Exploring the free energy surfaces of clusters using reconnaissance metadynamics.

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.

[1]  J. Doye,et al.  THE DOUBLE-FUNNEL ENERGY LANDSCAPE OF THE 38-ATOM LENNARD-JONES CLUSTER , 1998, cond-mat/9808265.

[2]  Michele Parrinello.  Eppur si muove , 2008 .

[3]  C. Millot,et al.  Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites. , 2005, The Journal of chemical physics.

[4]  Rose,et al.  Statistical mechanics and phase transitions in clustering. , 1990, Physical review letters.

[5]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[6]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[7]  J. B. Paul,et al.  Direct Measurement of Water Cluster Concentrations by Infrared Cavity Ringdown Laser Absorption Spectroscopy , 1997 .

[8]  Gerhard Stock,et al.  How complex is the dynamics of Peptide folding? , 2007, Physical review letters.

[9]  D. L. Freeman,et al.  Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles , 2000, physics/0003072.

[10]  D. Oxtoby.  Homogeneous nucleation: theory and experiment , 1992 .

[11]  Marcella Iannuzzi,et al.  Free energy surface of two- and three-dimensional transitions of Au 12 nanoclusters obtained by ab initio metadynamics , 2010 .

[12]  M. Kulmala.  Dynamical atmospheric cluster model , 2010 .

[13]  J. Anglada,et al.  Anharmonicity and the Eigen-Zundel Dilemma in the IR Spectrum of the Protonated 21 Water Cluster. , 2011, Journal of chemical theory and computation.

[14]  Hellmut Haberland,et al.  Clusters of Atoms and Molecules II , 1994 .

[15]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[16]  J. B. Paul,et al.  Infrared Cavity Ringdown Spectroscopy of the Water Cluster Bending Vibrations , 1999 .

[17]  Christopher M. Bishop,et al.  Mixtures of Probabilistic Principal Component Analyzers , 1999, Neural Computation.

[18]  Terry A. Ring,et al.  Fundamentals of crystallization: Kinetic effects on particle size distributions and morphology , 1991 .

[19]  Michele Parrinello,et al.  A self-learning algorithm for biased molecular dynamics , 2010, Proceedings of the National Academy of Sciences.

[20]  Alessandro Laio,et al.  Advillin folding takes place on a hypersurface of small dimensionality. , 2008, Physical review letters.

[21]  Zhongwei Zhu,et al.  Using novel variable transformations to enhance conformational sampling in molecular dynamics. , 2002, Physical review letters.

[22]  D. L. Freeman,et al.  Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble , 2000, physics/0003068.

[23]  J. Abbatt,et al.  Interactions of atmospheric trace gases with ice surfaces: adsorption and reaction. , 2003, Chemical reviews.

[24]  G. H. Nancollas.  The growth of crystals in solution , 1979 .

[25]  Berend Smit,et al.  Accelerating Monte Carlo Sampling , 2002 .

[26]  Marco Ronchetti,et al.  Icosahedral Bond Orientational Order in Supercooled Liquids , 1981 .

[27]  Massimiliano Bonomi,et al.  PLUMED: A portable plugin for free-energy calculations with molecular dynamics , 2009, Comput. Phys. Commun..

[28]  W Smith,et al.  DL_POLY_2.0: a general-purpose parallel molecular dynamics simulation package. , 1996, Journal of molecular graphics.

[29]  U. Buck,et al.  Structure and Spectra of Three-Dimensional ( H 2 O ) n Clusters, n = 8 , 9 , 10 , 1998 .

[30]  D. Holland-Moritz,et al.  Colloids as model systems for metals and alloys: a case study of crystallization , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[31]  D. Quigley,et al.  A metadynamics-based approach to sampling crystallisation events , 2009 .

[32]  N. Yan,et al.  Transition metal nanoparticle catalysis in green solvents , 2010 .

[33]  M. Maggioni,et al.  Determination of reaction coordinates via locally scaled diffusion map. , 2011, The Journal of chemical physics.

[34]  Lydia E Kavraki,et al.  Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction , 2006, Proc. Natl. Acad. Sci. USA.

[35]  A. Laio,et al.  Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science , 2008 .

[36]  G. Shields,et al.  Accurate predictions of water cluster formation, (H₂O)(n=2-10). , 2010, The journal of physical chemistry. A.

[37]  A. Laio,et al.  Predicting crystal structures: the Parrinello-Rahman method revisited. , 2002, Physical review letters.

[38]  A. Oganov,et al.  Crystal fingerprint space--a novel paradigm for studying crystal-structure sets. , 2010, Acta crystallographica. Section A, Foundations of crystallography.

[39]  Ahmed H. Zewail,et al.  Physical Biology: 4D Visualization of Complexity , 2008 .

[40]  David J. Wales,et al.  Global minima of water clusters (H2O)n, n≤21, described by an empirical potential , 1998 .

[41]  Alessandro Laio,et al.  Finite temperature properties of clusters by replica exchange metadynamics: the water nonamer. , 2011, Journal of the American Chemical Society.

[42]  E. Vanden-Eijnden,et al.  Large-scale conformational sampling of proteins using temperature-accelerated molecular dynamics , 2010, Proceedings of the National Academy of Sciences.

[43]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[44]  Helge J. Ritter,et al.  Resolution-Based Complexity Control for Gaussian Mixture Models , 2001, Neural Computation.

[45]  Krzysztof Szalewicz,et al.  Predictions of the Properties of Water from First Principles , 2007, Science.

[46]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[47]  Bertrand Guillot,et al.  A reappraisal of what we have learnt during three decades of computer simulations on water , 2002 .

[48]  Mario Valle,et al.  How to quantify energy landscapes of solids. , 2009, The Journal of chemical physics.

[49]  A. van der Avoird,et al.  TERAHERTZ VIBRATION-ROTATION-TUNNELING SPECTROSCOPY OF WATER CLUSTERS IN THE TRANSLATIONAL BAND REGION , 2001 .

[50]  Julius Jellinek,et al.  Energy Landscapes: With Applications to Clusters, Biomolecules and Glasses , 2005 .

[51]  M. Kahn,et al.  Organometallic chemistry: an alternative approach towards metal oxide nanoparticles , 2009 .

[52]  Giovanni Bussi,et al.  Langevin equation with colored noise for constant-temperature molecular dynamics simulations. , 2008, Physical review letters.

[53]  D. Quigley,et al.  Free energy and structure of calcium carbonate nanoparticles during early stages of crystallization. , 2008, The Journal of chemical physics.

[54]  M. Zwijnenburg,et al.  Isomorphism between ice and silica. , 2010, Physical chemistry chemical physics : PCCP.

[55]  V. F. Petrenko,et al.  Physics of Ice , 1999 .