Total Energy Of Cluster Research Articles

Ab initio study electronic structures of LiYF 4 crystal containing interstitial oxygen atoms

The positions of the interstitial oxygen atoms in LiYF 4 crystal are simulated by computer technologies. It is found that the total energy of cluster is low when interstitial oxygen atoms exist around the Li + ion. Basing on the computer results, the electronic structures of perfect LiYF 4 and the LiYF 4 containing interstitial oxygen atoms with the lattice structure optimized are studied within the framework of the density functional theory. By analyzing the calculated results it can be concluded that an interstitial oxygen atom could combine with formal lattice fluorine ions forming molecular ions, which cause the 260 nm absorption band.

High‐precision calculation of Hartree‐Fock energy of crystals

When using quantum chemistry techniques to calculate the energetics of bulk crystals, there is a need to calculate the Hartree-Fock (HF) energy of the crystal at the basis-set limit. We describe a strategy for achieving this, which exploits the fact that the HF energy of crystals can now be calculated using pseudopotentials and plane-wave basis sets, an approach that permits basis-set convergence to arbitrary precision. The errors due to the use of pseudopotentials are then computed from the difference of all-electron and pseudopotential total energies of atomic clusters, extrapolated to the bulk-crystal limit. The strategy is tested for the case of the LiH crystal, and it is shown that the HF cohesive energy can be converged with respect to all technical parameters to a precision approaching 0.1 mE(h) per atom. This cohesive energy and the resulting HF value of the equilibrium lattice parameter are compared with literature values obtained using Gaussian basis sets.

Large-Scale Molecular Dynamics Simulations of Energetic Ni Nanocluster Impact onto the Surface

On the atomic scale, Molecular Dynamics (MD) Simulation of Nano Ni cluster impact on Ni (100) substrate surface have been carried out for energies of Ea = 1–5 eV/atom and total energy of ET = 195 eV (the total energy of cluster is ET = nEa, n is the number of cluster atoms) to understand quantitatively the interaction mechanisms between the cluster atoms and the substrate atoms. The many-body Embedded Atom Method (EAM) was used in this simulation. We investigated the maximum substrate temperature Tmax and the time tmax within which this temperature is reached as a function of cluster sizes and the total energy ET. The temperature Tmax is linearly proportional to total cluster energy. For the constant energy per atom and for the cluster size increase, the correlated collisions rapidly transfers energy to the substrate, and the time tmax approached a constant value. For constant total energy the temperature Tmax and the time tmax versus different cluster sizes was studied. We showed that the cluster implantation and sputtering atoms from the surface are affected by the cluster size and total kinetic energy of the clusters. Finally time dependence of the number Ndis of disordered atoms in the substrate was observed.

Ab initio studies of small AlmFen clusters

The equilibrium geometrical structures of small AlmFen clusters have been determined through ab initio calculation of the cluster total energy at the UB3LYP/Lanl2dz level. For dimers of iron and aluminum, the dissociation energies, the equilibrium atomic distances, and the vibrational frequencies were calculated. The agreement between calculations and experiments is reasonable. The ground stable geometrical structures of Fe4, FeAl3, Fe3Al and Fe2Al2 clusters favor three-dimension configurations, but Al4 tetramers are planar structures. The Al-rich tetramers are more stable than the other two composition tetramers. This is different from that of bulk alloys.

Nonconventional tight-binding method for the calculation of the total energy and spectroscopic energies of atomic clusters: Transferable parameters for silicon

The principal differences between conventional tight-binding methods and a nonconventional tight-binding method proposed earlier by one of the authors [Z. M. Khakimov, Comput. Mater. Sci. 3, 95 (1994)] are highlighted here. The latter has been optimized for simulation of the structure, cohesive energies, ionization potentials, and electronic affinities of silicon clusters. A single tight-binding approximation has been used to predict all of the above properties with accuracy comparable to state-of-the-art ab initio methods. This demonstrates the potential of tight-binding methods as a quantitative, predictive tool, provided they are based on an accurate total energy functional and exploit properly the individual properties of chemical elements, accounting for both intra- and interatomic charge redistributions.

Fast electron correlation methods for molecular clusters in the ground and excited states*

An efficient and accurate electronic structure method for clusters of weakly interacting molecules has been proposed, on the basis of the pair-interaction method of Kitaura et al., and combined with density functional, many-body perturbation, coupled-cluster, equation-of-motion coupled-cluster, configuration-interaction singles, and time-dependent density functional theories. The method retains the one- and two-body (and, if necessary, also three-body) Coulomb, exchange, and correlation energies exactly and higher-order Coulomb energies in the leading order of multipole expansion (hence the dipole polarization or induction effects). The latter makes the combination of this method with existing implementations of any electronic structure theory extremely easy. It typically recovers the total energies within 0.001%, binding energies within a few kilocalories per mole, and excitation energies within a few hundredths of an electron volt of the conventional implementations. The size dependence of the computational cost of the method is asymptotically linear for total energies and constant for excitation energies. The method has been applied to the total energies of water clusters, to the total energies of zwitterionic and neutral glycine–water clusters, and to the excitation energies of formaldehyde–water clusters. The largest calculation was performed at an equation-of-motion coupled-cluster singles and doubles level for a formaldehyde–(H2O)81 cluster containing 247 atoms that predicted the solvatochromic shift of 1360 cm−1 in the lowest transition energy of formaldehyde in water.

Sputtering of Au (1 1 1) by 64 keV/atom Au clusters

Using molecular-dynamics simulation, we study the sputtering of a Au (111) surface due to impact of Aun clusters (n=1,2,4,8,13) with an energy of 64keV/atom. We measure the initial sputter yield Yinit at the time when the maximum number of atoms energized to above the cohesive energy of the material has been generated; this time is roughly 0.5ps after projectile impact. Yinit is proportional to the energy deposited near the surface, FD. We correlate FD to the final sputter yield Yfinal, measured at roughly 100ps after projectile impact. The good correlation between the deposited energy and the final sputter yield proves that sputter yield fluctuations mainly originate from the early phase of energy deposition. An overview over the available sputter yield simulations of Au cluster impact into Au shows a rough proportionality of the final yield to the total cluster energy. Deviations occur for small clusters and are believed to be due to range straggling, which induces a variation of the deposited energy at the surface.

Oxygen Position in Pb(Mg1/3Nb2/3)O3 from ab initio Cluster Calculations

Potential relief along the direction perpendicular to the face of the cube for oxygen atom located in Mg—O—Nb chain in Pb(Mg1/3Nb2/3)O3 (PMN) is considered. Accurate total energy cluster calculations are performed in the framework of ab initio restricted Hartree–Fock (RHF) method plus 2nd order Moller-Plesset perturbation theory (MP2) electron correlation corrections. It is found that the equilibrium oxygen position is shifted by 0.0664 Å from the middle point towards Nb atom. It is shown that electron correlation effects strongly influence on the equilibrium atomic positions in PMN.

Why is Al11B2− not a magic number in TOF-MS?

Bimetallic anionic and neutral clusters, consisting of group III elements (Aln−1B1, Aln−2B2, Aln−1In1, and Inn−1Al1, n=11–14), have been theoretically investigated by density functional theory at the B3LYP/6-31G* (LanL2DZ for the In element) level. The calculated optimized equilibrium geometries and total energies of neutral and anionic clusters give a satisfactory interpretation of magic number clusters observed in time of flight mass spectra (TOF-MS). Our results show that Al11B2− is the most stable among Aln−2B2− (n=11–14) cluster anions and keeps an icosahedronlike structure, contrary to what had been suggested previously. Whether a magic number turns out in TOF-MS likely depends more on the stability of the neutral clusters than on the stability of the anions. The Al11B2 neutral cluster is less stable than Al12B2, and this is why Al11B2− does not appear as a magic number in TOF-MS. In addition, we found that icosahedral structures do not always hold for the magic cluster anions considered in the present study.

Cluster Ab Initio Calculations of the Shape of Local Potential Well and of Positions for Oxygen Atoms in PCN (C=Cd)

Potential relief and equilibrium positions for oxygen atoms in Cd--O--Nb, Cd--O--Cd and Nb--O--Nb chains are studied in Pb(Cd 1/3 Nb 2/3 )O 3 (PCN) and Ba(Cd 1/3 Nb 2/3 )O 3 (BCN). Total energy cluster calculations are performed using ab initio restricted Hartree-Fock method. The electron correlation contribution is calculated within Møller-Plesset method. It is revealed that in PCN the oxygen atoms in Cd--O--Cd and Cd--O--Nb chains move in multi-well potentials with four minima shifted transversely to fourfold [001] axis. Whereas the oxygen atom in Nb--O--Nb chain in PCN and all oxygen atoms in BCN move in single-well potentials.

Chemically Induced Ferroelectric Lattice Instability in Disordered Mixed Perovskites

New mechanism of dipolar ordering is revealed in disordered mixed perovskites Pb( B 1/3 Nb 2/3 )O 3 [ B = Mg, Zn]. Local potentials for oxygen atoms situated in B --O--Nb, B --O-- B and Nb--O--Nb chains are examined in A ( B 1/3 Nb 2/3 )O 3 compounds where A = Pb, Ba. Total energy cluster calculations are performed using ab initio Hartree-Fock method and taking into account electron correlations within Möller-Plesset method. It is found that in B --O--Nb and B --O-- B chains the shapes of the local potentials depend crucially on the chemistry of A site and are also strongly influenced by electron correlation interactions in contrast to Nb--O--Nb chains. It is found for Pb( B 1/3 Nb 2/3 )O 3 that in B --O--Nb chain oxygen atom moves in multi-well potentials with four additional minima shifted along [010] or [100] axes and in B --O-- B chains a local potential surface for oxygen atom has either one minimum in the center of cubic face with very small positive harmonic force constant in the mirror plane (for B = Mg) or four minima shifted in [100] or [010] directions (for B = Zn). Whereas in Ba( B 1/3 Nb 2/3 )O 3 oxygen atoms with all types of chemical environments move in single-well local potentials.

Minimal interatomic distance in Morse clusters

In this paper we derive a lower bound, independent from the number of atoms N, for the minimal interatomic distances between atoms in a cluster whose total energy is modelled by means of the so called Morse potential. A similar result was previously proven for Lennard–Jones clusters but the proof can not be extended to Morse clusters. Besides the theoretical interest, the derivation of this lower bound is important for the definition of efficient procedures for the computation of the total energy of clusters with a large number of atoms.

Molecular-dynamics study of the interaction between energetic Al clusters and an Al surface

We have investigated the approximate transient temperature and transient time as a function of cluster size in the case of the same total energy and in the case of the same energy per atom. The approximate transient temperature was directly proportional to both energy per atom and total cluster energy. In the case of the same energy per atom, since the correlated collisions rapidly transferred energy to the substrate, the transient time was approximated by a constant value as the cluster size increased. The correlated collisions play an important role in the interaction between an energetic cluster and the surface, affecting their interaction as the size and energy of the cluster increases.

COMPARISON OF DENSITY FUNCTIONAL APPROXIMATIONS IN THE JELLIUM MODEL FOR METAL CLUSTERS

We calculated the exchange, correlation and total energies of clusters of alkali metals with N=1-150 atoms in the spherical jellium model. The calculations were made using the Kohn-Sham method with exchange and correlation energies evaluated in the meta-generalized gradient approximation (MGGA), proposed by J. P. Perdew, S. Kurth, A. Zupan and P. Blaha, in the generalized gradient approximation (GGA) of J. P. Perdew, K. Burke and M. Ernzerhof, and in the Local Density Approximation (LDA). We evaluated the relative deviations of MGGA and GGA energies with respect to LDA. Exchange energies of MGGA and GGA are more negative than the LDA exchange energy and become closer to this as the cluster size increases. On the other hand, the GGA and MGGA correlation energies, which are almost identical, are less negative than LDA. The deviations of GGA and MGGA exchange-correlation energies with respect to LDA are smaller than those of the exchange and correlation energies separately. For clusters with 18 and 20 atoms we have compared our jellium results with Variational and Diffusion Monte-Carlo results. Errors of LDA for exchange and correlation tend to cancel so that the total exchange-correlation energy is close to the Monte-Carlo results. Similar cancellations occur with GGA and MGGA. We also examined the validity of the liquid drop model.

Proton trapping and diffusion in SiO 2 thin films: a first-principles study

The behavior of mobile protons at the Si/SiO 2 interface has drawn substantial interest since it was found to play the critical role in a proposed non-volatile memory device based on Si/SiO 2/Si structures. We have investigated the bonding and diffusion properties of a proton at the interface by a first-principles local density cluster total energy approach. A 73-atom cluster model is used to simulate the Si/SiO 2 interface that is constructed from β-cristobalite SiO 2 on the Si(0 0 1) surface. In agreement with previous calculations of protons in bulk Si, the SiSi bond center is found to be a stable site for a proton on the Si side of the Si/SiO 2 interface. On the SiO 2 side, the proton is found to bond with O atoms. Furthermore, it is found that the binding energy of protonoxygen bond decreases as the proton penetrates into the oxide. Thus, an energy well is formed which confines protons in silicon oxide region in a Si/SiO 2/Si structure. The calculated diffusion barrier for proton hopping between the neighboring binding sites is 0.73 eV in LDA and 1.15 eV in GGA, in good agreement with the experimental activation energy.

Influence of Non-Stoichiometric Defects on Electrooptics in KNbO3

We present a band energy approach for a total energy cluster optimization which accounts for the various structural modifications caused by the non-stoichiometry of KNbO3 crystals. The variation of the optical properties with the deviation from the stoichiometric composition can be understood within this approach. The special role of the electron–phonon contributions to the electrooptic coefficient is shown. In particular, model calculations yield a large dependence of the electrooptic coefficient r22 on the crystal composition, in agreement with the experimental data. The observed experimental minimum of the linear electrooptic coefficient r22 in the plot versus degree of non-stoichiometry is interpreted as being due to a diminishing in the non-centrosymmetry of the electrostatic potential around [NbO6] clusters.

Hartree-Fock deformed jellium model for metallicclusters

We have developed the Hartree-Fock jellium modelfor deformed metal clusters, which treatsthe quantized electron motion in the field of thespheroidal ionic jellium backgroundin the Hartree-Fock approximation. Usingthis model, we have calculated single electron energy levelsas a function ofthe cluster deformation parameterfor a series of sodium clusters with the number of atoms N in a clusterranging from 4 to 40.We have established that the cluster deformationscorresponding to the minimum total energy of the oblate andprolate clusters are in a reasonable agreementwith the experimental data and predictions ofother theoretical models.

Approximate energy minimization for large Lennard-Jones clusters

We have designed a simple method to place particles on lattices, concentric shells and icosahedral concentric layers for minimizing the total energy of Lennard-Jones clusters, approximately, by analytical means. The most significant difference of our schemes from others is the dramatic reduction of parameters, which allows the study of large clusters, not possible otherwise. We present the derivation of formulae for minimal per-particle energy and for inter-particle distance. We also present their asymptotic values for large number of particles.

Ab initio study of small gold clusters

The most stable geometries (lowest energy configurations) as well as the lowest-lying isomers of Aun, n=2–6, clusters are determined through ab initio calculations of the cluster total energy. It is found that Hartree–Fock plus second-order perturbation method of Møller–Plesset combined with a double-zeta basis set and an 11 valence electrons relativistic pseudopotential provide reliable results for a qualitative and quantitative analysis of the structures. Two-dimensional planar configurations are obtained as the lowest energy structures for all the gold cluster sizes investigated. Vibrational frequencies for all the investigated isomers were obtained.

Simple energy minimization for huge Lennard-Jones clusters by dramatic parameter reduction

We have designed several schemes to reduce the number of parameters in the problem of minimizing the total energy of Lennard-Jones clusters. We will discuss our schemes development in three dimensions. The value of our work lies in the simplicity with which it provides a new approach to problems involving huge Lennard-Jones clusters.