Polarizabilities Of Clusters Research Articles

The Raman coupling coefficients of calcium and sodium silicate melts in high-frequency region - SiOT model study

The Raman coupling coefficient (CC), which was defined by Shuker and Gammon, of silicate melt in high-frequency region, is still an untouched subject but the key parameter for quantitatively processing the Raman spectra (RS) to achieve the abundance of microstructural units. In this paper, we present the results of a newly constructed model - SiOT model (Wu et al) about the Raman coupling coefficients of calcium and sodium silicate melts, especially in the high-frequency region. This new model combines classical MD simulation with decomposition of simulated configurations and vibrational analysis including Wilson's GF matrix method, electro-optical parameter method (EOPM) and bond polarizability model (BPM). The displacement dependence of the cluster polarizability through the combination of EOPM and BPM connotes the description of the frequency dependence of CC. This allows us to make a direct comparison for the first time between the calculated VDOS (vibrational density of states) and RS within the entire frequency range. A strong conclusion was given that the partial VDOS, RS and CC are all the intrinsic properties of respective Qi species, and the only variable inducing the change in total VDOS, RS and CC is the change of microstructure, i.e. the distribution of the Qi.

Electric dipole, polarizability and structure of cesium chloride clusters with one-excess electron

The measurement of the electric dipole of gas phase one-excess electron Cs n Cl n−1 clusters is reported together with a theoretical ab initio prediction of stable structures, dipole moments and electronic polarizabilities for these species in their ground state. Results are in agreement with NaCl cubic structures.

A Comparative Study of the Dipole Polarizability of Some Zn Clusters

We have employed a hierarchy of basis sets and computational techniques in order to approach the polarizability (alpha) of Zn(m), m = 2-20, in a systematic way. This procedure allows the proper approximate results to be selected and validated. More specifically, we have developed in a systematic way a series of basis sets that have been employed for the computation of the polarizability of the Zn atom. Comparison of the computed with the experimental and the best theoretical results allows us to comment on the quality of the basis sets, and to select some of the more successful ones in order to compute the polarizabilities of Zn(m), m = 2-20. We have employed a series of methods to take into account the correlation contribution. These include the following techniques: MP2, CC2, CCSD, CCSD(T), and DFT(B3LYP). We have used two effective core potentials, one small (3s2 3p6 3d10 4s2) and one large (4s2) core. The relativistic contribution to the properties is found to be significant. Thus we have studied in detail the relativistic effects on the polarizability of some small zinc clusters, by employing the Douglas-Kroll approximation in connection with the polarized basis sets developed by Kellö and Sadlej and the methods HF, CC2, and CCSD. Most of the polarizability values are static, but some frequency-dependent properties have also been computed in order to find out the difference between the dynamic and static ones. It is considered that the sharp changes of alpha(Zn(m))/m vs m may be correlated with the change of bonding, from van der Waals to covalent and finally to metallic bonding, in Zn(m). The present comprehensive study of the polarizabilities of Zn(m) includes a limited number of results for the first and second hyperpolarizability of some of the considered zinc clusters.

POST HARTREE–FOCK AND DENSITY FUNCTIONAL THEORY STUDIES ON (BN)n=1–10 CLUSTERS

Density functional theory and Møller–Plesset perturbation theory methods have been used to study the ring clusters of ( BN )n=1–10 employing 6-311++G** basis set. The binding energies have been corrected for the basis set superposition error (BSSE). Static polarizability of these ring clusters has been investigated. A simple expression for the size dependence of polarizability has been invoked, so that the same relation can be useful for predicting the polarizability of larger clusters. The topological properties were analyzed employing the Bader's atoms in molecules theory. A good correlation between the structural parameters and the properties of electron density is found. Localization and delocalization indices were also used for the analysis of molecular electronic structure by an electron pair perspective. The contribution of stereo electronic interactions to the molecular properties as a function of ring size is analyzed based on the natural bond orbital (NBO) analysis.

First-principles investigations of the polarizability of small-sized and intermediate-sized copper clusters

Density functional theory calculations are used to compute the dipole polarizabilities of copper clusters. Structures for the clusters are taken from the literature for n = 2-32 and several isomers are used for each cluster size for n < or = 10. The calculated polarizabilities are in good agreement with the prediction of a simple jellium model, but much smaller than experimental observations for n = 9-32 [M. B. Knickelbein, J. Chem. Phys., 120, 10450 (2004)]. To investigate this difference, the calculated polarizabilities are tested for the effects of basis set, electron correlation, and equilibrium geometry for small-size clusters (n = 2-10). These effects are too small to account for the theory-experiment gap. Temperature effects are also studied. Thermal expansion of the clusters leads to very small changes in polarizability. On the other hand, the presence of permanent dipoles in the clusters could account for the experimental observations if the rotational temperature of the clusters were sufficiently low. The potential importance of the cluster dipole moments implies that reliable ground-state structures and experimental temperatures are needed to find quantitative agreement between calculated and observed polarizabilities.

Resonant heating of a cluster plasma by intense laser light

Gases of atomic clusters are interaction media for laser pulse propagation with properties useful for applications such as extreme ultraviolet (EUV) and x-ray microscopy, harmonic generation, EUV lithography, and laser plasma acceleration. To understand cluster heating and expansion, a series of two- and three-dimensional electrostatic particle in cell simulations of the explosion of argon clusters of diameter in the range 20nm–53nm have been preformed. The studies show that heating is dominated by a nonlinear, resonant absorption process that gives rise to a size-dependent intensity threshold for strong absorption and that controls the dielectric properties of the cluster. Electrons are first accelerated out from the cluster and then driven back into it by the combined effects of the laser field and the electrostatic field produced by the laser-driven charge separation. Above the intensity threshold for strong heating there is a dramatic increase in the production of energetic particles and harmonic radiation. The dielectric properties of a gas of clusters are determined by the ensemble average cluster polarizability. Individual electrons contribute to the polarizability differently depending on whether they are in the core of the cluster or in the outer edge. Consequently, there can be large fluctuations in polarizability during the heating of a cluster.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Møller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

Spectral redshifts in the intense laser-cluster interaction

We study spectral shifts in intense ultrashort laser pulses propagating in clustered gas jets. Forward- and side-scattered laser pulse spectra were measured as a function of pulse width for chirped pulses, and the forward spectrum and absorption were measured for variably delayed colinear $2\ensuremath{\omega}$ probe pulses. The observation of redshifts is consistent with our model of rapidly increasing cluster polarizability early in the laser-heated cluster explosion. In addition, there is a blueshift contribution implying the presence of unclustered atoms in the jet. Simulations of intense pulse propagation in cluster jets are in reasonable agreement with the chirped pulse experiment.

Ab initio studies on the polarizability of lithium clusters: Some unusual results

AbstractThe polarizability of lithium clusters was studied using ab initio as well as Density Functional Theory (DFT)‐based methods. The electron correlation was found not to play any major role in the evaluation of polarizability of the lithium clusters, contrary to the case of sodium and other types of clusters. The theoretical methods used in the present study are not able to reproduce the unusual features in the size evolution of the polarizability observed experimentally. An interesting feature is that the polarizability of lithium clusters calculated by various methods at 0K temperature is found to be higher than the experimental results measured at higher temperature, which is quite unusual. The significance of these issues is highlighted and the need of highly accurate DFT exchange‐correlation functionals and ab initio methods in the study of the electronic properties of lithium clusters is emphasized. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Molecular polarizability of Si/Ge/GaAs semiconductors clusters

The interacting induced dipole polarization model implemented in our program for the calculation of molecular polarizabilities (POLAR) is used for the calculation of the molecular dipole-dipole polarizability ${\overline{\overline{α}}}$. POLAR is tested with Si$_{n}$, Ge$_{n}$ and Ga$_{n}$As$_{m}$ small clusters. The polarizability is an important quantity for the identification of clusters with different numbers of atoms and even for the separation of isomers. The results for the polarizability are in agreement with reference calculations performed with our version of the program PAPID (polarisabilites atomiques par interactions dipolaires) and with reference computations from Dr. J.R. Chelikowsky. The bulk limit for the polarizability is estimated from the Clausius-Mossotti relationship. The polarizability trend for the clusters as a function of size is different from what one might have expected. The clusters are more polarizable than what one might have inferred from the bulk polarizability. Previous experimental work yielded the opposite trend for somewhat larger clusters. At present, the origin of this difference is problematic. One might argue that smaller clusters need not behave like those of intermediate size. The high polarizability of small clusters is attributed to dangling bonds at the surface of the cluster. Indeed, most of the atoms within small clusters reside on the surface. In this respect, semiconductor clusters resemble metallic clusters.

Computational aspects of electric polarizability calculations: Atoms, molecules and clusters

This publication brings together contributions by eminent specialists in the field of the theoretical determination of electric polarizability. The contents of this book cover a wide area of subjects relevant to Chemical Physics, Molecular Physics, Nonlinear Optics and Materials Science. It covers such specific subjects as: Ab initio and Density functional theory calculations of electric polarizability and hyperpolarizability, intermolecular forces, aromaticity, molecular design, electric properties of solvated molecules, NLO materials, Raman intensities, polarizability of metal and semiconductor clusters, relativistic effects on electric properties, and more. Common experience had taught us that computational methods originally developed in a given basic science, e.g. physics, can be of paramount importance to other neighboring sciences, e.g. chemistry, as well as to engineering or technology and, in turn, to society as a whole.

The static dipole polarizability of aluminium atom: discrepancy between theory and experiment

A serious discrepancy of almost 20% has been found between the experimentally measured static dipole polarizability of aluminium atom and very exhaustive theoretical calculations. This fact is important because in some experimental works the dipole polarizability of atomic clusters is measured with respect to the one of aluminium atom.

Relationship between Ionization Potential, Polarizability, and Softness: A Case Study of Lithium and Sodium Metal Clusters

The properties of the alkali metal clusters have been investigated by using ab initio electronic structure calculations, with special reference to their structural evolution and the size dependence of several reactivity descriptors, such as ionization potential, electron affinity, polarizability, chemical potential, hardness, softness, etc. Also shown is a good inverse correlation between the dipole polarizability and the ionization potential of the neutral clusters. Similarly, the softness parameter has also been shown to correlate strongly with the dipole polarizability of the clusters. The present work thus will have some important implications in the calculation of polarizability of metal clusters in terms of the corresponding ionization potentials directly.

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.

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.

Polarizability of Fe n ( n⩽4) clusters: an all-electron density functional study

The first study of static polarizability and polarizability anisotropy of small iron clusters up to four atoms calculated in the framework of density functional theory is presented. The calculations were of all-electron type and performed using a finite field approach implemented in the density functional program A llC hem. A newly developed first-order field induced iron basis set for density functional calculations was employed. The calculated polarizability of iron clusters shows that the size dependency of the static polarizability per atom of iron clusters follows the same trend as that observed for sodium and copper clusters.

Size and Electric Dipole (Hyper)polarizability in Small Cadmium Sulfide Clusters: An ab initio Study on (CdS)n, n = 1, 2, and 4

AbstractFor Abstract see ChemInform Abstract in Full Text.

Size and Electric Dipole (Hyper)polarizability in Small Cadmium Sulfide Clusters: An ab Initio Study on (CdS)n, n = 1, 2, and 4

We report conventional ab initio and B3LYP/DFT calculations for the static electric (hyper)polarizability of small CdS clusters. Our results indicate a strong reduction of the (per atom) mean dipole polarizability with size, supporting the recent LDA findings by Troparevsky and Chelicowsky [J. Chem. Phys. 2001, 114, 943]. The same trend is observed for the second dipole hyperpolarizability. The computational complexity of the determination of the electric properties varies considerably with cluster size. B3LYP and conventional ab initio values are not in good agreement for the monomer but the gap is drastically reduced for the dimer and the tetramer.

Electron-energy-loss channels and plasmon confinement in supported silver particles

The present paper is aimed at distinguishing the surface and particle contributions to the electron-energy-loss reflection spectrum from supported metallic particles in the thin layer limit ${k}_{\ensuremath{\Vert}}{d}^{*}\ensuremath{\ll}1,$ where ${k}_{\ensuremath{\Vert}}$ is the electron parallel momentum transfer and ${d}^{*}$ the dielectric effective layer thickness. In the same way as with light excitation, the key constituents of the response of supported clusters are the cluster polarizabilities which create the long-range dipole oscillating field resulting in energy loss upon electron scattering. Contributions to the plasmon peak from either the substrate (Ag/Si, via the model) or a mixture of parallel and perpendicular excitations linked to the cluster shape (Ag/MgO, model and experiments) are identified. In the case Ag/MgO, a prototype for the study of plasmon excitation because of the negligible substrate contribution, a plasmon dispersion is observed even within a ${k}_{\ensuremath{\Vert}}$ range in which plasmon confinement is expected. This is interpreted as the signature of the island polarizabilities oscillatorlike behavior.

Accurate dipole polarizabilities of small silicon clusters from ab initio and density functional theory calculations

We report conventional ab initio and density functional theory calculations for the static dipole polarizability for the small silicon clusters Si3 to Si7. Our effort relies on the design of flexible basis sets of Gaussian-type functions. The dependence of the calculated mean polarizability per atom (ᾱ/n) on basis set type and level of theory is brought forth and discussed. The effect of electron correlation is found to be small for all studied clusters. The density functional theory based methods are seen to predict reliable values for (ᾱ/n). By introducing and analyzing the differential mean polarizability per atom, ᾱdiff/n=ᾱ(Sin)/n−ᾱ(Si), we show that in fact ab initio and density functional theory calculations yield distinctly different pictures of the polarizability of small silicon clusters. Computational strategies are proposed for the extension of theoretical studies to larger structures.

Polarizability of water clusters: An ab initio investigation

Ab initio calculations have been performed to obtain the polarizability of water clusters (H2O)n up to n=20. It is shown that a simple linear relation involving the aggregation number fits the polarizability results extremely well (with correlation coefficient &amp;gt;0.999) indicating a near additive nature of this quantity for weakly bonded molecular clusters. Calculated dynamic polarizabilities are also shown to follow the same trend. The effect of electron correlation on the static polarizability of water clusters has also been investigated.