On the transition from Van der Waals- to metallic bonding in Hg-clusters as a function of cluster size

Pastor, G. M.; Stampfli, P.; Bennemann, K. H.

doi:10.1088/0031-8949/38/4/022

Cited by 59 publications

(44 citation statements)

References 8 publications

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“…Our results for the relative variations of Eooh and An with n are in good agreement with those of [3]. The Ecoh calculated by exact diagonalization and recursion methods are shown in Fig.…”

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andsupporting

confidence: 84%

“…The rapid increase in E~oh for n= 13-19 shown in Fig. 3 indicates a transition from Van der Waals bonding to a much stronger covalent bonding [3,4]. For increasing cluster size the cohesive energy approaches the bulk cohesive energy.…”

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andmentioning

confidence: 90%

“…Small clusters, n = 2-9, have primarily s-like electronic structure, implying Van der Waals bonding. The appreciable increase in p-character around n=13-19 signals the onset of covalent bonding [3,4]. For clusters with n_>_ 79, the/-character approaches the bulk/-character.…”

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andmentioning

confidence: 98%

“…and the density of electronic states is n(E), the Fermi energy, measured with respect to the vacuum level, is Ev, the coordination number of an atom at site i is zi, and the internuclear separation is r. It is important to note that the constants 2 and p are determined by fitting to the bulk modulus and the bulk atomic volume [3]. Thus, for a given r the Er can be determined from (6).…”

Section: H (2) = Ev + H ~-H P O P H P + H P O ° H P O P H ~-mentioning

confidence: 99%

“…The electronic structure is then calculated by two methods; exact diagonalization [3] and recursion E8]. For n > 50, the latter method is computationally much more efficient.…”

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confidence: 99%

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Evolution of bulk-like properties in mercury microclusters

Singh

1990

Z Phys D - Atoms, Molecules and Clusters

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Abstract. The transition from non-metallic to metallic behavior of mercury microclusters, Hg,, with n ranging from 2 to 79, is investigated using first principles tightbinding linear muffin-tin orbital method. The n dependence of the ionization potential, the cohesive energy, the energy gap, and the nature of the bonding indicates metallic behavior for Hg, with n => 80. The average bond length of Hg clusters is found to be larger than that of the bulk. Our results are in good agreement with experiments.PACS: 71.30. + h; 36.40. + d Advances in experimental techniques for producing atomic clusters have opened up the possibility of studying changes in the electronic properties as atoms are added to the cluster [1]. An understanding of electronic properties of these clusters is prerequisite for overall characterization of such materials. Although one might expect atomic clusters to be not very different from bulk, many of them are found to have completely different properties. In particular, clusters of divalent metals (Hg, Be, Mg, etc.), with closed-shell configurations, show insulating behavior for small cluster sizes and a transition to metallic behavior for larger clusters [2]. In this paper we summarize the results of a new approach for studying the evolution of electronic properties in clusters, using Hg clusters (Hg,) as an example, and we show the good agreement of these calculations with data. A more detailed exposition will be published elsewhere.The striking difference in the electronic properties of Hg, from that of bulk-Hg has been under intense experimental investigation [2], but our theoretical understanding of electronic properties of clusters in general, and Hg, in particular, is still rudimentary. Using a parametrized tight-binding approach Pastor et al. E3, 4] studied Hg, in which the hopping integrals were adjusted to reproduce the electronic structure of bulk-Hg. Here we calculate the electronic behavior of Hg,, using the first principles tight-binding (TB) linear muffin-tin orbital (LMTO) method. (An introduction to the LMTO and the TB-LMTO methods is provided in [5] and [6].) We find Hg, to be insulating for n__< 13, semiconducting for 19<_n_<79, and metallic for n>79. The calculated increase in the bond length of small Hg clusters agrees with experiment.For bulk Hg we use a self-consistent electronic structure calculation, assuming a face centered cubic (FCC) lattice structure, for different Wigner-Seitz (WS) radii with the LMTO method [5][6][7], including the combined correction terms [5]. The atomic charge density is obtained by solving the fully relativistic Dirac equation, then freezing all but the 6 s 2 electrons during the bandstructure calculation. Then the total energy, E, approximated by the sum of the electronic band energy, Ee, and the Born-Mayer repulsive energy, Er, is minimized, to give the equilibrium internuclear separation, d, and the cohesive energy, E~o h.For Hg, we use the self-consistent potential parameters obtained from the bulk-Hg calculations to set up the TB hamiltoni...

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“…Our results for the relative variations of Eooh and An with n are in good agreement with those of [3]. The Ecoh calculated by exact diagonalization and recursion methods are shown in Fig.…”

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andsupporting

confidence: 84%

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andmentioning

confidence: 90%

Section: =C~e2/r-ev(n) Where Ev(n) Is the Fermi Energy Andmentioning

confidence: 98%

Section: H (2) = Ev + H ~-H P O P H P + H P O ° H P O P H ~-mentioning

confidence: 99%

“…The electronic structure is then calculated by two methods; exact diagonalization [3] and recursion E8]. For n > 50, the latter method is computationally much more efficient.…”

mentioning

confidence: 99%

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Evolution of bulk-like properties in mercury microclusters

Singh

1990

Z Phys D - Atoms, Molecules and Clusters

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Strukturübergänge in Clustern

Hartke

2002

Angew. Chem.

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Lagert man an einen Cluster aus einzelnen Teilchen weitere Teilchen an, so bleibt die energetisch günstigste Grundstruktur weder erhalten noch ändert sie sich kontinuierlich. Stattdessen findet man Größenbereiche mit jeweils einem stark dominierenden Bauprinzip und vergleichsweise schmale Grenzen zwischen diesen Bereichen. Die Struktur des Festkörpers wird in der Regel erst nach mehreren Strukturübergängen bei relativ großen Clustern erreicht. Für das Auftreten dieser Strukturübergänge scheint es keine Rolle zu spielen, ob die Teilchen Atome oder Moleküle sind und ob der Cluster homogen oder heterogen ist. Offenbar handelt es sich um ein kollektives Vielteilchenphänomen, das in rein reduktionistischer Sicht zwar prinzipiell berechnet, aber nicht einfach verstanden werden kann. Weil die tatsächliche Berechnung bei hinreichender Genauigkeit derzeit noch am viel zu hohen Rechenaufwand scheitert – auch beim Einsatz unkonventioneller evolutionärer Algorithmen zur globalen Geometrieoptimierung –, wären einfachere Strukturregeln sehr wertvoll. Denn bei diesen Strukturübergängen geht es nicht nur um die akademische Frage nach dem Zusammenhang zwischen Potentialenergiefläche und Clusterstruktur, sondern auch um wichtige Vorgänge in der Natur und in der technischen Chemie, vom Wachstum von Kristallkeimen bis zur Nanotechnologie. Hier wird eine exemplarische Übersicht über die Untersuchung von Strukturübergängen bei Clustern gegeben – von einfachen Modellsystemen, bei denen erste qualitative Erklärungsversuche bereits Erfolge zeigen, bis zu realistischeren, komplexen Systemen, die sich unserem Verständnis noch weitestgehend entziehen.

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Structural Transitions in Clusters

Hartke¹

2002

Angew. Chem. Int. Ed.

130

109

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If one adds more particles to a cluster, the energetically optimal structure is neither preserved nor does it change in a continuous fashion. Instead, one finds several cluster size regions where one structural principle dominates almost without exception, and rather narrow boundary regions in‐between. The structure of the solid is usually reached only at relatively large sizes, after more than one structural transition. The occurrence of this general phenomenon of size‐dependent structural transitions does not seem to depend on the nature of the particles, it is found for atomic, molecular, homogeneous, and heterogeneous clusters alike. Clearly, it is a collective many‐body phenomenon which can in principle be calculated but not understood in a fully reductionistic manner. Actual calculations with sufficient accuracy are not feasible today, because of the enormous computational expense, even when unconventional evolutionary algorithms are employed for global geometry optimization. Therefore, simple rules for cluster structures are highly desirable. In fact, we are dealing here not just with the academic quest for linkages between cluster structure and features of the potential energy surface, but structural transitions in clusters are also of immediate relevance for many natural and industrial processes, ranging from crystal growth all the way to nanotechnology. This article provides an exemplary overview of research on this topic, from simple model systems where first qualitative explanations start to be successful, up to more realistic complex systems which are still beyond our understanding.

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On the transition from Van der Waals- to metallic bonding in Hg-clusters as a function of cluster size

Cited by 59 publications

References 8 publications

Evolution of bulk-like properties in mercury microclusters

Evolution of bulk-like properties in mercury microclusters

Strukturübergänge in Clustern

Structural Transitions in Clusters

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