Convergence of the many-body expansion of interaction potentials: From van der Waals to covalent and metallic systems

The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual n-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semiempirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed.

[1]  D. Sánchez-Portal,et al.  Lowest Energy Structures of Gold Nanoclusters , 1998 .

[2]  Jaroslav V. Burda,et al.  Density functional study of structural and electronic properties of bimetallic silver–gold clusters: Comparison with pure gold and silver clusters , 2002 .

[3]  Şakir Erkoç,et al.  Molecular dynamics simulation of gold microclusters , 1988 .

[4]  A. Stone,et al.  Contribution of Many-Body Terms to the Energy for Small Water Clusters: A Comparison of ab Initio Calculations and Accurate Model Potentials , 1997 .

[5]  Han Myoung Lee,et al.  STRUCTURES AND ENERGETICS OF THE WATER HEPTAMER : COMPARISON WITH THE WATER HEXAMER AND OCTAMER , 1999 .

[6]  P. Schwerdtfeger.  Gold goes nano--from small clusters to low-dimensional assemblies. , 2003, Angewandte Chemie.

[7]  Jun Li,et al.  Au20: A Tetrahedral Cluster , 2003, Science.

[8]  Robert P. Krawczyk,et al.  Extension of the Lennard-Jones potential: Theoretical investigations into rare-gas clusters and crystal lattices of He, Ne, Ar, and Kr using many-body interaction expansions , 2006 .

[9]  Raju P. Gupta.  Lattice relaxation at a metal surface , 1981 .

[10]  Rosato,et al.  Tight-binding potentials for transition metals and alloys. , 1993, Physical review. B, Condensed matter.

[11]  Jinlan Wang,et al.  Structures and electronic properties of Cu20, Ag20, and Au20 clusters with density functional method , 2003 .

[12]  J. Murrell,et al.  Modelling Cu, Ag and Au surfaces using empirical potentials , 1998 .

[13]  Grimsditch,et al.  Brillouin scattering and three-body forces in argon at high pressures. , 1986, Physical review. B, Condensed matter.

[14]  I. L. Garzón,et al.  Ab initio study of small gold clusters , 1999 .

[15]  O. Novaro,et al.  Non-additive forces in atomic clusters , 1995 .

[16]  K. Raghavachari,et al.  Si3Si7. Experimental and theoretical infrared spectra , 1995 .

[17]  P. Morse.  Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels , 1929 .

[18]  Hannu Häkkinen,et al.  On the Electronic and Atomic Structures of Small AuN- (N = 4−14) Clusters: A Photoelectron Spectroscopy and Density-Functional Study , 2003 .

[19]  Hannu Häkkinen,et al.  When Gold Is Not Noble: Nanoscale Gold Catalysts , 1999 .

[20]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[21]  P. Schwerdtfeger,et al.  Relativistic effects in gold chemistry. V. Group 11 dipole polarizabilities and weak bonding in monocarbonyl compounds , 1994 .

[22]  Jijun Zhao,et al.  Density-functional study of Au n ( n = 2 – 2 0 ) clusters: Lowest-energy structures and electronic properties , 2002 .

[23]  A. Walker.  Structure and energetics of small gold nanoclusters and their positive ions. , 2005, The Journal of chemical physics.

[24]  Yuzuru Takamura,et al.  Modification of Escherichia coli single-stranded DNA binding protein with gold nanoparticles for electrochemical detection of DNA hybridization , 2004 .

[25]  L. Rincón,et al.  Many-Body Energy Decomposition Analysis of Cooperativity in Hydrogen Fluoride Clusters , 2005 .

[26]  Roy L. Johnston,et al.  A theoretical study of atom ordering in copper–gold nanoalloy clusters , 2002 .

[27]  O Engkvist,et al.  Accurate Intermolecular Potentials Obtained from Molecular Wave Functions: Bridging the Gap between Quantum Chemistry and Molecular Simulations. , 2000, Chemical reviews.

[28]  Roy L. Johnston,et al.  Modelling gold clusters with an empirical many-body potential , 2000 .

[29]  C. A. Murray,et al.  STRUCTURES AND COALESCENCE BEHAVIOR OF SIZE-SELECTED SILICON NANOCLUSTERS STUDIED BY SURFACE-PLASMON-POLARITON ENHANCED RAMAN SPECTROSCOPY , 1999 .

[30]  P. Schwerdtfeger,et al.  From the van der Waals dimer to the solid state of mercury with relativistic ab initio and density functional theory , 2006 .

[31]  S. Sasaki,et al.  High-pressure elastic properties of solid argon to 70 GPa. , 2001, Physical review letters.

[32]  J. Murrell,et al.  Molecular Potential Energy Functions , 1985 .

[33]  A. Sutton,et al.  Long-range Finnis–Sinclair potentials , 1990 .

[34]  G. Hutchings,et al.  Oxidation of glycerol using supported Pt, Pd and Au catalysts , 2003 .

[35]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[36]  Jens K Nørskov,et al.  Catalytic CO oxidation by a gold nanoparticle: a density functional study. , 2002, Journal of the American Chemical Society.

[37]  G. Bond.  Gold: A relatively new catalyst , 2001 .

[38]  Michele Parrinello,et al.  Simulation of gold in the glue model , 1988 .

[39]  Hannu Häkkinen,et al.  Bonding in Cu, Ag, and Au clusters: relativistic effects, trends, and surprises. , 2002, Physical review letters.

[40]  Pekka Pyykkö,et al.  Theoretical chemistry of gold. , 2004, Angewandte Chemie.

[41]  R. Johnston,et al.  Empirical Potentials for Modeling Solids, Surfaces, and Clusters , 1999 .

[42]  Robert P. Krawczyk,et al.  A comparison of structure and stability between the group 11 halide tetramers M4X4 (M = Cu, Ag, or Au; X = F, Cl, Br, or I) and the group 11 chloride and bromide phosphanes (XMPH3)4. , 2004, Inorganic chemistry.

[43]  R. Whetten,et al.  Coadsorption of CO and O(2) on selected gold clusters: evidence for efficient room-temperature CO(2) generation. , 2002, Journal of the American Chemical Society.

[44]  John E. Johnson,et al.  Fabrication of assembled virus nanostructures on templates of chemoselective linkers formed by scanning probe nanolithography. , 2003, Journal of the American Chemical Society.

[45]  Beate Paulus,et al.  Ab initio coupled-cluster calculations for the fcc and hcp structures of rare-gas solids , 2000 .

[46]  Bing Xu,et al.  Presenting Vancomycin on Nanoparticles to Enhance Antimicrobial Activities , 2003 .

[47]  D. Thompson,et al.  Developing new industrial applications for gold: Gold nanotechnology , 2002 .

[48]  Peter Schwerdtfeger,et al.  Strongly bonded water monomers on the ice Ih basal plane: Density-functional calculations , 2006 .

[49]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[50]  Masatake Haruta,et al.  When gold is not noble: catalysis by nanoparticles. , 2003, Chemical record.

[51]  Jonathan Doye,et al.  Global minima for transition metal clusters described by Sutton–Chen potentials , 1997 .

[52]  Janet E. Jones,et al.  On the Calculation of Certain Crystal Potential Constants, and on the Cubic Crystal of Least Potential Energy , 1925 .

[53]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi , 1985 .

[54]  Takayanagi,et al.  Synthesis and characterization of helical multi-shell gold nanowires , 2000, Science.

[55]  S. Penadés,et al.  Gold glyconanoparticles: synthetic polyvalent ligands mimicking glycocalyx-like surfaces as tools for glycobiological studies. , 2003, Chemistry.

[56]  Bernd Hartke.  Global geometry optimization of small silicon clusters at the level of density functional theory , 1998 .