Energy 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 (Au 5 – Au 14 )? 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 (Au 9 , Au 10 , and Au 12 ) 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] Au 13 / TiO 2 + O 2 Structure-property relationships Catalytic properties Charge state Relativistic effects Unravel metal-support interaction Gas-phase neutral Au 13 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 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 1 st 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 Au 13 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 Au 5 Au 6 Au 7 Au 8 Au 9 Au 10 Au 11 Au 12 Au 13 Au 14 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 Au 13 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 ∆E 3D→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 k B T = 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 Number of atoms Coordination similarity B. R. Goldsmith, P. Gruene, J. Lyon, D. Rayner, A. Fielicke, M. Scheffler, L. M. Ghiringhelli, In Progress Au 12 is ~50% planar at 300 K [9] Au 11 is exceptional case due to conformational entropy of 2D structures Typically fraction of 3D structures increases as size ↑ and temperature ↑ Au 11 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% Au 10 Kr Experiment Au 10 Kr 2 Experiment Ρ = 99% Ρ = 0% (a) (b) (c) (d) Au 12 Kr Experiment = 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 Au 9 , Au 10 , Au 12 2D to 3D crossover Au 11 at 0 K Au 10 or Au 9 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 (Au 5 -Au 14 ) No screening of polarizabilities FES of Au 8 clusters FES Au 10 clusters FES Au 9 clusters Au 9 Kr 2 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 Au 4 −Au 8 : P. Gruene et al. Z. Phys. Chem. 228, (2014) Au 7 , Au 19, Au 20 : 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 Au 9 , Au 10 and Au 12 Free Kr atom not shown Rigid shift in frequency