Structure and Stability of Atomic Clusters

Deformed jellium model for metal clusters and nanoparticles

We have developed the two-center jellium model for deformed metal clusters, which treats the quantized electron motion in the field of the axially symmetric deformed ionic jellium background of the cluster in the Hartree–Fock approximation. This approach can serve as a basis for a logical and systematic development of many-body (i.e. many-electron) theory of metal clusters within the random phase approximation with exchange (RPAE) method and allows one to construct models on the basis of fundamental physical principles, which can then be refined by extending the quality of the approximations. Geometry and electronic structure of sodium metal clusters has been studied. The model demonstrates close parallels between physics of atomic clusters and physics of nuclei. Important role of cluster's deformations is elucidated. Applicability of the jellium model to different types of metal clusters has been investigated. The model has been successfully used to describe physical properties of deformed nanosystems, such as metal nanoparticles, endohedral fullerenes, and nanoparticles deposited on a surface.

Figure: The effective potential binding valence electrons in a metal cluster, cluster deformations and size dependence of the binding energy of metal clusters calculated within the spherical and deformed jellium model.

Relevant publications

• • V. Semenikhina, A. Lyalin, A. V. Solov'yov, and W. Greiner, Droplet model of an atomic cluster at a solid surface, JETP 106, 678-689, (2008).

  • A. Matveentzev, A.G. Lyalin, I.A. Solov'yov, A.V. Solov'yov, and W. Greiner, On the applicability of jellium model to the description of alkali clusters, Int. J. Mod. Phys. E 12, 81-107, (2003).

  • A.G. Lyalin, S.K.Semenov, A.V.Solov'yov, N.A.Cherepkov, J-P.Connerade, and W.Greiner, Hartree-Fock deformed jellium calculations for metallic clusters, J. Chin. Chem. Soc. 48, 419-426, (2001).

  • J-P.Connerade, A.G.Lyalin, R.Semaoune, S.K.Semenov, and A.V.Solov'yov, A simple atomic model for hydrogen confined inside a prolate-shaped C₆₀ fullerene cage, J.Phys. B: At.Mol.Opt.Phys. 34, 2505-2511, (2001).

  • A.G.Lyalin, S.K.Semenov, A.Solov'yov, N.Cherepkov, and W.Greiner, Hartree-Fock deformed jellium model for metallic clusters, J.Phys. B: At.Mol.Opt.Phys. 33, 3653-3664, (2000).

Structure optimization of metal clusters

Geometry structure defines physical and chemical properties of atomic clusters and nanoparticles. In the size range of several nanometers or less, cluster's properties are not scalable with cluster size. This is "the regime in which each atom counts". We have systematically investigated the optimized structure and electronic properties of a number of neutral, singly, and doubly charged metal clusters using theoretical methods based on density-functional theory. The new effective “cluster fusion” algorithm has been used to study optimized structure of clusters of transition and rare-earth metals. We have studied such properties as optimized geometries, average bonding distances, electronic shell closures, binding energies per atom, the gap between the highest occupied and the lowest unoccupied molecular orbitals (HOMO-LUMO gap), spectra of the density of electronic states (DOS), etc. We have demonstrated that in many cases the size evolution of structural and electronic properties of metal clusters is governed by an interplay of the electronic and geometry shell closures. Thus, for example, influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. The excessive charge essentially affects the optimized geometry of metal clusters and ionization of small clusters results in the alteration of the magic numbers. The strong dependence of the DOS spectra on details of ionic structure allows one to perform a reliable geometry identification of clusters.

Figure: Mg₁₃ (left), Sr₁₃ (middle) and Au₁₃ (right) clusters with optimized geometries.

Relevant publications

• • A. Lyalin, I.A. Solov'yov, A.V. Solov'yov, and W. Greiner, Interplay of electronic and geometry shell effects in properties of neutral and charged Sr-clusters, Phys. Rev. A 75, 053201, (2007).

  • A. Lyalin, A.V. Solov'yov, and W. Greiner, Structure and magnetism of lanthanum clusters, Phys. Rev. A 74, 043201, (2006).

  • A. Lyalin, A.V. Solov'yov, C. Brechignac, and W. Greiner, Stability of small neutral and charged strontium clusters (Letter) J. Phys. B: At. Mol. Opt. Phys. 38, L129-L135, (2005).

  • I.A. Solov'yov, A. Lyalin, A.V. Solov'yov, and W. Greiner, Ab initio calculations and modelling of atomic cluster structure, in Latest Advances in Atomic Cluster Collisions: Fission, Fusion, Electron, Ion and Photon Impact (edited by J.-P. Connerade and A.V. Solov'yov), ISBN 1-86094-495-7, pp. 51-65, Imperial College Press, London (2004).

  • A.G. Lyalin, I.A. Solov'yov, A.V. Solov'yov, and W. Greiner, Evolution of electronic and ionic structure of Mg-clusters with the growth cluster size, Phys. Rev. A 67, 063203, (2003).

Fission of metal clusters: parallels with nuclear fission

Fission is an ubiquitous phenomenon that is encountered in various branches of science, from biology to nuclear physics. By cluster fission we understand the process of fragmentation of a charged cluster in which at least two of the daughter fragments are charged. Theory of cluster fission is a very interesting and important subject, not only because it has immediate applications in experiment and nanotechnology but also because cluster fission presents one of the instances of a long standing fundamental problem of stability of complex systems. A detailed description of different aspects of this process requires an interdisciplinary approach combining methods of atomic, molecular and nuclear physics, thermodynamics, statistics, mathematics and computational science. Fission of charged metal clusters provides especially close analogies to the corresponding process in nuclear systems. Coulomb repulsion is the driving force of the fission process. Depending on the excessive charge and cluster size, charged clusters can be found in the stable, metastable or unstable states. At lower degrees of the cluster ionization an interplay between the electronic binding and the Coulomb repulsion results in formation of a potential barrier which prevents the cluster from immediate decay. In our works we have made considerable contribution to the theory of cluster fission by using the original two-center deformed jellium model, models adapted from nuclear physics, and ab initio molecular dynamics simulations. An important impact of the thermodynamical aspects and the role of entropy on the branching ratios between different fission channels and their temperature dependence has been discussed. It has been argued theoretically and shown experimentally that dominant fission channels and the branching ratios between different channels are not governed by purely energetic considerations but by the free energy change which takes into account the number of possible different combinations of atoms which constitute the fragments.

Figure: Asymmetric and symmetric fission of Na₁₈²⁺ cluster.

Relevant publications

• • A. Lyalin, O.I. Obolensky, A.V. Solov'yov and W. Greiner, Fission of metal clusters (Review), Int. J. Mod. Phys. E 15, 153-195, (2006).

  • A. Lyalin, O.I. Obolensky, A.V. Solov'yov, and W. Greiner, Dissociation and fission of small sodium and strontium clusters, Eur. Phys. J. D 34, 93-96, (2005).

  • O. I. Obolensky, A.G. Lyalin, A.V. Solov'yov, and W. Greiner, Geometrical and statistical factors in fission of small metal clusters, Phys. Rev. B 72, 085433, (2005).

  • A.G. Lyalin, O.I. Obolensky, A.V. Solov'yov, I.A. Solov'yov, and W. Greiner, Rearrangement of cluster structure during fission processes (Letter), J. Phys. B: At.Mol.Opt.Phys. 37, L7-L13, (2004).

  • A.G. Lyalin, S.K. Semenov, A.V. Solov'yov, and W. Greiner, Hartree-Fock approach for metal-clusters fission, Phys. Rev. A 65, 023201, (2002).

  • A.G. Lyalin, A.V. Solov'yov, and W. Greiner, Comparative study of metal cluster fission in Hartree-Fock and local density approximation, Phys. Rev. A 65, 043202, (2002).

Giant enhancement of magnetism at nanoscale

Nonmagnetic materials can possess magnetic properties at nanoscale. Thus, small La clusters display unique, temperature-dependent magnetic behavior, even though bulk La has no magnetic ordering. We have investigated the optimized structure, electronic and magnetic properties of La clusters consisting of up to 14 atoms and demonstrated that increase in cluster symmetry can promote ferromagnetic instability in La clusters. A giant enhancement of magnetism in La₄, La₆, and La₁₃ clusters is predicted.The stability of the high spin state in La nanoparticles is associated with the valence electron ferromagnetism. Strong dependence of the magnetic moment on temperature for T > 300 K is predicted. Formation of the magnetic ordering in finite systems such as linear chains of Mn atoms and metal-organic molecules has also been studied.

Figure: Mn₃(C₆H₆)₄ (left) and La₁₃ (right) clusters with a giant magnetic moment.

Relevant publications

• • A. Lyalin, A.V. Solov'yov, and W. Greiner, Magnetism in atomic clusters, in Latest Advances in Atomic Cluster Collisions: structure and dynamics from the nuclear to the biological scale (edited by J.-P. Connerade and A.V. Solov'yov), pp. 86 - 104, Imperial College Press, London (2008).

  • A. Lyalin, A.V. Solov'yov, and W. Greiner, Structure and magnetism of lanthanum clusters, Phys. Rev. A 74, 043201, (2006).

Phase transitions at nanoscale: thermodynamics of atomic clusters and alloying effect

Thermodynamic properties of atomic clusters depend significantly on the size of the cluster. The melting temperature of a small spherical particle decreases with the reduction in its radius. This is due to the substantial increase in the relative number of weakly bounded atoms on the surface in comparison with those in the bulk. However for clusters having sizes smaller than 1–2 nm, the melting temperature is no longer a monotonic function of the cluster size. The origin of the nonmonotonic variation in the melting temperature with respect to cluster size lies in the interplay between electronic and geometric shell effects in the regime in which "each atom counts". Point defects can considerably affect melting of atomic clusters. We performed a systematic theoretical study regarding the effect of impurity on the thermodynamic properties of Ni clusters. Adding just a single carbon impurity can result in changes in the melting temperature of an Ni₁₄₇ cluster. The magnitude of the change induced is dependent on the parameters of the interaction between the Ni atoms and the C impurity. Hence, thermodynamic properties of Ni clusters can be effectively tuned by the addition of an impurity. We also show that the presence of a carbon impurity considerably changes the mobility of atoms in the Ni cluster at temperatures close to its melting point.

Figure: Caloric curve for the pure Ni₁₄₇ cluster. Temperatures T < T_freezing and T > T_melting correspond to the completely frozen and melted states, respectively.

Relevant publications

• • A. Lyalin, A. Hussien, A. Solov'yov, and W. Greiner, Impurity effect on the melting of nickel clusters as seen via molecular dynamics simulations, Phys. Rev. B 79, 165403, (2009).