Ener

gy

Order parameter

Estimate free energy surfaces (FES) and isomer populations from Replica-Exchange Molecular Dynamics

We address 1) What gold cluster structures are (meta)stable at finite temperature (Au5 – Au14)? 2) At what size do gold clusters turn three-dimensional? 3) Influence of intramolecular van der Waals on cluster stability? 4) Role of entropy on isomer populations? 5) Assign stable gold cluster structures at 100 K using IR (Au9, Au10, and Au12)

P. Ghosh et al., Adv. Drug Deliv. Rev. 60, (2008) J. Saavedra et al., Science 345, (2014)

Knowledge of free clusters gives insight into fundamental processes[1-4] Au13 / TiO2 + O2

Structure-property relationships Catalytic properties Charge state Relativistic effects Unravel metal-support interaction

Gas-phase neutral Au13 cluster

Role of Van der Waals and Entropy on Cluster (Meta)stability B. R. Goldsmith, P. Gruene, J. Lyon, D. Rayner, A. Fielicke, M. Scheffler, L. M. Ghiringhelli

Fritz Haber Institute of the Max Planck Society, Theory Department

Introduction

Gold cluster isomer populations

Pollution abatment Catalyst stability and dynamics under reaction conditions

Gold cluster structure search

Cluster stability and influence of intramolecular van der Waals

Structural assignment of clusters via Far-IR spectroscopy

Density-functional approximations

Schematic of dynamical trajectories crossing from state A to state B on a rough potential energy surface

Structure exploration find local minima and 1st order saddle points Free energy calculations estimate partition functions

Conclusions

References

Metal clusters display interesting phenomena and are technologically useful

[1] S. Arrii, F. Morfin, A. J. Renouprez, J. L. Rousset, J. Am. Chem. Soc. 126 (2014). [2] L. M. Ghiringhelli, P. Gruene, J. T. Lyon, D. M. Rayner, G. Meijer, A. Fielicke, M. Scheffler, New J. Phys. 15 (2013). [3] M. Boronat and A. Corma, Dalton Trans. 39 (2010). [4] A. Fielicke, C. Ratsch, G. von Helden, G. Meijer, J. Chem. Phys. 122 (2005). [5] M. P. Johansson, I. Warnke, A. Le, F. Furche, J. Phys. Chem. C 118 (2014). [6] M. R. Shirts and J. D. Chodera, J. Chem. Phys. 129 (2008). [7] A. R. Oganov and M. Valle, J. Chem. Phys. 130 (2009). [8] P. Gruene, B. Butschke, J. Lyon, D. Rayner, A. Fielicke, Z. Phys. Chem. 228 (2014). [9] G. Santarossa, A. Vargas, M. Iannuzzi, A. Baiker, Phys. Rev. B 81 (2010).

An accurate description of gold clusters at finite temperature is required Coexistence of isomers

Nearly energetically degenerate Au13 isomers Reactions Dynamically disordered system

-Entropic effects -Vibrational anharmonicity

Use Ab initio Molecular Dynamics Solve Newton’s equations of motion using forces from density-functional theory (DFT) Explore the gold cluster potential energy surface efficiently Use Replica Exchange Molecular Dynamics

1 2 3 4 5 6 7 8

Density Functional Approximations used for all replica-exchange simulations PBE + many body dispersion (PBE+MBD) atomic zora scalar relativistic correction spin polarized ‘light-tier 1’ settings

An enhanced, unbiased, sampling method

Simulated in the generalized canonical (NVT) ensemble

Au5 Au6 Au7 Au8 Au9

Au10 Au11 Au12 Au13 Au14

Crossover predicted at size 11 previously using RPA@TPSS[5]

MBD: Many body dispersion (screened long-range many-body vdW)

TS: Tkatchenko-Scheffler dispersion (pairwise interactions only)

PBE+MBD agrees well with HSE06+MBD and RPA until Au13

Planar to three-dimensional ground state transition is size 11 at zero kelvin for neutral gold clusters

Three-dimensional isomers are more stabilized by intramolecular dispersion than planar isomers

Planar isomers are more polarizable, but less stabilized by dispersion

MBD

TS

vdWs increasingly stabilizes 3D structures as size increases Dispersion is important to predict correct isomer energetics Influence of dispersion on ∆E3D→2D is larger than going from PBE to HSE06

Compact 3D structure leads to greater vdW stabilization

Mean relative bin error = 7.6% Mean bin error = 1.1 kBT = 19 meV 3 ns total per simulation Boltzmann Probability, Ρ

Free energy estimator Multistate Bennett Acceptance Ratio[6]

Order parameter Coordination similarity (cosine distance)[7]

Radius of gyration

Structure experimentally assigned at 100 K[8]

A

B

β∆F

Ρ(A) = 99%

T = 200 K Ρ(B) = 1%

Coordination number

Num

ber o

f ato

ms

Coordination similarity

B. R. Goldsmith, P. Gruene, J. Lyon, D. Rayner, A. Fielicke, M. Scheffler, L. M. Ghiringhelli, In Progress

Au12 is ~50% planar at 300 K[9]

Au11 is exceptional case due to conformational entropy of 2D structures

Typically fraction of 3D structures increases as size ↑ and temperature ↑

Au11

Experimental structure determination for gold clusters IR spectra obtained via molecular dynamics

A

C

B 100 K

Ρ(A) = 100%

Ρ(C) = 0%

Ρ(B) = 0%

(a)

(b)

(c)

(d)

All experimental IR spectra provided by P. Gruene, J. Lyon, D. Rayner and A. Fielicke

200 K

+ three additional 3D structures

Ρ = 68%

26%

1%

6%

Au10Kr Experiment

Au10Kr2 Experiment

Ρ = 99%

Ρ = 0%

(a)

(b)

(c)

(d)

Au12Kr Experiment

Ρ = X

Ρ = 90%

Ρ = 10%

Ρ = 0%

∆E = 0.0 eV

∆E = 0.13 eV

∆E = 0.57 eV

(a)

(b)

(c)

(d)

Conformational entropy typically stabilizes nonplanar isomers

van der Waals and entropy strongly influence cluster isomer (meta)stability

Free energy surface → isomer populations » IR spectra assignment of Au9, Au10, Au12

2D to 3D crossover Au11 at 0 K Au10 or Au9 at elevated T

Accurate description of van der Waals in clusters is needed for correct predictions of isomer energetics

J. Liu et al., J. Am. Chem. Soc. 135 (2013)

Support affects cluster reactivity and other properties

Heterogeneity, e.g., vacancy and substitutional defects, hydroxyl type and density, surface reconstruction

Understand physicochemical properties of condensed matter Improve simulation methodologies

Lowest energy planar and nonplanar gold cluster geometries found using replica-exchange molecular dynamics (Au5-Au14)

No screening of polarizabilities

FES of Au8 clusters FES Au10 clusters FES Au9 clusters

Au9Kr2 Experiment

Experiments and simulations are performed at 100 K

Ρ = 100%

Ρ = 0%

Ρ = 0%

Far-IR spectroscopy is a useful tool for the structural characterization of molecules and clusters in the gas phase

Fraction of isomers that are planar as a function of size and temperature

Au4−Au8: P. Gruene et al. Z. Phys. Chem. 228, (2014) Au7, Au19, Au20: P. Gruene et al. Science 321, (2008)

Includes anharmonic effects 100 ps per molecular dynamics trajectory PBE+MBD, ‘tier 2-tight’ numerical settings

Comparison of experimental IR spectra with simulated IR spectra for characterization of Au9, Au10 and Au12

Free Kr atom not shown Rigid shift in frequency