Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Structural isomerism in transition-metal clusters
T. R. Walsh
Dept. of Chemistry and Centre for Scientic Computing
www.warwick.ac.uk/go/nanoclusters
March 2, 2006
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
1 Background
2 Methods
3 Results for Niobium
4 Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Structural isomerism: the problem
For a given size n, a cluster can adopt many dierent
structures.
The number of structures grows exponentially with size!
In the case of transition-metal clusters, experiments indicate
some structures are more reactive than others ! catalysis
Despite recent advances, it is still dicult to assign cluster
structures from experimental data alone
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Structural isomerism: the problem
Calculations can complement experimental approaches by
identifying
which structures are observed and why
which structures are more reactive than others and why
The main ingredient used to answer these questions is the
potential energy landscape (PEL)
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
PEL and Structural Isomers
During experiments, observed clusters could be low-energy
structures, or they could be trapped metastable structures, or
a mix of both
Cannot address structural isomerism by studying minima alone
Instead, must determine the structure of the PEL to make
predictions about cluster relaxation dynamics
Predictions done using simulation techniques can tell us about
equilibrium and transient populations of structural isomers.
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Two Simulation Issues for Structural Isomers
1.
The relaxation simulations used here must be appropriate:
Can't use straightforward molecular dynamics :
can't
necessarily surmount high barriers
Rare-event simulation methods show promise:
thermally
activated dynamics
Can use kinetic models :
master equation approach
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Two Simulation Issues for Structural Isomers
2.
The PEL must be accurately represented:
Energy/Forces evaluated thousands of times in a run!
Full electronic
simulations
structure theory not practical
for
Even density-functional theory (DFT) using Car-Parrinello
takes too long
Need a good
bonding
model potential
to describe metal-metal
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Interpreting results
Simulations are limited ! they suggest possible structural
isomers.
Must complement these results with other calculated data for
comparison with experiment.
Ionization potentials.
IR spectra.
Franck-Condon factors for simulated ZEKE or MATI spectra.
Reaction kinetics (wrt small molecule adsorbates).
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Master Equation approach
Potential energy landscape (PEL) information supplied via
calculating 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 frequencies
calculated using DFT
These rates are used as input to the Master Equation
This approach yields the relative population of each isomer as
a function of time (coupled dierentials equations solved
numerically).
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Master Equation approach
Potential energy landscape (PEL) information supplied via
calculating 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 frequencies
calculated using DFT
These rates are used as input to the Master Equation
This approach yields the relative population of each isomer as
a function of time (coupled dierentials equations solved
numerically).
This simulates cluster relaxation in the beam
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
The catch:
We must pre-suppose the rearrangement mechanisms for
interconversion.
How we do it: a `two-stage' procedure
Use Basin-Hopping with existing (unsuitable) potential to nd
candidate structures
Rened these minima using DFT optimisations
Mapped out connectivities between minima using a known
interconversion mechanism
Diamond-Square-Diamond (DSD) and Cap Migration (CM)
mechanism
Connectivity was mapped outwards from global minimum
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Nb10 : Experimental motivation
Knickelbein and Yang claim observation of two isomers of
Nb10 with practically same ionization potential
Bondybey and coworkers observe bi-exponential reaction
kinetics of Nb+
10 with ethene
Smalley and coworkers did not observe structural isomerism of
Nb10 when reacting with H2 .
No structural assignment to date
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Example barrier heights for neutral and cationic systems
Connection
1{2
2{3
2{4
4{6
5{6
Forward
Reverse
Barrier (eV) Barrier (eV)
1.42 (1.06) 0.43 (0.48)
0.71 (0.79) 0.32 (0.33)
0.97 (0.92) 0.38 (0.47)
0.70 (0.77) 0.46 (0.13)
0.62 (0.65) 0.59 (0.23)
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Isomer
1
2
4
7
VIP (eV)
6.47 (5.24)
5.84 (4.88)
6.00 (4.61)
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 all
others
Suggests they may have observed structure 2 and 4.
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
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 vibrational
frequencies
Seek IR spectra of structures 1, 2, 4 and 7: are they
distinctive?
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Niobium Conclusions
Structures 2 and 4 identied as candidate isomers observed by
Knickelbein and Yang
Structures 1, 2 and 7 identied as candidate isomers for
cationic system
Structures 4 and 7 have distinctive IR spectra - could be
identied by FIR-MPD?
Greater chance of nding more than one isomer signicantly
populated in cation system
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Possible structural isomerism in Rh+
6
Taken from M. S. Ford et.al., PCCP,
7,
975 (2005)
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Candidate minima for Rh6
No need to run simulations (?). Two isoenergetic structures
emerge from the `two-stage' procedure : the octahedron and
the trigonal prism.
Work done with Dan Harding
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Path1
Energy/kJ mol 1
Forward Barrier
156
Reverse Barrier
99
Products Reactants
57
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Path2
Energy/kJ mol 1
Forward Barrier
107
Reverse Barrier
137
Products Reactants
30
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Path3
Energy/kJ mol 1
Forward Barrier
149
Reverse Barrier
52
Products Reactants
97
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Summary for Rh+
6 so far:
The second reaction shown is the clear favourite so far.
All pre-dissociation minima have binding energies between 250
and 300 kJ mol 1 (wrt separated fragments).
Many more possibilities { other pathways currently under
investigation
Crucial for comparison is the behaviour of N2 O { currently
underway
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Outlook
Potential energy landscape is crucial for suggesting/predicting
structural isomerism.
Master equation is a plausible way forward: but rare-event
dynamics needed to supplement assumed mechanisms.
Need model potential designed for transition-metal clusters!
Complementary calculations (IP) are critical for assigning
structures.
Reaction pathways with small molecules appears promising.
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters
Overview
Background
Methods
Results for Niobium
Rhodium reactivity
Acknowledgements
Computing facilities of the Centre for Scientic Computing,
University of Warwick
Helpful discussions with Stuart Mackenzie
T. R. Walsh Dept. of Chemistry and Centre for Scientic Computing
Structural
www.warwick.ac.uk/go/nanoclusters
isomerism in transition-metal clusters