Clifford Boundary Conditions for Periodic Systems: the Madelung Constant of Cubic Crystals in 1, 2 and 3 Dimensions
| Autor: | J. Arjan Berger, Véronique Brumas, Nicolas Tavernier, Stefano Evangelisti, Gian Luigi Bendazzoli |
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| Přispěvatelé: | Groupe Méthodes et outils de la chimie quantique (LCPQ) (GMO), Laboratoire de Chimie et Physique Quantiques Laboratoire (LCPQ), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), European Theoretical Spectroscopy Facility (ETSF), Laboratoire de Chimie et Physique Quantiques (LCPQ), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC), Universita di Bologna |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Condensed Matter - Materials Science 010304 chemical physics Mathematical analysis Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Clifford torus Space (mathematics) 01 natural sciences Madelung constant Manifold [CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry 0103 physical sciences Supercell (crystal) Periodic boundary conditions Boundary value problem Physical and Theoretical Chemistry 010306 general physics Topology (chemistry) ComputingMilieux_MISCELLANEOUS |
| Zdroj: | Theoretical Chemistry Accounts: Theory, Computation, and Modeling Theoretical Chemistry Accounts: Theory, Computation, and Modeling, 2021, 140, pp.106. ⟨10.1007/s00214-021-02805-1⟩ Theoretical Chemistry Accounts: Theory, Computation, and Modeling, Springer Verlag, 2021, 140, pp.106. ⟨10.1007/s00214-021-02805-1⟩ |
| ISSN: | 1432-881X 1432-2234 |
| DOI: | 10.1007/s00214-021-02805-1⟩ |
| Popis: | In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed (Tavernier et al in J Phys Chem Lett 17:7090, 2000). In our approach we extract a fragment, i.e., a supercell, out of the infinite system, and then modifying its topology into the that of a Clifford torus which is a flat, finite and border-less manifold. We then renormalize the distance between two points by defining it as the Euclidean distance in the embedding space of the Clifford torus. With our method we have been able to calculate the reference results available in the literature with a remarkable accuracy, and at a very low computational effort. In this work we show that our approach is robust with respect to the shape of the supercell. In particular, we show that the Madelung constants converge to the same values but that the convergence properties are different. Our approach scales linearly with the number of atoms. The calculation of Madelung constants only takes a few seconds on a laptop computer for a relative precision of about 10 $$^{-6}$$ . |
| Databáze: | OpenAIRE |
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