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Rivic F, Lehr A, Schäfer R. Dielectric Behavior and Prolate Growth Patterns of Silicon Clusters Si N with N = 12-30 by Cryogenic Electric Beam Deflection. J Phys Chem A 2024. [PMID: 38442276 DOI: 10.1021/acs.jpca.3c08432] [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
We present a comprehensive investigation of the dielectric behavior and geometric structures of cold neutral SiN clusters of intermediate size with N = 12-30 atoms. For this, cryogenic electric beam deflection experiments were carried out for the first time for Si clusters at nozzle temperatures below 30 K. In combination with quantum chemical calculations based on density functional theory and classical trajectory simulations of the rotational dynamics in the electric field, the geometric structures of the clusters are discriminated. Clusters with N < 15 favor a single-capped square antiprism as a nucleus for cluster growth, forming compact geometries in the molecular beam. Starting with 15 atoms, a prolate-like growth is observed. The prolate structures are based on stable building blocks which reappear for numerous sizes throughout the cluster growth. Finally, the transition from prolate to quasi-spherical shapes is shown to take place around Si29/Si30 as predicted theoretically by the literature. The influence of the exchange-correlation functional on the predicted structure and dielectric properties is discussed in detail for some clusters. Relaxation of the electric-dipole moment and therefore quenching of the observed electric response due to vibrational excitation and collisions with the background gas are also considered, which explains deviations between experiment and theory.
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Affiliation(s)
- Filip Rivic
- Eduard-Zintl Institute, Technical University of Darmstadt, Peter-Grünberg-Straße 8, 64287 Darmstadt, Germany
| | - Andreas Lehr
- Eduard-Zintl Institute, Technical University of Darmstadt, Peter-Grünberg-Straße 8, 64287 Darmstadt, Germany
| | - Rolf Schäfer
- Eduard-Zintl Institute, Technical University of Darmstadt, Peter-Grünberg-Straße 8, 64287 Darmstadt, Germany
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2
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Zhong Q. Size-dependent linear and nonlinear optical responses of silicon clusters. Phys Chem Chem Phys 2024; 26:6022-6028. [PMID: 38294058 DOI: 10.1039/d3cp05678c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2024]
Abstract
Owing to strong quantum confinement effects and no periodic constraints, the geometric and electronic structures of silicon clusters differ from those of crystalline silicon. Although previous studies have elucidated the optical properties of silicon clusters, some issues remain unresolved. To address these, this study examined the size-dependent linear and nonlinear optical responses of silicon clusters through first-principles calculations. Silicon clusters exhibited lone-pair-electron-dominated optical response behaviors. With the investigated size range, the orientationally average polarizability (αave) and second-order hyperpolarizability (γave) increased with cluster size. However, αave and γave per atom exhibited no evident size-dependent trends owing to co-modulation of the lone-pair-number-to-atomic-number ratio and geometry. αave and γave were notably sensitive to the nuclear binding strength of lone-pair electrons. Thus, the nonlinear optical effects of silicon clusters are superior to those of phosphorus and sulfur clusters. This investigation offers valuable insights into the optical responses of atomic-precision clusters.
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Affiliation(s)
- Quanjie Zhong
- School of Materials Science and Physics, Nanhu Campus, China University of Mining and Technology, No. 1 University Road, Xuzhou 221116, Jiangsu Province, China.
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Rivic F, Lehr A, Schäfer R. Scaling of the permanent electric dipole moment in isolated silicon clusters with near-spherical shape. Phys Chem Chem Phys 2023; 25:13376-13382. [PMID: 37145168 DOI: 10.1039/d3cp00926b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
In silicon clusters a structural transition from prolate to near-spherical structures takes place at a size of about 25-30 atoms. While some of the prolate clusters are very polar, there has been no experimental evidence of the presence of dipole moments in larger silicon clusters with near-spherical shape. By means of electric molecular beam deflection experiments at cryogenic temperatures, it was possible to prove for the first time that SiN clusters with more than N = 30 atoms are also polar. Interestingly, the dipole moment per atom for clusters in the range between 30 and 80 or 90 atoms is almost constant and amounts to 0.02 D. This unusual behaviour manifests in effective polarizabilities increasing linearly with cluster size. The dipolar contribution to the polarizability means that SiN clusters with N = 80 atoms can be polarized more than twice as well as a correspondingly small sphere with the dielectric properties of bulk α-Si. This finding is analysed with quantum chemical calculations concerning the geometric structure as well as the charge distribution and is related to the dielectric behaviour of polar semiconductor nanocrystals.
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Affiliation(s)
- Filip Rivic
- Technical University of Darmstadt, Eduard-Zintl-Institute, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany.
| | - Andreas Lehr
- Technical University of Darmstadt, Eduard-Zintl-Institute, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany.
| | - Rolf Schäfer
- Technical University of Darmstadt, Eduard-Zintl-Institute, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany.
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Affiliation(s)
- Jijun Zhao
- Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
| | - Qiuying Du
- Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
| | - Si Zhou
- Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
| | - Vijay Kumar
- Center for Informatics, School of Natural Sciences, Shiv Nadar University, NH-91, Tehsil Dadri, Gautam Buddha Nagar 201314, U. P., India
- Dr. Vijay Kumar Foundation, 1969 Sector 4, Gurgaon 122001, Haryana, India
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Silva FT, Yoshinaga M, Galvão BRL. A method for predicting basins in the global optimization of nanoclusters with applications to Al xCu y alloys. Phys Chem Chem Phys 2020; 22:16914-16925. [PMID: 32672291 DOI: 10.1039/d0cp01327g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
The problem of obtaining the geometrical configuration of a molecule that minimizes its potential energy is a very complicated one for a series of applications, ranging from determining the structure of biological macromolecules to nanoclusters of atoms. Global optimization tools are available for this task, and many of them are based in performing successive local optimizations, where the starting geometries for these steps are determined by an intelligent algorithm. Here we develop a method to save computing time in the optimization of nanoclusters by predicting if a given minimum has been previously visited during local optimization steps. Our application to Cu-Al nanoalloys indicates that it is possible to save a substantial amount of computational cost. The application also reveals new promising AlxCuy clusters and explain their stabilities in terms of the jellium model.
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Affiliation(s)
- F T Silva
- Prime Systems, Av. Afonso Pena 3577, 7F, Belo Horizonte, Minas Gerais, Brazil
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Galvão BRL, Viegas LP. What Electronic Structure Method Can Be Used in the Global Optimization of Nanoclusters? J Phys Chem A 2019; 123:10454-10462. [DOI: 10.1021/acs.jpca.9b09309] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Breno R. L. Galvão
- Centro Federal de Educação Tecnológica de Minas Gerais, CEFET-MG, Av. Amazonas 5253, 30421-169 Belo Horizonte, Minas Gerais, Brazil
| | - Luís P. Viegas
- Aarhus Institute of Advanced Studies, Aarhus University, Aarhus DK-8000, Denmark
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Silva FT, Silva MX, Belchior JC. A New Genetic Algorithm Approach Applied to Atomic and Molecular Cluster Studies. Front Chem 2019; 7:707. [PMID: 31750290 PMCID: PMC6848380 DOI: 10.3389/fchem.2019.00707] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2019] [Accepted: 10/09/2019] [Indexed: 12/16/2022] Open
Abstract
A new procedure is suggested to improve genetic algorithms for the prediction of structures of nanoparticles. The strategy focuses on managing the creation of new individuals by evaluating the efficiency of operators (o1, o2,…,o13) in generating well-adapted offspring. This is done by increasing the creation rate of operators with better performance and decreasing that rate for the ones which poorly fulfill the task of creating favorable new generation. Additionally, several strategies (thirteen at this level of approach) from different optimization techniques were implemented on the actual genetic algorithm. Trials were performed on the general case studies of 26 and 55-atom clusters with binding energy governed by a Lennard-Jones empirical potential with all individuals being created by each of the particular thirteen operators tested. A 18-atom carbon cluster and some polynitrogen systems were also studied within REBO potential and quantum approaches, respectively. Results show that our management strategy could avoid bad operators, keeping the overall method performance with great confidence. Moreover, amongst the operators taken from the literature and tested herein, the genetic algorithm was faster when the generation of new individuals was carried out by the twist operator, even when compared to commonly used operators such as Deaven and Ho cut-and-splice crossover. Operators typically designed for basin-hopping methodology also performed well on the proposed genetic algorithm scheme.
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Affiliation(s)
- Frederico T Silva
- Departamento de Química Fundamental-CCEN, Universidade Federal de Pernambuco, Cidade Universitária, Recife, Brazil
| | - Mateus X Silva
- Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Belo Horizonte, Brazil
| | - Jadson C Belchior
- Departamento de Química-ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
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Gleditzsch M, Fuchs TM, Schäfer R. N-Doping at the Sub-Nanoscale: Dielectric and Magnetic Response of Neutral Phosphorus-Doped Tin Clusters. J Phys Chem A 2019; 123:1434-1444. [DOI: 10.1021/acs.jpca.8b12049] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Martin Gleditzsch
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
| | - Thomas M. Fuchs
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
| | - Rolf Schäfer
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
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Kohaut S, Thiel P, Springborg M. Growth patterns, shapes, and electronic properties of mixed Si m Ge n clusters with n+m⩽30. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2016.12.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Affiliation(s)
- Koblar Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Julius Jellinek
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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Götz DA, Shayeghi A, Johnston RL, Schwerdtfeger P, Schäfer R. Structural evolution and metallicity of lead clusters. NANOSCALE 2016; 8:11153-11160. [PMID: 27181365 DOI: 10.1039/c6nr02080a] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The evolution of the metallic state in lead clusters and its structural implications are subject to ongoing discussions. Here we present molecular beam electric deflection studies of neutral PbN (N = 19-25, 31, 36, 54) clusters. Many of them exhibit dipole moments or anomalies of the polarizability indicating a non-metallic state. In order to resolve their structures, the configurational space is searched using the Pool Birmingham Cluster Genetic algorithm based on density functional theory. Spin-orbit effects on the geometries and dipole moments are taken into account by further relaxing them with two-component density functional theory. Geometries and dielectric properties from quantum chemical calculations are then used to simulate beam deflection profiles. Structures are assigned by the comparison of measured and simulated beam profiles. Energy gaps are calculated using time-dependent density functional theory. They are compared to Kubo gaps, which are an indicator of the metallicity in finite particles. Both, experimental and theoretical data suggest that lead clusters are not metallic up to at least 36 atoms.
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Affiliation(s)
- Daniel A Götz
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany.
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Shayeghi A, Götz D, Davis JBA, Schäfer R, Johnston RL. Pool-BCGA: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters. Phys Chem Chem Phys 2014; 17:2104-12. [PMID: 25482360 DOI: 10.1039/c4cp04323e] [Citation(s) in RCA: 75] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The Birmingham cluster genetic algorithm is a package that performs global optimisations for homo- and bimetallic clusters based on either first principles methods or empirical potentials. Here, we present a new parallel implementation of the code which employs a pool strategy in order to eliminate sequential steps and significantly improve performance. The new approach meets all requirements of an evolutionary algorithm and contains the main features of the previous implementation. The performance of the pool genetic algorithm is tested using the Gupta potential for the global optimisation of the Au10Pd10 cluster, which demonstrates the high efficiency of the method. The new implementation is also used for the global optimisation of the Au10 and Au20 clusters directly at the density functional theory level.
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Affiliation(s)
- A Shayeghi
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany.
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Shayeghi A, Heard CJ, Johnston RL, Schäfer R. Optical and electronic properties of mixed Ag-Au tetramer cations. J Chem Phys 2014; 140:054312. [PMID: 24511945 DOI: 10.1063/1.4863443] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
We present experimental and theoretical studies of the optical response of mixed Ag(n)Au(+)(4-n) (n=1-3) clusters in the photon energy range ℏω = 1.9-3.5 eV. Absorption spectra are recorded by a newly built longitudinal molecular beam depletion spectroscopy apparatus providing lower limits to absolute photodissociation cross sections. The experimental data are compared to optical response calculations in the framework of long-range corrected time-dependent density functional theory with initial cluster geometries obtained by the unbiased Birmingham Cluster Genetic Algorithm coupled with density functional theory. Experiments and excited state calculations shed light on the structural and electronic properties of the mixed Ag-Au tetramer cations.
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Affiliation(s)
- A Shayeghi
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
| | - C J Heard
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - R L Johnston
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - R Schäfer
- Eduard-Zintl-Institut, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
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14
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Rohrmann U, Schwerdtfeger P, Schäfer R. Atomic domain magnetic nanoalloys: interplay between molecular structure and temperature dependent magnetic and dielectric properties in manganese doped tin clusters. Phys Chem Chem Phys 2014; 16:23952-66. [DOI: 10.1039/c4cp02994a] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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Götz DA, Shayeghi A, Johnston RL, Schwerdtfeger P, Schäfer R. Influence of spin-orbit effects on structures and dielectric properties of neutral lead clusters. J Chem Phys 2014; 140:164313. [DOI: 10.1063/1.4872369] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Götz DA, Schäfer R, Schwerdtfeger P. The performance of density functional and wavefunction-based methods for 2D and 3D structures of Au10. J Comput Chem 2013; 34:1975-81. [DOI: 10.1002/jcc.23338] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2013] [Revised: 04/24/2013] [Accepted: 04/25/2013] [Indexed: 12/20/2022]
Affiliation(s)
- Daniel A. Götz
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt; Germany
| | - Rolf Schäfer
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt; Germany
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics; The New Zealand Institute for Advanced Study, Massey University Albany; 0745; Auckland; New Zealand
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Shayeghi A, Johnston RL, Schäfer R. Evaluation of photodissociation spectroscopy as a structure elucidation tool for isolated clusters: a case study of Ag4+ and Au4+. Phys Chem Chem Phys 2013; 15:19715-23. [DOI: 10.1039/c3cp52160e] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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Li S, Chen W, Yu G, Huang X, Sun C. Theoretical investigation on structures, stability and properties of [P, X, Y] (X=C, Si; Y = O, S) isomers. Mol Phys 2012. [DOI: 10.1080/00268976.2012.724184] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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