Theoretical Simulation of

Nanoclusters

Xiaohu Yu

Moscow Institute of Physics and Technology

Contents

• Introduction of nanoscience and

theoretical methods;

• The geometric structure of nanocluster;

• The stability of nanocluster;

• The growth of nanocluster;

• The structural transformation of

nanocluster;

• The sintering of nanocluster

Introduction

Science 327 (2010) 278-279.

Bulk Au is noble;

Au nanoclusters are

active in catalysis;

High-surface area gold

catalysts exhibit

promising properties

suitable for industrial

application.

Green gold catalysis

Introduction

Nanotechnology defination

Coarse particles: 2500-10000 nm;

Fine particles: 100-2500 nm

Nanoparticles: Ultrafine particle,

1-100 nm;

Nanoclusters: 1-10 nm;

Nanopowers: agglomerates of

nanoparticles or nanoclusters.

Introduction

• In chemistry, a cluster

(a) an ensemble of bound atoms or molecules;

(b) intermediate in size between a molecule and a bulk

solid;

(c)diverse stoichiometries and nuclearities.

• In physics, the term clusters

(a)small, multiatom particles;

(b)between 3 and 3*107 atoms

• The phase cluster was coined by F.A.Cotton in the early

1960s to refer to compounds containing metal-metal

bonds.

Introduction

• Atomic cluster can be either pure, formed from a

single atomic species, or mixed, formed from a mixed

atomic species.

• Classifications criteria:

(a)bond nature; (b)atomic count;(c) electric/magnetic

properties

• “magic number” representation in the mass spectra.

• The number of atoms N in perfect icosahedra as well as

fcc cuboctahedra with n complete atomic shells is given by

the sequence; 13, 55, 147, 309, 561, etc.

• N =(10n3+15n2+11n+3)/3Phys. Rev. Lett. 99 (2007) 083402.

Introduction

• Molecular clusters: Atomic and molecular clusters

are aggregates of 5-105 atomic or molecular units.

• Classified according to the forces holding them together:

Van der Waals clusters; Metallic clusters; ionic clusters;

• Transition metal carbonyl clusters:Ni(CO)4

and Fe(CO)5, Fe2(CO)9,

• Transition metal halide clusters:

• Boron Hydrides: ( Wade’s rule)

• Fe-S clusters in biology: Fe4S4

Theoretical Methods

• Molecular mechanics

• Finite element methods

• Molecular dynamics

• Monte Carlo methods

• Quantum molecular dynamics

• Nonequilibrium molecular dynamics

• Monte Carlo method

• Brownian dynamics

• Density functional theory

Theoretical method

• Basin hopping (BH)

• Simulated annealing

• Minima hopping (MH)

• Genetic algorithm (GA)

• Random sampling methods

• Particle swarm optimization (PSO)

• Evolutionary program (USPEX)

Bottom-up

Bottom-up (metal)

Top-down

Top-down

Chem. Commun. 2010, 46, 5936.J. Mater. Chem. 2010, 20, 10535.

O vacancy formation is greatly facilitated in nanoscale ceria

Ce3+ occupy edge and corner sites

Ce4+ in highly coordinated positions

The geometric of nanocluster

Phys. Rev. Lett. 75 (1995) 288-291.

Nature 392 (1998) 582-585.

Stability of nanocluster

• Bind energy: Eb =Eatom-Ecluster/n

• Second energy difference:

Δ2En=En-1+En+1-2En

• Fragmentation energy:ΔEn= Eb(n)-Eb(n-1)

• Ionization potentials (IP):

E(IP) = En+-En

• Electron affinities (EA):

E(EA)=En-En-

• Detachment energies(ED)

Stability of nanocluster

Stability of nanocluster

Number of vertices Polyhedron

4 Tetrahedron

5 Trigonal bipyramid

6 Octahedron

7 Pentagonal bipyramid

8 D2d (trigonal)Dodecahedron

9 Tricapped trigonal prism

10 Bicapped square antiprism

11 Edge-contracted icosahedron

12 Icosahedron

4n rules

Stability of nanocluster

Stability of nanocluster

Stability of Cs clusters

Phys. Rev. B 78 (2008) 245423.

Stability of Cs clusters

Phys. Rev. B 78 (2008) 245423.

Structures of iron clusters

Comp. Mater. Sci. 35 (2006) 275-278.

Stability of iron clusters

J. Chem. Phys. 139 (2013) 034314.

Structures of Au clusters

Phys. Rev. B 66 (2002) 035418.

Stability of gold clusters

Phys. Rev. B 66 (2002) 035418.

Optimization of Atomic Clusters

J. Am. Chem. Soc. 132, 6596-6605 (2010).

Optimization of Atomic Clusters

ACS Nano 3, 1225-1230 (2009).

Optimization of Atomic Clusters

Nature materials 11, 49-52(2012)

Mg, Ti, Zn oxides

Nat. Mater. 7 (2008) 937-946.

Modelling nano-clusters and nucleation

Phys. Chem. Chem. Phys. 12 (2010) 786-811.

The growth of In2O3

Phys. Chem. Chem. Phys. 12 (2010) 8446-8453.

The growth of SiO2

Phys. Chem. Chem. Phys. 12 (2010) 786-811.

The growth of TiO2

Phys. Chem. Chem. Phys. 12 (2010) 786-811.

The growth of dimer

Phys. Rev. Lett. 77, 51-54 (1996).

Dimer Growth, Structure Transition and Antiferromagnetic

Ordering in Small Cr Clusters

The growth of Ti cluster

J. Chem. Phys. 118, 2116-2123 (2003).

Oxidation of Fe cluster

Phys. Rev. Lett. 76, 4853-4856 (1996).

Oxidation of Si3Ox(1-6) cluster

Phys. Rev. Lett. 78, 4450-4453 (1997).

Oxidation of Ta cluster

J. Phys. Chem. A. 113, 9804-9813 (2009).

Doping of nanocluster

Physical Review B 86, 205320 (2012)

Structural transformations

Phys. Rev. Lett. 99 (2007) 083402.

John-Teller effect

Structural transformations

The lowest energy structures of 13-atom Fe13-nPtn clusters.The blue and

yellow balls represent the Fe and Pt atoms, respectively.

Frau Sanjubala Sahoo, 2011, dissertation

Structural transformations

Evolution of the lowest isomer for Ag8 (left) and Au4Ag4 (right), relative

to the energy of the GM isomer (E0)

Nanoscale 4 (2012) 1109-1115.

Global minimum isomers for the 8-atom Au-Ag clusters, as function of

composition. For Au6Ag2 the two nearly degenerate isomers are shown.

Structural transformations

Nanoscale 4 (2012) 1109-1115.

Structural transformations

J. Chem. Phys. 138 (2013) 094312.

Sintering of nanocluster

• Molecular dynamics

Sintering of Ni nanocluster

Acknowledgements

Thank you for your attention!

grant of the Government of the Russian

Cuderation № 14.A12.31.0003.