http://fielicke.lmsu.tu-berlin.de/

Methods to produce and study clusters

André Fielicke Institut für Optik und Atomare Physik Technische Universität Berlin, Germany Program

1. What are clusters and why to study them? 2. Making and characterizing free clusters 3. Probing the structures 1. What are clusters and why to study them? Clusters

Oxford English Dictionary:

1. A collection of things of the same kind, as fruits or flowers, growing closely together; a bunch. a. Originally of grapes (in which sense bunch is now the usual term). b. Of other fruits, or of flowers; also of other natural growths, as the eggs of reptiles, the air-cells of the lungs, etc. Cluster compounds • Thermodynamically and kinetically stable • Chemical synthesis in bulk quantities • Characterization with “classical” spectroscopic methods (IR, NMR, XRD etc.) Co (CO) 2- 4 12 B12H12

Isolated clusters • Generation through aggregation of the (atomic or molecular) constituents

• (Nearly) free choice of size (n), + B V8 16 z composition (n/m) and charge (z): MnLm PRL 93 (2004) 023401 JCP 137 (2012) 014317 • Most clusters are not stable towards aggregation • Experimental investigations are usually performed in the gas phase  Molecular beam techniques + H6O13 (“Zundel” cation) Clusters of atoms and molecules

• multiples of a simple subunit, e.g. Cn, Arn, or (H2O)n • The cluster size n can vary and determines the properties

Clusters Nano-crystals 2 3 4 5 6 7 8 Number of atoms 11010 10 10 10 10 10 10 2 3 4 5 Surface atoms 10 10 10 10 10 2 radius [nm] 11?0 10

• small clusters have (nearly) all atoms on the surface

+ Nbn

567 8 10 11 12 13 9 Volume and surface of a cluster with n atoms

Spherical cluster approximation 4   RV 3 3 R  4 RS 2 2r

Assignment 1.1 How many Krypton atoms are in a spherical cluster of a) 1 nm, b) 10 nm, c) 100 nm radius? Assume that a single Kr atom fills an effective volume with 0.2 nm diameter in this cluster. 1.2 What is the ratio for surface vs. volume atoms for these clusters? The surface atoms contribute to the cluster surface by only ¼ of their ‚atomic surface‘, ¾ point toward the inside of the cluster. Clusters: nano and smaller

Effects at the (sub)nano-scale quantum confinement large surface/volume ratio structural changes Emergence of new properties e.g.: magnetic optical / luminescence chemical / catalytic Size dependence of properties: Each atom counts

Ionization energy

Stability

Magnetism Reactivity

Fen + H2 Motivations for the study of free metal clusters

Fundamental aspects How are properties emerging when going from the atom to the bulk?

Reference systems Test and further development of theoretical model methods

New materials

Inspiration from particularly stable clusters application Model systems in heterogeneous catalysis 2. Making and characterizing free clusters Bonding in clusters

EB≈100 neV 1s 1s

dispersion HeHe2 He induction - + + increasing - - - dipole/dipole ++ + bond strength EB≈1-5 eV - + - - and cluster + ion/dipole stability

Cn metallic

C=C=C or C≡C–C covalent EB≈4-6 eV

ionic + - (Na Cl )n EB≈7-8 eV Experimental techniques for Cluster studies

Cluster production: Top-down vs. Bottom-up Sputtering or Aggregation of the constituents

sputtering

bulk clusters material

vaporization condensation supersaturated cooling vapor Cluster production

Supersonic expansion of a gas Adiabatic and isenthalpic expansion leads to strong cooling  formation of a cold supersonic beam

Cluster formation via 3-body collisions near the nozzle

e.g. Ar + Ar + Ar  Ar* + Ar2 (conservation of energy and momentum) Dimers are condensation nuclei for larger clusters

Seeded molecular beam: cooling of the internal degrees of freedom Cluster Production

Gas aggregation (thermal) evaporation into a cold gas

 (°C) Typical vapour Na 289 pressures of ~10-2 mbar need to be Al 1217 reached Ag 1027 Smoke source for the production Au 1397 of C60, C70 and larger carbon clusters Cluster Production Laser ablation heating of a small surface part of a solid target by a focused, intense short- pulse laser (typically Nd-YAG, 532 nm) formation of a plasma that contains ions and electrons cooling with rare gas induces aggregation  formation of neutral and charged (anionic and cationic) clusters

Converts practically any solid into clusters, very frequently used! Can be easily combined with reaction or thermalization channels, etc.

see: M.A. Duncan, Rev. Sci. Instr. 83 (2012) 041101. A molecular beam cluster experiment

Experiments under collision-free conditions

Mean free path length (identical particles)

Vacuum range Pressure in mbar Molecules / cm3 mean free path Ambient pressure 1013 2.7*1019 68 nm Medium vacuum 1-10-3 1016-1013 0.1-100 mm High vacuum 10-3-10-7 1013-109 10 cm - 1 km Ultra high vacuum 10-7-10-12 109-104 1 km-105 km Metal cluster lab at the FHI-FEL in Berlin

VUV laser Source chamber operators time-of-flight mass spectrometer

small pump

big pump

fore vacuum pump infrared laser beam from FEL Mass spectrometric characterization

Ionization techniques for neutral clusters Electron impact Efficient ionization at 60-100 eV Ionization potentials (IPs) are on the order of 5-15 eV excess energy leads to fragmentation and changes mass distribution

Photoionization

 B  EEh kin UV lasers (nm) E (eV) Nd-YAG, 3rd 355 3.5 Nd-YAG, 4th 266 4.7 KrF 249 5.0 ArF 193 6.4

F2 157 7.9 single photon resonant multi photon Nd-YAG, 9th 118 10.5 species and state selective Mass spectrometric characterization

Time-of-flight mass spectrometry acceleration of charged particles (ions) in an electric field particles having the same charge but different mass are accelerated to the same kinetic energy mv2 zeEs  2 2zeEs v  m m t   sDD 2zeEs

Measurement of the arrival time on the detector gives mass information typical experimental conditions: s=1 cm, D=10-300 cm, E=100-10000 kV/cm A single mass spectrum can be measured within 5-100 µs. Mass resolution up to 10 000 amu can be achieved Mass spectrometric characterization

Example: Cobalt cluster cations produced by Laser ablation (arb. units) intensity

time-of-flight (µs) time-of-flight (µs)

t mass resolution: R max  340 2t 2/1 2. Dirty Terbium clusters, what is in there? Mass spectrometric characterization

Other types of mass spectrometers I Magnetic sector field

II Quadrupole moderate to high (104) resolution experiments on beams of mass selected ions (MS/MS)

III Ion traps, FT-ICR (ion cyclotron resonance) very high resolution (106), long storage times simultaneous detection of all ions expensive zeB  m

I-II are often used as mass filters, measurement of a full mass spectrum requires scanning (of voltages) and is relatively time consuming. Experiments are often performed on pulsed molecular beams, usage of a ToF-MS allows rapid and full mass analysis of a single ion pulse. Mass spectrometers: mass analyzer mass filters ion traps

Approaches for size-selectivity in cluster studies: a) Mass selection, accumulation, spectroscopy b) Size-specific detection ( Action spectroscopy) 3. Probing the structures Linus Carl Pauling

(1901-1994) Nobel Prize in Chemistry 1954

We like to understand, and to explain, observed facts in terms of structure.

“The place of Chemistry in the Integration of the Sciences”, Main Currents in Modern Thought, 1950, 7, 110 Experimental methods for structure determination of clusters

Anion PES Trapped Ion Ion Mobility Electron Diffraction

Theory CLUSTER STRUCTURE

Raman Chemical probe Spectroscopy method

Vibrational Infrared Multiple Photon spectroscopies Dissociation Spectroscopy The chemical probe method

Ligand molecules are brought into reaction with a cluster Complexes of the cluster with one or more ligands are formed depending on PL and T via consecutive reactions

X + L  XL + L XL2 + L  …  XLsat

 saturation numbers The chemical probe method

plot (average) saturation number as function of P, plateaus indicate stable complexes

8 6 5

E.K. Parks, et al., The structure of nickel-iron clusters probed by adsorption of molecular nitrogen. Chem. Phys. 262 (2000) 151. Ion chromatography

• The collision cross section is a measure of size (number of atoms) and shape of a cluster

rotationally averaged collision cross sections: spherical < oblate < prolate Ion mobility measurements

source: bowers.chem.ucsb.edu/theory_analysis/ion-mobility

Mass selected ions are pulled through a collision gas (He) by a weak electric field leading to a resulting drift velocity: vd = K·E Mobility K in the gas is related to L2 3q  12 K the collision cross section   Ut 16 BTkN 

More compact structures have higher mobilities Comparison with collision cross sections for various isomers from theory  geometric structure IMS-MS: a commercial technique

Waters Synapt-G2 HDMS Si cations and anions

oblate?

‘more prolate spherical’

Several families of cluster structures Similar transition size from prolate to oblate structures

R.R. Hudgins, M. Imai, M.F. Jarrold, P. Dugourd, J. Chem. Phys. 111 (1999) 7865. Electron diffraction of trapped cluster ions

wave - particle duality

de Broglie wavelength on electrons:

 12 pm for Ekin=10 keV Electron diffraction of trapped cluster ions

mass selection, trapping, thermalization ~107 ions per cm3 40 keV e-beam, ~µA current J.H. Parks, X. Xing in The Chemical Physics of Solid Surfaces, Vol. 12 Atomic Clusters. (2007) 377. Overview: TIED of anionic gold clusters

Total scattering intensity shows little size specific features  use of reduced molecular intensity Gold clusters, some example structures from TIED

observation of 2D and 3D isomer for Au12-: size for 2D/3D transition for anionic Au clusters Anion photoelectron spectroscopy (Photoemission)

Ekin=h-EB

• Anions can be mass selected • Excitation energies are within the UV-vis range

• Electron affinity: vertical EA > adiabatic EA Measurement of photoelectron spectra

1. Production of cluster anions 2. Mass selection 3. Photo excitation with vis/UV Laser 4. Measure kinetic energies of electrons

K.H. Meiwes-Broer, Appl. Phys. A 55 (1992) 430-441. - Anion Photoelectron Spectroscopy of Au20

Au20: minimum in EA (2.75 eV) A-X separation = energy to reach first excited state in the neutral ≈ HOMO-LUMO gap

“… Au20 possesses a tetrahedral structure, which is a fragment of the face-centered cubic lattice of bulk gold with a small structural relaxation.”

simulation

J. Li, X. Li, H.-J. Zhai, L.-S. Wang, Science 299 (2003) 864. - Structure and bonding of Au20

large HOMO-LUMO gap: sign of stability

1.77 eV in Au20 vs. 1.57 eV in C60 20 e: magic shell closing

5d10 are localized 6s1 form 4-center- 2-electron bonds (10x)

D.Y. Zubarev, A.I. Boldyrev, J. Phys. Chem. A 113 (2008) 866. Isomerism in gold clusters

Isomer identification by: Ion chromatography (different cross section) Electron diffraction (different atomic positions) Chemical reactions (different reactivity)

Example: using O2 to remove contribution of more reactive isomers of - Au10 to anion photoelectron spectrum

W. Huang, L.-S. Wang, Phys. Chem. Chem. Phys. 11 (2009) 2663. Origin of vibrational spectroscopy

1800 discovery of “invisible Rays of the Sun” by W. Herschel

1905 Coblentz: “Investigations of Infrared Spectra” (120 organic compounds) 1920/30’s Foundations of theoretical molecular spectroscopy 1928 Discovery of the Raman effect 1940’s structure of penicillin from group frequencies

R.N.Jones Can. J. Spectr. 26 (1981) 1 Vibrational spectroscopy

=1

h=E -E Infrared absorption =1 =0 =0

virtual state

h h( h h h h(   Raman scattering      =1

=0 Rayleigh-S. Raman-S. Raman-S. (Stokes) (anti-Stokes) Selection rules for vibrational transitions

Infrared absorption

      0  q eq Selection rules for vibrational transitions

s as  Infrared absorption

      0  q eq

Raman scattering

      0  q eq IR spectroscopy of clusters in molecular beams

σnl  0eII Absorption spectroscopy

Not sensitive enough (low particle density) Not species specific (cluster distribution)

σF  0eNN Action Spectroscopy: More sensitive and selective: Mass spectrometric detection of absorption Changes of the charge state (ionization) Changes of particle mass (dissociation)

An intense and tunable IR source is needed for the excitation IR photo dissociation of most systems requires absorption of multiple IR photons

(M-M) “fingerprint” region (C=O) (X-H)

DFM / OPO CO2

Chemisorption energies: 1-3 eV Binding energies in transition metal clusters 3-6 eV Physisorption energies <0.1 eV

Dissociation of rare gas complexes: Messenger technique Free Electron Lasers as source of IR radiation

2 U K E  2 1(  1)  2 2 2 ecm

Wavelength depends on: kinetic energy of the electrons

Undulator period u magnetic field (~K) The Free Electron Laser for Infrared eXperiments (FELIX) FOM Institute for Plasma Physics “Rijnhuizen”, Nieuwegein, The Netherlands

15-45 MeV electron beam tunable between 40-2400 cm-1 (up to ~3700 cm-1 on 3rd harmonic) up to 100 mJ per macropulse (1010 W/cm2 in a micropulse) bandwidth typically 0.5-2 % of the central wavelength Magnetism in small rhodium clusters

8910

12 13 A.J. Cox et al. Phys. Rev. B 49 (1994) 12295.

► Cubic growth can explain magnetic properties ► Eight-center bonding through d orbitals

Y.-C. Bae et al. Phys. Rev. B 72 (2005) 125427. Far-IR multiple photon dissociation spectroscopy of metal cluster rare-gas complexes IR multiple photon excitation spectroscopy

IR excitation

Internal vibrational redistribution  thermal heating

action Far-IR multiple photon dissociation spectroscopy of metal cluster rare-gas complexes

IR: 205 cm-1

IR absorption spectrum depletion spectrum resonant absorption Fragmentation of the Ar complexes intensity cross section frequency frequency The cubic structures of rhodium clusters

8910 1312

Rh8 cube, Oh symmetry  1 IR active mode (t1u) + Assignment of the structure of Rh8

+0.92 eV

+0.56 eV

+0.18 eV

0 b2

 bicapped octahedral e structure as identified also for other transition metals

J. Chem. Phys. 132 (2010) 011101. J. Chem. Phys. 133 (2010) 214304. Infrared spectroscopy of metal cluster complexes

Structure of “bare” metal clusters

internal cluster modes < 500 cm-1 (0.06 eV)

Exploring the cluster’s surface chemistry

ligand modes 500-3500 cm-1 (0.06-0.43 eV) + CO at Rhn : Size dependence of the binding site

M() CO(5) donation

M()  CO(2) back donation

Binding to each additional M atom leads to a shift of the C-O stetch of about 100-150 cm-1 to lower frequencies.

 Observation of CO bound in 3-fold face capping (µ3), 2-fold bridging (µ2), and linear (µ1) geometries

JACS 125 (2003) 15716 J. Phys. Chem. B 108 (2004) 14591 Assignment

3.1 Rh4(CO)12 has the structure shown to the right. For the cation we measured the infrared spectrum plotted below. What can you say + about the structure of Rh4(CO)12 ?

+ + 3.2 Make suggestions for the structures of Rh3(CO)9 and Ru3(CO)12 based on their given IR spectra. Both are actually very similar.

Hint: Rh2(CO)8 shown below follows the 18 e valence electron rule for each metal atom, where CO is a 2e donor ligand and metal-metal single bonds are counted to contribute with one extra electron to each metal center. This gives in total 2x9 (from Rh) + 8x2 (from CO) + 2 (1 Rh-Rh bond) = 36 valence electrons, or 18 per Rh atom. + For the trimers only Ru3(CO)12 obeys this rule for each metal atom, so, first figure out how many metal-metal single bonds are in this cluster. Summary

Physical and chemical properties of small clusters (<100 atoms) are often strongly size-dependent

Model and reference systems

Investigation under (close to) collision free conditions

Mass spectrometry: Cluster size separation vs. size selective detection (action spectroscopy)

Variation of size (n), composition (n/m) and charge (z): z MnLm Cluster-size specific methods for characterization Adsorption probes Ion mobility spectrometry Trapped ion electron diffraction Anion photo electron spectroscopy Infrared spectroscopy