T. R. Walsh · Cannot address structural isomerism by studying minima alone Instead, must determine...

OverviewBackgroundMethodsResults for NiobiumRhodium reactivity

Structural isomerism in transition-metal clusters

T. R. WalshDept. of Chemistry and Centre for Scienti�c Computing

www.warwick.ac.uk/go/nanoclusters

March 2, 2006

T. R. Walsh Dept. of Chemistry and Centre for Scienti�c Computing www.warwick.ac.uk/go/nanoclustersStructural isomerism in transition-metal clusters


1 Background

2 Methods

3 Results for Niobium

4 Rhodium reactivity



Structural isomerism: the problem

For a given size n, a cluster can adopt many di�erentstructures.

The number of structures grows exponentially with size!

In the case of transition-metal clusters, experiments indicatesome structures are more reactive than others ! catalysis

Despite recent advances, it is still di�cult to assign clusterstructures from experimental data alone



Structural isomerism: the problem

Calculations can complement experimental approaches byidentifying

which structures are observed and why

which structures are more reactive than others and why

The main ingredient used to answer these questions is thepotential energy landscape (PEL)





PEL and Structural Isomers

During experiments, observed clusters could be low-energystructures, or they could be trapped metastable structures, ora mix of both

Cannot address structural isomerism by studying minima alone

Instead, must determine the structure of the PEL to makepredictions about cluster relaxation dynamics

Predictions done using simulation techniques can tell us aboutequilibrium and transient populations of structural isomers.



Two Simulation Issues for Structural Isomers

1. The relaxation simulations used here must be appropriate:

Can't use straightforward molecular dynamics : can'tnecessarily surmount high barriers

Rare-event simulation methods show promise: thermally

activated dynamics

Can use kinetic models : master equation approach



Two Simulation Issues for Structural Isomers

2. The PEL must be accurately represented:

Energy/Forces evaluated thousands of times in a run!

Full electronic structure theory not practical forsimulations

Even density-functional theory (DFT) using Car-Parrinellotakes too long

Need a good model potential to describe metal-metalbonding



Interpreting results

Simulations are limited ! they suggest possible structuralisomers.

Must complement these results with other calculated data forcomparison with experiment.

Ionization potentials.IR spectra.Franck-Condon factors for simulated ZEKE or MATI spectra.Reaction kinetics (wrt small molecule adsorbates).



Master Equation approach

Potential energy landscape (PEL) information supplied viacalculating the rate of interconversion between isomers

Obviates need for expensive `on-the- y' dynamics

We only need relative rates here!RRKM theory is used to calculate these rates

Input for RRKM { energies and harmonic frequenciescalculated using DFT

These rates are used as input to the Master Equation

This approach yields the relative population of each isomer asa function of time (coupled di�erentials equations solvednumerically).

This simulates cluster relaxation in the beam



Master Equation approach

Potential energy landscape (PEL) information supplied viacalculating the rate of interconversion between isomers

Obviates need for expensive `on-the- y' dynamics

We only need relative rates here!RRKM theory is used to calculate these rates

Input for RRKM { energies and harmonic frequenciescalculated using DFT

These rates are used as input to the Master Equation

This approach yields the relative population of each isomer asa function of time (coupled di�erentials equations solvednumerically).

This simulates cluster relaxation in the beam



The catch:

We must pre-suppose the rearrangement mechanisms forinterconversion.How we do it: a `two-stage' procedure

Use Basin-Hopping with existing (unsuitable) potential to �ndcandidate structures

Re�ned these minima using DFT optimisations

Mapped out connectivities between minima using a knowninterconversion mechanism

Diamond-Square-Diamond (DSD) and Cap Migration (CM)mechanismConnectivity was mapped outwards from global minimum





Nb10 : Experimental motivation

Knickelbein and Yang claim observation of two isomers ofNb10 with practically same ionization potential

Bondybey and coworkers observe bi-exponential reactionkinetics of Nb+10 with ethene

Smalley and coworkers did not observe structural isomerism ofNb10 when reacting with H2.

No structural assignment to date





Example barrier heights for neutral and cationic systems

Connection Forward ReverseBarrier (eV) Barrier (eV)

1{2 1.42 (1.06) 0.43 (0.48)2{3 0.71 (0.79) 0.32 (0.33)2{4 0.97 (0.92) 0.38 (0.47)4{6 0.70 (0.77) 0.46 (0.13)5{6 0.62 (0.65) 0.59 (0.23)















Isomer VIP (eV)

1 6.47 (5.24)2 5.84 (4.88)4 6.00 (4.61)7 5.89 (4.92)

Relation to Knickelbein experiments

LDA and BLYP IP's are not always consistent

However, IP for structure 1 is consistently higher than allothers

Suggests they may have observed structure 2 and 4.



IR Spectra

Recently reported FIR-MPD experiments show great promise

(Fielicke, von Helden, Meijer and co-workers)

But occasional ambiguities reported for structural isomerism

IR spectra are easy to calculate, given the vibrationalfrequencies

Seek IR spectra of structures 1, 2, 4 and 7: are theydistinctive?







Niobium Conclusions

Structures 2 and 4 identi�ed as candidate isomers observed byKnickelbein and Yang

Structures 1, 2 and 7 identi�ed as candidate isomers forcationic system

Structures 4 and 7 have distinctive IR spectra - could beidenti�ed by FIR-MPD?

Greater chance of �nding more than one isomer signi�cantlypopulated in cation system



Possible structural isomerism in Rh+6

Taken from M. S. Ford et.al., PCCP, 7, 975 (2005)



Candidate minima for Rh6

No need to run simulations (?). Two isoenergetic structuresemerge from the `two-stage' procedure : the octahedron andthe trigonal prism.

Work done with Dan Harding



Path1 Energy/kJmol�1

Forward Barrier 156Reverse Barrier 99Products � Reactants 57




Forward Barrier 107Reverse Barrier 137Products � Reactants �30




Forward Barrier 149Reverse Barrier 52Products � Reactants 97



Summary for Rh+6 so far:

The second reaction shown is the clear favourite so far.

All pre-dissociation minima have binding energies between 250and 300 kJmol�1 (wrt separated fragments).

Many more possibilities { other pathways currently underinvestigation

Crucial for comparison is the behaviour of N2O { currentlyunderway



Outlook

Potential energy landscape is crucial for suggesting/predictingstructural isomerism.

Master equation is a plausible way forward: but rare-eventdynamics needed to supplement assumed mechanisms.

Need model potential designed for transition-metal clusters!

Complementary calculations (IP) are critical for assigningstructures.

Reaction pathways with small molecules appears promising.



Acknowledgements

Computing facilities of the Centre for Scienti�c Computing,University of Warwick

Helpful discussions with Stuart Mackenzie


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T. R. Walsh · Cannot address structural isomerism by studying minima alone Instead, must determine...

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