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Sahre MJ, von Rudorff GF, Marquetand P, von Lilienfeld OA. Transferability of atomic energies from alchemical decomposition. J Chem Phys 2024; 160:054106. [PMID: 38341696 DOI: 10.1063/5.0187298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 01/09/2024] [Indexed: 02/13/2024] Open
Abstract
We study alchemical atomic energy partitioning as a method to estimate atomization energies from atomic contributions, which are defined in physically rigorous and general ways through the use of the uniform electron gas as a joint reference. We analyze quantitatively the relation between atomic energies and their local environment using a dataset of 1325 organic molecules. The atomic energies are transferable across various molecules, enabling the prediction of atomization energies with a mean absolute error of 23 kcal/mol, comparable to simple statistical estimates but potentially more robust given their grounding in the physics-based decomposition scheme. A comparative analysis with other decomposition methods highlights its sensitivity to electrostatic variations, underlining its potential as a representation of the environment as well as in studying processes like diffusion in solids characterized by significant electrostatic shifts.
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Affiliation(s)
- Michael J Sahre
- Vienna Doctoral School in Chemistry (DoSChem) and Institute of Theoretical Chemistry and Faculty of Physics, University of Vienna, 1090 Vienna, Austria
| | - Guido Falk von Rudorff
- Department of Chemistry, University Kassel, Heinrich-Plett-Str.40, 34132 Kassel, Germany
- Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), Heinrich-Plett-Straße 40, 34132 Kassel, Germany
| | - Philipp Marquetand
- Faculty of Chemistry, Institute of Theoretical Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - O Anatole von Lilienfeld
- Vienna Doctoral School in Chemistry (DoSChem) and Institute of Theoretical Chemistry and Faculty of Physics, University of Vienna, 1090 Vienna, Austria
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, St. George Campus, Toronto, M5S 3H6 Ontario, Canada
- Department of Materials Science and Engineering, University of Toronto, St. George Campus, Toronto, M5S 3E4 Ontario, Canada
- Vector Institute for Artificial Intelligence, Toronto, M5S 1M1 Ontario, Canada
- ML Group, Technische Universität Berlin and Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
- Berlin Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
- Department of Physics, University of Toronto, St. George Campus, Toronto, M5S 1A7 Ontario, Canada
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2
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Loos PF, Seidl M. Transient uniform electron gases. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2061388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Michael Seidl
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modelling, FEW, Vrije Universiteit, Amsterdam, The Netherlands
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3
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Traore D, Giner E, Toulouse J. Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model. J Chem Phys 2022; 156:044113. [DOI: 10.1063/5.0076128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Diata Traore
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
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4
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Loos PF, Fromager E. A weight-dependent local correlation density-functional approximation for ensembles. J Chem Phys 2020; 152:214101. [DOI: 10.1063/5.0007388] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Université de Strasbourg, Strasbourg, France
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Marut C, Senjean B, Fromager E, Loos PF. Weight dependence of local exchange–correlation functionals in ensemble density-functional theory: double excitations in two-electron systems. Faraday Discuss 2020; 224:402-423. [DOI: 10.1039/d0fd00059k] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We discuss the construction of first-rung weight-dependent exchange–correlation density-functional approximations for He and H2 specifically designed for the computation of double excitations within Gross–Oliveira–Kohn-DFT.
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Affiliation(s)
- Clotilde Marut
- Laboratoire de Chimie et Physique Quantiques
- Université de Toulouse
- CNRS
- UPS
- France
| | - Bruno Senjean
- Instituut-Lorentz
- Universiteit Leiden
- 2300 RA Leiden
- The Netherlands
- Division of Theoretical Chemistry
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique
- Institut de Chimie
- CNRS
- Université de Strasbourg
- Strasbourg
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6
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Distributed Gaussian orbitals for the description of electrons in an external potential. J Mol Model 2018; 24:216. [PMID: 30051296 DOI: 10.1007/s00894-018-3749-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2018] [Accepted: 07/03/2018] [Indexed: 10/28/2022]
Abstract
In this work, we demonstrate the viability of using distributed Gaussian orbitals as a basis set for the calculation of the properties of electrons subjected to an external potential. We validate our method by studying one-electron systems for which we can compare to exact analytical results. We highlight numerical aspects that require particular care when using a distributedGaussian basis set. In particular, we discuss the optimal choice for the distance between two neighboring Gaussian orbitals. Finally, we show how our approach can be applied to many-electron problems.
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Loos PF. Exchange functionals based on finite uniform electron gases. J Chem Phys 2017; 146:114108. [DOI: 10.1063/1.4978409] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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8
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Affiliation(s)
- Fergus J. M. Rogers
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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Sun J, Perdew JP, Yang Z, Peng H. Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems. J Chem Phys 2016; 144:191101. [DOI: 10.1063/1.4950845] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Affiliation(s)
- Jianwei Sun
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Zenghui Yang
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Haowei Peng
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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Loos P, Gill PMW. The uniform electron gas. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1257] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
| | - Peter M. W. Gill
- Research School of Chemistry Australian National University Canberra Australia
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Tognetti V, Loos PF. Natural occupation numbers in two-electron quantum rings. J Chem Phys 2016; 144:054108. [PMID: 26851909 DOI: 10.1063/1.4940919] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.
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Affiliation(s)
- Vincent Tognetti
- Normandy Univ., COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont Saint Aignan, Cedex, France
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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Agboola D, Knol AL, Gill PMW, Loos PF. Uniform electron gases. III. Low-density gases on three-dimensional spheres. J Chem Phys 2015; 143:084114. [DOI: 10.1063/1.4929353] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Davids Agboola
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Anneke L. Knol
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Peter M. W. Gill
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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13
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Loos PF, Bressanini D. Nodal surfaces and interdimensional degeneracies. J Chem Phys 2015; 142:214112. [DOI: 10.1063/1.4922159] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Dario Bressanini
- Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Lucini 3, I-22100 Como, Italy
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Sun J, Perdew JP, Ruzsinszky A. Semilocal density functional obeying a strongly tightened bound for exchange. Proc Natl Acad Sci U S A 2015; 112:685-9. [PMID: 25561554 PMCID: PMC4311813 DOI: 10.1073/pnas.1423145112] [Citation(s) in RCA: 69] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb-Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic "meta-GGA made very simple" (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew-Burke-Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.
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Affiliation(s)
| | - John P Perdew
- Departments of Physics and Chemistry, Temple University, Philadelphia, PA 19122
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Abstract
Orbital basis functions in a one-dimensional triatomic molecule ABC.
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Affiliation(s)
- Pierre-François Loos
- Research School of Chemistry
- Australian National University
- Canberra ACT 0200
- Australia
| | - Caleb J. Ball
- Research School of Chemistry
- Australian National University
- Canberra ACT 0200
- Australia
| | - Peter M. W. Gill
- Research School of Chemistry
- Australian National University
- Canberra ACT 0200
- Australia
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Gill PMW, Loos PF, Agboola D. Basis functions for electronic structure calculations on spheres. J Chem Phys 2014; 141:244102. [DOI: 10.1063/1.4903984] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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