On the polarizability of the sulfur atom

Using both Thole's and Birge's semiclassical models, the atomic polarizability of the sulfur atom is calculated. It is concluded that the former model is adequate for calculating polarizabilities of atoms belonging to the second row of the periodic table.     

The effective polarizability of the electrical image of a physisorbed atom

The elementary theory of electrical images may be extended to include the concept of linear dynamic polarizability of the image of an atom. Four different applications are proposed: they allow us to find easily the long-range expressions of the physisorption energy for one and for two atoms and of the electric polarization and polarizability of an atom near a solid surface.     

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

The 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     

Static polarizability of small simple metal clusters in dielectric media

Using the local-density-functional method and spherical jellium model, the electronic structure and static polarizability α(0) of small simple metal clusters (Al, Li, Na, K, Rb, and Cs) surrounding by media with dielectric constants ε = 1 ÷ 25 have been calculated. It has been obtained that α(0) of the smallest clusters with a low mean valence electron density is a decreasing function of ε, whereas for the clusters with a high valence electron density it rises with ε.     

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.     

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 Kell? 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.     

Atom distributions in binary atom clusters: a perturbational approach and its validation in a case study

An approach to describe heteroatomic clusters A(n)B(N-n) as perturbed homoatomic ones is presented. By first treating the homoatomic systems A(N) or/and B(N) and subsequent application of first-order perturbation theory it is possible to estimate relative stabilities of the 2(N) possible distributions of the atom types A and B at the N atomic sites in a very efficient manner. The approach was tested considering Ir(n)Pt(13-n) as an example (treated with density functional methods). One observes good correlation between relative stabilities estimated from the homoatomic cases and those obtained from explicit treatments of the binary systems. Moreover we rationalize the observed correlation of atom type and atom position in Ir(n)Pt(13-n).     

Impact of anion polarizability on ion pairing in microhydrated salt clusters

Despite longstanding interest in the mechanism of salt dissolution in aqueous media, a molecular level understanding remains incomplete. Here, cryogenic ion trap vibrational action spectroscopy is combined with electronic structure calculations to track salt hydration in a gas phase model system one water molecule at a time. The infrared photodissociation spectra of microhydrated lithium dihalide anions [LiXX′(H₂O)_n]⁻ (XX′ = I₂, ClI and Cl₂; n = 1–3) in the OH stretching region (3800–2800 cm⁻¹) provide a detailed picture of how anion polarizability influences the competition among ion–ion, ion–water and water–water interactions. While exclusively contact ion pairs are observed for n = 1, the formation of solvent-shared ion pairs, identified by markedly red-shifted OH stretching bands (<3200 cm⁻¹), originating from the bridging water molecules, is favored already for n = 2. For n = 3, Li⁺ reaches its maximum coordination number of four only in [LiI₂(H₂O)₃]⁻, in accordance with the hard and soft Lewis acid and base principle. Water–water hydrogen bond formation leads to a different solvent-shared ion pair motif in [LiI₂(H₂O)₃]⁻ and network formation even restabilizes the contact ion pair motif in [LiCl₂(H₂O)₃]⁻. Structural assignments are exclusively possible after the consideration of anharmonic effects. Molecular dynamics simulations confirm that the significance of large amplitude motion (of the water molecules) increases with increasing anion polarizability and that needs to be considered already at cryogenic temperatures.

Infrared spectroscopy of microhydrated salt clusters provides a detailed picture of how anion polarizability influences the interactions between ions and water.     

Signatures of critical phenomena in rare atom clusters

We study the occurrence of a critical behaviour related to a liquid-gas phase transition in an atomic cluster. In particular, we analyse some experimental possibilities to investigate the role of finite size effects on the phase behaviour. In mass distributions, conditional moments, as well as scaled factorial moments of fragment mass distributions we find evidence for the presence of critical behaviour. It can be connected, by the use of Fisher's droplet model and Campi analysis, to a liquid-gas phase transition.     

Three-body contributions to the dipole polarizability of He3 clusters

Quantum-mechanical calculations of three-body contributions to the dipole polarizability in linear and triangular He₃ clusters are presented. Account is taken of electron correlation. For short distances, three-body terms can be large, dependent upon geometry, although for distances greater than the van der Waals minimum these three-body terms are small, their effect may still be of importance for dense fluids because of the number ratio of three- to two-body terms.     

Origin and control of superlinear polarizability scaling in chemical potential equalization methods

Many common chemical potential equalization (muEq) methods are known to suffer from a superlinear scaling of the polarizability with increasing molecular size that interferes with model transferability and prevents the straightforward application of these methods to large, biochemically relevant molecules. In the present work, we systematically investigate the origins of this scaling and the mechanisms whereby some existing methods successfully temper the scaling. We demonstrate several types of topological charge constraints distinct from the usual single molecular charge constraint that can successfully achieve linear polarizability scaling in atomic charge based equilibration models. We find the use of recently employed charge conservation constraints tied to small molecular units to be an effective and practical approach for modulating the polarizability scaling in atomic muEq schemes. We also analyze the scaling behavior of several muEq schemes in the bond representation and derive closed-form expressions for the polarizability scaling in a linear atomic chain model; for a single molecular charge constraint these expressions demonstrate a cubic dependence of the polarizability on molecular size compared with linear scaling obtainable in the case of the atom-atom charge transfer (AACT) and split-charge equilibration (SQE) schemes. Application of our results to the trans N-alkane series reveals that in certain situations, the AACT and SQE schemes can become unstable due to an indefinite Hessian matrix. Consequently, we discuss sufficient criteria for ensuring stability within these schemes.     

The polarizability of iodoform in the crystal

The optical polarizability of iodoform in the crystal is calculated using: the submolecule approach. The results are compatible with solution data and lack the excessive anisotropy found with the point-dipolc approach. The effective dipole moment in the crystal field is about twice the free dipole moment.     

Electronic spectroscopy of toluene-rare-gas clusters: the external heavy atom effect and vibrational predissociation

Toluene-X van der Waals clusters (where X = Ne, Ne2, Ar, Ar2, Kr, Xe) have been investigated by fluorescence excitation spectroscopy in the region of the S1-S0 transition. With the exception of Xe, for each rare-gas studied, we have assigned cluster transitions in the region of all the strong monomer vibrational bands up to 1000 cm(-1) above the origin band. We have further investigated the S1 relaxation dynamics for each vibrational level of each complex, via their fluorescence decay profiles. Clustering with neon has little appreciable effect on the vibrationless S1 lifetime. By contrast, the clusters with argon and krypton exhibit markedly shorter fluorescence lifetimes compared with the monomer. The effect is so severe in the case of toluene-Xe clusters that no fluorescence signals were observed. We interpret these results in terms of an external heavy atom effect in which the rate of intersystem crossing in toluene is influenced by the cluster partner. For clusters built upon excited S1 vibrational levels, the situation is potentially complicated by intramolecular vibrational redistribution and vibrational predissociation (VP). The majority of the fluorescence decay profiles were satisfactorily modeled using single exponential decays. The emission following pumping of the 37(1) level in the toluene-Kr cluster, however, is an exception. We have modeled the decay of this level with a simple kinetic scheme including VP and determined a predissociation rate of (1.04 +/- 0.54) x 10(7) s(-1).     

The effect of geometry on cluster polarizability: studies of sodium, copper, and silicon clusters at shape-transition sizes

The electronic properties of Na(16), Cu(16,) and Si(20-28) clusters were calculated using density functional theory with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof. These clusters are special, as transitions in cluster shape occur at these sizes in the Na(n), Cu(n), and Si(n) cluster systems, respectively. Low-energy isomers that are comparable in stability, but possess distinctly different shapes, exist at each of these sizes, making these sets of isomers useful as probes of geometrical effects on cluster properties. Results for ionization potentials, electron affinities, and polarizabilities are shown to have a characteristic dependence on cluster shape. An analysis of the results reveals a close relationship between polarizability and cluster volume for all the isomers studied, despite the differences in cluster type and geometry. This relationship accounts for variations in polarizabilities among isomers of the same size, but different shapes, whereas previously published rules relating the polarizability to other cluster properties do not.     

The polarizability of LiBr

Finite field SCF MO calculations are reported for LiBr over a range of bond distance from 3.8 a_o to 15 a_o Values of the pair potential, dipole moment and polarizability tensor are reported, and the polarizability curves compared with those of LiF and LiCl.     

The polarizability of KCl

We report near-Hartree-Fock limit SCF MO calculations of the variation of the polarizability of KCl with bond distance. The results are compared with those obtained previously for LiCl and Ar₂.     

Vacuum-UV photoemission-photoion coincidence spectroscopy of neutral metal atom clusters

A newly developed photoion-photoelectron Vacuum-UV coincidence spectrometer has been coupled to a supersonic metal atom cluster beam source and has been used to investigate the electronic structure of isolated mercury clusters in the size range from 1 to 110 at several selected discrete excitation energies between 11.3 and 7.1 eV. Excitation of the van der Waals cluster Hg₁₀ at the center of the strongD _3/2-autoionization line at 10.7 eV yields a photoelectron kinetic energy distribution between 0 and 2.5 eV indicating the population of Hg₁₀ ionic states, which are also accessible by threshold ionization.     

Origin of the oxygen atom in metalloporphyrin-catalyzed epoxidations with LiOCl as oxidant

Abstract – The origin of the oxygen atom incorporated into epoxides during the oxidation of olefins with the catalytic system Mn(TPP)Cl/LiOCl in the presence of ¹⁸O-labelled water has been investigated. One molar equivalent of H₂¹⁸O with respect to Li¹⁶OCl led to a 53 % ¹⁸O-incorporation within the epoxide formed, and near complete incorporation of ¹⁸O from water was achieved when no limiting amount of water was used. These results clearly indicate that the epoxidic oxygen atom arose from the high-valent metal-oxo species generated by LiOCl, but the exchange of the oxygen atom of hypochlorite with bulk water is fast, compared to the oxidation of the manganese(III) porphyrin by LiOCl. Therefore hypochlorite is not a suitable oxidant for mechanistic studies of metal-catalyzed oxygenation reactions involving high-valent metal-oxo species. Potassium monopersulfate is the adequate oxidant for such studies, because of its slow oxygen atom exchange with bulk water.     

Description of spin-crossover in a heterogeneous chain of exchange clusters

Spin transition theory is developed for periodic chains with two and more exchange clusters in a unit cell. A general expression is obtained for the effective magnetic moment of a unit cell μ_eff with several exchange clusters. For heterospin complexes Cu(hfac)₂L^R characterized by chains with the head-to-head motif a twosite approximation for the statistical sum of the Cu²⁺ Jahn-Teller paramagnetic center Cu²⁺ with spin 1/2 is proposed, within which a comparison with the available experimental data is performed. It is shown that the model developed describes both smooth and abrupt (cooperative) spin-crossover cases for the chains of three-spin exchange clusters.