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Angeli C, Bendazzoli GL, Evangelisti S, Berger JA. The localization spread and polarizability of rings and periodic chains. J Chem Phys 2021; 155:124107. [PMID: 34598588 DOI: 10.1063/5.0056226] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The localization spread gives a criterion to decide between metallic and insulating behavior of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with open or periodic boundary conditions. In particular, in the case of periodic systems, we use the complex position definition, which was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius R with open boundary conditions leads, in the large R limit, to the same formula derived by Resta and co-workers [C. Sgiarovello, M. Peressi, and R. Resta, Phys. Rev. B 64, 115202 (2001)] for 1D systems with periodic Born-von Kármán boundary conditions. A second formula, alternative to Resta's, is also given based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities.
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Affiliation(s)
- Celestino Angeli
- Dipartimento di Scienze Chimiche, Farmaceutiche ed Agrarie, Università di Ferrara, via Borsari 46, 44121 Ferrara, Italy
| | | | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques, UMR5626, Université de Toulouse (UPS), CNRS, 118 Route de Narbonne, F-31062 Toulouse, France
| | - J Arjan Berger
- Laboratoire de Chimie et Physique Quantiques, UMR5626, Université de Toulouse (UPS), CNRS, and European Theoretical Spectroscopy Facility, 118 Route de Narbonne, F-31062 Toulouse, France
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Diaz-Marquez A, Battaglia S, Bendazzoli GL, Evangelisti S, Leininger T, Berger JA. Signatures of Wigner localization in one-dimensional systems. J Chem Phys 2018; 148:124103. [PMID: 29604812 DOI: 10.1063/1.5017118] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a simple and efficient approach to study Wigner localization in one-dimensional systems using ab initio theory. In particular, we propose a suitable basis for the study of localization which consists of equally spaced overlapping gaussians. We illustrate our approach with full-configuration interaction which yields exact results for a given basis set. With our approach, we were able to study up to 8 electrons with full-configuration interaction. Finally, we propose the total-position spread tensor and the total electron entropy as convenient quantities to obtain signatures of Wigner localization.
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Affiliation(s)
- Alejandro Diaz-Marquez
- Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Stefano Battaglia
- Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | | | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Thierry Leininger
- Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - J A Berger
- Laboratoire de Chimie et Physique Quantiques, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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Huran AW, Leininger T, Bendazzoli GL, Evangelisti S. Computing the position-spread tensor in the CAS-SCF formalism II: Spin partition. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.10.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Brea O, El Khatib M, Bendazzoli GL, Evangelisti S, Leininger T, Angeli C. The Spin-Partitioned Total-Position Spread Tensor: An Application To Diatomic Molecules. J Phys Chem A 2016; 120:5230-8. [DOI: 10.1021/acs.jpca.6b01043] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Oriana Brea
- Laboratoire
de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, Toulouse Cedex 31062, France
- Departamento
de Química, Facultad de Ciencias, Universidad Autónoma de Madrid, Módulo 13 Cantoblanco, 28049 Madrid, Spain
| | - Muammar El Khatib
- Laboratoire
de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, Toulouse Cedex 31062, France
| | - Gian Luigi Bendazzoli
- Dipartimento
di Chimica Industriale “Toso Montanari”, Università di Bologna, Viale Risorgimento 4, I−40136 Bologna, Italy
| | - Stefano Evangelisti
- Laboratoire
de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, Toulouse Cedex 31062, France
| | - Thierry Leininger
- Laboratoire
de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, Toulouse Cedex 31062, France
| | - Celestino Angeli
- Dipartimento
di Scienze Chimiche e Farmaceutiche, Università di Ferrara, Via Fossato
di Mortara 17, 44121 Ferrara, Italy
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Fertitta E, El Khatib M, Bendazzoli GL, Paulus B, Evangelisti S, Leininger T. The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains. J Chem Phys 2015; 143:244308. [PMID: 26723672 DOI: 10.1063/1.4936585] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.
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Affiliation(s)
- Edoardo Fertitta
- Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin, Germany
| | - Muammar El Khatib
- Laboratoire de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118 Route de Narbonne, Toulouse Cedex 31062, France
| | - Gian Luigi Bendazzoli
- Dipartimento di Chimica Industriale "Toso Montanari," Università di Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy
| | - Beate Paulus
- Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin, Germany
| | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118 Route de Narbonne, Toulouse Cedex 31062, France
| | - Thierry Leininger
- Laboratoire de Chimie et Physique Quantiques-LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118 Route de Narbonne, Toulouse Cedex 31062, France
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El Khatib M, Brea O, Fertitta E, Bendazzoli GL, Evangelisti S, Leininger T. The total position-spread tensor: Spin partition. J Chem Phys 2015; 142:094113. [DOI: 10.1063/1.4913734] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Muammar El Khatib
- Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex, France
| | - Oriana Brea
- Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex, France
- Departamento de Química, Facultad de Ciencias, Módulo 13, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
| | - Edoardo Fertitta
- Institut für Chemie und Biochemie - Physikalische und Theoretische Chemie, Freie Universität Berlin, Takustr. 3, D-14195 Berlin, Germany
| | - Gian Luigi Bendazzoli
- Dipartimento di Chimica Industriale “Toso Montanari”, Università di Bologna, Viale Risorgimento 4, I–40136 Bologna, Italy
| | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex, France
| | - Thierry Leininger
- Laboratoire de Chimie et Physique Quantiques - LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118, Route de Narbonne, 31062 Toulouse Cedex, France
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