The discovery of unexpected isomers in sodium heptamers by Born-Oppenheimer molecular dynamics.

This work presents a density functional study of neutral, cationic, and anionic sodium cluster heptamers. The cluster structures were optimized with the local density approximation as well as with the generalized gradient approximation. For the neutral and cationic clusters new unexpected isomers are found closed in energy to the well known ground state structures. In the case of the neutral heptamer the new isomer was first noticed by inspection of a first-principles Born-Oppenheimer molecular dynamics (BOMD) simulations at 300 K. A structure alignment algorithm is presented which facilitates the discovery of new structures from such BOMD simulations. With this algorithm the structural evolution of the two low-lying isomers of the neutral, cationic, and anionic heptamer was analyzed at different temperatures. This work demonstrates the capability of reasonably long (approximately 100 ps) first-principles BOMD simulations to explore the potential energy landscape of metallic clusters.

[1]  J. Munkres ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[2]  Andreas M Köster,et al.  A hierarchical transition state search algorithm. , 2008, The Journal of chemical physics.

[3]  E. Carter,et al.  Ab initio molecular dynamics simulated annealing at the generalized valence bond level. Application to a small nickel cluster , 1993 .

[4]  Walt A. de Heer,et al.  The physics of simple metal clusters: experimental aspects and simple models , 1993 .

[5]  Emily A. Carter,et al.  Ab initio molecular dynamics with correlated molecular wave functions: Generalized valence bond molecular dynamics and simulated annealing , 1992 .

[6]  E. Carter,et al.  Multiple time scale Hartree–Fock molecular dynamics , 1993 .

[7]  Michael Vollmer,et al.  Optical properties of metal clusters , 1995 .

[8]  Andreoni,et al.  Equilibrium structures and finite temperature properties of silicon microclusters from ab initio molecular-dynamics calculations. , 1988, Physical review letters.

[9]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[10]  Keith Bonin,et al.  Electric-Dipole Polarizabilities Of Atoms, Molecules, And Clusters , 1997 .

[11]  P. Calaminici,et al.  Static polarizabilities of Nan (n⩽9) clusters: An all-electron density functional study , 1999 .

[12]  Gerhard Klebe,et al.  Superposition of molecules: Electron density fitting by application of fourier transforms , 1997 .

[13]  S. Kearsley On the orthogonal transformation used for structural comparisons , 1989 .

[14]  A. Köster,et al.  Growth pattern and bonding of copper clusters , 2002 .

[15]  A. Peter Johnson,et al.  An algorithm for the multiple common subgraph problem , 1992, Journal of chemical information and computer sciences.

[16]  W. Andreoni,et al.  Structural and electronic properties of sodium microclusters (n=2–20) at low and high temperatures: New insights from ab initio molecular dynamics studies , 1991 .

[17]  R. Fletcher Practical Methods of Optimization , 1988 .

[18]  P. Calaminici,et al.  Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. , 2007, The Journal of chemical physics.

[19]  Electronic polarizability of small sodium clusters. , 1986, Physical review. B, Condensed matter.

[20]  Andreas M Köster,et al.  Efficient and reliable numerical integration of exchange-correlation energies and potentials. , 2004, The Journal of chemical physics.

[21]  James Arvo,et al.  Fast Random Rotation matrices , 1992, Graphics Gems III.

[22]  M. T. Barakat,et al.  Molecular structure matching by simulated annealing. I. A comparison between different cooling schedules , 1990, J. Comput. Aided Mol. Des..

[23]  S. Nosé A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[24]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[25]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[26]  David Robert,et al.  TGSA: A molecular superposition program based on topo‐geometrical considerations , 2001, J. Comput. Chem..

[27]  Andreas M. Köster,et al.  Geometry optimization in density functional methods , 2004, J. Comput. Chem..

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

[29]  J. Nørskov,et al.  Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals , 1999 .

[30]  How important are temperature effects for cluster polarizabilities? , 2008, The journal of physical chemistry. A.

[31]  D. Hohl,et al.  Structure of phosphorus clusters using simulated annealing—P2 to P8 , 1990 .

[32]  P. Dirac Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[33]  Structure and properties of small sodium clusters , 2001, physics/0112038.

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

[35]  Andreoni,et al.  Transferability of bulk empirical potentials to silicon microclusters: A critical study. , 1990, Physical review. B, Condensed matter.

[36]  Ken Shoemake,et al.  Uniform Random Rotations , 1992, Graphics Gems III.

[37]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[38]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[39]  Winston A. Saunders,et al.  Electronic Shell Structure and Abundances of Sodium Clusters , 1984 .

[40]  B. K. Rao,et al.  Physics and Chemistry of Finite Systems: From Clusters to Crystals , 1992 .

[41]  A. Castleman,et al.  CLUSTERS: PROPERTIES AND FORMATION , 1986 .

[42]  Martins,et al.  Static electric polarizabilities as evidence for cluster geometries. , 1990, Physical review letters.

[43]  J. Mintmire,et al.  Fitting the Coulomb potential variationally in linear-combination-of-atomic-orbitals density-functional calculations , 1982 .

[44]  Swapan K. Ghosh,et al.  Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods. , 2004, The Journal of chemical physics.

[45]  Andreas M Köster,et al.  Calculation of exchange-correlation potentials with auxiliary function densities. , 2004, The Journal of chemical physics.

[46]  J. Connolly,et al.  On first‐row diatomic molecules and local density models , 1979 .

[47]  Jordi Mestres,et al.  MIMIC: A molecular‐field matching program. Exploiting applicability of molecular similarity approaches , 1997 .

[48]  K. I. Peterson,et al.  Photoionization of sodium clusters , 1984 .