Research Proposal

Nanomagnetism of Rhodium Nanoclusters via Tight-Binding Molecular Dynamics and Molecular Dynamics with Empirical Potential

Name                   :               Soon Yee Yeen

Supervisor         :               Dr. Yoon Tiem Leong

University          :               Universiti Sains Malaysia

Program             :               Master of Science (M. Sc.)

Field of Study    :               Physics (Computational Condensed Matter Physics)

I.          OBJECTIVES

The objective of this project is to study the magnetic properties of rhodium nanoclusters theoretically by using different approaches.

II.        INTRODUCTION

The 4d-element Rhodium (Rh) is non-magnetic in the bulk form but it becomes magnetic in the form of a nanoscale-cluster. The size-dependence of electronic and thermal properties of Rh is a specific example of a more generic phenomenon in the study of nanoclusters. The ground-state (GS) configuration of nanocluster is the origin of the size-dependence of its electronic and chemical properties, including the magnetic property.

Existing model for atomic magnetism alone may provide a good description of the magnetic properties of a single Rh atom. The orbital electrons, which are the origin of the magnetic dipole moment in the Rh atom, are treated quantum mechanically in the model. When a bunch of atoms are put together and form a stable Rh cluster, determining the magnetic moment will become a highly non-trivial problem.

The landscape of the potential energy surface (PES) of the cluster becomes increasingly complex at an exponential rate as the number of atoms increases. This results in the search for the global energy minima, which corresponds to a most stable configuration, a very difficult task. Once the GS structure of a given cluster is known, the magnetic property can be determined via standard theoretical procedures.

III.       LITERATURE REVIEW

There have been much research works published on magnetic properties of Rh clusters; each uses different combination of total energy calculating program and global minimum search strategies. The following is a list of the works in sequence of decreasing computational cost.

The most expensive approach involves the use of first-principles molecular dynamics. Ref. [1] used the high-temperature first-principles molecular dynamics simulation to identify the 13-atom Rh structures. No intelligent global minimum (GM) search is involved but the method is considered reliable and effective for such purpose.

The second most expensive approach is that using density functional theory (DFT) coupled with an alternative form of simulated annealing method known as dynamical simulated annealing (DSA) sampling [2]. The results are accurate and reliable but suffer the draw-back that the size of the cluster accessible is small, which is only up to 13 atoms. At the same level of costliness is Ref. [3], in which the GS of 13-atom Rh cluster was searched using a new GM search algorithm known as ab initio random structure searching (AIRSS) that is coupled to DFT.

Going down the ladder is the combination of using DFT for total energy calculation but not coupled to any intelligent GM search algorithm. For example, in Refs. [4] and [5], DFT is employed to calculate educated guess structures, or those obtained from other established sources, such as experiments or those constructed following a mathematical prescription, for cluster size of up to around 15 atoms. Ref. [6] calculated up to 23 atoms, whereas in Ref. [7], which is an extension of [4], included a cluster as large as 64 atoms. Ref. [8] is so far the most ambitious who has calculated the magnetic moment of Rh clusters as large as 147 atoms via DFT based on random initial guess.

Ref. [9] attempted a large cluster size up to 55, using a less expensive total-energy calculating theory, which is density functional tight-binding (DFTB) theory. However, it used only intelligent guess instead of intelligent-search algorithm for the global minimum in the PES. Ref. [10] developed the Slater-Koster (SK) files for Rh and Palladium (Pd) and used them in the DFTB calculation to obtain the GS of clusters with sizes up to 112 atoms. No intelligent GM search algorithm is included as the main purpose of this paper is to report the values of SK parameters for Rh and Pd.

The computationally cheapest GS structures search was done by Ref. [11] where Gupta potential and a global evaluative search for the global minima strategy are used. Electronic structures and related magnetic properties were derived using tight-binding method, without involving DFT. At the same level of costliness is that of Ref. [12] who developed a Rh empirical force field and used it to determine the GS structures up to 58 atoms through a GM search algorithm.

All of the existing literature does not treat temperature-dependent effect of the magnetic properties of the Rh clusters. As can be concluded from the literature search, intelligent GM search algorithms are not usually integrated into the GS determination especially for large cluster size. The ideal choice to obtain most reliable results of GS structures is the combination of DFT and intelligent GM search algorithms, or ab initio molecular dynamics (MD) assisted by a simulated annealing GM search algorithm. However, these are over expensive combinations.

A strategic way to overcome the computational bottle neck is to first use DFTB (or MD) integrated with intelligent GM search algorithms to generate a host of low-energy candidate structures. Then, these candidate structures are fed into DFT for re-optimization via its built-in local-minimum search algorithm. By using this way, electronics features of the cluster can be preserved and hence, the magnetic properties can be calculated reliable. The GS structures obtained can be more confidently claimed as the true global minima. This strategy was advocated by Refs. [13] and [14].

Hence, this proposal proposed a project to fill up the gap on determinations of GS structures and magnetic properties of large Rh clusters. If time permits, determination of the temperature-dependence of the magnetic properties of these nanoclusters will be attempted.
 

IV.       OBJECTIVES OF RESEARCH

i.        To find the ground state structures of large Rh_n clusters, where n is the number of atoms which is up to 100.

ii.       To investigate the magnetic dipole moments of the clusters as a function of n.

iii.    To determine the conditions where the cluster would develop superatomic state, which is the most stable state relative to its neighbor of similar size, and how would these conditions be manipulated for optimum functionality in realistic applications.

iv.     To calculate the temperature-dependence of the magnetic properties of Rh cluster.

V.         METHODOLOGY

i.              Ground State Structures

To perform a search for the ground state structure, two computational tools are required. First of all is the theoretical framework which has to be adopted to calculate the total energy of the system. It can be classical MD using empirical potential, first-principles approaches such as DFT or semi-empirical approach such as density functional tight-binding DFTB theory. Secondly, GM search algorithm such as simulated annealing, genetic algorithms or basin-hoping methods, is employed to search for the configuration such that the total energy of the system is a global minimum.

A search algorithm known as parallel tempering multi-canonical basin-hoping plus genetic algorithm (PTMBHGA) will be used in this work. It is developed by the research group in Physics Department, National Central University (NCU), Taiwan [15]. Energy of each configuration is calculated by using Gupta many-body potential which is default energy-calculating algorithm in PTMBHGA.

By coupling open-source MD software LAMMPS with PTMBHGA, energy of each configuration is calculated by using different types of force field. These potentials, including Gupta potential, are classical potentials. By adopting classical limit in the potential, the system investigated is devoid of any quantum mechanical description of the interaction among electrons.

The TB formalism acts as a “bridge” between the first-principles interactions as obtained from electronic structure methods and empirical classical potentials where the electronic degrees of freedom have been formally eliminated. With this approach, energy of each configuration is calculated by the TBMD software known as DFTB+. This software is coupled with PTMBHGA to generate GS structures. The GS structures obtained from different approaches will be compared.

ii.            Optimization

The lowest-energy candidate GS structures obtained by using both approaches are then optimized via a built-in local-minimization algorithm. This can be done by feeding them into a DFT program such as ABINIT, VASP, CRYSTAL or GAUSSIAN. The optimization process lowers states on the phase space from one PES to another. Denote the global minimum structure as GS configuration.

iii.           Determination of Magnetic Properties

To obtain magnetic dipole moment of a nanostructure, its GS configuration is fed into a DFT to be calculated as a function of spin multiplicity in a spin-orbital mode.  The total energy when minimized against the spin multiplicity will allow us to determine the magnetic configuration of the cluster, hence the magnetic dipole moment, at zero temperature.

Then the magnetic dipole moment of the cluster as a function of the composition of the cluster will be investigated to find out whether there exist any magnetic superatomic states in the range of composition. Temperature-dependence magnetic moment of the cluster can be determined from the DFTB+ software by heating up the temperature of the GS structures from zero temperature.

iv.           Flow Chart of Research Activities

VI.       HYPOTHESIS OF RESEARCH

The GS structures of Rh clusters which obtained by using different approaches should have similar in structural and energy levels. The structures obtained should have similar structures and magnetic properties as reported in present literatures. By analyzing the results, the structures which have higher order of symmetry are expected to have lower energies and higher stability. Besides, the magnetic properties are expected to change with the compositions of Rh clusters. The magnetic properties of the cluster may change as temperature of the system changes in simulation.

VII.      ACCESS TO EQUIPMENT & MATERIAL

VIII.    GANTT CHART OF RESEARCH ACTIVITIES

IX.       MILESTONES AND DATES

X.         EXPECTED RESULTS

i.              Novel Theories and Findings

First of all, the ground state structures of rhodium clusters, up to 100 atoms, can be obtained from an all rounded intelligent guided approach at the level of PTMBHGA with added values. The input structures can be lowered to the lowest potential energy state with a concluded approach at DFT level. Based on these ground state structures, variation of magnetic properties as a function of cluster size can be observed through calculations. Finally, observation on the changes of magnetic moment with temperature can be made by simulations.

ii.            Publications

Several papers on the following topics, which might serve as a method for other elements, will be written and submitted for publication in reputable international journals:

•             Ground state structures of large Rh_n clusters, where n is the number of atoms which is up to 100.

•             Structural and magnetic properties of Rhn clusters.

•             Temperature-dependence magnetic moment of rhodium clusters

XI.       CONTRIBUTION TO THE COUNTRY

One of the most important challenges that the field of magnetism will face in the near future, is the understanding and the technological application of advanced magnetic materials, which requires the cluster geometry for a complete understanding of the electronics properties. Unfortunately, the experiments can only provide some pieces information that is not enough to determine accurately the geometrical structure. Theory and computational methods are essential to determine the most stable geometrical structure.

In a developing country like Malaysia, carrying out real experiments to determine properties of materials may be difficult due to the difficulty caused by technical or financial reasons. In principle the properties of any functional materials, not limited only to the Rh system proposed, can be determined in simulations without much cost. The potential for use in commercial devices, such as magnetic storage media and catalyst converter, is the biggest motivation to pursue cluster research.

XII.      CONCLUSION

There is a need to carry out the research of Rh clusters via theory and computational simulations due to the limitations in real experiments. Through the theoretical studies, a better understanding on the electronics properties of Rh clusters can be obtained.  Subsequently, the magnetic properties of the cluster and how it can be influenced by temperature can be investigated. Eventually, this research work may contribute significant advancement and development in related technological area.

XIII.    REFERENCE

[1]    M. J. Piotrowski, P. Piquini, J. L. F. Da Silva, Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters, Phys. Rev. B 81 (2010) 155446.

[2]    T. Futschek, M. Marsman, J. Hafner, Structural and magnetic isomers of small Pd and Rh clusters: an ab initio density functional study, Journal of Physics: Condensed Matter 17 (38) (2005) 5927.

[3]    J. P. Chou, C. R. Hsing, C. M. Wei, C. Cheng, C. M. Chang, Ab initio random structure search for 13-atom clusters of fcc elements, Journal of Physics: Condensed Matter 25 (12) (2013) 125305.

[4]    Y. –C. Bae, H. Osanai, V. Kumar, Y. Kawazoe, Nonicosahedral growth and magnetic behavior of rhodium clusters, Phys. Rev. B 70 (2004) 195413.

[5]    Y. Jinlong, F. Toigo, W. Kelin, Structural, electronic, and magnetic properties of small rhodium clusters, Phys. Re. B 50 (1994) 7915 – 7924.

[6]   F. Aguilera-Granja, A. Garcia-Fuente, A. Vega, Comparative ab initio study of the structural, electronic, and magnetic trends of isoelectronic late 3d and 4d transition metal clusters, Phys. Rev. B 78 (2008) 134425.

[7]    Y. –C. Bae, V. Kumar, H. Osanai, Y. Kawazoe, Cubic magnetic clusters of rhodium stabilized with eight-center bonding: magnetism and growth, Phys. Rev. B 72 (2005) 125427.

[8]    V. Kumar, Y. Kawazoe, Magnetism in clusters of non-magnetic elements: Rd, Rh, and Ru, The European Physical Journal D – Atomic, Molecular, Optical and Plasma Physics 24 (1) (2003) 81 – 84.

[9]   P. Villasenor-Gonzalez, J. Dorantes-Davila, H. Dreysse, G. M. Pastor, Size and structural dependence of the magnetic properties of rhodium clusters, Phys. Rev. B 55 (1997) 15084 – 15091.

[10]  C. Barreteau, R. Guirado-Lopez, D. Spanjaard, M. C. Desjonqueres, A. M. Oles, spd tight-binding model of magnetism in transition metals: application of Rh and Pd clusters and slabs, Phys. Rev. B 61 (2000) 7781 – 7794.

[11]  F. Aguilera-Granja, J. L. Rodriquez Lopez, K. Michaelian, E. O. Berlanga-Ramirez, A. Vega, Structure and magnetism of small rhodium clusters, Phys. Rev. B 66 (2002) 224410.

[12]  C. –H. Chien, E. Blaisten-Barojas, M. R. Pederson, Many-body potential and structure for rhodium clusters, The Journal of Chemical Physics 112 (5) (2000) 2301 – 2307.

[13]  R. Ferrando, A. Fortunelli, R. L. Johnston, Searching for the optimum structures of alloy nanoclusters, Phys. Chem. Chem. Phys. 10 (2008) 640 – 649.

[14]  J. Rogan, G. Garcia, C. Loyola, W. Orellana, R. Ramirez, M. Kiwi, Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver, The Journal of Chemical Physics 125 (21) (2006) 214708.

[15]  P. J. Hsu, S. K. Lai, Structures of bimetallic clusters, The Journal of Chemical Physics 124 (4) (2006) 0447711.