DETERMINATION OF THE GROUND-STATE GEOMETRIES OF COPPER CLUSTERS BY SIMULATED ANNEALING WITHIN AN EQUIVALENT CRYSTAL APPROACH

We determine the lowest energy structures of small (11–20 atoms) copper clusters. The semi-empirical Equivalent Crystal Theory (ECT) is used in conjunction with the Metropolis Monte Carlo algorithm to determine the equilibrium geometry of each cluster via simulated annealing. The optimum structures of the clusters in this size range are found to be derived from icosahedral structures. The 13-atom cluster is an icosahedron and the 19-atom is a double-icosahedron. The other sizes show structures related to these. The 11-atom clusters, however, show somewhat different structures. We propose the ECT as an efficient tool for developing starting structures for more chemically accurate, first principles and therefore computationally very demanding, approaches.

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Determination of the Ground State Geometries of Copper Clusters by Simulated Annealing

International Journal of Modern Physics B ◽

10.1142/s0217979297001192 ◽

1997 ◽

Vol 11 (19) ◽

pp. 2333-2341

Author(s):

Amitava Banerjea ◽

Radhika Prosad Datta ◽

Abhijit Mookerjee ◽

A. K. Bhattacharyya

Keyword(s):

Simulated Annealing ◽

Cluster Size ◽

Size Range ◽

Monte Carlo Algorithm ◽

Equilibrium Geometry ◽

Copper Clusters ◽

Atom Clusters ◽

Metropolis Monte Carlo ◽

Semi Empirical

We determine the lowest energy structures of small (10–20 atoms) copper clusters. The semi-empirical Equivalent Crystal Theory (ECT) is used in conjunction with the Metropolis Monte Carlo algorithm to determine the equilibrium geometry of each cluster via simulated annealing. The optimum structures of the clusters in this size range are found to be derived from icosahedral structures. The 13-atom cluster is an icosahedron and the 19-atom one a double-icosahedron. The other sizes show structures related to these. The 10- and 11-atom clusters, however, show somewhat different structures. We report the variation of binding energy, as obtained from ECT, with cluster size.

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Determination of Total Energy Tight Binding Parameters from First Principles Calculations Using Adaptive Simulated Annealing

MRS Proceedings ◽

10.1557/proc-700-s7.4 ◽

2001 ◽

Vol 700 ◽

Author(s):

Anders G. Froseth ◽

Peter Derlet ◽

Ragnvald Hoier

Keyword(s):

Simulated Annealing ◽

Total Energy ◽

First Principles ◽

Linear Optimization ◽

Tight Binding ◽

Accurate Method ◽

Optimization Method ◽

Binding Parameters ◽

Non Linear

AbstractEmpirical Total Energy Tight Binding (TETB) has proven to be a fast and accurate method for calculating materials properties for various system, including bulk, surface and amorphous structures. The determination of the tight binding parameters from first-principles results is a multivariate, non-linear optimization problem with multiple local minima. Simulated annealing is an optimization method which is flexible and “guaranteed” to find a global minimum, opposed to classical methods like non-linear least squares algorithms. As an example results are presented for a nonorthogonal s,p parameterization for Silicon based on the NRL tight binding formalism.

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Semi-Experimental Determination of the Linear Clamped Electro-Optical Coefficients of Polar Crystals from Vibrational Spectroscopic Data

Crystals ◽

10.3390/cryst12010052 ◽

2021 ◽

Vol 12 (1) ◽

pp. 52

Author(s):

Eric Bouhari ◽

Ballo Mohamadou ◽

Patrice Bourson

Keyword(s):

First Principles ◽

Soft Mode ◽

Dielectric Susceptibility ◽

First Principles Calculations ◽

Mode Behavior ◽

Direct Measurements ◽

Semi Empirical ◽

General Method ◽

Good Agreement

The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations are based on the formula analog to that of the Lyddane–Sachs–Teller relation, which is systematically used for the calculations of the clamped linear electro-optical coefficient of oxide ferroelectric crystals such as LiNbO3, LiTaO3, BaTiO3, PbTiO3, and KNbO3. The computed electro-optical coefficients are in good agreement with those obtained from direct measurements and the first-principles calculations or other semi-empirical models. In addition, the famous r51 or r42 coefficients of the tetragonal BaTiO3, PbTiO3, and KNbO3 crystals are finally calculated with high accuracy and discussed in connection with the soft mode behavior.

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FINITE-TEMPERATURE SIMULATION OF ABSORPTION SPECTRA IN SMALL ARGON-CLUSTER IONS ${\rm Ar}_n^ + $(n=3, 4, 8, 13, AND 19)

Surface Review and Letters ◽

10.1142/s0218625x96000425 ◽

1996 ◽

Vol 03 (01) ◽

pp. 211-215 ◽

Cited By ~ 24

Author(s):

M. GRIGOROV ◽

F. SPIEGELMANN

Keyword(s):

Absorption Spectra ◽

Finite Temperature ◽

Potential Energy Surfaces ◽

Monte Carlo Algorithm ◽

Cluster Ions ◽

Nuclear Motion ◽

Spin Orbit Coupling ◽

Metropolis Monte Carlo ◽

Energy Surfaces

We report finite-temperature simulations of the absorption spectra of argon-cluster ions using a diatomics in molecules (DIM) Hamiltonian (including spin-orbit coupling) for the determination of the potential-energy surfaces (PES), a point-charge approximation for the dipole transition moments and a Metropolis Monte-Carlo algorithm for the nuclear motion. The dependency of the absorption spectrum on cluster size (3≤n≤19) and on temperature (100 K≤T≤500 K) is analyzed.

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