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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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Vu N, Mejia-Rodriguez D, Bauman NP, Panyala A, Mutlu E, Govind N, Foley JJ. Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction Theory. J Chem Theory Comput 2024; 20:1214-1227. [PMID: 38291561 PMCID: PMC10876286 DOI: 10.1021/acs.jctc.3c01207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 12/21/2023] [Accepted: 12/26/2023] [Indexed: 02/01/2024]
Abstract
Polariton chemistry has attracted great attention as a potential route to modify chemical structure, properties, and reactivity through strong interactions among molecular electronic, vibrational, or rovibrational degrees of freedom. A rigorous theoretical treatment of molecular polaritons requires the treatment of matter and photon degrees of freedom on equal quantum mechanical footing. In the limit of molecular electronic strong or ultrastrong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach we refer to as ab initio cavity quantum electrodynamics, where the photon degrees of freedom are treated at the level of cavity quantum electrodynamics. Here, we present an approach called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction theory to provide ground- and excited-state polaritonic surfaces with a balanced description of strong correlation effects among electronic and photonic degrees of freedom. This method provides a platform for ab initio cavity quantum electrodynamics when both strong electron correlation and strong light-matter coupling are important and is an important step toward computational approaches that yield multiple polaritonic potential energy surfaces and couplings that can be leveraged for ab initio molecular dynamics simulations of polariton chemistry.
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Affiliation(s)
- Nam Vu
- Department
of Chemistry, University of North Carolina
Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223, United States
| | - Daniel Mejia-Rodriguez
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Nicholas P. Bauman
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Ajay Panyala
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Erdal Mutlu
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Niranjan Govind
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Jonathan J. Foley
- Department
of Chemistry, University of North Carolina
Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223, United States
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Coe JP. Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock. J Chem Theory Comput 2023; 19:8053-8065. [PMID: 37939698 PMCID: PMC10687870 DOI: 10.1021/acs.jctc.3c00601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 10/24/2023] [Accepted: 10/25/2023] [Indexed: 11/10/2023]
Abstract
We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.
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Affiliation(s)
- Jeremy P. Coe
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
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4
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Dey M, Ghosh D. Machine Learning the Quantum Mechanical Wave Function. J Phys Chem A 2023; 127:9159-9166. [PMID: 37906959 DOI: 10.1021/acs.jpca.3c05322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
Strongly correlated systems have been challenging to computational chemists for a long time. To solve these systems, multireference methods have been developed over the years. Recently, with the fast development of machine learning and artificial intelligence methods, these methods have also influenced the quest for optimal wave function ansatz. Machine learning approaches have been used in many different flavors. From this perspective, we will discuss the different milestones achieved in the use of machine learning for solving the quantum many body problem.
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Affiliation(s)
- Mandira Dey
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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Bilous P, Pálffy A, Marquardt F. Deep-Learning Approach for the Atomic Configuration Interaction Problem on Large Basis Sets. PHYSICAL REVIEW LETTERS 2023; 131:133002. [PMID: 37832007 DOI: 10.1103/physrevlett.131.133002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Revised: 06/29/2023] [Accepted: 08/09/2023] [Indexed: 10/15/2023]
Abstract
High-precision atomic structure calculations require accurate modeling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily become challenging or infeasibly large even for advanced supercomputers. Here, we develop a deep-learning approach which allows us to preselect the most relevant configurations out of large CI basis sets until the targeted energy precision is achieved. The large CI computation is thereby replaced by a series of smaller ones performed on an iteratively expanding basis subset managed by a neural network. While dense architectures as used in quantum chemistry fail, we show that a convolutional neural network naturally accounts for the physical structure of the basis set and allows for robust and accurate CI calculations. The method was benchmarked on basis sets of moderate size allowing for the direct CI calculation, and further demonstrated on prohibitively large sets where the direct computation is not possible.
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Affiliation(s)
- Pavlo Bilous
- Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - Adriana Pálffy
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany
- Institute of Theoretical Physics and Astrophysics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Florian Marquardt
- Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
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Jones GM, Li RR, DePrince AE, Vogiatzis KD. Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory. J Phys Chem Lett 2023:6377-6385. [PMID: 37418691 DOI: 10.1021/acs.jpclett.3c01382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies relative to reference values from configuration-interaction-based calculations.
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Affiliation(s)
- Grier M Jones
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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Herzog B, Casier B, Lebègue S, Rocca D. Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning. J Chem Theory Comput 2023; 19:2484-2490. [PMID: 37043718 DOI: 10.1021/acs.jctc.2c01216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2023]
Abstract
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.
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Affiliation(s)
- Basile Herzog
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Bastien Casier
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Sébastien Lebègue
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Dario Rocca
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
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Abstract
We develop analytic gradients for selected configuration interaction wave functions. Despite all pairs of molecular orbitals now potentially having to be considered for the coupled perturbed Hartree-Fock equations, we show that degenerate orbital pairs belonging to different irreducible representations in the largest abelian subgroup do not need to be included and instabilities due to degeneracies are avoided. We introduce seminumerical gradients and use them to validate the analytic approach even when near degeneracies are present due to high-symmetry geometries being slightly distorted to break symmetry. The method is applied to carbon monoxide, ammonia, square planar H4, hexagonal planar H6, and methane for a range of bond lengths where we demonstrate that analytic gradients for selected configuration interaction can approach the quality of full configuration interaction yet only use a very small fraction of its determinants.
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Seth K, Ghosh D. Active Learning Assisted MCCI to Target Spin States. J Chem Theory Comput 2023; 19:524-531. [PMID: 36607601 DOI: 10.1021/acs.jctc.2c00935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Strongly correlated systems and their accurate solutions have been challenging to quantum chemistry. Several methods have been developed over the years for the accurate understanding of such systems, and selected configuration interaction and Monte Carlo configuration interaction (MCCI) form important classes of systems in this category. However, MCCI is plagued by slow convergence. This is further exacerbated by the fact that most of the current MCCI implementations do not target specific spin states. In our work, we use active learning assisted MCCI to speed up the convergence manyfold and also develop a method for spin targeting. This method has been tested with several model Hamiltonian systems akin to molecular systems and has shown improved convergence and accuracy.
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Affiliation(s)
- Koushik Seth
- School of Chemical Sciences, Indian Association for the Cultivation of Sciences, Jadavpur, Kolkata700032, India
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Sciences, Jadavpur, Kolkata700032, India
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Lunghi A, Sanvito S. Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations. Nat Rev Chem 2022; 6:761-781. [PMID: 37118096 DOI: 10.1038/s41570-022-00424-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/15/2022] [Indexed: 11/09/2022]
Abstract
Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.
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