Frederiksen O, Billinge SJL, Jensen KMØ. MLstructureMining: a machine learning tool for structure identification from X-ray pair distribution functions. DIGITAL DISCOVERY 2024; 3:908-918. [PMID: 38756225 PMCID: PMC11094694 DOI: 10.1039/d4dd00001c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Accepted: 03/27/2024] [Indexed: 05/18/2024]
Abstract
Synchrotron X-ray techniques are essential for studies of the intrinsic relationship between synthesis, structure, and properties of materials. Modern synchrotrons can produce up to 1 petabyte of data per day. Such amounts of data can speed up materials development, but also comes with a staggering growth in workload, as the data generated must be stored and analyzed. We present an approach for quickly identifying an atomic structure model from pair distribution function (PDF) data from (nano)crystalline materials. Our model, MLstructureMining, uses a tree-based machine learning (ML) classifier. MLstructureMining has been trained to classify chemical structures from a PDF and gives a top-3 accuracy of 99% on simulated PDFs not seen during training, with a total of 6062 possible classes. We also demonstrate that MLstructureMining can identify the chemical structure from experimental PDFs from nanoparticles of CoFe2O4 and CeO2, and we show how it can be used to treat an in situ PDF series collected during Bi2Fe4O9 formation. Additionally, we show how MLstructureMining can be used in combination with the well-known methods, principal component analysis (PCA) and non-negative matrix factorization (NMF) to analyze data from in situ experiments. MLstructureMining thus allows for real-time structure characterization by screening vast quantities of crystallographic information files in seconds.
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Affiliation(s)
- Emil T S Kjær
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Andy S Anker
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Andrea Kirsch
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | - Joakim Lajer
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
| | | | - Simon J L Billinge
- Department of Applied Physics and Applied Mathematics Science, Columbia University New York NY 10027 USA
| | - Kirsten M Ø Jensen
- Department of Chemistry and Nano-Science Center, University of Copenhagen 2100 Copenhagen Ø Denmark
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21
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Zhao H, Gould T, Vuckovic S. Deep Mind 21 functional does not extrapolate to transition metal chemistry. Phys Chem Chem Phys 2024; 26:12289-12298. [PMID: 38597718 DOI: 10.1039/d4cp00878b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2024]
Abstract
The development of density functional approximations stands at a crossroads: while machine-learned functionals show potential to surpass their human-designed counterparts, their extrapolation to unseen chemistry lags behind. Here we assess how well the recent Deep Mind 21 (DM21) machine-learned functional [Science, 2021, 374, 1385-1389], trained on main-group chemistry, extrapolates to transition metal chemistry (TMC). We show that DM21 demonstrates comparable or occasionally superior accuracy to B3LYP for TMC, but consistently struggles with achieving self-consistent field convergence for TMC molecules. We also compare main-group and TMC machine-learning DM21 features to shed light on DM21's challenges in TMC. We finally propose strategies to overcome limitations in the extrapolative capabilities of machine-learned functionals in TMC.
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Affiliation(s)
- Heng Zhao
- Department of Chemistry, University of Fribourg, Fribourg, Switzerland.
| | - Tim Gould
- Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111, Australia
| | - Stefan Vuckovic
- Department of Chemistry, University of Fribourg, Fribourg, Switzerland.
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22
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Dral PO. AI in computational chemistry through the lens of a decade-long journey. Chem Commun (Camb) 2024; 60:3240-3258. [PMID: 38444290 DOI: 10.1039/d4cc00010b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/07/2024]
Abstract
This article gives a perspective on the progress of AI tools in computational chemistry through the lens of the author's decade-long contributions put in the wider context of the trends in this rapidly expanding field. This progress over the last decade is tremendous: while a decade ago we had a glimpse of what was to come through many proof-of-concept studies, now we witness the emergence of many AI-based computational chemistry tools that are mature enough to make faster and more accurate simulations increasingly routine. Such simulations in turn allow us to validate and even revise experimental results, deepen our understanding of the physicochemical processes in nature, and design better materials, devices, and drugs. The rapid introduction of powerful AI tools gives rise to unique challenges and opportunities that are discussed in this article too.
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Affiliation(s)
- Pavlo O Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen University, Xiamen, Fujian 361005, China.
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23
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Tang WH, Sim SR, Aik DYK, Nelanuthala AVS, Athilingam T, Röllin A, Wohland T. Deep learning reduces data requirements and allows real-time measurements in imaging FCS. Biophys J 2024; 123:655-666. [PMID: 38050354 PMCID: PMC10995408 DOI: 10.1016/j.bpj.2023.11.3403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 11/18/2023] [Accepted: 11/30/2023] [Indexed: 12/06/2023] Open
Abstract
Imaging fluorescence correlation spectroscopy (FCS) is a powerful tool to extract information on molecular mobilities, actions, and interactions in live cells, tissues, and organisms. Nevertheless, several limitations restrict its applicability. First, FCS is data hungry, requiring 50,000 frames at 1-ms time resolution to obtain accurate parameter estimates. Second, the data size makes evaluation slow. Third, as FCS evaluation is model dependent, data evaluation is significantly slowed unless analytic models are available. Here, we introduce two convolutional neural networks-FCSNet and ImFCSNet-for correlation and intensity trace analysis, respectively. FCSNet robustly predicts parameters in 2D and 3D live samples. ImFCSNet reduces the amount of data required for accurate parameter retrieval by at least one order of magnitude and makes correct estimates even in moderately defocused samples. Both convolutional neural networks are trained on simulated data, are model agnostic, and allow autonomous, real-time evaluation of imaging FCS measurements.
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Affiliation(s)
- Wai Hoh Tang
- Department of Biological Sciences, National University of Singapore, Singapore, Singapore; NUS Centre for Bio-Imaging Sciences, National University of Singapore, Singapore, Singapore; Department of Statistics and Data Science, National University of Singapore, Singapore, Singapore; Institute of Digital Molecular Analytics and Science, National University of Singapore, Singapore, Singapore
| | - Shao Ren Sim
- Department of Biological Sciences, National University of Singapore, Singapore, Singapore; NUS Centre for Bio-Imaging Sciences, National University of Singapore, Singapore, Singapore
| | - Daniel Ying Kia Aik
- Department of Biological Sciences, National University of Singapore, Singapore, Singapore; NUS Centre for Bio-Imaging Sciences, National University of Singapore, Singapore, Singapore; Institute of Digital Molecular Analytics and Science, National University of Singapore, Singapore, Singapore; Department of Chemistry, National University of Singapore, Singapore, Singapore
| | - Ashwin Venkata Subba Nelanuthala
- Department of Biological Sciences, National University of Singapore, Singapore, Singapore; NUS Centre for Bio-Imaging Sciences, National University of Singapore, Singapore, Singapore
| | | | - Adrian Röllin
- Department of Statistics and Data Science, National University of Singapore, Singapore, Singapore
| | - Thorsten Wohland
- Department of Biological Sciences, National University of Singapore, Singapore, Singapore; NUS Centre for Bio-Imaging Sciences, National University of Singapore, Singapore, Singapore; Institute of Digital Molecular Analytics and Science, National University of Singapore, Singapore, Singapore; Department of Chemistry, National University of Singapore, Singapore, Singapore.
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24
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Wodyński A, Lauw B, Reimann M, Kaupp M. Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density. J Chem Theory Comput 2024; 20:2033-2048. [PMID: 38411554 PMCID: PMC10938646 DOI: 10.1021/acs.jctc.3c01422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2023] [Revised: 02/02/2024] [Accepted: 02/07/2024] [Indexed: 02/28/2024]
Abstract
A small set of mononuclear manganese complexes evaluated previously for their Mn hyperfine couplings (HFCs) has been analyzed using density functionals based on the exact-exchange energy density─in particular, the spin symmetry breaking (SSB) found previously when using hybrid functionals. Employing various strong-correlation corrected local hybrids (scLHs) and strong-correlation corrected range-separated local hybrids (scRSLHs) with or without additional corrections to their local mixing functions (LMFs) to mitigate delocalization errors (DE), the SSB and the associated dipolar HFCs of [Mn(CN)4]2-, MnO3, [Mn(CN)4N]-, and [Mn(CN)5NO]2- (the latter with cluster embedding) have been examined. Both strong-correlation (sc)-correction and DE-correction terms help to diminish SSB and correct the dipolar HFCs. The DE corrections are more effective, and the effects of the sc corrections depend on their damping factors. Interestingly, the DE-corrections reduce valence-shell spin polarization (VSSP) and thus SSB by locally enhancing exact-exchange (EXX) admixture near the metal center and thereby diminishing spin-density delocalization onto the ligand atoms. In contrast, sc corrections diminish EXX admixture locally, mostly on specific ligand atoms. This then reduces VSSP and SSB as well. The performance of scLHs and scRSLHs for the isotropic Mn HFCs has also been analyzed, with particular attention to core-shell spin-polarization contributions. Further sc-corrected functionals, such as the KP16/B13 construction and the DM21 deep-neural-network functional, have been examined.
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Affiliation(s)
- Artur Wodyński
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Bryan Lauw
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Marc Reimann
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
| | - Martin Kaupp
- Technische Universität
Berlin, Institut für Chemie, Theoretische
Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, Berlin, D-10623, Germany
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25
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Zhang H, Liu S, You J, Liu C, Zheng S, Lu Z, Wang T, Zheng N, Shao B. Overcoming the barrier of orbital-free density functional theory for molecular systems using deep learning. NATURE COMPUTATIONAL SCIENCE 2024; 4:210-223. [PMID: 38467870 DOI: 10.1038/s43588-024-00605-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 02/07/2024] [Indexed: 03/13/2024]
Abstract
Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. Here we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep learning functional model. We build the essential non-locality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy to Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those seen in training, which unleashes the appealing scaling of OFDFT for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.
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Affiliation(s)
- He Zhang
- National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an, China
- Microsoft Research AI4Science, Beijing, China
| | - Siyuan Liu
- Microsoft Research AI4Science, Beijing, China
| | | | - Chang Liu
- Microsoft Research AI4Science, Beijing, China.
| | | | - Ziheng Lu
- Microsoft Research AI4Science, Beijing, China
| | - Tong Wang
- Microsoft Research AI4Science, Beijing, China
| | - Nanning Zheng
- National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, and Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an, China
| | - Bin Shao
- Microsoft Research AI4Science, Beijing, China.
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26
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Zope RR, Yamamoto Y, Baruah T. How well do one-electron self-interaction-correction methods perform for systems with fractional electrons? J Chem Phys 2024; 160:084102. [PMID: 38385511 DOI: 10.1063/5.0182773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/28/2024] [Indexed: 02/23/2024] Open
Abstract
Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (zσ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew-Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of H2+ and He2+ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li+ to F- at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.
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Affiliation(s)
- Rajendra R Zope
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
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27
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Ayres LB, Gomez FJV, Silva MF, Linton JR, Garcia CD. Predicting the formation of NADES using a transformer-based model. Sci Rep 2024; 14:2715. [PMID: 38388549 PMCID: PMC10883925 DOI: 10.1038/s41598-022-27106-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 12/26/2022] [Indexed: 02/24/2024] Open
Abstract
The application of natural deep eutectic solvents (NADES) in the pharmaceutical, agricultural, and food industries represents one of the fastest growing fields of green chemistry, as these mixtures can potentially replace traditional organic solvents. These advances are, however, limited by the development of new NADES which is today, almost exclusively empirically driven and often derivative from known mixtures. To overcome this limitation, we propose the use of a transformer-based machine learning approach. Here, the transformer-based neural network model was first pre-trained to recognize chemical patterns from SMILES representations (unlabeled general chemical data) and then fine-tuned to recognize the patterns in strings that lead to the formation of either stable NADES or simple mixtures of compounds not leading to the formation of stable NADES (binary classification). Because this strategy was adapted from language learning, it allows the use of relatively small datasets and relatively low computational resources. The resulting algorithm is capable of predicting the formation of multiple new stable eutectic mixtures (n = 337) from a general database of natural compounds. More importantly, the system is also able to predict the components and molar ratios needed to render NADES with new molecules (not present in the training database), an aspect that was validated using previously reported NADES as well as by developing multiple novel solvents containing ibuprofen. We believe this strategy has the potential to transform the screening process for NADES as well as the pharmaceutical industry, streamlining the use of bioactive compounds as functional components of liquid formulations, rather than simple solutes.
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Affiliation(s)
- Lucas B Ayres
- Department of Chemistry, Clemson University, 211 S. Palmetto Blvd, Clemson, SC, 29634, USA
| | - Federico J V Gomez
- Facultad de Ciencias Agrarias, Instituto de Biología Agrícola de Mendoza (IBAM-CONICET), Universidad Nacional de Cuyo, Mendoza, Argentina
| | - Maria Fernanda Silva
- Facultad de Ciencias Agrarias, Instituto de Biología Agrícola de Mendoza (IBAM-CONICET), Universidad Nacional de Cuyo, Mendoza, Argentina
| | - Jeb R Linton
- Department of Chemistry, Clemson University, 211 S. Palmetto Blvd, Clemson, SC, 29634, USA
- IBM Cloud, Armonk, NY, 10504, USA
| | - Carlos D Garcia
- Department of Chemistry, Clemson University, 211 S. Palmetto Blvd, Clemson, SC, 29634, USA.
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28
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Lee AJ, Rackers JA, Pathak S, Bricker WP. Building an ab initio solvated DNA model using Euclidean neural networks. PLoS One 2024; 19:e0297502. [PMID: 38358990 PMCID: PMC10868815 DOI: 10.1371/journal.pone.0297502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2023] [Accepted: 01/06/2024] [Indexed: 02/17/2024] Open
Abstract
Accurately modeling large biomolecules such as DNA from first principles is fundamentally challenging due to the steep computational scaling of ab initio quantum chemistry methods. This limitation becomes even more prominent when modeling biomolecules in solution due to the need to include large numbers of solvent molecules. We present a machine-learned electron density model based on a Euclidean neural network framework that includes a built-in understanding of equivariance to model explicitly solvated double-stranded DNA. By training the machine learning model using molecular fragments that sample the key DNA and solvent interactions, we show that the model predicts electron densities of arbitrary systems of solvated DNA accurately, resolves polarization effects that are neglected by classical force fields, and captures the physics of the DNA-solvent interaction at the ab initio level.
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Affiliation(s)
- Alex J. Lee
- Department of Chemical and Biological Engineering, University of New Mexico, Albuquerque, NM, United States of America
| | - Joshua A. Rackers
- Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, United States of America
| | - Shivesh Pathak
- Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, United States of America
| | - William P. Bricker
- Department of Chemical and Biological Engineering, University of New Mexico, Albuquerque, NM, United States of America
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29
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Xi B, Chan MK, Bao K, Zhao W, Chan HM, Chen H, Zhu J. Parameter-Free and Electron Counting Satisfied Material Representation for Machine Learning Potential Energy and Force Fields. J Phys Chem Lett 2024; 15:1636-1643. [PMID: 38306617 PMCID: PMC10875669 DOI: 10.1021/acs.jpclett.3c03250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Revised: 01/28/2024] [Accepted: 01/29/2024] [Indexed: 02/04/2024]
Abstract
We proposed a parameter-free volume element representation that satisfies the electron counting model and obtains accurate machine learning potential energy and direct force fitting of randomly perturbed hexagonal BN. Our method preserves permutational, translational, and rotational invariance and can be extended to three-dimensional systems, verified by a system of bulk Si. As a result, we obtained 0.57 meV/atom potential energy root mean squared error (RMSE) and 59 meV/Å force RMSE for perturbed bulk BN systems and 0.43 meV/atom potential energy RMSE and 36 meV/Å force RMSE for perturbed Si systems. In addition, an unbiased perturbation-based data set construction scheme is introduced and a continuous population distribution is obtained with a training data set of 4500, which is about 1 order of magnitude smaller than standard methods based on first-principles molecular dynamics simulations and saves a large amount of computing resources. General validity of our model is verified by structure optimization, molecular dynamics simulations, and extrapolations.
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Affiliation(s)
- Bin Xi
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Man Kit Chan
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Kejie Bao
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Wenjing Zhao
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Ho Ming Chan
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Hang Chen
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Junyi Zhu
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
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30
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Hölzer C, Gordiy I, Grimme S, Bursch M. Hybrid DFT Geometries and Properties for 17k Lanthanoid Complexes─The LnQM Data Set. J Chem Inf Model 2024; 64:825-836. [PMID: 38238264 DOI: 10.1021/acs.jcim.3c01832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/13/2024]
Abstract
The unique properties of lanthanoids and their diverse applications make them an indispensable part of modern research and industry. While the field has garnered attention, there remains a gap in available molecule data sets that facilitate both classical quantum chemistry calculations and the burgeoning field of machine learning in data science applications. This research addresses the need for a comprehensive data set that allows for a comparative analysis of various lanthanoids. The herein presented, curated data set includes 17269 monolanthanoid complexes derived from 1205 distinct ligand motifs. Structures encompass all 15 lanthanoids in the +3 oxidation state and exhibit molecular charges ranging from -1 to +3, including structures with a high spin multiplicity up to 8. Starting from lanthanum complexes, samples were processed with a permutation of the central lanthanoid atom, resulting in highly comparable subsets, facilitating comparative studies in which the influence of the lanthanoid can be investigated independently of ligand effects. The data set provides a broad range of features such as PBE0-D4/def2-SVP optimized geometries and optimization trajectories, while also covering ωB97M-V/def2-SVPD energies, rotational constants, dipole moments, highest occupied molecular orbital-lowest-unoccupied molecular orbital (HOMO-LUMO) energies, and Mulliken, Löwdin, and Hirshfeld population analyses. Additionally, coordination numbers, polarizabilities, and partial charges from D4, electronegativity equilibration (EEQ), GFN2-xTB, and charge extended Hückel (CEH) calculations are included. The data set is openly accessible and may serve as a basis for further investigations into the properties of lanthanoids.
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Affiliation(s)
- Christian Hölzer
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - Igor Gordiy
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, 53115 Bonn, Germany
| | - Markus Bursch
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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31
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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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32
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Shi Y, Shi Y, Wasserman A. Stretching Bonds without Breaking Symmetries in Density Functional Theory. J Phys Chem Lett 2024; 15:826-833. [PMID: 38232318 DOI: 10.1021/acs.jpclett.3c03073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Kohn-Sham density functional theory (KS-DFT) stands out among electronic structure methods due to its balance of accuracy and computational efficiency. However, to achieve chemically accurate energies, standard density functional approximations in KS-DFT often need to break underlying symmetries, a long-standing "symmetry dilemma". By employing fragment spin densities as the main variables in calculations (rather than total molecular densities, as in KS-DFT), we present an embedding framework in which this symmetry dilemma is understood and partially resolved. The spatial overlap between fragment densities is used as the main ingredient to construct a simple, physically motivated approximation to a universal functional of the fragment densities. This "overlap approximation" is shown to significantly improve semilocal KS-DFT binding energies of molecules without artificially breaking either charge or spin symmetries. The approach is shown to be applicable to covalently bonded molecules and to systems of the "strongly correlated" type.
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Affiliation(s)
- Yuming Shi
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yi Shi
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Adam Wasserman
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
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33
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Tancogne-Dejean N, Penz M, Laestadius A, Csirik MA, Ruggenthaler M, Rubio A. Exchange energies with forces in density-functional theory. J Chem Phys 2024; 160:024103. [PMID: 38189616 DOI: 10.1063/5.0177346] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 12/12/2023] [Indexed: 01/09/2024] Open
Abstract
We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.
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Affiliation(s)
- Nicolas Tancogne-Dejean
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Penz
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Basic Research Community for Physics, Innsbruck, Austria
| | - Andre Laestadius
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, 0315 Oslo, Norway
| | - Mihály A Csirik
- Department of Computer Science, Oslo Metropolitan University, 0130 Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, 0315 Oslo, Norway
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science and Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
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34
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Powell A, Gerrits N, Tchakoua T, Somers MF, Busnengo HF, Meyer J, Kroes GJ, Doblhoff-Dier K. Best-of-Both-Worlds Predictive Approach to Dissociative Chemisorption on Metals. J Phys Chem Lett 2024; 15:307-315. [PMID: 38169287 PMCID: PMC10788952 DOI: 10.1021/acs.jpclett.3c02972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Revised: 12/21/2023] [Accepted: 12/28/2023] [Indexed: 01/05/2024]
Abstract
Predictive capability, accuracy, and affordability are essential features of a theory that is capable of describing dissociative chemisorption on a metal surface. This type of reaction is important for heterogeneous catalysis. Here we present an approach in which we use diffusion Monte Carlo (DMC) to pin the minimum barrier height and construct a density functional that reproduces this value. This predictive approach allows the construction of a potential energy surface at the cost of density functional theory while retaining near DMC accuracy. Scrutinizing effects of energy dissipation and quantum tunneling, dynamics calculations suggest the approach to be of near chemical accuracy, reproducing molecular beam sticking experiments for the showcase H2 + Al(110) system to ∼1.4 kcal/mol.
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Affiliation(s)
- Andrew
D. Powell
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Nick Gerrits
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Theophile Tchakoua
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Mark F. Somers
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Heriberto F. Busnengo
- Instituto
de Física Rosario (IFIR), CONICET-UNR, 2000 Rosario, Argentina
- Facultad
de Ciencias Exatas, Ingeniería y
Agrimensura, UNR, 2000 Rosario, Argentina
| | - Jörg Meyer
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Geert-Jan Kroes
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
| | - Katharina Doblhoff-Dier
- Leiden
Institute of Chemistry, Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
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35
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Perdew JP. My life in science: Lessons for yours? J Chem Phys 2024; 160:010402. [PMID: 38180261 DOI: 10.1063/5.0179606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 10/26/2023] [Indexed: 01/06/2024] Open
Abstract
Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.
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Affiliation(s)
- John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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36
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Chen Z, Yang W. Development of a machine learning finite-range nonlocal density functional. J Chem Phys 2024; 160:014105. [PMID: 38180254 DOI: 10.1063/5.0179149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Accepted: 12/12/2023] [Indexed: 01/06/2024] Open
Abstract
Kohn-Sham density functional theory has been the most popular method in electronic structure calculations. To fulfill the increasing accuracy requirements, new approximate functionals are needed to address key issues in existing approximations. It is well known that nonlocal components are crucial. Current nonlocal functionals mostly require orbital dependence such as in Hartree-Fock exchange and many-body perturbation correlation energy, which, however, leads to higher computational costs. Deviating from this pathway, we describe functional nonlocality in a new approach. By partitioning the total density to atom-centered local densities, a many-body expansion is proposed. This many-body expansion can be truncated at one-body contributions, if a base functional is used and an energy correction is approximated. The contribution from each atom-centered local density is a single finite-range nonlocal functional that is universal for all atoms. We then use machine learning to develop this universal atom-centered functional. Parameters in this functional are determined by fitting to data that are produced by high-level theories. Extensive tests on several different test sets, which include reaction energies, reaction barrier heights, and non-covalent interaction energies, show that the new functional, with only the density as the basic variable, can produce results comparable to the best-performing double-hybrid functionals, (for example, for the thermochemistry test set selected from the GMTKN55 database, BLYP based machine learning functional gives a weighted total mean absolute deviations of 3.33 kcal/mol, while DSD-BLYP-D3(BJ) gives 3.28 kcal/mol) with a lower computational cost. This opens a new pathway to nonlocal functional development and applications.
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Affiliation(s)
- Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
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37
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Burgess AC, Linscott E, O'Regan DD. The convexity condition of density-functional theory. J Chem Phys 2023; 159:211102. [PMID: 38038199 DOI: 10.1063/5.0174159] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 11/08/2023] [Indexed: 12/02/2023] Open
Abstract
It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham bandgap and the exchange-correlation derivative discontinuity of DFT.
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Affiliation(s)
- Andrew C Burgess
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
| | - Edward Linscott
- Theory and Simulation of Materials (THEOS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - David D O'Regan
- School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Ireland
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38
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Mazo-Sevillano PD, Hermann J. Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy functional. J Chem Phys 2023; 159:194107. [PMID: 37971033 DOI: 10.1063/5.0166432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/26/2023] [Indexed: 11/19/2023] Open
Abstract
Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange-correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work, we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange-correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.
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Affiliation(s)
- Pablo Del Mazo-Sevillano
- Departamento de Química Física Aplicada, Universidad Autónoma de Madrid, Módulo 14, 28049 Madrid, Spain
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Jan Hermann
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195 Berlin, Germany
- Microsoft Research AI4Science, Karl-Liebknecht-Str. 32, 10178 Berlin, Germany
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39
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Fürst S, Kaupp M, Wodyński A. Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals. J Chem Theory Comput 2023. [PMID: 37972297 DOI: 10.1021/acs.jctc.3c00877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2023]
Abstract
Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn-Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.
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Affiliation(s)
- Susanne Fürst
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Artur Wodyński
- Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
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40
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de Mendonça JPA, Mariano LA, Devijver E, Jakse N, Poloni R. Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes. J Chem Theory Comput 2023; 19:7555-7566. [PMID: 37843492 DOI: 10.1021/acs.jctc.3c00600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.
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Affiliation(s)
| | | | - Emilie Devijver
- Université Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France
| | - Noel Jakse
- Université Grenoble Alpes, CNRS, Grenoble INP, SIMaP, 38000 Grenoble, France
| | - Roberta Poloni
- Université Grenoble Alpes, CNRS, Grenoble INP, SIMaP, 38000 Grenoble, France
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41
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Palos E, Caruso A, Paesani F. Consistent density functional theory-based description of ion hydration through density-corrected many-body representations. J Chem Phys 2023; 159:181101. [PMID: 37947509 DOI: 10.1063/5.0174577] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023] Open
Abstract
Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.
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Affiliation(s)
- Etienne Palos
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Alessandro Caruso
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, USA
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42
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Mi W, Luo K, Trickey SB, Pavanello M. Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations. Chem Rev 2023; 123:12039-12104. [PMID: 37870767 DOI: 10.1021/acs.chemrev.2c00758] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2023]
Abstract
Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.
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Affiliation(s)
- Wenhui Mi
- Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, PR China
- State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, PR China
- International Center of Future Science, Jilin University, Changchun 130012, PR China
| | - Kai Luo
- Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, PR China
| | - S B Trickey
- Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Michele Pavanello
- Department of Physics and Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
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43
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Ai W, Su NQ, Fang WH. Short-range screened density matrix functional for proper descriptions of thermochemistry, thermochemical kinetics, nonbonded interactions, and singlet diradicals. J Chem Phys 2023; 159:174110. [PMID: 37933778 DOI: 10.1063/5.0169234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 10/09/2023] [Indexed: 11/08/2023] Open
Abstract
Common one-electron reduced density matrix (1-RDM) functionals that depend on Coulomb and exchange-only integrals tend to underestimate dynamic correlation, preventing reduced density matrix functional theory (RDMFT) from achieving comparable accuracy to density functional theory in main-group thermochemistry and thermochemical kinetics. The recently developed ωP22 functional introduces a semi-local density functional to screen the erroneous short-range portion of 1-RDM functionals without double-counting correlation, potentially providing a better treatment of dynamic correlation around equilibrium geometries. Herein, we systematically evaluate the performance of this functional model, which consists of two parameters, on main-group thermochemistry, thermochemical kinetics, nonbonded interactions, and more. Tests on atomization energies, vibrational frequencies, and reaction barriers reveal that the ωP22 functional model can reliably predict properties at equilibrium and slightly away from equilibrium geometries. In particular, it outperforms commonly used density functionals in the prediction of reaction barriers, nonbonded interactions, and singlet diradicals, thus enhancing the predictive power of RDMFT for routine calculations of thermochemistry and thermochemical kinetics around equilibrium geometries. Further development is needed in the future to refine short- and long-range approximations in the functional model in order to achieve an excellent description of properties both near and far from equilibrium geometries.
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Affiliation(s)
- Wenna Ai
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
| | - Neil Qiang Su
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
| | - Wei-Hai Fang
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
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44
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Casetti N, Alfonso-Ramos JE, Coley CW, Stuyver T. Combining Molecular Quantum Mechanical Modeling and Machine Learning for Accelerated Reaction Screening and Discovery. Chemistry 2023; 29:e202301957. [PMID: 37526059 DOI: 10.1002/chem.202301957] [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: 06/20/2023] [Revised: 07/30/2023] [Accepted: 07/31/2023] [Indexed: 08/02/2023]
Abstract
Molecular quantum mechanical modeling, accelerated by machine learning, has opened the door to high-throughput screening campaigns of complex properties, such as the activation energies of chemical reactions and absorption/emission spectra of materials and molecules; in silico. Here, we present an overview of the main principles, concepts, and design considerations involved in such hybrid computational quantum chemistry/machine learning screening workflows, with a special emphasis on some recent examples of their successful application. We end with a brief outlook of further advances that will benefit the field.
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Affiliation(s)
- Nicholas Casetti
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts, 02139, United States
| | - Javier E Alfonso-Ramos
- Ecole Nationale Supérieure de Chimie de Paris, Université PSL, CNRS, Institute of Chemistry for Life and Health Sciences, 75005, Paris, France
| | - Connor W Coley
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts, 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts, 02139, United States
| | - Thijs Stuyver
- Ecole Nationale Supérieure de Chimie de Paris, Université PSL, CNRS, Institute of Chemistry for Life and Health Sciences, 75005, Paris, France
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45
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Riemelmoser S, Verdi C, Kaltak M, Kresse G. Machine Learning Density Functionals from the Random-Phase Approximation. J Chem Theory Comput 2023; 19:7287-7299. [PMID: 37800677 PMCID: PMC10601474 DOI: 10.1021/acs.jctc.3c00848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Indexed: 10/07/2023]
Abstract
Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.
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Affiliation(s)
- Stefan Riemelmoser
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse
5, A-1090 Vienna, Austria
| | - Carla Verdi
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- School
of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia
- School
of Mathematics and Physics, The University
of Queensland, Brisbane, Queensland 4072, Australia
| | - Merzuk Kaltak
- VASP
Software GmbH, Sensengasse
8/12, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse
8/12, A-1090 Vienna, Austria
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46
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Linscott EB, Colonna N, De Gennaro R, Nguyen NL, Borghi G, Ferretti A, Dabo I, Marzari N. koopmans: An Open-Source Package for Accurately and Efficiently Predicting Spectral Properties with Koopmans Functionals. J Chem Theory Comput 2023; 19:7097-7111. [PMID: 37610300 PMCID: PMC10601481 DOI: 10.1021/acs.jctc.3c00652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Indexed: 08/24/2023]
Abstract
Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity condition to the entire electronic manifold, ensuring that orbital energies match the corresponding electron removal/addition energy differences (in contrast to semilocal DFT, where a mismatch between the two lies at the heart of the band gap problem and, more generally, the unreliability of Kohn-Sham orbital energies). This strategy has proven to be very powerful, yielding molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost while preserving a functional formulation. This paper reviews the theory of Koopmans functionals, discusses the algorithms necessary for their implementation, and introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials.
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Affiliation(s)
- Edward B. Linscott
- Theory
and Simulation of Materials (THEOS), École
Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Nicola Colonna
- Laboratory
for Neutron Scattering and Imaging, Paul
Scherrer Institut, 5232 Villigen, Switzerland
- National
Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale
de Lausanne, 1015 Lausanne, Switzerland
| | - Riccardo De Gennaro
- Theory
and Simulation of Materials (THEOS), École
Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Ngoc Linh Nguyen
- Faculty
of Materials Science and Engineering, Phenikaa
University, Hanoi 12116, Vietnam
- A&A
Green Phoenix Group JSC, Phenikaa Research
and Technology Institute (PRATI), No. 167 Hoang Ngan, Trung Hoa, Cau Giay, Hanoi 11313, Vietnam
| | - Giovanni Borghi
- Theory
and Simulation of Materials (THEOS), École
Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | | | - Ismaila Dabo
- Department
of Materials Science and Engineering, Materials Research Institute,
and Institutes of Energy and the Environment, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Nicola Marzari
- Theory
and Simulation of Materials (THEOS), École
Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National
Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale
de Lausanne, 1015 Lausanne, Switzerland
- Laboratory
for Materials Simulations, Paul Scherrer
Institut, 5232 Villigen, Switzerland
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47
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Jana S, Śmiga S, Constantin LA, Samal P. Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations. J Phys Chem A 2023; 127:8685-8697. [PMID: 37811903 PMCID: PMC10591512 DOI: 10.1021/acs.jpca.3c03976] [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: 06/12/2023] [Revised: 08/24/2023] [Indexed: 10/10/2023]
Abstract
The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.
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Affiliation(s)
- Subrata Jana
- Department
of Chemistry & Biochemistry, The Ohio
State University, Columbus, Ohio 43210, United States
| | - Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudzikadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Istituto
di Nanoscienze, Consiglio Nazionale delle
Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School
of Physical Sciences, National Institute of Science Education and
Research, HBNI, Bhubaneswar 752050, India
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48
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Remme R, Kaczun T, Scheurer M, Dreuw A, Hamprecht FA. KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory. J Chem Phys 2023; 159:144113. [PMID: 37830452 DOI: 10.1063/5.0158275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 09/14/2023] [Indexed: 10/14/2023] Open
Abstract
Orbital-free density functional theory (OF-DFT) holds promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of electron density alone. Here, we set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths, and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two-electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.
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Affiliation(s)
- R Remme
- IWR, Heidelberg University Im Neuenheimer Feld 205, 69120 Heidelberg Baden-Württemberg, Germany
| | - T Kaczun
- IWR, Heidelberg University Im Neuenheimer Feld 205, 69120 Heidelberg Baden-Württemberg, Germany
| | - M Scheurer
- IWR, Heidelberg University Im Neuenheimer Feld 205, 69120 Heidelberg Baden-Württemberg, Germany
| | - A Dreuw
- IWR, Heidelberg University Im Neuenheimer Feld 205, 69120 Heidelberg Baden-Württemberg, Germany
| | - F A Hamprecht
- IWR, Heidelberg University Im Neuenheimer Feld 205, 69120 Heidelberg Baden-Württemberg, Germany
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Terayama K, Osaki Y, Fujita T, Tamura R, Naito M, Tsuda K, Matsui T, Sumita M. Koopmans' Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules. J Chem Theory Comput 2023; 19:6770-6781. [PMID: 37729470 DOI: 10.1021/acs.jctc.3c00764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans' theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans' theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans' theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals.
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Affiliation(s)
- Kei Terayama
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku Kanagawa 230-0045, Japan
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- MDX Research Center for Element Strategy, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8501, Japan
| | - Yamato Osaki
- Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
| | - Takehiro Fujita
- Research Center for Macromolecules and Biomaterials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Ryo Tamura
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- Center for Basic Research on Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Masanobu Naito
- Research Center for Macromolecules and Biomaterials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
| | - Koji Tsuda
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
- Center for Basic Research on Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
- Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
| | - Toru Matsui
- Department of Chemistry, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
| | - Masato Sumita
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
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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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